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Mathematics Subject Classification 2010
a: 1: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysison metric spaces
a: 2: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)a: 3: 53D18 Generalized geometries (a la Hitchin)a: 4: 58B34 Noncommutative geometry (a la Connes)
the: 1: 01-XX History and biography [See also]the classification number–03 in the other sectionsfor: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86for: 2: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30for: 3: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45for: 4: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52for: 5: 03D78 Computation over the reals For constructive aspects, see 03F60for: 6: 05-XX Combinatorics For finite fields, see 11Txxfor: 7: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30for: 8: 05Bxx Designs and configurations For applications of design theory, see 94C30for: 9: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C15for: 10: 06D22 Frames, locales For topological questions see 54-XXfor: 11: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80for: 12: 11Axx Elementary number theory For analogues in number fields, see 11R04for: 13: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A15for: 14: 11A63 Radix representation; digital problems For metric results, see 11K16for: 15: 11B37 Recurrences For applications to special functions, see 33-XXfor: 16: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63for: 17: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45for: 18: 11Hxx Geometry of numbers For applications in coding theory, see 94B75for: 19: 11Lxx Exponential sums and character sums For finite fields, see 11Txxfor: 20: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72for: 21: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15for: 22: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15for: 23: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxfor: 24: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxfor: 25: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13for: 26: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32for: 27: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxfor: 28: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35for: 29: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45for: 30: 16-XX Associative rings and algebras For the commutative case, see 13-XXfor: 31: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxfor: 32: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30for: 33: 16K20 Finite-dimensional For crossed products, see 16S35for: 34: 16N80 General radicals and rings For radicals in module categories, see 16S90for: 35: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxfor: 36: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxfor: 37: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
1 Run: December 14, 2009
Mathematics Subject Classification 2010
see 15A75; for Clifford algebras, see 11E88, 15A66for: 38: 16Yxx Generalizations For nonassociative rings, see 17-XXfor: 39: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxfor: 40: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
for: 41: 20A10 Metamathematical considerations For word problems, see 20F10for: 42: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
for: 43: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
for: 44: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
for: 45: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.For abstract harmonic analysis, see 43-XX
for: 46: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see12Jxx, 13Jxx, 16W80
for: 47: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;for analysis thereon, see 43A80, 43A85, 43A90
for: 48: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methodsFor the purely algebraic theory, see 20G05
for: 49: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxfor: 50: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20for: 51: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40for: 52: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
for: 53: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
for: 54: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see49J52, 58Cxx, 90Cxx
for: 55: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scalesor measure chains see 34N05
for: 56: 28-XX Measure and integration For analysis on manifolds, see 58-XXfor: 57: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXfor: 58: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10for: 59: 31-XX Potential theory For probabilistic potential theory, see 60J45for: 60: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12for: 61: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30for: 62: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35for: 63: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27for: 64: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15for: 65: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see 32A22for: 66: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22for: 67: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxfor: 68: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for
2 Run: December 14, 2009
Mathematics Subject Classification 2010
representation theory see 22Exxfor: 69: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxfor: 70: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxfor: 71: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70for: 72: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70for: 73: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxfor: 74: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15for: 75: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35for: 76: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05for: 77: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15for: 78: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 79: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 80: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
for: 81: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30
for: 82: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30for: 83: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxfor: 84: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxfor: 85: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 86: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 87: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxfor: 88: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxfor: 89: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxfor: 90: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxfor: 91: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxfor: 92: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxfor: 93: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J10for: 94: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15for: 95: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20for: 96: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20for: 97: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20for: 98: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxx
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Mathematics Subject Classification 2010
for: 99: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,58-XX, especially 58Cxx
for: 100: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For globaland geometric aspects, see 58-XX
for: 101: 51-XX Geometry For algebraic geometry, see 14-XXfor: 102: 51M16 Inequalities and extremum problems For convex problems, see 52A40for: 103: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxfor: 104: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxfor: 105: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxfor: 106: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80for: 107: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80for: 108: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxfor: 109: 55Pxx Homotopy theory For simple homotopy type, see 57Q10for: 110: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxfor: 111: 57M25 Knots and links in S3 For higher dimensions, see 57Q45for: 112: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25for: 113: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxfor: 114: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15for: 115: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXfor: 116: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxfor: 117: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35for: 118: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxfor: 119: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30for: 120: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30for: 121: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areafor: 122: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30for: 123: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxfor: 124: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXfor: 125: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXfor: 126: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80for: 127: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15for: 128: 82D25 Crystals For crystallographic group theory, see 20H15for: 129: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15for: 130: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15for: 131: 85A40 Cosmology For relativistic cosmology, see 83F05for: 132: 91Bxx Mathematical economics For econometrics, see 62P20for: 133: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXfor: 134: 92D10 Genetics For genetic algebras, see 17D92for: 135: 92Exx Chemistry For biochemistry, see 92C40for: 136: 93-XX Systems theory; control For optimal control, see 49-XXfor: 137: 97B50 Teacher education For research aspects, see 97C70for: 138: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxx
cech: 1: 55N05 Cech types-codimensional: 1: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-space
4 Run: December 14, 2009
Mathematics Subject Classification 2010
15th: 1: 01A40 15th and 16th centuries, Renaissance16th: 1: 01A40 15th and 16th centuries, Renaissance16th: 2: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)17th: 1: 01A45 17th century18th: 1: 01A50 18th century19th: 1: 01A55 19th century
2-person: 1: 91A05 2-person games20th: 1: 01A60 20th century
3-manifolds: 1: 57M27 Invariants of knots and 3-manifolds30: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G3532: 1: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)32: 2: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)32: 3: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)40: 1: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)40: 2: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)47: 1: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)47: 2: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)49: 1: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)49: 2: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)70: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 8670: 2: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
70–86: 1: 51Pxx Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
70–86: 2: 51P05 Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
86: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)86: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 8692: 1: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)94: 1: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1094: 2: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10$<>$: 1: 11B50 Sequences (mod m)$<>$: 2: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20$<>$: 3: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithms$<>$: 4: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheses$<>$: 5: 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p;
tight closure [See also]13B22$<>$: 6: 14J40 n-folds (n > 4)$<>$: 7: 30C65 Quasiconformal mappings in Rn, other generalizations$<>$: 8: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)$<>$: 9: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxx$<>$: 10: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
5 Run: December 14, 2009
Mathematics Subject Classification 2010
metric taking values in an ordered structure more general than R, etc.)$<>$: 11: 46A63 Topological invariants ((DN), (Ω), etc.)$<>$: 12: 54D10 Lower separation axioms (T0–T3, etc.)$<>$: 13: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A03$<>$: 14: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)$<>$: 15: 55R45 Homology and homotopy of BO and BU; Bott periodicity$<>$: 16: 57N15 Topology of En, n-manifolds (4 < n <∞)$<>$: 17: 57N50 Sn − 1⊂ En, Schoenflies problem$<>$: 18: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
$<>$-: 1: 19D06 Q- and plus-constructions$<>$-: 2: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)
[See also]22D25, 47Lxx$<>$-: 3: 47C15 Operators in C∗- or von Neumann algebras
$<>$-adic: 1: 11D88 p-adic and power series fields$<>$-adic: 2: 11E95 p-adic theory$<>$-adic: 3: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50$<>$-adic: 4: 11F85 p-adic theory, local fields [See also]14G20, 22E50$<>$-adic: 5: 11K41 Continuous, p-adic and abstract analogues$<>$-adic: 6: 11Sxx Algebraic number theory: local and p-adic fields$<>$-adic: 7: 11S31 Class field theory; p-adic formal groups [See also]14L05$<>$-adic: 8: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)$<>$-adic: 9: 12H25 p-adic differential equations [See also]11S80, 14G20$<>$-adic: 10: 12J12 Formally p-adic fields$<>$-adic: 11: 14F30 p-adic cohomology, crystalline cohomology$<>$-adic: 12: 20C11 p-adic representations of finite groups$<>$-adic: 13: 22E35 Analysis on p-adic Lie groups$<>$-adic: 14: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, andrelated topics
$<>$-algebra: 1: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,58B34, 58J22
$<>$-algebras: 1: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxx$<>$-algebras: 2: 37A55 Relations with the theory of C∗-algebras [See mainly]46L55$<>$-algebras: 3: 43A20 L1-algebras on groups, semigroups, etc.$<>$-algebras: 4: 46L05 General theory of C∗-algebras$<>$-algebras: 5: 46L06 Tensor products of C∗-algebras$<>$-algebras: 6: 46L09 Free products of C∗-algebras$<>$-algebras: 7: 46L35 Classifications of C∗-algebras$<>$-algebras: 8: 46L45 Decomposition theory for C∗-algebras$<>$-algebras: 9: 46L57 Derivations, dissipations and positive semigroups in C∗-algebras$<>$-algebras: 10: 47C10 Operators in ∗-algebras$<>$-algebras: 11: 47L40 Limit algebras, subalgebras of C∗-algebras$<>$-algebras: 12: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
$<>$-analytic: 1: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)$<>$-arcs: 1: 51E21 Blocking sets, ovals, k-arcs$<>$-beta: 1: 33D05 q-gamma functions, q-beta functions and integrals$<>$-body: 1: 70F10 n-body problems$<>$-body: 2: 81U05 2-body potential scattering theory [See also]34E20 for WKB methods$<>$-body: 3: 81U10 n-body potential scattering theory
$<>$-calculus: 1: 05A30 q-calculus and related topics [See also]33Dxx$<>$-categories: 1: 18D05 Double categories, 2-categories, bicategories and generalizations$<>$-cobordism: 1: 57R75 O- and SO-cobordism$<>$-cobordism: 2: 57R77 Complex cobordism (U- and SU-cobordism) [See also]55N22$<>$-cobordism: 3: 57R80 h- and s-cobordism
$<>$-compactness: 1: 54D45 Local compactness, σ-compactness$<>$-completeness: 1: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
6 Run: December 14, 2009
Mathematics Subject Classification 2010
completeness)$<>$-concavity: 1: 32F10 q-convexity, q-concavity
$<>$-control: 1: 93B36 H∞-control$<>$-convex: 1: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)
$<>$-differences: 1: 39A13 Difference equations, scaling (q-differences) [See also]33Dxx$<>$-dimensional: 1: 52B11 n-dimensional polytopes
$<>$-divisible: 1: 14L05 Formal groups, p-divisible groups [See also]55N22$<>$-embedding: 1: 54C45 C- and C∗-embedding
$<>$-folds: 1: 14J30 3-folds [See also]32Q25$<>$-folds: 2: 14J35 4-folds$<>$-folds: 3: 32J17 Compact 3-folds$<>$-folds: 4: 32J18 Compact n-folds
$<>$-functions: 1: 11F66 Langlands L-functions; one variable Dirichlet series and functional equations$<>$-functions: 2: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10$<>$-functions: 3: 11Mxx Zeta and L-functions: analytic theory$<>$-functions: 4: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F27$<>$-functions: 5: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxx$<>$-functions: 6: 11S40 Zeta functions and L-functions [See also]11M41, 19F27$<>$-functions: 7: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G10$<>$-functions: 8: 26E10 C∞-functions, quasi-analytic functions [See also]58C25
$<>$-groups: 1: 20D15 Nilpotent groups, p-groups$<>$-homology: 1: 19K33 EXT and K-homology [See also]55N22
$<>$-homomorphism: 1: 19L20 J-homomorphism, Adams operations [See also]55Q50$<>$-ideals: 1: 16R10 T -ideals, identities, varieties of rings and algebras
$<>$-identities: 1: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A30$<>$-invariants: 1: 55S45 Postnikov systems, k-invariants$<>$-laplacian: 1: 35J92 Quasilinear elliptic equations with p-Laplacian$<>$-laplacian: 2: 35K92 Quasilinear parabolic equations with p-Laplacian
$<>$-length: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks[See also]20F17
$<>$-limit: 1: 60F25 Lp-limit theorems$<>$-manifolds: 1: 57N05 Topology of E2, 2-manifolds$<>$-manifolds: 2: 57N10 Topology of general 3-manifolds [See also]57Mxx$<>$-manifolds: 3: 57N13 Topology of E4, 4-manifolds [See also]14Jxx, 32Jxx
$<>$-matrix: 1: 81U20 S-matrix theory, etc.$<>$-modules: 1: 11J93 Transcendence theory of Drinfel′d and t-modules$<>$-modules: 2: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J15$<>$-modules: 3: 32S40 Monodromy; relations with differential equations and D-modules$<>$-modules: 4: 46L08 C∗-modules
$<>$-morphism: 1: 55Q50 J-morphism [See also]19L20$<>$-neumann: 1: 32W05 ∂ and ∂-Neumann operators$<>$-neumann: 2: 32W10 ∂b and ∂b-Neumann operators$<>$-neumann: 3: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J10$<>$-numbers: 1: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operators$<>$-pair: 1: 20E42 Groups with a BN -pair; buildings [See also]51E24
$<>$-periodicity: 1: 55Q51 vn-periodicity$<>$-proper: 1: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
$<>$-rings: 1: 17D20 (γ, δ)-rings, including (1,−1)-rings$<>$-rings: 2: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
$<>$-schur: 1: 20G43 Schur and q-Schur algebras
7 Run: December 14, 2009
Mathematics Subject Classification 2010
$<>$-semigroups: 1: 47D60 C-semigroups, regularized semigroups$<>$-series: 1: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbols$<>$-set: 1: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.
$<>$-space: 1: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-space$<>$-spaces: 1: 30H25 Besov spaces and Qp-spaces$<>$-spaces: 2: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J15$<>$-spaces: 3: 42B30 Hp-spaces$<>$-spaces: 4: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.$<>$-spaces: 5: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)$<>$-spaces: 6: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30$<>$-spaces: 7: 53C70 Direct methods (G-spaces of Busemann, etc.)$<>$-spaces: 8: 54D50 k-spaces$<>$-spaces: 9: 54E18 p-spaces, M -spaces, σ-spaces, etc.$<>$-spaces: 10: 54G05 Extremally disconnected spaces, F -spaces, etc.$<>$-spaces: 11: 54G10 P -spaces$<>$-spaces: 12: 55P45 H-spaces and duals$<>$-spaces: 13: 55R35 Classifying spaces of groups and H-spaces$<>$-spaces: 14: 57T25 Homology and cohomology of H-spaces$<>$-spaces: 15: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
$<>$-structure: 1: 20D20 Sylow subgroups, Sylow properties, π-groups, π-structure$<>$-structures: 1: 53C10 G-structures$<>$-summing: 1: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20$<>$-theory: 1: 11E70 K-theory of quadratic and Hermitian forms$<>$-theory: 2: 11G55 Polylogarithms and relations with K-theory$<>$-theory: 3: 11R70 K-theory of global fields [See also]19Fxx$<>$-theory: 4: 11S70 K-theory of local fields [See also]19Fxx$<>$-theory: 5: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D50$<>$-theory: 6: 14C35 Applications of methods of algebraic K-theory [See also]19Exx$<>$-theory: 7: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D50$<>$-theory: 8: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R67$<>$-theory: 9: 19-XX K-theory [See also]16E20, 18F25$<>$-theory: 10: 19Dxx Higher algebraic K-theory$<>$-theory: 11: 19D10 Algebraic K-theory of spaces$<>$-theory: 12: 19D25 Karoubi-Villamayor-Gersten K-theory$<>$-theory: 13: 19D35 Negative K-theory, NK and Nil$<>$-theory: 14: 19D45 Higher symbols, Milnor K-theory$<>$-theory: 15: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E20$<>$-theory: 16: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G60$<>$-theory: 17: 19Exx K-theory in geometry$<>$-theory: 18: 19E08 K-theory of schemes [See also]14C35$<>$-theory: 19: 19Fxx K-theory in number theory [See also]11R70, 11S70$<>$-theory: 20: 19Gxx K-theory of forms [See also]11Exx$<>$-theory: 21: 19G24 L-theory of group rings [See also]11E81$<>$-theory: 22: 19G38 Hermitian K-theory, relations with K-theory of rings$<>$-theory: 23: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M20$<>$-theory: 24: 19K35 Kasparov theory (KK-theory) [See also]58J22$<>$-theory: 25: 19Lxx Topological K-theory [See also]55N15, 55R50, 55S25$<>$-theory: 26: 19L41 Connective K-theory, cobordism [See also]55N22$<>$-theory: 27: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S91$<>$-theory: 28: 19L50 Twisted K-theory; differential K-theory$<>$-theory: 29: 19Mxx Miscellaneous applications of K-theory$<>$-theory: 30: 19M05 Miscellaneous applications of K-theory
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Mathematics Subject Classification 2010
$<>$-theory: 31: 43A17 Analysis on ordered groups, Hp-theory$<>$-theory: 32: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22$<>$-theory: 33: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20$<>$-theory: 34: 55N15 K-theory [See also]19Lxx For algebraic K-theory, see 18F25, 19-XX$<>$-theory: 35: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XX$<>$-theory: 36: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxx$<>$-vertex: 1: 51L15 n-vertex theorems via direct methods
for: 1: 05C62 Graph representations (geometric and intersection representations, etc.) For graphdrawing, see also 68R10
=: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology andderived functors for triples [See also]18Gxx
=: 2: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,braided categories [See also]19D23
=: 3: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE ininfinitely many variables) [See also]46Gxx, 58D25
=: 4: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)[See also]46B70, 46M35
=: 5: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, includingde Branges-Rovnyak and other structured spaces) [See also]47B32
=: 6: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,realizations, etc.
=: 7: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07“$<>$-closed”: 1: 54D25 “P -minimal” and “P -closed” spaces
“noncommutative”: 1: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,58B34, 58J22
“skew”: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,see 15A75; for Clifford algebras, see 11E88, 15A66
“smart: 1: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxx“smooth”: 1: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theorems“special”: 1: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometry“super”: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66“topological”: 1: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)a: 1: 35B45 A priori estimatesa: 2: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)a: 3: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)
abel: 1: 40G10 Abel, Borel and power series methodsabel: 2: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35abelian: 1: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40abelian: 2: 11G10 Abelian varieties of dimension > 1 [See also]14Kxxabelian: 3: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K22abelian: 4: 11J89 Transcendence theory of elliptic and abelian functionsabelian: 5: 11J95 Results involving abelian varietiesabelian: 6: 11R20 Other abelian and metabelian extensionsabelian: 7: 14Kxx Abelian varieties and schemesabelian: 8: 14K20 Analytic theory; abelian integrals and differentialsabelian: 9: 18Exx Abelian categoriesabelian: 10: 18E10 Exact categories, abelian categoriesabelian: 11: 20Kxx Abelian groupsabelian: 12: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]abelian: 13: 22Bxx Locally compact abelian groups (LCA groups)abelian: 14: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
9 Run: December 14, 2009
Mathematics Subject Classification 2010
Abelian integrals, etc.)abelian: 15: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupsabelian: 16: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05
about: 1: 74B15 Equations linearized about a deformed state (small deformations superposed on large)absolute: 1: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)absolute: 2: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)absolute: 3: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriesabsolute: 4: 42A24 Summability and absolute summability of Fourier and trigonometric seriesabsolute: 5: 51F05 Absolute planesabsolute: 6: 51F10 Absolute spacesabsolute: 7: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15absolute: 8: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15absolute: 9: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15absolute: 10: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15absolute: 11: 55M15 Absolute neighborhood retracts [See also]54C55absolute: 12: 76E15 Absolute and convective instability and stability
absolutely: 1: 26A46 Absolutely continuous functionsabsolutely: 2: 26B30 Absolutely continuous functions, functions of bounded variation
absoluteness: 1: 03E57 Generic absoluteness and forcing axioms [See also]03E50absorption: 1: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorptionproblems, etc.) [See also]92Dxx
abstract: 1: 03B22 Abstract deductive systemsabstract: 2: 03C48 Abstract elementary classes and related topics [See also]03C45abstract: 3: 03C95 Abstract model theoryabstract: 4: 03D75 Abstract and axiomatic computability and recursion theoryabstract: 5: 03G27 Abstract algebraic logicabstract: 6: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65abstract: 7: 11K41 Continuous, p-adic and abstract analoguesabstract: 8: 12H20 Abstract differential equations [See also]34Mxxabstract: 9: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxxabstract: 10: 20Dxx Abstract finite groupsabstract: 11: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXabstract: 12: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24abstract: 13: 28Bxx Set functions, measures and integrals with values in abstract spacesabstract: 14: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D25abstract: 15: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxxabstract: 16: 35K90 Abstract parabolic equationsabstract: 17: 35L90 Abstract hyperbolic equationsabstract: 18: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxabstract: 19: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B15abstract: 20: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)abstract: 21: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)abstract: 22: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)abstract: 23: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exx
10 Run: December 14, 2009
Mathematics Subject Classification 2010
abstract: 24: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exx
abstract: 25: 45Nxx Abstract integral equations, integral equations in abstract spacesabstract: 26: 45Nxx Abstract integral equations, integral equations in abstract spacesabstract: 27: 45N05 Abstract integral equations, integral equations in abstract spacesabstract: 28: 45N05 Abstract integral equations, integral equations in abstract spacesabstract: 29: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12abstract: 30: 46M35 Abstract interpolation of topological vector spaces [See also]46B70abstract: 31: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15abstract: 32: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E09abstract: 33: 47L30 Abstract operator algebras on Hilbert spacesabstract: 34: 49J27 Problems in abstract spaces [See also]90C48, 93C25abstract: 35: 49K27 Problems in abstract spaces [See also]90C48, 93C25abstract: 36: 51D05 Abstract (Maeda) geometriesabstract: 37: 51D10 Abstract geometries with exchange axiomabstract: 38: 51D15 Abstract geometries with parallelismabstract: 39: 55U05 Abstract complexesabstract: 40: 55U35 Abstract and axiomatic homotopy theoryabstract: 41: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)abstract: 42: 58E07 Abstract bifurcation theoryabstract: 43: 65Jxx Numerical analysis in abstract spacesabstract: 44: 65J08 Abstract evolution equationsabstract: 45: 68Q65 Abstract data types; algebraic specification [See also]18C50abstract: 46: 90C48 Programming in abstract spacesabstract: 47: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q25abstract: 48: 93C25 Systems in abstract spaces
abstract-valued: 1: 30G30 Other generalizations of analytic functions (including abstract-valued functions)abstracts: 1: 00B05 Collections of abstracts of lectures
academies: 1: 01A74 Other institutions and academiesacceleration: 1: 65Bxx Acceleration of convergence
accessible: 1: 18C35 Accessible and locally presentable categoriesaccretive: 1: 47B44 Accretive operators, dissipative operators, etc.accretive: 2: 47H06 Accretive operators, dissipative operators, etc.
achievement: 1: 97D60 Student assessment, achievement control and ratingacting: 1: 20E08 Groups acting on trees [See also]20F65acting: 2: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10acting: 3: 57S25 Groups acting on specific manifoldsaction: 1: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20action-minimizing: 1: 37J50 Action-minimizing orbits and measures
actions: 1: 05E18 Group actions on combinatorial structuresactions: 2: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24actions: 3: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17actions: 4: 14R20 Group actions on affine varieties [See also]13A50, 14L30actions: 5: 16S40 Smash products of general Hopf actions [See also]16T05actions: 6: 16W22 Actions of groups and semigroups; invariant theoryactions: 7: 16W25 Derivations, actions of Lie algebrasactions: 8: 19J35 Obstructions to group actionsactions: 9: 20M30 Representation of semigroups; actions of semigroups on setsactions: 10: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20actions: 11: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axxactions: 12: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40actions: 13: 37B05 Transformations and group actions with special properties (minimality, distality,
11 Run: December 14, 2009
Mathematics Subject Classification 2010
proximality, etc.)actions: 14: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxactions: 15: 57M60 Group actions in low dimensionsactions: 16: 58D19 Group actions and symmetry propertiesactions: 17: 58E40 Group actions
actuarial: 1: 62P05 Applications to actuarial sciences and financial mathematicsadele: 1: 11R56 Adele rings and groupsadele: 2: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05adeles: 1: 20G35 Linear algebraic groups over adeles and other rings and schemesadams: 1: 19L20 J-homomorphism, Adams operations [See also]55Q50adams: 2: 55T15 Adams spectral sequences
adaptive: 1: 62F35 Robustness and adaptive proceduresadaptive: 2: 68T05 Learning and adaptive systems [See also]68Q32, 91E40adaptive: 3: 93C40 Adaptive controladaptive: 4: 93D21 Adaptive or robust stabilizationadaptive: 5: 93E35 Stochastic learning and adaptive control
additional: 1: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)[See also]03G25, 03F45additional: 2: 16Wxx Rings and algebras with additional structureadditional: 3: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20additional: 4: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)additional: 5: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXadditive: 1: 11B13 Additive bases, including sumsets [See also]05B10additive: 2: 11N60 Distribution functions associated with additive and positive multiplicative functionsadditive: 3: 11Pxx Additive number theory; partitionsadditive: 4: 11P32 Goldbach-type theorems; other additive questions involving primesadditive: 5: 11P70 Inverse problems of additive number theory, including sumsetsadditive: 6: 18B10 Category of relations, additive relationsadditive: 7: 18E05 Preadditive, additive categoriesadditive: 8: 39A10 Difference equations, additiveadditive: 9: 60J55 Local time and additive functionals
additivity: 1: 39B55 Orthogonal additivity and other conditional equationsadiabatic: 1: 70H11 Adiabatic invariants
adjoint: 1: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)adjoints: 1: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
adjunction: 1: 14N30 Adjunction problemsadjunction: 2: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction ofinverses, etc.)adjunction: 3: 54B17 Adjunction spaces and similar constructions
adjunctions: 1: 18D25 Strong functors, strong adjunctionsadministrative: 1: 97R70 User programs, administrative applications
admissibility: 1: 62C15 Admissibilityadmissible: 1: 03C70 Logic on admissible setsadmissible: 2: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.admitting: 1: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionsadult: 1: 97B60 Adult and further education
advertising: 1: 90B60 Marketing, advertising [See also]91B60aero-: 1: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
aero-acoustics: 1: 76Qxx Hydro- and aero-acousticsaero-acoustics: 2: 76Q05 Hydro- and aero-acousticsaerodynamics: 1: 76Gxx General aerodynamics and subsonic flowsaerodynamics: 2: 76G25 General aerodynamics and subsonic flows
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Mathematics Subject Classification 2010
affective: 1: 97C20 Affective behavioraffective: 2: 97Q20 Affective aspects in teaching computer science
affine: 1: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D35affine: 2: 14Rxx Affine geometryaffine: 3: 14R05 Classification of affine varietiesaffine: 4: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)affine: 5: 14R20 Group actions on affine varieties [See also]13A50, 14L30affine: 6: 14R25 Affine fibrations [See also]14D06affine: 7: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrasaffine: 8: 32B15 Analytic subsets of affine spaceaffine: 9: 32M17 Automorphism groups of Cn and affine manifoldsaffine: 10: 51A35 Non-Desarguesian affine and projective planesaffine: 11: 51E15 Affine and projective planesaffine: 12: 51N10 Affine analytic geometryaffine: 13: 53A15 Affine differential geometryaffine: 14: 53B05 Linear and affine connectionsagent: 1: 68T42 Agent technologyagent: 2: 91B69 Heterogeneous agent models
aggregation: 1: 82B24 Interface problems; diffusion-limited aggregationaggregation: 2: 82C24 Interface problems; diffusion-limited aggregation
aided: 1: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07aids: 1: 97U30 Teachers’ manuals and planning aidsair: 1: 76Z10 Biopropulsion in water and in air
airfoil: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil andhydrofoil theory, sloshing
airy: 1: 33C10 Bessel and Airy functions, cylinder functions, 0F1
al: 1: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)aleksandrov: 1: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)
algebra: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C05algebra: 2: 03C60 Model-theoretic algebra [See also]08C10, 12Lxx, 13L05algebra: 3: 03E20 Other classical set theory (including functions, relations, and set algebra)algebra: 4: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65algebra: 5: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)algebra: 6: 05E40 Combinatorial aspects of commutative algebraalgebra: 7: 08A70 Applications of universal algebra in computer sciencealgebra: 8: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63algebra: 9: 12Hxx Differential and difference algebraalgebra: 10: 12H05 Differential algebra [See also]13Nxxalgebra: 11: 12H10 Difference algebra [See also]39Axxalgebra: 12: 13-XX Commutative algebraalgebra: 13: 13J30 Real algebra [See also]12D15, 14Pxxalgebra: 14: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxxalgebra: 15: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxxalgebra: 16: 13Nxx Differential algebra [See also]12H05, 14F10algebra: 17: 13P20 Computational homological algebra [See also]13Dxxalgebra: 18: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)algebra: 19: 14A05 Relevant commutative algebra [See also]13-XXalgebra: 20: 15-XX Linear and multilinear algebra; matrix theoryalgebra: 21: 15Axx Basic linear algebraalgebra: 22: 15A69 Multilinear algebra, tensor productsalgebra: 23: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L24algebra: 24: 15A75 Exterior algebra, Grassmann algebrasalgebra: 25: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
13 Run: December 14, 2009
Mathematics Subject Classification 2010
algebra: 26: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txxalgebra: 27: 18G25 Relative homological algebra, projective classesalgebra: 28: 18G50 Nonabelian homological algebraalgebra: 29: 18G55 Homotopical algebraalgebra: 30: 20Jxx Connections with homological algebra and category theoryalgebra: 31: 20M50 Connections of semigroups with homological algebra and category theoryalgebra: 32: 32A65 Banach algebra techniques [See mainly]46Jxxalgebra: 33: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15algebra: 34: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxalgebra: 35: 55S10 Steenrod algebraalgebra: 36: 55Uxx Applied homological algebra and category theory [See also]18Gxxalgebra: 37: 65Fxx Numerical linear algebraalgebra: 38: 76M60 Symmetry analysis, Lie group and algebra methodsalgebra: 39: 81R15 Operator algebra methods [See also]46Lxx, 81T05algebra: 40: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30algebra: 41: 97G70 Analytic geometry. Vector algebraalgebra: 42: 97Hxx Algebraalgebra: 43: 97H20 Elementary algebraalgebra: 44: 97H60 Linear algebraalgebra: 45: 97N30 Numerical algebra
algebraic: 1: 03Gxx Algebraic logicalgebraic: 2: 03G27 Abstract algebraic logicalgebraic: 3: 05Exx Algebraic combinatoricsalgebraic: 4: 06-XX Order, lattices, ordered algebraic structures [See also]18B35algebraic: 5: 06A11 Algebraic aspects of posetsalgebraic: 6: 08-XX General algebraic systemsalgebraic: 7: 08Axx Algebraic structures [See also]03C05algebraic: 8: 08A72 Fuzzy algebraic structuresalgebraic: 9: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63algebraic: 10: 11E72 Galois cohomology of linear algebraic groups [See also]20G10algebraic: 11: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24algebraic: 12: 11F23 Relations with algebraic geometry and topologyalgebraic: 13: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxxalgebraic: 14: 11J68 Approximation to algebraic numbersalgebraic: 15: 11J85 Algebraic independence; Gel′fond’s methodalgebraic: 16: 11N45 Asymptotic results on counting functions for algebraic and topological structuresalgebraic: 17: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15algebraic: 18: 11R04 Algebraic numbers; rings of algebraic integersalgebraic: 19: 11R04 Algebraic numbers; rings of algebraic integersalgebraic: 20: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measurealgebraic: 21: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10algebraic: 22: 11R58 Arithmetic theory of algebraic function fields [See also]14-XXalgebraic: 23: 11Sxx Algebraic number theory: local and p-adic fieldsalgebraic: 24: 11T71 Algebraic coding theory; cryptographyalgebraic: 25: 11Y40 Algebraic number theory computationsalgebraic: 26: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15algebraic: 27: 12F05 Algebraic extensionsalgebraic: 28: 14-XX Algebraic geometryalgebraic: 29: 14A20 Generalizations (algebraic spaces, stacks)algebraic: 30: 14A22 Noncommutative algebraic geometry [See also]16S38algebraic: 31: 14C25 Algebraic cyclesalgebraic: 32: 14C35 Applications of methods of algebraic K-theory [See also]19Exx
14 Run: December 14, 2009
Mathematics Subject Classification 2010
algebraic: 33: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,see 32G13
algebraic: 34: 14H05 Algebraic functions; function fields [See also]11R58algebraic: 35: 14H10 Families, moduli (algebraic)algebraic: 36: 14J10 Families, moduli, classification: algebraic theoryalgebraic: 37: 14K05 Algebraic theoryalgebraic: 38: 14K10 Algebraic moduli, classification [See also]11G15algebraic: 39: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45algebraic: 40: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45algebraic: 41: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D35algebraic: 42: 14L40 Other algebraic groups (geometric aspects)algebraic: 43: 14Pxx Real algebraic and real analytic geometryalgebraic: 44: 14P05 Real algebraic sets [See also]12D15, 13J30algebraic: 45: 14P25 Topology of real algebraic varietiesalgebraic: 46: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W30algebraic: 47: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxxalgebraic: 48: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22algebraic: 49: 17B10 Representations, algebraic theory (weights)algebraic: 50: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxxalgebraic: 51: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
algebraic: 52: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30algebraic: 53: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R67algebraic: 54: 19Dxx Higher algebraic K-theoryalgebraic: 55: 19D10 Algebraic K-theory of spacesalgebraic: 56: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F42algebraic: 57: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXalgebraic: 58: 20F29 Representations of groups as automorphism groups of algebraic systemsalgebraic: 59: 20F70 Algebraic geometry over groups; equations over groupsalgebraic: 60: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
algebraic: 61: 20G15 Linear algebraic groups over arbitrary fieldsalgebraic: 62: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionsalgebraic: 63: 20G25 Linear algebraic groups over local fields and their integersalgebraic: 64: 20G30 Linear algebraic groups over global fields and their integersalgebraic: 65: 20G35 Linear algebraic groups over adeles and other rings and schemesalgebraic: 66: 20G40 Linear algebraic groups over finite fieldsalgebraic: 67: 20M32 Algebraic monoidsalgebraic: 68: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W80algebraic: 69: 22A30 Other topological algebraic systems and their representationsalgebraic: 70: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05algebraic: 71: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05algebraic: 72: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10algebraic: 73: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10algebraic: 74: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05algebraic: 75: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05algebraic: 76: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxx
15 Run: December 14, 2009
Mathematics Subject Classification 2010
algebraic: 77: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros offunctions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10
algebraic: 78: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,14J10 [See also]14H15, 14J15
algebraic: 79: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraictheory, see 14Jxx
algebraic: 80: 32J10 Algebraic dependence theoremsalgebraic: 81: 32J25 Transcendental methods of algebraic geometry [See also]14C30algebraic: 82: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)algebraic: 83: 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)algebraic: 84: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxalgebraic: 85: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70algebraic: 86: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresalgebraic: 87: 37P55 Arithmetic dynamics on general algebraic varietiesalgebraic: 88: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxalgebraic: 89: 47Cxx Individual linear operators as elements of algebraic systemsalgebraic: 90: 51-XX Geometry For algebraic geometry, see 14-XXalgebraic: 91: 51H30 Geometries with algebraic manifold structure [See also]14-XXalgebraic: 92: 51N35 Questions of classical algebraic geometry [See also]14Nxxalgebraic: 93: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxalgebraic: 94: 54C40 Algebraic properties of function spaces [See also]46J10algebraic: 95: 54H10 Topological representations of algebraic systems [See also]22-XXalgebraic: 96: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80algebraic: 97: 55-XX Algebraic topologyalgebraic: 98: 57N65 Algebraic topology of manifoldsalgebraic: 99: 57R19 Algebraic topology on manifoldsalgebraic: 100: 57R91 Equivariant algebraic topology of manifoldsalgebraic: 101: 58K20 Algebraic and analytic properties of mappingsalgebraic: 102: 60Bxx Probability theory on algebraic and topological structuresalgebraic: 103: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)algebraic: 104: 65Hxx Nonlinear algebraic or transcendental equationsalgebraic: 105: 68Q65 Abstract data types; algebraic specification [See also]18C50algebraic: 106: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M35algebraic: 107: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F10algebraic: 108: 70G55 Algebraic geometry methodsalgebraic: 109: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40algebraic: 110: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40algebraic: 111: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B37algebraic: 112: 93B25 Algebraic methodsalgebraic: 113: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50algebraic: 114: 97H50 Ordered algebraic structures
algebraically: 1: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetriesalgebraization: 1: 51A25 Algebraization [See also]12Kxx, 20N05
algebras: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,03G25, 06E25
algebras: 2: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,03G25, 06E25
algebras: 3: 03G05 Boolean algebras [See also]06Exxalgebras: 4: 03G15 Cylindric and polyadic algebras; relation algebrasalgebras: 5: 03G15 Cylindric and polyadic algebras; relation algebras
16 Run: December 14, 2009
Mathematics Subject Classification 2010
algebras: 6: 03G20 Lukasiewicz and Post algebras [See also]06D25, 06D30algebras: 7: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F35algebras: 8: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C80algebras: 9: 06D20 Heyting algebras [See also]03G25algebras: 10: 06D25 Post algebras [See also]03G20algebras: 11: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G20algebras: 12: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G20algebras: 13: 06D72 Fuzzy lattices (soft algebras) and related topicsalgebras: 14: 06Exx Boolean algebras (Boolean rings) [See also]03G05algebras: 15: 06E10 Chain conditions, complete algebrasalgebras: 16: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45algebras: 17: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45algebras: 18: 06E75 Generalizations of Boolean algebrasalgebras: 19: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80algebras: 20: 08A40 Operations, polynomials, primal algebrasalgebras: 21: 08A55 Partial algebrasalgebras: 22: 08A60 Unary algebrasalgebras: 23: 08A62 Finitary algebrasalgebras: 24: 08A65 Infinitary algebrasalgebras: 25: 08A68 Heterogeneous algebrasalgebras: 26: 08B20 Free algebrasalgebras: 27: 08Cxx Other classes of algebrasalgebras: 28: 08C05 Categories of algebras [See also]18C05algebras: 29: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A30algebras: 30: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A66algebras: 31: 11F22 Relationship to Lie algebras and finite simple groupsalgebras: 32: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsalgebras: 33: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxxalgebras: 34: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxxalgebras: 35: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S10algebras: 36: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)algebras: 37: 13E10 Artinian rings and modules, finite-dimensional algebrasalgebras: 38: 13F50 Rings with straightening laws, Hodge algebrasalgebras: 39: 13F60 Cluster algebrasalgebras: 40: 13J07 Analytical algebras and rings [See also]32B05algebras: 41: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45algebras: 42: 15A66 Clifford algebras, spinorsalgebras: 43: 15A75 Exterior algebra, Grassmann algebrasalgebras: 44: 15A78 Other algebras built from modulesalgebras: 45: 15A80 Max-plus and related algebrasalgebras: 46: 16-XX Associative rings and algebras For the commutative case, see 13-XXalgebras: 47: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)algebras: 48: 16E45 Differential graded algebras and applicationsalgebras: 49: 16Gxx Representation theory of rings and algebrasalgebras: 50: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxxalgebras: 51: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30algebras: 52: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)algebras: 53: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)algebras: 54: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)algebras: 55: 16H10 Orders in separable algebrasalgebras: 56: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxx
17 Run: December 14, 2009
Mathematics Subject Classification 2010
algebras: 57: 16R10 T -ideals, identities, varieties of rings and algebrasalgebras: 58: 16Sxx Rings and algebras arising under various constructionsalgebras: 59: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)algebras: 60: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B35algebras: 61: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B35algebras: 62: 16S37 Quadratic and Koszul algebrasalgebras: 63: 16Txx Hopf algebras, quantum groups and related topicsalgebras: 64: 16T05 Hopf algebras and their applications [See also]16S40, 57T05algebras: 65: 16Wxx Rings and algebras with additional structurealgebras: 66: 16W25 Derivations, actions of Lie algebrasalgebras: 67: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66algebras: 68: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66algebras: 69: 17-XX Nonassociative rings and algebrasalgebras: 70: 17A15 Noncommutative Jordan algebrasalgebras: 71: 17A20 Flexible algebrasalgebras: 72: 17A30 Algebras satisfying other identitiesalgebras: 73: 17A32 Leibniz algebrasalgebras: 74: 17A35 Division algebrasalgebras: 75: 17A45 Quadratic algebras (but not quadratic Jordan algebras)algebras: 76: 17A45 Quadratic algebras (but not quadratic Jordan algebras)algebras: 77: 17A50 Free algebrasalgebras: 78: 17A75 Composition algebrasalgebras: 79: 17A80 Valued algebrasalgebras: 80: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxalgebras: 81: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B23algebras: 82: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxxalgebras: 83: 17B63 Poisson algebrasalgebras: 84: 17B66 Lie algebras of vector fields and related (super) algebrasalgebras: 85: 17B66 Lie algebras of vector fields and related (super) algebrasalgebras: 86: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrasalgebras: 87: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrasalgebras: 88: 17B68 Virasoro and related algebrasalgebras: 89: 17B69 Vertex operators; vertex operator algebras and related structuresalgebras: 90: 17Cxx Jordan algebras (algebras, triples and pairs)algebras: 91: 17Cxx Jordan algebras (algebras, triples and pairs)algebras: 92: 17C20 Simple, semisimple algebrasalgebras: 93: 17C60 Division algebrasalgebras: 94: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70algebras: 95: 17Dxx Other nonassociative rings and algebrasalgebras: 96: 17D10 Mal′cev (Mal′tsev) rings and algebrasalgebras: 97: 17D25 Lie-admissible algebrasalgebras: 98: 17D92 Genetic algebrasalgebras: 99: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxalgebras: 100: 18C20 Algebras and Kleisli categories associated with monadsalgebras: 101: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M20algebras: 102: 20C08 Hecke algebras and their representationsalgebras: 103: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50algebras: 104: 20G43 Schur and q-Schur algebrasalgebras: 105: 22B10 Structure of group algebras of LCA groupsalgebras: 106: 22Dxx Locally compact groups and their algebrasalgebras: 107: 22D15 Group algebras of locally compact groups
18 Run: December 14, 2009
Mathematics Subject Classification 2010
algebras: 108: 22D20 Representations of group algebrasalgebras: 109: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxalgebras: 110: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxalgebras: 111: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05algebras: 112: 28A60 Measures on Boolean rings, measure algebras [See also]54H10algebras: 113: 30Hxx Spaces and algebras of analytic functionsalgebras: 114: 30H50 Algebras of analytic functionsalgebras: 115: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J15algebras: 116: 32B05 Analytic algebras and generalizations, preparation theoremsalgebras: 117: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15algebras: 118: 33C80 Connections with groups and algebras, and related topicsalgebras: 119: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and
related topicsalgebras: 120: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresalgebras: 121: 43A10 Measure algebras on groups, semigroups, etc.algebras: 122: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J10algebras: 123: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15algebras: 124: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15algebras: 125: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 126: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 127: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 128: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 129: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 130: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20algebras: 131: 46H05 General theory of topological algebrasalgebras: 132: 46H15 Representations of topological algebrasalgebras: 133: 46H20 Structure, classification of topological algebrasalgebras: 134: 46H30 Functional calculus in topological algebras [See also]47A60algebras: 135: 46H35 Topological algebras of operators [See mainly]47Lxxalgebras: 136: 46H70 Nonassociative topological algebras [See also]46K70, 46L70algebras: 137: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25algebras: 138: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25algebras: 139: 46J05 General theory of commutative topological algebrasalgebras: 140: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25algebras: 141: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25algebras: 142: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30algebras: 143: 46J25 Representations of commutative topological algebrasalgebras: 144: 46J40 Structure, classification of commutative topological algebrasalgebras: 145: 46J45 Radical Banach algebrasalgebras: 146: 46Kxx Topological (rings and) algebras with an involution [See also]16W10algebras: 147: 46K05 General theory of topological algebras with involutionalgebras: 148: 46K10 Representations of topological algebras with involutionalgebras: 149: 46K15 Hilbert algebrasalgebras: 150: 46K50 Nonselfadjoint (sub)algebras in algebras with involutionalgebras: 151: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L70
19 Run: December 14, 2009
Mathematics Subject Classification 2010
algebras: 152: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)[See also]22D25, 47Lxx
algebras: 153: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)[See also]22D25, 47Lxx
algebras: 154: 46L10 General theory of von Neumann algebrasalgebras: 155: 46L54 Free probability and free operator algebrasalgebras: 156: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C10algebras: 157: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K70algebras: 158: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22algebras: 159: 47B48 Operators on Banach algebrasalgebras: 160: 47C05 Operators in algebrasalgebras: 161: 47C15 Operators in C∗- or von Neumann algebrasalgebras: 162: 47Lxx Linear spaces and algebras of operators [See also]46Lxxalgebras: 163: 47L10 Algebras of operators on Banach spaces and other topological linear spacesalgebras: 164: 47L15 Operator algebras with symbol structurealgebras: 165: 47L30 Abstract operator algebras on Hilbert spacesalgebras: 166: 47L35 Nest algebras, CSL algebrasalgebras: 167: 47L35 Nest algebras, CSL algebrasalgebras: 168: 47L40 Limit algebras, subalgebras of C∗-algebrasalgebras: 169: 47L45 Dual algebras; weakly closed singly generated operator algebrasalgebras: 170: 47L45 Dual algebras; weakly closed singly generated operator algebrasalgebras: 171: 47L50 Dual spaces of operator algebrasalgebras: 172: 47L55 Representations of (nonselfadjoint) operator algebrasalgebras: 173: 47L60 Algebras of unbounded operators; partial algebras of operatorsalgebras: 174: 47L60 Algebras of unbounded operators; partial algebras of operatorsalgebras: 175: 47L65 Crossed product algebras (analytic crossed products)algebras: 176: 47L70 Nonassociative nonselfadjoint operator algebrasalgebras: 177: 47L75 Other nonselfadjoint operator algebrasalgebras: 178: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)algebras: 179: 47L90 Applications of operator algebras to physicsalgebras: 180: 57T05 Hopf algebras [See also]16T05algebras: 181: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)algebras: 182: 81Rxx Groups and algebras in quantum theoryalgebras: 183: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70algebras: 184: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
algebras: 185: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
algebras: 186: 81T05 Axiomatic quantum field theory; operator algebrasalgebras: 187: 92D10 Genetics For genetic algebras, see 17D92
algebro-geometric: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72
algebro-geometric: 2: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E57algebro-geometric: 3: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson,
Deligne (co)homologies)algebroids: 1: 53D17 Poisson manifolds; Poisson groupoids and algebroidsalgorithm: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsalgorithm: 2: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40algorithmic: 1: 03D32 Algorithmic randomness and dimension [See also]68Q30algorithmic: 2: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32
20 Run: December 14, 2009
Mathematics Subject Classification 2010
algorithms: 1: 05C85 Graph algorithms [See also]68R10, 68W05algorithms: 2: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmsalgorithms: 3: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension[See also]11N99, 28Dxxalgorithms: 4: 11Y16 Algorithms; complexity [See also]68Q25algorithms: 5: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30algorithms: 6: 52B55 Computational aspects related to convexity For computational geometry andalgorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxalgorithms: 7: 52B55 Computational aspects related to convexity For computational geometry andalgorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxalgorithms: 8: 65Dxx Numerical approximation and computational geometry (primarily algorithms) Fortheory, see 41-XX and 68Uxxalgorithms: 9: 65D15 Algorithms for functional approximationalgorithms: 10: 65F30 Other matrix algorithmsalgorithms: 11: 65G20 Algorithms with automatic result verificationalgorithms: 12: 65Yxx Computer aspects of numerical algorithmsalgorithms: 13: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M07algorithms: 14: 65Y10 Algorithms for specific classes of architecturesalgorithms: 15: 65Y20 Complexity and performance of numerical algorithms [See also]68Q25algorithms: 16: 68Q12 Quantum algorithms and complexity [See also]68Q05, 81P68algorithms: 17: 68Q25 Analysis of algorithms and problem complexity [See also]68W40algorithms: 18: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,see 05C85, 68Rxxalgorithms: 19: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,see 05C85, 68Rxxalgorithms: 20: 68W05 Nonnumerical algorithmsalgorithms: 21: 68W10 Parallel algorithmsalgorithms: 22: 68W15 Distributed algorithmsalgorithms: 23: 68W20 Randomized algorithmsalgorithms: 24: 68W25 Approximation algorithmsalgorithms: 25: 68W27 Online algorithmsalgorithms: 26: 68W32 Algorithms on stringsalgorithms: 27: 68W35 VLSI algorithmsalgorithms: 28: 68W40 Analysis of algorithms [See also]68Q25algorithms: 29: 76M27 Visualization algorithms
all: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
all: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
all: 3: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
all: 4: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
all: 5: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
all: 6: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
all: 7: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)[See also]28-XX, 46Txx
all: 8: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxallocation: 1: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxxallocation: 2: 91B32 Resource and cost allocation
almost: 1: 11K70 Harmonic analysis and almost periodicity
21 Run: December 14, 2009
Mathematics Subject Classification 2010
almost: 2: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quiversalmost: 3: 32M12 Almost homogeneous manifolds and spaces [See also]14M17almost: 4: 32Q60 Almost complex manifoldsalmost: 5: 34C27 Almost and pseudo-almost periodic solutionsalmost: 6: 34K14 Almost and pseudo-periodic solutionsalmost: 7: 35B15 Almost and pseudo-almost periodic solutionsalmost: 8: 39A24 Almost periodic solutionsalmost: 9: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60almost: 10: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsalmost: 11: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsalmost: 12: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)almost: 13: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)almost: 14: 53D15 Almost contact and almost symplectic manifoldsalmost: 15: 53D15 Almost contact and almost symplectic manifoldsalmost: 16: 70H12 Periodic and almost periodic solutions
along: 1: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.alphabets: 1: 94A55 Shift register sequences and sequences over finite alphabets
also: 1: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30also: 2: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45also: 3: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10also: 4: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80also: 5: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72also: 6: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S10also: 7: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
also: 8: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M20also: 9: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35also: 10: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)also: 11: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)also: 12: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)also: 13: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15also: 14: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxalso: 15: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXalso: 16: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)also: 17: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)also: 18: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)also: 19: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)also: 20: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)
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also: 21: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 forother integral operators; see also 32A25, 32M15
also: 22: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; seealso 20M20
also: 23: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)
also: 24: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)
also: 25: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)
also: 26: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)
also: 27: 51Pxx Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
also: 28: 51P05 Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
also: 29: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numericalmethods in conformal mapping, see also 30C30
also: 30: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numericalmethods in conformal mapping, see also 30C30
also: 31: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned atleast one other classification number in this section)
also: 32: 92Fxx Other natural sciences (should also be assigned at least one other classification numberin this section)
also: 33: 92F05 Other natural sciences (should also be assigned at least one other classification numberin section 92)alternating: 1: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxalternative: 1: 17D05 Alternative ringsalternative: 2: 17D15 Right alternative ringsalternative: 3: 81Q65 Alternative quantum mechanics
amalgamated: 1: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30amalgamation: 1: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsamalgams: 1: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamsamenable: 1: 43A07 Means on groups, semigroups, etc.; amenable groupsamericas: 1: 01A12 Indigenous cultures of the Americas
among: 1: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)[See also]03D15, 68Q17, 68Q19analogous: 1: 34D30 Structural stability and analogous concepts [See also]37C20analogues: 1: 11Axx Elementary number theory For analogues in number fields, see 11R04analogues: 2: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)analogues: 3: 11K41 Continuous, p-adic and abstract analoguesanalogues: 4: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)analogues: 5: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
subordinationanalogues: 6: 83C80 Analogues in lower dimensions
analysis: 1: 00A73 Dimensional analysisanalysis: 2: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S30analysis: 3: 11K70 Harmonic analysis and almost periodicityanalysis: 4: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05analysis: 5: 20F38 Other groups related to topology or analysisanalysis: 6: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXanalysis: 7: 22A10 Analysis on general topological groupsanalysis: 8: 22A20 Analysis on topological semigroupsanalysis: 9: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
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Mathematics Subject Classification 2010
for analysis thereon, see 43A80, 43A85, 43A90analysis: 10: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXanalysis: 11: 22E35 Analysis on p-adic Lie groupsanalysis: 12: 22E66 Analysis on and representations of infinite-dimensional Lie groupsanalysis: 13: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxxanalysis: 14: 26E30 Non-Archimedean analysis [See also]12J25analysis: 15: 26E35 Nonstandard analysis [See also]03H05, 28E05, 54J05analysis: 16: 26E40 Constructive real analysis [See also]03F60analysis: 17: 26E50 Fuzzy real analysis [See also]03E72, 28E10analysis: 18: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05analysis: 19: 28-XX Measure and integration For analysis on manifolds, see 58-XXanalysis: 20: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXanalysis: 21: 30Exx Miscellaneous topics of analysis in the complex domainanalysis: 22: 30Lxx Analysis on metric spacesanalysis: 23: 32A50 Harmonic analysis of several complex variables [See mainly]43-XXanalysis: 24: 32A70 Functional analysis techniques [See mainly]46Exxanalysis: 25: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)analysis: 26: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)analysis: 27: 32V20 Analysis on CR manifoldsanalysis: 28: 32W50 Other partial differential equations of complex analysisanalysis: 29: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxanalysis: 30: 34E18 Methods of nonstandard analysisanalysis: 31: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70analysis: 32: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70analysis: 33: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxanalysis: 34: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxanalysis: 35: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70analysis: 36: 37M10 Time series analysisanalysis: 37: 37N30 Dynamical systems in numerical analysisanalysis: 38: 39A12 Discrete version of topics in analysisanalysis: 39: 42-XX Harmonic analysis on Euclidean spacesanalysis: 40: 42Axx Harmonic analysis in one variableanalysis: 41: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30analysis: 42: 42B35 Function spaces arising in harmonic analysisanalysis: 43: 42B37 Harmonic analysis and PDE [See also]35-XXanalysis: 44: 42Cxx Nontrigonometric harmonic analysisanalysis: 45: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxanalysis: 46: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxanalysis: 47: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxanalysis: 48: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxanalysis: 49: 43A17 Analysis on ordered groups, Hp-theoryanalysis: 50: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05analysis: 51: 43A75 Analysis on specific compact groupsanalysis: 52: 43A77 Analysis on general compact groupsanalysis: 53: 43A80 Analysis on other specific Lie groups [See also]22Exxanalysis: 54: 43A85 Analysis on homogeneous spacesanalysis: 55: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxx
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analysis: 56: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxanalysis: 57: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxanalysis: 58: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)analysis: 59: 46Mxx Methods of category theory in functional analysis [See also]18-XXanalysis: 60: 46Nxx Miscellaneous applications of functional analysis [See also]47Nxxanalysis: 61: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsanalysis: 62: 46N40 Applications in numerical analysis [See also]65Jxxanalysis: 63: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxxanalysis: 64: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05analysis: 65: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05analysis: 66: 46S20 Nonstandard functional analysis [See also]03H05analysis: 67: 46S30 Constructive functional analysis [See also]03F60analysis: 68: 46S40 Fuzzy functional analysis [See also]03E72analysis: 69: 46S50 Functional analysis in probabilistic metric linear spacesanalysis: 70: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50analysis: 71: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxxanalysis: 72: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsanalysis: 73: 47N40 Applications in numerical analysis [See also]65Jxxanalysis: 74: 49J52 Nonsmooth analysis [See also]46G05, 58C50, 90C56analysis: 75: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C06analysis: 76: 49Q12 Sensitivity analysisanalysis: 77: 53A45 Vector and tensor analysisanalysis: 78: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesanalysis: 79: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXanalysis: 80: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15analysis: 81: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15analysis: 82: 58C50 Analysis on supermanifolds or graded manifoldsanalysis: 83: 58J42 Noncommutative global analysis, noncommutative residuesanalysis: 84: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60analysis: 85: 60G46 Martingales and classical analysisanalysis: 86: 60Hxx Stochastic analysis [See also]58J65analysis: 87: 60H30 Applications of stochastic analysis (to PDE, etc.)analysis: 88: 62A86 Fuzzy analysis in statisticsanalysis: 89: 62Hxx Multivariate analysis [See also]60Exxanalysis: 90: 62H25 Factor analysis and principal components; correspondence analysisanalysis: 91: 62H25 Factor analysis and principal components; correspondence analysisanalysis: 92: 62H30 Classification and discrimination; cluster analysis [See also]68T10, 91C20analysis: 93: 62H35 Image analysisanalysis: 94: 62H86 Multivariate analysis and fuzzinessanalysis: 95: 62J10 Analysis of variance and covarianceanalysis: 96: 62L10 Sequential analysisanalysis: 97: 62M15 Spectral analysisanalysis: 98: 62M40 Random fields; image analysisanalysis: 99: 62Nxx Survival analysis and censored dataanalysis: 100: 62N86 Fuzziness, and survival analysis and censored dataanalysis: 101: 65-XX Numerical analysisanalysis: 102: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05analysis: 103: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
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Mathematics Subject Classification 2010
methods in conformal mapping, see also 30C30analysis: 104: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30analysis: 105: 65Gxx Error analysis and interval analysisanalysis: 106: 65Gxx Error analysis and interval analysisanalysis: 107: 65G40 General methods in interval analysisanalysis: 108: 65Jxx Numerical analysis in abstract spacesanalysis: 109: 65Txx Numerical methods in Fourier analysisanalysis: 110: 68Q25 Analysis of algorithms and problem complexity [See also]68W40analysis: 111: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40analysis: 112: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30analysis: 113: 68W40 Analysis of algorithms [See also]68Q25analysis: 114: 70J10 Modal analysisanalysis: 115: 70K05 Phase plane analysis, limit cyclesanalysis: 116: 74N15 Analysis of microstructureanalysis: 117: 76M35 Stochastic analysisanalysis: 118: 76M55 Dimensional analysis and similarityanalysis: 119: 76M60 Symmetry analysis, Lie group and algebra methodsanalysis: 120: 78M35 Asymptotic analysisanalysis: 121: 80M35 Asymptotic analysisanalysis: 122: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysisanalysis: 123: 91B84 Economic time series analysis [See also]62M10analysis: 124: 93C70 Time-scale analysis and singular perturbationsanalysis: 125: 97Ixx Analysisanalysis: 126: 97I80 Complex analysisanalysis: 127: 97N40 Numerical analysisanalytic: 1: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)analytic: 2: 11Mxx Zeta and L-functions: analytic theoryanalytic: 3: 11P82 Analytic theory of partitionsanalytic: 4: 11R47 Other analytic theory [See also]11Nxxanalytic: 5: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)analytic: 6: 11Y35 Analytic computationsanalytic: 7: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15analytic: 8: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsanalytic: 9: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13analytic: 10: 14G22 Rigid analytic geometryanalytic: 11: 14H15 Families, moduli (analytic) [See also]30F10, 32G15analytic: 12: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxanalytic: 13: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13analytic: 14: 14K20 Analytic theory; abelian integrals and differentialsanalytic: 15: 14Pxx Real algebraic and real analytic geometryanalytic: 16: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C05analytic: 17: 17B15 Representations, analytic theoryanalytic: 18: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05analytic: 19: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exxanalytic: 20: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H05analytic: 21: 30B40 Analytic continuationanalytic: 22: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10analytic: 23: 30D05 Functional equations in the complex domain, iteration and composition of analytic
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Mathematics Subject Classification 2010
functions [See also]34Mxx, 37Fxx, 39-XXanalytic: 24: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxanalytic: 25: 30G25 Discrete analytic functionsanalytic: 26: 30G30 Other generalizations of analytic functions (including abstract-valued functions)analytic: 27: 30Hxx Spaces and algebras of analytic functionsanalytic: 28: 30H05 Bounded analytic functionsanalytic: 29: 30H50 Algebras of analytic functionsanalytic: 30: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12analytic: 31: 32Bxx Local analytic geometry [See also]13-XX and 14-XXanalytic: 32: 32B05 Analytic algebras and generalizations, preparation theoremsanalytic: 33: 32B10 Germs of analytic sets, local parametrizationanalytic: 34: 32B15 Analytic subsets of affine spaceanalytic: 35: 32Cxx Analytic spacesanalytic: 36: 32C09 Embedding of real analytic manifoldsanalytic: 37: 32C18 Topology of analytic spacesanalytic: 38: 32C20 Normal analytic spacesanalytic: 39: 32C22 Embedding of analytic spacesanalytic: 40: 32C25 Analytic subsets and submanifoldsanalytic: 41: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27analytic: 42: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N30analytic: 43: 32C36 Local cohomology of analytic spacesanalytic: 44: 32Dxx Analytic continuationanalytic: 45: 32D15 Continuation of analytic objectsanalytic: 46: 32Gxx Deformations of analytic structuresanalytic: 47: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15analytic: 48: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxanalytic: 49: 32J05 Compactification of analytic spacesanalytic: 50: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)analytic: 51: 32K05 Banach analytic spaces [See also]58Bxxanalytic: 52: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25analytic: 53: 32S10 Invariants of analytic local ringsanalytic: 54: 32S15 Equisingularity (topological and analytic) [See also]14E15analytic: 55: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundariesanalytic: 56: 32V25 Extension of functions and other analytic objects from CR manifoldsanalytic: 57: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)analytic: 58: 35A20 Analytic methods, singularitiesanalytic: 59: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemsanalytic: 60: 37P10 Analytic and meromorphic mapsanalytic: 61: 40Hxx Functional analytic methods in summabilityanalytic: 62: 40H05 Functional analytic methods in summabilityanalytic: 63: 46E05 Lattices of continuous, differentiable or analytic functionsanalytic: 64: 46E10 Topological linear spaces of continuous, differentiable or analytic functionsanalytic: 65: 46E15 Banach spaces of continuous, differentiable or analytic functionsanalytic: 66: 46E20 Hilbert spaces of continuous, differentiable or analytic functionsanalytic: 67: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15analytic: 68: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J15analytic: 69: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40analytic: 70: 46G15 Functional analytic lifting theory [See also]28A51
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Mathematics Subject Classification 2010
analytic: 71: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,32A35, 32A37, 32A38, 42B30
analytic: 72: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,including analytic and meromorphic ones)
analytic: 73: 47L65 Crossed product algebras (analytic crossed products)analytic: 74: 51Nxx Analytic and descriptive geometryanalytic: 75: 51N10 Affine analytic geometryanalytic: 76: 51N15 Projective analytic geometryanalytic: 77: 51N20 Euclidean analytic geometryanalytic: 78: 51N25 Analytic geometry with other transformation groupsanalytic: 79: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05analytic: 80: 58J52 Determinants and determinant bundles, analytic torsionanalytic: 81: 58K20 Algebraic and analytic properties of mappingsanalytic: 82: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)analytic: 83: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)analytic: 84: 94C05 Analytic circuit theoryanalytic: 85: 97G70 Analytic geometry. Vector algebra
analytical: 1: 13J07 Analytical algebras and rings [See also]32B05analytical: 2: 26D20 Other analytical inequalitiesanalytical: 3: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)analytical: 4: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XXand: 1: 01A80 Sociology (and profession) of mathematicsand: 2: 19J10 Whitehead (and related) torsionand: 3: 37A40 Nonsingular (and infinite-measure preserving) transformationsand: 4: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesand: 5: 46Kxx Topological (rings and) algebras with an involution [See also]16W10
and/or: 1: 39B52 Equations for functions with more general domains and/or rangesandre-quillen: 1: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)anelastic: 1: 74R20 Anelastic fracture and damage
angelic: 1: 46A50 Compactness in topological linear spaces; angelic spaces, etc.animal: 1: 92D50 Animal behavior
animals: 1: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41animals: 2: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50
anisotropy: 1: 74E10 Anisotropyannihilators: 1: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimensionanomalies: 1: 81T50 Anomalies
anosov: 1: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)anr: 1: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15ansatz: 1: 82B23 Exactly solvable models; Bethe ansatz
antennas: 1: 78A50 Antennas, wave-guidesanthropology: 1: 91Dxx Mathematical sociology (including anthropology)
antidifferentiation: 1: 26A36 Antidifferentiationaperiodic: 1: 52C23 Quasicrystals, aperiodic tilings
appell: 1: 33C65 Appell, Horn and Lauricella functionsapplicable: 1: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics ingeneral)application: 1: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05application: 2: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,35K05, 35L05application: 3: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
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Mathematics Subject Classification 2010
[See also]81T13, etc.application: 4: 94A11 Application of orthogonal and other special functionsapplication: 5: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30
applications: 1: 03B80 Other applications of logicapplications: 2: 03C98 Applications of model theory [See also]03C60applications: 3: 03D80 Applications of computability and recursion theoryapplications: 4: 03E75 Applications of set theoryapplications: 5: 03H10 Other applications of nonstandard models (economics, physics, etc.)applications: 6: 05Bxx Designs and configurations For applications of design theory, see 94C30applications: 7: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C15applications: 8: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15applications: 9: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q55applications: 10: 08A70 Applications of universal algebra in computer scienceapplications: 11: 11B37 Recurrences For applications to special functions, see 33-XXapplications: 12: 11Hxx Geometry of numbers For applications in coding theory, see 94B75applications: 13: 11J87 Schmidt Subspace Theorem and applicationsapplications: 14: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasapplications: 15: 11N36 Applications of sieve methodsapplications: 16: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxapplications: 17: 11P55 Applications of the Hardy-Littlewood method [See also]11D85applications: 18: 11Zxx Miscellaneous applications of number theoryapplications: 19: 11Z05 Miscellaneous applications of number theoryapplications: 20: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxxapplications: 21: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxxapplications: 22: 13Pxx Computational aspects and applications [See also]14Qxx, 68W30applications: 23: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)applications: 24: 14C35 Applications of methods of algebraic K-theory [See also]19Exxapplications: 25: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxapplications: 26: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B40applications: 27: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05applications: 28: 16B70 Applications of logic [See also]03Cxxapplications: 29: 16E45 Differential graded algebras and applicationsapplications: 30: 16T05 Hopf algebras and their applications [See also]16S40, 57T05applications: 31: 17B80 Applications to integrable systemsapplications: 32: 17B81 Applications to physicsapplications: 33: 17C90 Applications to physicsapplications: 34: 19L64 Computations, geometric applicationsapplications: 35: 19Mxx Miscellaneous applications of K-theoryapplications: 36: 19M05 Miscellaneous applications of K-theoryapplications: 37: 20A15 Applications of logic to group theoryapplications: 38: 20C35 Applications of group representations to physicsapplications: 39: 20G45 Applications to physicsapplications: 40: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F30applications: 41: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10applications: 42: 30C40 Kernel functions and applicationsapplications: 43: 32C81 Applications to physicsapplications: 44: 32G81 Applications to physicsapplications: 45: 32J81 Applications to physicsapplications: 46: 32L81 Applications to physicsapplications: 47: 33C90 Applications
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Mathematics Subject Classification 2010
applications: 48: 33D90 Applicationsapplications: 49: 34B60 Applicationsapplications: 50: 37Nxx Applicationsapplications: 51: 39A60 Applicationsapplications: 52: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxapplications: 53: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C10applications: 54: 46Nxx Miscellaneous applications of functional analysis [See also]47Nxxapplications: 55: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsapplications: 56: 46N20 Applications to differential and integral equationsapplications: 57: 46N30 Applications in probability theory and statisticsapplications: 58: 46N40 Applications in numerical analysis [See also]65Jxxapplications: 59: 46N50 Applications in quantum physicsapplications: 60: 46N55 Applications in statistical physicsapplications: 61: 46N60 Applications in biology and other sciencesapplications: 62: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationsapplications: 63: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxapplications: 64: 47L90 Applications of operator algebras to physicsapplications: 65: 47Nxx Miscellaneous applications of operator theory [See also]46Nxxapplications: 66: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsapplications: 67: 47N20 Applications to differential and integral equationsapplications: 68: 47N30 Applications in probability theory and statisticsapplications: 69: 47N40 Applications in numerical analysis [See also]65Jxxapplications: 70: 47N50 Applications in the physical sciencesapplications: 71: 47N60 Applications in chemistry and life sciencesapplications: 72: 47N70 Applications in systems theory, circuits, and control theoryapplications: 73: 49N90 Applications of optimal control and differential games [See also]90C90, 93C95applications: 74: 53B50 Applications to physicsapplications: 75: 53C80 Applications to physicsapplications: 76: 53Zxx Applications to physicsapplications: 77: 53Z05 Applications to physicsapplications: 78: 54Hxx Connections with other structures, applicationsapplications: 79: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXapplications: 80: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T20applications: 81: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)applications: 82: 58E10 Applications to the theory of geodesics (problems in one independent variable)applications: 83: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05applications: 84: 58E17 Pareto optimality, etc., applications to economics [See also]90C29applications: 85: 58E25 Applications to control theory [See also]49-XX, 93-XXapplications: 86: 58E50 Applicationsapplications: 87: 58J90 Applicationsapplications: 88: 58Zxx Applications to physicsapplications: 89: 58Z05 Applications to physicsapplications: 90: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXapplications: 91: 60H30 Applications of stochastic analysis (to PDE, etc.)applications: 92: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40applications: 93: 60J28 Applications of continuous-time Markov processes on discrete state spacesapplications: 94: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxapplications: 95: 60J85 Applications of branching processes [See also]92Dxx
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Mathematics Subject Classification 2010
applications: 96: 60K10 Applications (reliability, demand theory, etc.)applications: 97: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxapplications: 98: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxxapplications: 99: 60K40 Other physical applications of random processesapplications: 100: 62Pxx Applications [See also]90-XX, 91-XX, 92-XXapplications: 101: 62P05 Applications to actuarial sciences and financial mathematicsapplications: 102: 62P10 Applications to biology and medical sciencesapplications: 103: 62P12 Applications to environmental and related topicsapplications: 104: 62P15 Applications to psychologyapplications: 105: 62P20 Applications to economics [See also]91Bxxapplications: 106: 62P25 Applications to social sciencesapplications: 107: 62P30 Applications in engineering and industryapplications: 108: 62P35 Applications to physicsapplications: 109: 65Zxx Applications to physicsapplications: 110: 65Z05 Applications to physicsapplications: 111: 68Uxx Computing methodologies and applicationsapplications: 112: 78A55 Technical applicationsapplications: 113: 78A70 Biological applications [See also]91D30, 92C30applications: 114: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40applications: 115: 81Vxx Applications to specific physical systemsapplications: 116: 82Dxx Applications to specific types of physical systemsapplications: 117: 90C90 Applications of mathematical programmingapplications: 118: 91A80 Applications of game theoryapplications: 119: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)applications: 120: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)applications: 121: 92C50 Medical applications (general)applications: 122: 93C95 Applicationsapplications: 123: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50applications: 124: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
[See also]11H31, 11H71applications: 125: 94C15 Applications of graph theory [See also]05Cxx, 68R10applications: 126: 94C30 Applications of design theory [See also]05Bxxapplications: 127: 97Mxx Mathematical modeling, applications of mathematicsapplications: 128: 97Rxx Computer science applicationsapplications: 129: 97R20 Applications in mathematicsapplications: 130: 97R30 Applications in sciencesapplications: 131: 97R70 User programs, administrative applications
applied: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86applied: 2: 55Uxx Applied homological algebra and category theory [See also]18Gxxapplied: 3: 97K80 Applied statistics
approach: 1: 58A03 Topos-theoretic approach to differentiable manifoldsapproach: 2: 76F20 Dynamical systems approach to turbulence [See also]37-XX
approaches: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionisticand similar approaches see 03F55approaches: 2: 62M45 Neural nets and related approachesapproaches: 3: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C30approaches: 4: 70Gxx General models, approaches, and methods [See also]37-XXapproaches: 5: 93D25 Input-output approaches
approximate: 1: 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)approximate: 2: 41A55 Approximate quadraturesapproximate: 3: 81P50 Quantum state estimation, approximate cloningapproximate: 4: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanics
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Mathematics Subject Classification 2010
approximation: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,40A15
approximation: 2: 11Jxx Diophantine approximation, transcendental number theory [See also]11K60approximation: 3: 11J04 Homogeneous approximation to one numberapproximation: 4: 11J13 Simultaneous homogeneous approximation, linear formsapproximation: 5: 11J17 Approximation by numbers from a fixed fieldapproximation: 6: 11J61 Approximation in non-Archimedean valuationsapproximation: 7: 11J68 Approximation to algebraic numbersapproximation: 8: 11K60 Diophantine approximation [See also]11Jxxapproximation: 9: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
14B25approximation: 10: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10approximation: 11: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
approximation: 12: 30E10 Approximation in the complex domainapproximation: 13: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolationapproximation: 14: 33F05 Numerical approximation and evaluation [See also]65D20approximation: 15: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxapproximation: 16: 34K07 Theoretical approximation of solutionsapproximation: 17: 34K28 Numerical approximation of solutionsapproximation: 18: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumapproximation: 19: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxapproximation: 20: 37L65 Special approximation methods (nonlinear Galerkin, etc.)approximation: 21: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxapproximation: 22: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)approximation: 23: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15approximation: 24: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 25: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 26: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 27: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 28: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 29: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximation: 30: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
approximation: 31: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
approximation: 32: 41A15 Spline approximationapproximation: 33: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)approximation: 34: 41A20 Approximation by rational functionsapproximation: 35: 41A21 Pade approximationapproximation: 36: 41A25 Rate of convergence, degree of approximationapproximation: 37: 41A28 Simultaneous approximation
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Mathematics Subject Classification 2010
approximation: 38: 41A29 Approximation with constraintsapproximation: 39: 41A30 Approximation by other special function classesapproximation: 40: 41A35 Approximation by operators (in particular, by integral operators)approximation: 41: 41A36 Approximation by positive operatorsapproximation: 42: 41A45 Approximation by arbitrary linear expressionsapproximation: 43: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropyapproximation: 44: 41A50 Best approximation, Chebyshev systemsapproximation: 45: 41A52 Uniqueness of best approximationapproximation: 46: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)approximation: 47: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)approximation: 48: 41A80 Remainders in approximation formulasapproximation: 49: 42A10 Trigonometric approximationapproximation: 50: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxapproximation: 51: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxapproximation: 52: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20approximation: 53: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L20approximation: 54: 47A58 Operator approximation theoryapproximation: 55: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsapproximation: 56: 52A27 Approximation by convex setsapproximation: 57: 62L20 Stochastic approximationapproximation: 58: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxapproximation: 59: 65D15 Algorithms for functional approximationapproximation: 60: 65T40 Trigonometric approximation and interpolationapproximation: 61: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15approximation: 62: 68W25 Approximation algorithmsapproximation: 63: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)approximation: 64: 74G15 Numerical approximation of solutionsapproximation: 65: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)approximation: 66: 74H15 Numerical approximation of solutionsapproximation: 67: 83C25 Approximation procedures, weak fieldsapproximation: 68: 90C59 Approximation methods and heuristicsapproximation: 69: 97N50 Interpolation and approximation
approximations: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximations: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
approximations: 3: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)[See also]30E15
approximations: 4: 49M25 Discrete approximationsapproximations: 5: 57Q55 Approximationsapproximations: 6: 57R12 Smooth approximationsapproximations: 7: 62E17 Approximations to distributions (nonasymptotic)
aptitudes: 1: 97C40 Intelligence and aptitudesarakelov: 1: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30
arbitrary: 1: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25arbitrary: 2: 11L26 Sums over arbitrary intervals
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arbitrary: 3: 20G15 Linear algebraic groups over arbitrary fieldsarbitrary: 4: 41A45 Approximation by arbitrary linear expressionsarbitrary: 5: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
arches: 1: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)architecture: 1: 00A67 Mathematics and architecturearchitecture: 2: 68M07 Mathematical problems of computer architecturearchitecture: 3: 97M80 Arts, music, language, architecture
architectures: 1: 65Y10 Algorithms for specific classes of architecturesarcs: 1: 14E18 Arcs and motivic integrationare: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05are: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05are: 3: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)area: 1: 26B15 Integration: length, area, volume [See also]28A75, 51M25area: 2: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15area: 3: 51M25 Length, area and volume [See also]26B15area: 4: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q20area: 5: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areaarea: 1: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areaareal: 1: 53B40 Finsler spaces and generalizations (areal metrics)areal: 2: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B20areas: 1: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L05areas: 2: 97G30 Areas and volumes
areolar: 1: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenicfunctions)
arising: 1: 16Sxx Rings and algebras arising under various constructionsarising: 2: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22arising: 3: 37G30 Infinite nonwandering sets arising in bifurcationsarising: 4: 42B35 Function spaces arising in harmonic analysisarising: 5: 70J50 Systems arising from the discretization of structural vibration problems
arithmetic: 1: 03C62 Models of arithmetic and set theory [See also]03Hxxarithmetic: 2: 03F30 First-order arithmetic and fragmentsarithmetic: 3: 03F35 Second- and higher-order arithmetic and fragments [See also]03B30arithmetic: 4: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L05arithmetic: 5: 11A25 Arithmetic functions; related numbers; inversion formulasarithmetic: 6: 11B25 Arithmetic progressions [See also]11N13arithmetic: 7: 11B30 Arithmetic combinatorics; higher degree uniformityarithmetic: 8: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,20H10, 22E40arithmetic: 9: 11F75 Cohomology of arithmetic groupsarithmetic: 10: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxxarithmetic: 11: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G35arithmetic: 12: 11G42 Arithmetic mirror symmetry [See also]14J33arithmetic: 13: 11K65 Arithmetic functions [See also]11Nxxarithmetic: 14: 11N37 Asymptotic results on arithmetic functionsarithmetic: 15: 11N56 Rate of growth of arithmetic functionsarithmetic: 16: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsarithmetic: 17: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsarithmetic: 18: 11R58 Arithmetic theory of algebraic function fields [See also]14-XXarithmetic: 19: 11T55 Arithmetic theory of polynomial rings over finite fieldsarithmetic: 20: 11U10 Nonstandard arithmetic [See also]03H15arithmetic: 21: 11Y70 Values of arithmetic functions; tables
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arithmetic: 22: 12E30 Field arithmeticarithmetic: 23: 12L15 Nonstandard arithmetic [See also]03H15arithmetic: 24: 13Fxx Arithmetic rings and other special ringsarithmetic: 25: 14D10 Arithmetic ground fields (finite, local, global)arithmetic: 26: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxxarithmetic: 27: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30arithmetic: 28: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxxarithmetic: 29: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32arithmetic: 30: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxxarithmetic: 31: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxxarithmetic: 32: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-tion theory, see 16G30arithmetic: 33: 19F15 Symbols and arithmetic [See also]11R37arithmetic: 34: 20D60 Arithmetic and combinatorial problemsarithmetic: 35: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55arithmetic: 36: 20M13 Arithmetic theory of monoidsarithmetic: 37: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A45arithmetic: 38: 37P35 Arithmetic properties of periodic pointsarithmetic: 39: 37P55 Arithmetic dynamics on general algebraic varietiesarithmetic: 40: 65G30 Interval and finite arithmeticarithmetic: 41: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M07arithmetic: 42: 94B40 Arithmetic codes [See also]11T71, 14G50arithmetic: 43: 97Fxx Arithmetic, number theoryarithmetic: 44: 97F90 Real life mathematics, practical arithmetic
arnol′: 1: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionaronszajn: 1: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35arrangements: 1: 14N20 Configurations and arrangements of linear subspacesarrangements: 2: 32S22 Relations with arrangements of hyperplanes [See also]52C35arrangements: 3: 52C30 Planar arrangements of lines and pseudolinesarrangements: 4: 52C35 Arrangements of points, flats, hyperplanes [See also]32S22
arrays: 1: 05B15 Orthogonal arrays, Latin squares, Room squaresarticles: 1: 00B10 Collections of articles of general interestarticles: 2: 00B15 Collections of articles of miscellaneous specific contentarticles: 3: 00B60 Collections of reprinted articles [See also]01A75
artificial: 1: 68Txx Artificial intelligenceartificial: 2: 68T27 Logic in artificial intelligenceartificial: 3: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxartificial: 4: 97R40 Artificial intelligence
artin: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,14B25
artin: 2: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10artin: 3: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A30artin: 4: 20F36 Braid groups; Artin groups
artinian: 1: 13E10 Artinian rings and modules, finite-dimensional algebrasartinian: 2: 16G10 Representations of Artinian ringsartinian: 3: 16P20 Artinian rings and modules
arts: 1: 00A66 Mathematics and visual arts, visualizationarts: 2: 97M80 Arts, music, language, architecture
as: 1: 11D68 Rational numbers as sums of fractionsas: 2: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXas: 3: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)as: 4: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionas: 5: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XX
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as: 6: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,20L05, 20Mxx
as: 7: 19K14 K0 as an ordered group, tracesas: 8: 20F29 Representations of groups as automorphism groups of algebraic systemsas: 9: 22F50 Groups as automorphisms of other structuresas: 10: 32Q35 Complex manifolds as subdomains of Euclidean spaceas: 11: 32V15 CR manifolds as boundaries of domainsas: 12: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
as: 13: 33C75 Elliptic integrals as hypergeometric functionsas: 14: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemsas: 15: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40as: 16: 47Cxx Individual linear operators as elements of algebraic systemsas: 17: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S05as: 18: 81Q80 Special quantum systems, such as solvable systemsas: 19: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)asia: 1: 01A29 Southeast Asia
askey: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
askey-wilson: 1: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)aspects: 1: 03Axx Philosophical aspects of logic and foundationsaspects: 2: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52aspects: 3: 03D78 Computation over the reals For constructive aspects, see 03F60aspects: 4: 03E40 Other aspects of forcing and Boolean-valued modelsaspects: 5: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
57M25aspects: 6: 05E10 Combinatorial aspects of representation theory [See also]20C30aspects: 7: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C80aspects: 8: 05E40 Combinatorial aspects of commutative algebraaspects: 9: 05E45 Combinatorial aspects of simplicial complexesaspects: 10: 06A11 Algebraic aspects of posetsaspects: 11: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G35aspects: 12: 11Txx Finite fields and commutative rings (number-theoretic aspects)aspects: 13: 12E20 Finite fields (field-theoretic aspects)aspects: 14: 12Yxx Computational aspects of field theory and polynomialsaspects: 15: 12Y05 Computational aspects of field theory and polynomialsaspects: 16: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxaspects: 17: 13Pxx Computational aspects and applications [See also]14Qxx, 68W30aspects: 18: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E57aspects: 19: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32aspects: 20: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N30aspects: 21: 14L40 Other algebraic groups (geometric aspects)aspects: 22: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W30aspects: 23: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30aspects: 24: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R50aspects: 25: 16Zxx Computational aspects of associative ringsaspects: 26: 16Z05 Computational aspects of associative rings [See also]68W30aspects: 27: 20Fxx Special aspects of infinite or finite groupsaspects: 28: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D24aspects: 29: 32Q55 Topological aspects of complex manifoldsaspects: 30: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants
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Mathematics Subject Classification 2010
aspects: 31: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
aspects: 32: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
aspects: 33: 33Fxx Computational aspectsaspects: 34: 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)aspects: 35: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J15aspects: 36: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxaspects: 37: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXaspects: 38: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxaspects: 39: 53C08 Gerbes, differential characters: differential geometric aspectsaspects: 40: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R32aspects: 41: 53C43 Differential geometric aspects of harmonic maps [See also]58E20aspects: 42: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J33aspects: 43: 53D40 Floer homology and cohomology, symplectic aspectsaspects: 44: 54D05 Connected and locally connected spaces (general aspects)aspects: 45: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05aspects: 46: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80aspects: 47: 58K45 Singularities of vector fields, topological aspectsaspects: 48: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)aspects: 49: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)aspects: 50: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35aspects: 51: 65Yxx Computer aspects of numerical algorithmsaspects: 52: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)aspects: 53: 76A25 Superfluids (classical aspects)aspects: 54: 97B50 Teacher education For research aspects, see 97C70aspects: 55: 97C60 Sociological aspects of learningaspects: 56: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxxaspects: 57: 97Q20 Affective aspects in teaching computer scienceaspects: 58: 97Q40 Sociological aspects
asphericity: 1: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericityassessment: 1: 97D60 Student assessment, achievement control and ratingassessment: 2: 97Q70 Student assessment
asset: 1: 91B25 Asset pricing modelsassigned: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35assigned: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)assigned: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)assigned: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)assigned: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)assigned: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)assigned: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
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Mathematics Subject Classification 2010
tion number in Section 40)assigned: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)assigned: 9: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)assigned: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)assigned: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)assigned: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)assigned: 13: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)assigned: 14: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)assigned: 15: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)assigned: 16: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)assigned: 17: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)assigned: 18: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)assignment: 1: 90B80 Discrete location and assignment [See also]90C10
assisted: 1: 97U50 Computer assisted instruction; e-learningassociated: 1: 11F52 Modular forms associated to Drinfel′d modulesassociated: 2: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weylgroup multiple Dirichlet seriesassociated: 3: 11N60 Distribution functions associated with additive and positive multiplicative functionsassociated: 4: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and relatedtopicsassociated: 5: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)[See also]16W10, 17C40, 17C50associated: 6: 17C30 Associated groups, automorphismsassociated: 7: 17C36 Associated manifoldsassociated: 8: 17C37 Associated geometriesassociated: 9: 17C50 Jordan structures associated with other structures [See also]16W10associated: 10: 18C20 Algebras and Kleisli categories associated with monadsassociated: 11: 20F40 Associated Lie structuresassociated: 12: 33C52 Orthogonal polynomials and functions associated with root systemsassociated: 13: 33C67 Hypergeometric functions associated with root systemsassociated: 14: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonaldpolynomials, etc.)associated: 15: 33D67 Basic hypergeometric functions associated with root systems
association: 1: 05E30 Association schemes, strongly regular graphsassociation: 2: 62H20 Measures of association (correlation, canonical correlation, etc.)associative: 1: 16-XX Associative rings and algebras For the commutative case, see 13-XXassociative: 2: 16Zxx Computational aspects of associative ringsassociative: 3: 16Z05 Computational aspects of associative rings [See also]68W30associative: 4: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)[See also]16W10, 17C40, 17C50associative: 5: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topologyastronomy: 1: 35Q85 PDEs in connection with astronomy and astrophysicsastronomy: 2: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15astronomy: 3: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15
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astronomy: 4: 85A35 Statistical astronomyastronomy: 5: 97M50 Physics, astronomy, technology, engineering
astrophysical: 1: 76E20 Stability and instability of geophysical and astrophysical flowsastrophysics: 1: 35Q85 PDEs in connection with astronomy and astrophysicsastrophysics: 2: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15astrophysics: 3: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15asymmetric: 1: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric fieldtheories
asymmetric: 2: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric fieldtheoriesasymptotic: 1: 05A16 Asymptotic enumerationasymptotic: 2: 11N37 Asymptotic results on arithmetic functionsasymptotic: 3: 11N45 Asymptotic results on counting functions for algebraic and topological structuresasymptotic: 4: 20F69 Asymptotic properties of groupsasymptotic: 5: 30E15 Asymptotic representations in the complex domainasymptotic: 6: 34C41 Equivalence, asymptotic equivalenceasymptotic: 7: 34D05 Asymptotic propertiesasymptotic: 8: 34Exx Asymptotic theoryasymptotic: 9: 34E05 Asymptotic expansionsasymptotic: 10: 34K25 Asymptotic theoryasymptotic: 11: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionsasymptotic: 12: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionsasymptotic: 13: 35B40 Asymptotic behavior of solutionsasymptotic: 14: 35C20 Asymptotic expansionsasymptotic: 15: 35P20 Asymptotic distribution of eigenvalues and eigenfunctionsasymptotic: 16: 37K40 Soliton theory, asymptotic behavior of solutionsasymptotic: 17: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)[See also]30E15asymptotic: 18: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)[See also]30E15asymptotic: 19: 46B06 Asymptotic theory of Banach spaces [See also]52A23asymptotic: 20: 52A23 Asymptotic theory of convex bodies [See also]46B06asymptotic: 21: 58K55 Asymptotic behaviorasymptotic: 22: 62E20 Asymptotic distribution theoryasymptotic: 23: 62F05 Asymptotic properties of testsasymptotic: 24: 62F12 Asymptotic properties of estimatorsasymptotic: 25: 62G20 Asymptotic propertiesasymptotic: 26: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,etc.)asymptotic: 27: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,etc.)asymptotic: 28: 76M45 Asymptotic methods, singular perturbationsasymptotic: 29: 78M35 Asymptotic analysisasymptotic: 30: 80M35 Asymptotic analysisasymptotic: 31: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)asymptotic: 32: 93D20 Asymptotic stability
asymptotics: 1: 34E10 Perturbations, asymptoticsasymptotics: 2: 34M30 Asymptotics, summation methodsasymptotics: 3: 45M05 Asymptoticsasymptotics: 4: 58J37 Perturbations; asymptotics
at: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assignedat least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35
at: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)
at: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
at: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
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number from Section 32 describing the type of problem)at: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)at: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)at: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)at: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)at: 9: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)at: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)at: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)at: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)at: 13: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)at: 14: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)at: 15: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)at: 16: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)at: 17: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)at: 18: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)atmospheres: 1: 85A20 Planetary atmospheresatmospheric: 1: 76B60 Atmospheric waves [See also]86A10atmospheric: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U05atomic: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M05atomic: 2: 81V45 Atomic physics
attainable: 1: 93B03 Attainable setsattracting: 1: 37L25 Inertial manifolds and other invariant attracting setsattractors: 1: 34D45 Attractors [See also]37C70, 37D45attractors: 2: 35B41 Attractorsattractors: 3: 37B25 Lyapunov functions and stability; attractors, repellersattractors: 4: 37C70 Attractors and repellers, topological structureattractors: 5: 37D45 Strange attractors, chaotic dynamicsattractors: 6: 37G35 Attractors and their bifurcationsattractors: 7: 37L30 Attractors and their dimensions, Lyapunov exponents
auctions: 1: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)audiovisual: 1: 97U80 Audiovisual media
auslander-reiten: 1: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quiversauslander-reiten: 2: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
authentication: 1: 94A62 Authentication and secret sharing [See also]81P94auto-correlation: 1: 62M10 Time series, auto-correlation, regression, etc. [See also]91B84
automata: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,68Q70, 68R15automata: 2: 11B85 Automata sequencesautomata: 3: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxxautomata: 4: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70
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automata: 5: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50automata: 6: 37B15 Cellular automata [See also]68Q80automata: 7: 68Q45 Formal languages and automata [See also]03D05, 68Q70, 94A45automata: 8: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M35automata: 9: 68Q80 Cellular automata [See also]37B15
automated: 1: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q05automatic: 1: 46H40 Automatic continuityautomatic: 2: 65G20 Algorithms with automatic result verificationautomatic: 3: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
automorphic: 1: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms andfunctions)
automorphic: 2: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45
automorphic: 3: 11F03 Modular and automorphic functionsautomorphic: 4: 11F12 Automorphic forms, one variableautomorphic: 5: 11F30 Fourier coefficients of automorphic formsautomorphic: 6: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20automorphic: 7: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20automorphic: 8: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formsautomorphic: 9: 11F55 Other groups and their modular and automorphic forms (several variables)automorphic: 10: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsautomorphic: 11: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesautomorphic: 12: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsautomorphic: 13: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxautomorphic: 14: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxxautomorphic: 15: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F35automorphic: 16: 32N05 General theory of automorphic functions of several complex variablesautomorphic: 17: 32N10 Automorphic formsautomorphic: 18: 32N15 Automorphic functions in symmetric domainsautomorphic: 19: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30automorphic: 20: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30automorphic: 21: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsautomorphism: 1: 11H56 Automorphism groups of latticesautomorphism: 2: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXautomorphism: 3: 20B27 Infinite automorphism groups [See also]12F10automorphism: 4: 20F28 Automorphism groups of groups [See also]20E36automorphism: 5: 20F29 Representations of groups as automorphism groups of algebraic systemsautomorphism: 6: 22D45 Automorphism groups of locally compact groupsautomorphism: 7: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10automorphism: 8: 32M17 Automorphism groups of Cn and affine manifoldsautomorphism: 9: 51A10 Homomorphism, automorphism and dualities
automorphisms: 1: 08A35 Automorphisms, endomorphismsautomorphisms: 2: 14E07 Birational automorphisms, Cremona group and generalizationsautomorphisms: 3: 14H37 Automorphismsautomorphisms: 4: 14J50 Automorphisms of surfaces and higher-dimensional varietiesautomorphisms: 5: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)automorphisms: 6: 16W20 Automorphisms and endomorphisms
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automorphisms: 7: 17A36 Automorphisms, derivations, other operatorsautomorphisms: 8: 17B40 Automorphisms, derivations, other operatorsautomorphisms: 9: 17C30 Associated groups, automorphismsautomorphisms: 10: 20D45 Automorphismsautomorphisms: 11: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]automorphisms: 12: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]automorphisms: 13: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxxautomorphisms: 14: 20K30 Automorphisms, homomorphisms, endomorphisms, etc.automorphisms: 15: 22F50 Groups as automorphisms of other structuresautomorphisms: 16: 32Mxx Complex spaces with a group of automorphismsautomorphisms: 17: 46L40 Automorphisms
availability: 1: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N05averaging: 1: 34C29 Averaging methodaveraging: 2: 34K33 Averagingaveraging: 3: 70K65 Averaging of perturbations
axially: 1: 35B07 Axially symmetric solutionsaxiom: 1: 03E25 Axiom of choice and related propositionsaxiom: 2: 03E50 Continuum hypothesis and Martin’s axiom [See also]03E57axiom: 3: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)axiom: 4: 51D10 Abstract geometries with exchange axiom
axiomatic: 1: 03D75 Abstract and axiomatic computability and recursion theoryaxiomatic: 2: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C60axiomatic: 3: 31Dxx Axiomatic potential theoryaxiomatic: 4: 31D05 Axiomatic potential theoryaxiomatic: 5: 52A01 Axiomatic and generalized convexityaxiomatic: 6: 55U35 Abstract and axiomatic homotopy theoryaxiomatic: 7: 81T05 Axiomatic quantum field theory; operator algebrasaxiomatic: 8: 93A05 Axiomatic system theory
axiomatics: 1: 03E30 Axiomatics of classical set theory and its fragmentsaxiomatics: 2: 20A05 Axiomatics and elementary propertiesaxiomatics: 3: 70Axx Axiomatics, foundationsaxiomatics: 4: 70A05 Axiomatics, foundationsaxiomatics: 5: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solidsaxiomatics: 6: 81Pxx Axiomatics, foundations, philosophy
axioms: 1: 03E57 Generic absoluteness and forcing axioms [See also]03E50axioms: 2: 03E65 Other hypotheses and axiomsaxioms: 3: 54D10 Lower separation axioms (T0–T3, etc.)axioms: 4: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)axioms: 5: 55N40 Axioms for homology theory and uniqueness theoremsaxioms: 6: 60A05 Axioms; other general questions
azumaya: 1: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)babylonian: 1: 01A17 Babylonian
backgrounds: 1: 81T20 Quantum field theory on curved space backgroundsbaire: 1: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05baire: 2: 54E52 Baire category, Baire spacesbaire: 3: 54E52 Baire category, Baire spaces
baker’s: 1: 11J86 Linear forms in logarithms; Baker’s methodbanach: 1: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70banach: 2: 32A65 Banach algebra techniques [See mainly]46Jxxbanach: 3: 32K05 Banach analytic spaces [See also]58Bxxbanach: 4: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxbanach: 5: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxbanach: 6: 46B03 Isomorphic theory (including renorming) of Banach spaces
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banach: 7: 46B04 Isometric theory of Banach spacesbanach: 8: 46B06 Asymptotic theory of Banach spaces [See also]52A23banach: 9: 46B07 Local theory of Banach spacesbanach: 10: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07banach: 11: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxbanach: 12: 46B25 Classical Banach spaces in the general theorybanach: 13: 46B26 Nonseparable Banach spacesbanach: 14: 46B42 Banach lattices [See also]46A40, 46B40banach: 15: 46B45 Banach sequence spaces [See also]46A45banach: 16: 46B50 Compactness in Banach (or normed) spacesbanach: 17: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsbanach: 18: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxbanach: 19: 46E15 Banach spaces of continuous, differentiable or analytic functionsbanach: 20: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15banach: 21: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20banach: 22: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)banach: 23: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25banach: 24: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25banach: 25: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30banach: 26: 46J45 Radical Banach algebrasbanach: 27: 47B48 Operators on Banach algebrasbanach: 28: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesbanach: 29: 47L10 Algebras of operators on Banach spaces and other topological linear spacesbanach: 30: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxbandwidth: 1: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)bang-bang: 1: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,etc.)
bar: 1: 57T30 Bar and cobar constructions [See also]18G55, 55Uxxbarbilian: 1: 51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)barbilian: 2: 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
bargaining: 1: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)barrelled: 1: 46A08 Barrelled spaces, bornological spaces
base: 1: 54D70 Base propertiesbased: 1: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J22based: 2: 49M05 Methods based on necessary conditionsbases: 1: 11B13 Additive bases, including sumsets [See also]05B10bases: 2: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)bases: 3: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)bases: 4: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)bases: 5: 33D65 Bibasic functions and multiple basesbases: 6: 46A35 Summability and bases [See also]46B15bases: 7: 46B15 Summability and bases [See also]46A35bases: 8: 97R50 Data bases, information systemsbasic: 1: 03C07 Basic properties of first-order languages and structuresbasic: 2: 15Axx Basic linear algebrabasic: 3: 33Dxx Basic hypergeometric functionsbasic: 4: 33D15 Basic hypergeometric functions in one variable, rϕs
basic: 5: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)basic: 6: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
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hypergeometric functions in one variablebasic: 7: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)basic: 8: 33D60 Basic hypergeometric integrals and functions defined by thembasic: 9: 33D67 Basic hypergeometric functions associated with root systemsbasic: 10: 33D70 Other basic hypergeometric functions and integrals in several variablesbasic: 11: 54Bxx Basic constructionsbasic: 12: 76Mxx Basic methods in fluid mechanics [See also]65-XXbasic: 13: 78Mxx Basic methodsbasic: 14: 80Mxx Basic methodsbasic: 15: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)bayes: 1: 62C10 Bayesian problems; characterization of Bayes proceduresbayes: 2: 62C12 Empirical decision procedures; empirical Bayes procedures
bayesian: 1: 62C10 Bayesian problems; characterization of Bayes proceduresbayesian: 2: 62F15 Bayesian inference
bci: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
bci-algebras: 1: 06F35 BCK-algebras, BCI-algebras [See also]03G25bck: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52bck-algebras: 1: 06F35 BCK-algebras, BCI-algebras [See also]03G25
be: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assignedat least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35
be: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)
be: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
be: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
be: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classificationnumber in this section)
be: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
be: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
be: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)
be: 9: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
be: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)
be: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)
be: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)
be: 13: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)
be: 14: 51Pxx Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
be: 15: 51P05 Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
be: 16: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned atleast one other classification number in this section)
be: 17: 92Fxx Other natural sciences (should also be assigned at least one other classification numberin this section)
be: 18: 92F05 Other natural sciences (should also be assigned at least one other classification number
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in section 92)beams: 1: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
behavior: 1: 30B30 Boundary behavior of power series, over-convergencebehavior: 2: 30D40 Cluster sets, prime ends, boundary behaviorbehavior: 3: 31A20 Boundary behavior (theorems of Fatou type, etc.)behavior: 4: 31B25 Boundary behaviorbehavior: 5: 32A40 Boundary behavior of holomorphic functionsbehavior: 6: 32E35 Global boundary behavior of holomorphic functionsbehavior: 7: 34C28 Complex behavior, chaotic systems [See also]37Dxxbehavior: 8: 34K23 Complex (chaotic) behavior of solutionsbehavior: 9: 34M35 Singularities, monodromy, local behavior of solutions, normal formsbehavior: 10: 35B40 Asymptotic behavior of solutionsbehavior: 11: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setsbehavior: 12: 37Dxx Dynamical systems with hyperbolic behaviorbehavior: 13: 37K40 Soliton theory, asymptotic behavior of solutionsbehavior: 14: 39A33 Complex (chaotic) behavior of solutionsbehavior: 15: 45Mxx Qualitative behaviorbehavior: 16: 58K55 Asymptotic behaviorbehavior: 17: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D45behavior: 18: 74G55 Qualitative behavior of solutionsbehavior: 19: 74H40 Long-time behavior of solutionsbehavior: 20: 74H65 Chaotic behaviorbehavior: 21: 91B42 Consumer behavior, demand theorybehavior: 22: 92D50 Animal behaviorbehavior: 23: 97C20 Affective behavior
behavioral: 1: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencesbehavioral: 2: 91-XX Game theory, economics, social and behavioral sciencesbehavioral: 3: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXbehavioral: 4: 91Fxx Other social and behavioral sciences (mathematical treatment)behavioral: 5: 97M70 Behavioral and social sciences
belief: 1: 03B42 Logics of knowledge and belief (including belief change)belief: 2: 03B42 Logics of knowledge and belief (including belief change)belief: 3: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45bell: 1: 11B73 Bell and Stirling numbers
belonging: 1: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-vonNeumann classes, etc.) [See also]47L20belonging: 2: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)belonging: 3: 49K30 Optimal solutions belonging to restricted classes
belyı: 1: 11G32 Dessins d’enfants, Belyı theorybergman: 1: 30H20 Bergman spaces, Fock spacesbergman: 2: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)bergman: 3: 32A36 Bergman spaces
berkovich: 1: 37P50 Dynamical systems on Berkovich spacesbernoulli: 1: 11B68 Bernoulli and Euler numbers and polynomialsbernoulli: 2: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)bernstein: 1: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)
bernstein-sato: 1: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals andpolynomials [See also]13Nxx, 32C38
berry: 1: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.bers: 1: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)
besov: 1: 30H25 Besov spaces and Qp-spacesbessel: 1: 33C10 Bessel and Airy functions, cylinder functions, 0F1
bessel: 2: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)best: 1: 41A44 Best constantsbest: 2: 41A50 Best approximation, Chebyshev systems
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best: 3: 41A52 Uniqueness of best approximationbeta: 1: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)beta: 2: 33B15 Gamma, beta and polygamma functionsbeta: 3: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)bethe: 1: 82B23 Exactly solvable models; Bethe ansatz
bethe-salpeter: 1: 81Q40 Bethe-Salpeter and other integral equationsbetween: 1: 46B70 Interpolation between normed linear spaces [See also]46M35between: 2: 55P92 Relations between equivariant and nonequivariant homotopy theorybetween: 3: 55R37 Maps between classifying spacesbetween: 4: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
bi-hamiltonian: 1: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)
bi-laplacian: 1: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianbi-laplacian: 2: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
bialgebras: 1: 16T10 Bialgebrasbialgebras: 2: 17B62 Lie bialgebras; Lie coalgebras
bibasic: 1: 33D65 Bibasic functions and multiple basesbibliographic: 1: 01A90 Bibliographic studies
bibliographies: 1: 00A15 Bibliographiesbibliographies: 2: 01A70 Biographies, obituaries, personalia, bibliographiesbibliographies: 3: 97A50 Bibliographies [See also]01-00
bicategories: 1: 18D05 Double categories, 2-categories, bicategories and generalizationsbidding: 1: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)
bifurcation: 1: 34C23 Bifurcation [See also]37Gxxbifurcation: 2: 34F10 Bifurcationbifurcation: 3: 34H20 Bifurcation controlbifurcation: 4: 34K18 Bifurcation theorybifurcation: 5: 35B32 Bifurcation [See also]37Gxx, 37K50bifurcation: 6: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K18bifurcation: 7: 37G40 Symmetries, equivariant bifurcation theorybifurcation: 8: 37H20 Bifurcation theory [See also]37Gxxbifurcation: 9: 37J20 Bifurcation problemsbifurcation: 10: 37K50 Bifurcation problemsbifurcation: 11: 37L10 Normal forms, center manifold theory, bifurcation theorybifurcation: 12: 37M20 Computational methods for bifurcation problemsbifurcation: 13: 39A28 Bifurcation theorybifurcation: 14: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E09bifurcation: 15: 58E07 Abstract bifurcation theorybifurcation: 16: 58E09 Group-invariant bifurcation theorybifurcation: 17: 58J55 Bifurcation [See also]35B32bifurcation: 18: 65P30 Bifurcation problemsbifurcation: 19: 74G60 Bifurcation and bucklingbifurcation: 20: 74H60 Dynamical bifurcation
bifurcations: 1: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationsbifurcations: 2: 37G10 Bifurcations of singular pointsbifurcations: 3: 37G15 Bifurcations of limit cycles and periodic orbitsbifurcations: 4: 37G25 Bifurcations connected with nontransversal intersectionbifurcations: 5: 37G30 Infinite nonwandering sets arising in bifurcationsbifurcations: 6: 37G35 Attractors and their bifurcationsbifurcations: 7: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and theirbifurcations, reduction
bifurcations: 8: 70K50 Bifurcations and instabilitybiharmonic: 1: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationbiharmonic: 2: 31B30 Biharmonic and polyharmonic equations and functions
bijective: 1: 05A19 Combinatorial identities, bijective combinatoricsbilinear: 1: 11D09 Quadratic and bilinear equations
46 Run: December 14, 2009
Mathematics Subject Classification 2010
bilinear: 2: 11E39 Bilinear and Hermitian formsbilinear: 3: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exxbilinear: 4: 47A07 Forms (bilinear, sesquilinear, multilinear)billiards: 1: 37D50 Hyperbolic systems with singularities (billiards, etc.)
bimodules: 1: 16Dxx Modules, bimodules and idealsbimodules: 2: 16D20 Bimodules
binary: 1: 11E16 General binary quadratic formsbinary: 2: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05binary: 3: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05binary: 4: 20N02 Sets with a single binary operation (groupoids)
binomial: 1: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxxbinomial: 2: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A30
biochemical: 1: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)[See also]80A30
biochemistry: 1: 92C40 Biochemistry, molecular biologybiochemistry: 2: 92Exx Chemistry For biochemistry, see 92C40
biographies: 1: 01A70 Biographies, obituaries, personalia, bibliographiesbiography: 1: 01-XX History and biography [See also]the classification number–03 in the other sectionsbiological: 1: 76Zxx Biological fluid mechanics [See also]74F10, 74L15, 92Cxxbiological: 2: 78A70 Biological applications [See also]91D30, 92C30biological: 3: 92B25 Biological rhythms and synchronization
biology: 1: 35Q92 PDEs in connection with biology and other natural sciencesbiology: 2: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXbiology: 3: 46N60 Applications in biology and other sciencesbiology: 4: 62P10 Applications to biology and medical sciencesbiology: 5: 92-XX Biology and other natural sciencesbiology: 6: 92Bxx Mathematical biology in generalbiology: 7: 92B05 General biology and biomathematicsbiology: 8: 92C15 Developmental biology, pattern formationbiology: 9: 92C20 Neural biologybiology: 10: 92C37 Cell biologybiology: 11: 92C40 Biochemistry, molecular biologybiology: 12: 92C42 Systems biology, networksbiology: 13: 92C80 Plant biologybiology: 14: 97M60 Biology, chemistry, medicine
biomathematics: 1: 92B05 General biology and biomathematicsbiomechanical: 1: 74L15 Biomechanical solid mechanics [See also]92C10biomechanics: 1: 92C10 Biomechanics [See also]74L15
biomedical: 1: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A12biophysics: 1: 92C05 Biophysics
biopropulsion: 1: 76Z10 Biopropulsion in water and in airbiostatistics: 1: 92B15 General biostatistics [See also]62P10
birational: 1: 14Exx Birational geometrybirational: 2: 14E05 Rational and birational mapsbirational: 3: 14E07 Birational automorphisms, Cremona group and generalizations
birch-swinnerton-dyer: 1: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture[See also]14G10
birch-swinnerton-dyer: 2: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyerconjecture)
birth-and-death: 1: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)bisimulation: 1: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)bistability: 1: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80
bitopologies: 1: 54E55 Bitopologiesblack: 1: 83C57 Black holes
47 Run: December 14, 2009
Mathematics Subject Classification 2010
blaschke: 1: 30J10 Blaschke productsblast: 1: 76Lxx Shock waves and blast waves [See also]35L67blast: 2: 76L05 Shock waves and blast waves [See also]35L67bloch: 1: 30D45 Bloch functions, normal functions, normal familiesbloch: 2: 30H30 Bloch spacesbloch: 3: 32A18 Bloch functions, normal functionsblock: 1: 05B05 Block designs [See also]51E05, 62K10block: 2: 51E05 General block designs [See also]05B05block: 3: 55R60 Microbundles and block bundles [See also]57N55, 57Q50block: 4: 57N55 Microbundles and block bundles [See also]55R60, 57Q50block: 5: 57Q50 Microbundles and block bundles [See also]55R60, 57N55block: 6: 62K10 Block designs
blocking: 1: 51E21 Blocking sets, ovals, k-arcsblow-up: 1: 35B44 Blow-upblowup: 1: 74H35 Singularities, blowup, stress concentrations
bmo-spaces: 1: 30H35 BMO-spacesbmoa: 1: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxbockstein: 1: 55U20 Universal coefficient theorems, Bockstein operator
bodies: 1: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C07bodies: 2: 11H16 Nonconvex bodiesbodies: 3: 52A23 Asymptotic theory of convex bodies [See also]46B06bodies: 4: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P21bodies: 5: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P21bodies: 6: 70F35 Collision of rigid or pseudo-rigid bodiesbodies: 7: 74Kxx Thin bodies, structures
body: 1: 70B10 Kinematics of a rigid bodybody: 2: 70Exx Dynamics of a rigid body and of multibody systemsbody: 3: 70E15 Free motion of a rigid body [See also]70M20body: 4: 70E17 Motion of a rigid body with a fixed pointbody: 5: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25body: 6: 70E20 Perturbation methods for rigid body dynamics
boltzmann: 1: 35Q20 Boltzmann equationsboltzmann: 2: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05boltzmann: 3: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05
book: 1: 00A17 External book reviewsbooks: 1: 00A07 Problem booksbooks: 2: 01A05 General histories, source booksbooks: 3: 97A10 Comprehensive works, reference booksbooks: 4: 97U40 Problem books. Competitions. Examinations
boolean: 1: 03G05 Boolean algebras [See also]06Exxboolean: 2: 06Exx Boolean algebras (Boolean rings) [See also]03G05boolean: 3: 06Exx Boolean algebras (Boolean rings) [See also]03G05boolean: 4: 06E15 Stone spaces (Boolean spaces) and related structuresboolean: 5: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45boolean: 6: 06E30 Boolean functions [See also]94C10boolean: 7: 06E75 Generalizations of Boolean algebrasboolean: 8: 15B34 Boolean and Hadamard matricesboolean: 9: 28A60 Measures on Boolean rings, measure algebras [See also]54H10boolean: 10: 90C09 Boolean programmingboolean: 11: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30boolean: 12: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30
boolean-valued: 1: 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)boolean-valued: 2: 03E40 Other aspects of forcing and Boolean-valued models
bootstrap: 1: 62F40 Bootstrap, jackknife and other resampling methodsborder: 1: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)
48 Run: December 14, 2009
Mathematics Subject Classification 2010
bordism: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,57R77, 57R85, 57R90
borel: 1: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
borel: 2: 40G10 Abel, Borel and power series methodsborel: 3: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05bornological: 1: 46A08 Barrelled spaces, bornological spacesbornologies: 1: 46A17 Bornologies and related structures; Mackey convergence, etc.
bott: 1: 55R45 Homology and homotopy of BO and BU; Bott periodicityboundaries: 1: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundariesboundaries: 2: 32V15 CR manifolds as boundaries of domainsboundaries: 3: 46J20 Ideals, maximal ideals, boundariesboundaries: 4: 74N20 Dynamics of phase boundaries
boundary: 1: 30B30 Boundary behavior of power series, over-convergenceboundary: 2: 30D40 Cluster sets, prime ends, boundary behaviorboundary: 3: 30E25 Boundary value problems [See also]45Exxboundary: 4: 30F25 Ideal boundary theoryboundary: 5: 31A20 Boundary behavior (theorems of Fatou type, etc.)boundary: 6: 31A25 Boundary value and inverse problemsboundary: 7: 31B20 Boundary value and inverse problemsboundary: 8: 31B25 Boundary behaviorboundary: 9: 31C35 Martin boundary theory [See also]60J50boundary: 10: 32A40 Boundary behavior of holomorphic functionsboundary: 11: 32E35 Global boundary behavior of holomorphic functionsboundary: 12: 32H12 Boundary uniqueness of mappingsboundary: 13: 32H40 Boundary regularity of mappingsboundary: 14: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxboundary: 15: 34B05 Linear boundary value problemsboundary: 16: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterboundary: 17: 34B08 Parameter dependent boundary value problemsboundary: 18: 34B09 Boundary eigenvalue problemsboundary: 19: 34B10 Nonlocal and multipoint boundary value problemsboundary: 20: 34B15 Nonlinear boundary value problemsboundary: 21: 34B16 Singular nonlinear boundary value problemsboundary: 22: 34B18 Positive solutions of nonlinear boundary value problemsboundary: 23: 34B37 Boundary value problems with impulsesboundary: 24: 34B40 Boundary value problems on infinite intervalsboundary: 25: 34B45 Boundary value problems on graphs and networksboundary: 26: 34K10 Boundary value problemsboundary: 27: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxboundary: 28: 35F15 Boundary value problems for linear first-order equationsboundary: 29: 35F30 Boundary value problems for nonlinear first-order equationsboundary: 30: 35F45 Boundary value problems for linear first-order systemsboundary: 31: 35F60 Boundary value problems for nonlinear first-order systemsboundary: 32: 35G15 Boundary value problems for linear higher-order equationsboundary: 33: 35G30 Boundary value problems for nonlinear higher-order equationsboundary: 34: 35G45 Boundary value problems for linear higher-order systemsboundary: 35: 35G60 Boundary value problems for nonlinear higher-order systemsboundary: 36: 35J25 Boundary value problems for second-order elliptic equationsboundary: 37: 35J40 Boundary value problems for higher-order elliptic equationsboundary: 38: 35J56 Boundary value problems for first-order elliptic systemsboundary: 39: 35J57 Boundary value problems for second-order elliptic systemsboundary: 40: 35J58 Boundary value problems for higher-order elliptic systemsboundary: 41: 35J65 Nonlinear boundary value problems for linear elliptic equationsboundary: 42: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsboundary: 43: 35J67 Boundary values of solutions to elliptic equations
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Mathematics Subject Classification 2010
boundary: 44: 35M12 Boundary value problems for equations of mixed typeboundary: 45: 35M32 Boundary value problems for systems of mixed typeboundary: 46: 35N25 Overdetermined boundary value problemsboundary: 47: 35R35 Free boundary problemsboundary: 48: 35R37 Moving boundary problemsboundary: 49: 35S15 Boundary value problems for pseudodifferential operatorsboundary: 50: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40boundary: 51: 58J32 Boundary value problems on manifoldsboundary: 52: 60J50 Boundary theoryboundary: 53: 65L10 Boundary value problemsboundary: 54: 65M38 Boundary element methodsboundary: 55: 65Nxx Partial differential equations, boundary value problemsboundary: 56: 65N38 Boundary element methodsboundary: 57: 65N45 Method of contraction of the boundaryboundary: 58: 74S15 Boundary element methodsboundary: 59: 76F40 Turbulent boundary layersboundary: 60: 76M15 Boundary element methodsboundary: 61: 78M15 Boundary element methodsboundary: 62: 80M15 Boundary element methods
boundary-layer: 1: 76D10 Boundary-layer theory, separation and reattachment, higher-order effectsboundary-layer: 2: 76N20 Boundary-layer theory
bounded: 1: 26A45 Functions of bounded variation, generalizationsbounded: 2: 26B30 Absolutely continuous functions, functions of bounded variationbounded: 3: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10bounded: 4: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)bounded: 5: 30H05 Bounded analytic functionsbounded: 6: 30K15 Bounded universal functionsbounded: 7: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxbounded: 8: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15bounded: 9: 40D20 Summability and bounded fields of methodsbounded: 10: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)bounded: 11: 46L07 Operator spaces and completely bounded maps [See also]47L25
boundedness: 1: 34C11 Growth, boundednessboundedness: 2: 34K12 Growth, boundedness, comparison of solutionsboundedness: 3: 39A22 Growth, boundedness, comparison of solutions
bounds: 1: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)
bounds: 2: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundsbounds: 3: 35P15 Estimation of eigenvalues, upper and lower boundsbounds: 4: 65L70 Error boundsbounds: 5: 65M15 Error boundsbounds: 6: 65N15 Error boundsbounds: 7: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15bounds: 8: 74G45 Bounds for solutionsbounds: 9: 74Q20 Bounds on effective propertiesbounds: 10: 94B65 Bounds on codes
braid: 1: 20F36 Braid groups; Artin groupsbraided: 1: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23branch-and-bound: 1: 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
50 Run: December 14, 2009
Mathematics Subject Classification 2010
branch-and-cut: 1: 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cutbranched: 1: 57M12 Special coverings, e.g. branchedbranches: 1: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)branching: 1: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)branching: 2: 60J85 Applications of branching processes [See also]92Dxx
branes: 1: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30branges: 1: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35branges: 2: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22branges-rovnyak: 1: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32branges-rovnyak: 2: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22brauer: 1: 14F22 Brauer groups of schemes [See also]12G05, 16K50brauer: 2: 16K50 Brauer groups [See also]12G05, 14F22brauer: 3: 19C30 K2 and the Brauer group
breaking: 1: 81R40 Symmetry breakingbrewer: 1: 11L10 Jacobsthal and Brewer sums; other complete character sums
brill-noether: 1: 14H51 Special divisors (gonality, Brill-Noether theory)brittle: 1: 74R05 Brittle damagebrittle: 2: 74R10 Brittle fracture
brownian: 1: 60G22 Fractional processes, including fractional Brownian motionbrownian: 2: 60J65 Brownian motion [See also]58J65brownian: 3: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxbubbly: 1: 76T10 Liquid-gas two-phase flows, bubbly flows
buchsbaum: 1: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05buckling: 1: 74G60 Bifurcation and buckling
buildings: 1: 20E42 Groups with a BN -pair; buildings [See also]51E24buildings: 2: 51E24 Buildings and the geometry of diagrams
built: 1: 15A78 Other algebras built from modulesbulk: 1: 74J10 Bulk waves
bundle: 1: 32L15 Bundle convexity [See also]32F10bundle: 2: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxbundle: 3: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxbundles: 1: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13bundles: 2: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxbundles: 3: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05bundles: 4: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxbundles: 5: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxxbundles: 6: 32G08 Deformations of fiber bundlesbundles: 7: 32L05 Holomorphic bundles and generalizationsbundles: 8: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30bundles: 9: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
[See also]32Q20bundles: 10: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25bundles: 11: 55R10 Fiber bundlesbundles: 12: 55R25 Sphere bundles and vector bundlesbundles: 13: 55R25 Sphere bundles and vector bundles
51 Run: December 14, 2009
Mathematics Subject Classification 2010
bundles: 14: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-theory, see 18F25, 19-XX
bundles: 15: 55R60 Microbundles and block bundles [See also]57N55, 57Q50bundles: 16: 55R65 Generalizations of fiber spaces and bundlesbundles: 17: 55R91 Equivariant fiber spaces and bundles [See also]19L47bundles: 18: 55S40 Sectioning fiber spaces and bundlesbundles: 19: 57N55 Microbundles and block bundles [See also]55R60, 57Q50bundles: 20: 57Q50 Microbundles and block bundles [See also]55R60, 57N55bundles: 21: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxxbundles: 22: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxxbundles: 23: 58A30 Vector distributions (subbundles of the tangent bundles)bundles: 24: 58A32 Natural bundlesbundles: 25: 58J52 Determinants and determinant bundles, analytic torsion
burnside: 1: 19A22 Frobenius induction, Burnside and representation ringsburnside: 2: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)burst-correcting: 1: 94B20 Burst-correcting codes
busemann: 1: 53C70 Direct methods (G-spaces of Busemann, etc.)but: 1: 17A45 Quadratic algebras (but not quadratic Jordan algebras)but: 2: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXbut: 3: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)by: 1: 11E25 Sums of squares and representations by other particular quadratic formsby: 2: 11J17 Approximation by numbers from a fixed fieldby: 3: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuesby: 4: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M05by: 5: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H10by: 6: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)by: 7: 16S70 Extensions of rings by idealsby: 8: 20F22 Other classes of groups defined by subgroup chainsby: 9: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
by: 10: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
by: 11: 30D10 Representations of entire functions by series and integralsby: 12: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)by: 13: 33D60 Basic hypergeometric integrals and functions defined by themby: 14: 33E20 Other functions defined by series and integralsby: 15: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsby: 16: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see
42A10by: 17: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see
42A10by: 18: 41A20 Approximation by rational functionsby: 19: 41A30 Approximation by other special function classesby: 20: 41A35 Approximation by operators (in particular, by integral operators)by: 21: 41A35 Approximation by operators (in particular, by integral operators)by: 22: 41A36 Approximation by positive operatorsby: 23: 41A45 Approximation by arbitrary linear expressionsby: 24: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropyby: 25: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)by: 26: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40
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Mathematics Subject Classification 2010
by: 27: 47B07 Operators defined by compactness propertiesby: 28: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y30by: 29: 52A27 Approximation by convex setsby: 30: 54Cxx Maps and general types of spaces defined by mapsby: 31: 54C50 Special sets defined by functions [See also]26A21by: 32: 57R95 Realizing cycles by submanifoldsby: 33: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70by: 34: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
by: 35: 93C15 Systems governed by ordinary differential equations [See also]34H05by: 36: 93C20 Systems governed by partial differential equationsby: 37: 93C23 Systems governed by functional-differential equations [See also]34K35by: 38: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)by: 39: 93D15 Stabilization of systems by feedback
calabi-yau: 1: 14J32 Calabi-Yau manifoldscalabi-yau: 2: 32Q25 Calabi-Yau theory [See also]14J30
calculation: 1: 11Y55 Calculation of integer sequencescalculations: 1: 11Y65 Continued fraction calculationscalculators: 1: 97U70 Technological tools, calculators
calculi: 1: 44A40 Calculus of Mikusinski and other operational calculicalculus: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52calculus: 2: 05A40 Umbral calculuscalculus: 3: 14N15 Classical problems, Schubert calculuscalculus: 4: 20F12 Commutator calculuscalculus: 5: 26A06 One-variable calculuscalculus: 6: 26B12 Calculus of vector functionscalculus: 7: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxxcalculus: 8: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxcalculus: 9: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XXcalculus: 10: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
calculus: 11: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
calculus: 12: 44A40 Calculus of Mikusinski and other operational calculicalculus: 13: 44A45 Classical operational calculuscalculus: 14: 44A55 Discrete operational calculuscalculus: 15: 46H30 Functional calculus in topological algebras [See also]47A60calculus: 16: 47A60 Functional calculuscalculus: 17: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)calculus: 18: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XXcalculus: 19: 57M05 Fundamental group, presentations, free differential calculuscalculus: 20: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxxcalculus: 21: 60H07 Stochastic calculus of variations and the Malliavin calculuscalculus: 22: 60H07 Stochastic calculus of variations and the Malliavin calculuscalculus: 23: 68N18 Functional programming and lambda calculus [See also]03B40calculus: 24: 81S25 Quantum stochastic calculuscalculus: 25: 83C27 Lattice gravity, Regge calculus and other discrete methodscalculus: 26: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
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Mathematics Subject Classification 2010
SPDE, dynamical systems)calculus: 27: 97I40 Differential calculuscalculus: 28: 97I50 Integral calculus
calderon-zygmund: 1: 42B20 Singular and oscillatory integrals (Calderon-Zygmund, etc.)calibrated: 1: 53C38 Calibrations and calibrated geometries
calibrations: 1: 53C38 Calibrations and calibrated geometriescanard: 1: 34E17 Canard solutions
cancellation: 1: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)cancellation: 2: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-tion
cancellation: 3: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05canonical: 1: 15A21 Canonical forms, reductions, classificationcanonical: 2: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)canonical: 3: 47A45 Canonical models for contractions and nonselfadjoint operatorscanonical: 4: 53D22 Canonical transformationscanonical: 5: 62H20 Measures of association (correlation, canonical correlation, etc.)canonical: 6: 70H15 Canonical and symplectic transformationscanonical: 7: 81S05 Canonical quantization, commutation relations and statisticscanonical: 8: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)canonical: 9: 93B10 Canonical structure
cantor: 1: 26A30 Singular functions, Cantor functions, functions with other special propertiescapacities: 1: 28A12 Contents, measures, outer measures, capacitiescapacities: 2: 31B15 Potentials and capacities, extremal lengthcapacities: 3: 31C15 Potentials and capacities
capacity: 1: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15capacity: 2: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85capacity: 3: 32U20 Capacity theory and generalizations
capillarity: 1: 76B45 Capillarity (surface tension) [See also]76D45capillarity: 2: 76D45 Capillarity (surface tension) [See also]76B45
caps: 1: 51E22 Linear codes and caps in Galois spaces [See also]94B05cardinal: 1: 03E10 Ordinal and cardinal numberscardinal: 2: 03E17 Cardinal characteristics of the continuumcardinal: 3: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80cardinality: 1: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)[See also]03Exx For ultrafilters, see 54D80
cardinals: 1: 03E55 Large cardinalscareer: 1: 97M20 Mathematics in vocational training and career education
carlo: 1: 11K45 Pseudo-random numbers; Monte Carlo methodscarlo: 2: 65C05 Monte Carlo methodscarlo: 3: 78M31 Monte Carlo methodscarlo: 4: 80M31 Monte Carlo methodscarlo: 5: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80carlo: 6: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)carlo: 7: 91G60 Numerical methods (including Monte Carlo methods)
carnot: 1: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.cartan: 1: 58A15 Exterior differential systems (Cartan theory)
cartesian: 1: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)case: 1: 16-XX Associative rings and algebras For the commutative case, see 13-XXcase: 2: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25case: 3: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
case-oriented: 1: 90B90 Case-oriented studiescases: 1: 70E40 Integrable cases of motion
casimir: 1: 81T55 Casimir effectcatastrophe: 1: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XXcatastrophe: 2: 58K35 Catastrophe theorycategorical: 1: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C10
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categorical: 2: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q65categorical: 3: 20K40 Homological and categorical methodscategorical: 4: 43A95 Categorical methods [See also]46Mxxcategorical: 5: 54B30 Categorical methods [See also]18B30
categoricity: 1: 03C35 Categoricity and completeness of theoriescategories: 1: 08C05 Categories of algebras [See also]18C05categories: 2: 13C60 Module categoriescategories: 3: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxcategories: 4: 13D09 Derived categoriescategories: 5: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M20categories: 6: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitycategories: 7: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxcategories: 8: 16E35 Derived categoriescategories: 9: 16N80 General radicals and rings For radicals in module categories, see 16S90categories: 10: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxcategories: 11: 18Axx General theory of categories and functorscategories: 12: 18A25 Functor categories, comma categoriescategories: 13: 18A25 Functor categories, comma categoriescategories: 14: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionscategories: 15: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionscategories: 16: 18Bxx Special categoriescategories: 17: 18B15 Embedding theorems, universal categories [See also]18E20categories: 18: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxxcategories: 19: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxxcategories: 20: 18B30 Categories of topological spaces and continuous mappings [See also]54-XXcategories: 21: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XXcategories: 22: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
20L05, 20Mxxcategories: 23: 18Cxx Categories and theoriescategories: 24: 18C05 Equational categories [See also]03C05, 08C05categories: 25: 18C20 Algebras and Kleisli categories associated with monadscategories: 26: 18C35 Accessible and locally presentable categoriescategories: 27: 18Dxx Categories with structurecategories: 28: 18D05 Double categories, 2-categories, bicategories and generalizationscategories: 29: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23categories: 30: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23categories: 31: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23categories: 32: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23categories: 33: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)categories: 34: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)categories: 35: 18D20 Enriched categories (over closed or monoidal categories)categories: 36: 18D20 Enriched categories (over closed or monoidal categories)categories: 37: 18D30 Fibered categoriescategories: 38: 18Exx Abelian categoriescategories: 39: 18E05 Preadditive, additive categoriescategories: 40: 18E10 Exact categories, abelian categories
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categories: 41: 18E10 Exact categories, abelian categoriescategories: 42: 18E15 Grothendieck categoriescategories: 43: 18E30 Derived categories, triangulated categoriescategories: 44: 18E30 Derived categories, triangulated categoriescategories: 45: 18E35 Localization of categoriescategories: 46: 18Fxx Categories and geometrycategories: 47: 18F05 Local categories and functorscategories: 48: 19D23 Symmetric monoidal categories [See also]18D10categories: 49: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05categories: 50: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05categories: 51: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20categories: 52: 55U40 Topological categories, foundations of homotopy theory
category: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
category: 2: 18B05 Category of sets, characterizations [See also]03-XXcategory: 3: 18B10 Category of relations, additive relationscategory: 4: 18D35 Structured objects in a category (group objects, etc.)category: 5: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10category: 6: 20Jxx Connections with homological algebra and category theorycategory: 7: 20J15 Category of groupscategory: 8: 20M50 Connections of semigroups with homological algebra and category theorycategory: 9: 46Mxx Methods of category theory in functional analysis [See also]18-XXcategory: 10: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J33category: 11: 54E52 Baire category, Baire spacescategory: 12: 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirel′man) category of a spacecategory: 13: 55Uxx Applied homological algebra and category theory [See also]18Gxx
category-theoretic: 1: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXcategory-theoretic: 2: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitycatenary: 1: 13C15 Dimension theory, depth, related rings (catenary, etc.)
cauchy: 1: 15B05 Toeplitz, Cauchy, and related matricescauchy: 2: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxcauchy: 3: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)cauchy: 4: 45E05 Integral equations with kernels of Cauchy type [See also]35J15cauchy: 5: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10cauchy: 6: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
cauchy-kovalevskaya: 1: 35A10 Cauchy-Kovalevskaya theoremscavitation: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingcavities: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingcelestial: 1: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxxcelestial: 2: 70Fxx Dynamics of a system of particles, including celestial mechanicscelestial: 3: 70F15 Celestial mechanicscelestial: 4: 70F16 Collisions in celestial mechanics, regularizationcelestial: 5: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15celestial: 6: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15
cell: 1: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxcell: 2: 92C17 Cell movement (chemotaxis, etc.)cell: 3: 92C37 Cell biology
cellular: 1: 37B15 Cellular automata [See also]68Q80
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cellular: 2: 68Q80 Cellular automata [See also]37B15cellular: 3: 92Cxx Physiological, cellular and medical topics
cellularity: 1: 57N60 Cellularitycensored: 1: 62Nxx Survival analysis and censored datacensored: 2: 62N01 Censored data modelscensored: 3: 62N86 Fuzziness, and survival analysis and censored data
censorship: 1: 83C75 Space-time singularities, cosmic censorship, etc.center: 1: 16U70 Center, normalizer (invariant elements)center: 2: 37L10 Normal forms, center manifold theory, bifurcation theory
central: 1: 19C09 Central extensions and Schur multiplierscentral: 2: 20F14 Derived series, central series, and generalizationscentral: 3: 60F05 Central limit and other weak theorems
centralizing: 1: 16S20 Centralizing and normalizing extensionscentrally: 1: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)centuries: 1: 01A40 15th and 16th centuries, Renaissance
century: 1: 01A45 17th centurycentury: 2: 01A50 18th centurycentury: 3: 01A55 19th centurycentury: 4: 01A60 20th centurycentury: 5: 01A61 Twenty-first century
cesaro: 1: 40G05 Cesaro, Euler, Norlund and Hausdorff methodscev: 1: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionscev: 2: 17D10 Mal′cev (Mal′tsev) rings and algebras
chain: 1: 06E10 Chain conditions, complete algebraschain: 2: 13Exx Chain conditions, finiteness conditionschain: 3: 16Pxx Chain conditions, growth conditions, and other forms of finitenesschain: 4: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions
[See also]16U20, Krull dimensionchain: 5: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherencechain: 6: 18G35 Chain complexes [See also]18E30, 55U15chain: 7: 55U15 Chain complexes
chains: 1: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F22chains: 2: 20F22 Other classes of groups defined by subgroup chainschains: 3: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05chains: 4: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05chains: 5: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70chains: 6: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70chains: 7: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70chains: 8: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.chains: 9: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.chains: 10: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)chains: 11: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40chains: 12: 60J22 Computational methods in Markov chains [See also]65C40chains: 13: 65C40 Computational Markov chains
change: 1: 03B42 Logics of knowledge and belief (including belief change)change: 2: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)changes: 1: 80A22 Stefan problems, phase changes, etc. [See also]74Nxxchannel: 1: 94A40 Channel models (including quantum)
chaos: 1: 34H10 Chaos controlchaos: 2: 65P20 Numerical chaos
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chaos: 3: 81Q50 Quantum chaos [See also]37Dxxchaotic: 1: 34C28 Complex behavior, chaotic systems [See also]37Dxxchaotic: 2: 34K23 Complex (chaotic) behavior of solutionschaotic: 3: 37D45 Strange attractors, chaotic dynamicschaotic: 4: 39A33 Complex (chaotic) behavior of solutionschaotic: 5: 47A16 Cyclic vectors, hypercyclic and chaotic operatorschaotic: 6: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D45chaotic: 7: 74H65 Chaotic behavior
character: 1: 11Lxx Exponential sums and character sums For finite fields, see 11Txxcharacter: 2: 11L10 Jacobsthal and Brewer sums; other complete character sumscharacter: 3: 11L40 Estimates on character sumscharacter: 4: 11T24 Other character sums and Gauss sumscharacter: 5: 43A40 Character groups and dual objects
characteristic: 1: 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p;tight closure [See also]13B22
characteristic: 2: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15characteristic: 3: 14G17 Positive characteristic ground fieldscharacteristic: 4: 33E50 Special functions in characteristic p (gamma functions, etc.)characteristic: 5: 34D08 Characteristic and Lyapunov exponentscharacteristic: 6: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.characteristic: 7: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R20characteristic: 8: 57R20 Characteristic classes and numberscharacteristic: 9: 60E10 Characteristic functions; other transforms
characteristics: 1: 03E17 Cardinal characteristics of the continuumcharacteristics: 2: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J72characteristics: 3: 65M25 Method of characteristics
characterization: 1: 05C75 Structural characterization of families of graphscharacterization: 2: 11N64 Other results on the distribution of values or the characterization of arithmetic functionscharacterization: 3: 20B10 Characterization theoremscharacterization: 4: 62C10 Bayesian problems; characterization of Bayes procedurescharacterization: 5: 62E10 Characterization and structure theorycharacterization: 6: 62H05 Characterization and structure theorycharacterization: 7: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
characterizations: 1: 18B05 Category of sets, characterizations [See also]03-XXcharacterizations: 2: 46C15 Characterizations of Hilbert spacescharacterizations: 3: 54F65 Topological characterizations of particular spacescharacterizations: 4: 57M40 Characterizations of E3 and S3 (Poincare conjecture) [See also]57N12
characters: 1: 19L10 Riemann-Roch theorems, Chern characterscharacters: 2: 20C15 Ordinary representations and characterscharacters: 3: 20C20 Modular representations and characterscharacters: 4: 53C08 Gerbes, differential characters: differential geometric aspects
charge: 1: 78A20 Space charge wavescharged: 1: 78A35 Motion of charged particles
chebyshev: 1: 41A50 Best approximation, Chebyshev systemschecking: 1: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70chemical: 1: 74E40 Chemical structurechemical: 2: 74F25 Chemical and reactive effectschemical: 3: 80A30 Chemical kinetics [See also]76V05, 92C45, 92E20
chemically: 1: 80A32 Chemically reacting flows [See also]92C45, 92E20chemistry: 1: 47N60 Applications in chemistry and life scienceschemistry: 2: 80A50 Chemistry (general) [See mainly]92Exxchemistry: 3: 92Exx Chemistry For biochemistry, see 92C40chemistry: 4: 97M60 Biology, chemistry, medicine
chemotaxis: 1: 92C17 Cell movement (chemotaxis, etc.)chern: 1: 19L10 Riemann-Roch theorems, Chern characters
chern-simons: 1: 58J28 Eta-invariants, Chern-Simons invariants
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chevalley: 1: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, andrelated topics
china: 1: 01A25 Chinachoice: 1: 03E25 Axiom of choice and related propositionschoice: 2: 91B14 Social choice
choquet: 1: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07chow: 1: 14C05 Parametrization (Chow and Hilbert schemes)chow: 2: 14C15 (Equivariant) Chow groups and rings; motives
chromodynamics: 1: 81V05 Strong interaction, including quantum chromodynamicscircle: 1: 37E10 Maps of the circlecircle: 2: 52C26 Circle packings and discrete conformal geometry
circuit: 1: 94C05 Analytic circuit theorycircuits: 1: 47N70 Applications in systems theory, circuits, and control theorycircuits: 2: 94-XX Information and communication, circuitscircuits: 3: 94Cxx Circuits, networkscircular: 1: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)
cladistics: 1: 92B10 Taxonomy, cladistics, statisticsclass: 1: 11E41 Class numbers of quadratic and Hermitian formsclass: 2: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F05class: 3: 11R29 Class numbers, class groups, discriminantsclass: 4: 11R29 Class numbers, class groups, discriminantsclass: 5: 11R37 Class field theoryclass: 6: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55class: 7: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)class: 8: 11R65 Class groups and Picard groups of ordersclass: 9: 11S31 Class field theory; p-adic formal groups [See also]14L05class: 10: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50class: 11: 13C20 Class groups [See also]11R29class: 12: 19F05 Generalized class field theory [See also]11G45class: 13: 30H15 Nevanlinna class and Smirnov classclass: 14: 30H15 Nevanlinna class and Smirnov classclass: 15: 62C07 Complete class results
classes: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C05classes: 2: 03C48 Abstract elementary classes and related topics [See also]03C45classes: 3: 03C52 Properties of classes of modelsclasses: 4: 08Cxx Other classes of algebrasclasses: 5: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C60classes: 6: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A30classes: 7: 11N69 Distribution of integers in special residue classesclasses: 8: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15classes: 9: 16D80 Other classes of modules and ideals [See also]16G50classes: 10: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceclasses: 11: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsclasses: 12: 18G25 Relative homological algebra, projective classesclasses: 13: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17classes: 14: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17classes: 15: 20E45 Conjugacy classesclasses: 16: 20F17 Formations of groups, Fitting classes [See also]20D10classes: 17: 20F22 Other classes of groups defined by subgroup chainsclasses: 18: 26A16 Lipschitz (Holder) classesclasses: 19: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H05classes: 20: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)classes: 21: 30D15 Special classes of entire functions and growth estimates
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classes: 22: 30D60 Quasi-analytic and other classes of functionsclasses: 23: 41A30 Approximation by other special function classesclasses: 24: 47Bxx Special classes of linear operatorsclasses: 25: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20classes: 26: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)classes: 27: 49K30 Optimal solutions belonging to restricted classesclasses: 28: 55Q05 Homotopy groups, general; sets of homotopy classesclasses: 29: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R20classes: 30: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XXclasses: 31: 57R20 Characteristic classes and numbersclasses: 32: 65Y10 Algorithms for specific classes of architecturesclasses: 33: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q19classes: 34: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q19classes: 35: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
classical: 1: 03B05 Classical propositional logicclassical: 2: 03B10 Classical first-order logicclassical: 3: 03B20 Subsystems of classical logic (including intuitionistic logic)classical: 4: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35classical: 5: 03C68 Other classical first-order model theoryclassical: 6: 03E20 Other classical set theory (including functions, relations, and set algebra)classical: 7: 03E30 Axiomatics of classical set theory and its fragmentsclassical: 8: 11E57 Classical groups [See also]14Lxx, 20Gxxclassical: 9: 14F25 Classical real and complex (co)homologyclassical: 10: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N30classical: 11: 14N15 Classical problems, Schubert calculusclassical: 12: 28Axx Classical measure theoryclassical: 13: 33Bxx Elementary classical functionsclassical: 14: 33C05 Classical hypergeometric functions, 2F1
classical: 15: 35A09 Classical solutionsclassical: 16: 35Q79 PDEs in connection with classical thermodynamics and heat transferclassical: 17: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxxclassical: 18: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60classical: 19: 44A45 Classical operational calculusclassical: 20: 46B25 Classical Banach spaces in the general theoryclassical: 21: 51N30 Geometry of classical groups [See also]20Gxx, 14L35classical: 22: 51N35 Questions of classical algebraic geometry [See also]14Nxxclassical: 23: 53Axx Classical differential geometryclassical: 24: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxclassical: 25: 60G46 Martingales and classical analysisclassical: 26: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XXclassical: 27: 74B05 Classical linear elasticityclassical: 28: 76A25 Superfluids (classical aspects)classical: 29: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15classical: 30: 80A10 Classical thermodynamics, including relativisticclassical: 31: 81Txx Quantum field theory; related classical field theories [See also]70Sxxclassical: 32: 82B05 Classical equilibrium statistical mechanics (general)classical: 33: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)classical: 34: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A32classical: 35: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)classics: 1: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60
classification: 1: 01-XX History and biography [See also]the classification number–03 in the other sections
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classification: 2: 03C45 Classification theory, stability and related concepts [See also]03C48classification: 3: 13C05 Structure, classification theoremsclassification: 4: 14J10 Families, moduli, classification: algebraic theoryclassification: 5: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13classification: 6: 14K10 Algebraic moduli, classification [See also]11G15classification: 7: 14R05 Classification of affine varietiesclassification: 8: 15A21 Canonical forms, reductions, classificationclassification: 9: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionclassification: 10: 20D05 Finite simple groups and their classificationclassification: 11: 20Exx Structure and classification of infinite or finite groupsclassification: 12: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05classification: 13: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05classification: 14: 30F20 Classification theory of Riemann surfacesclassification: 15: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35classification: 16: 32J27 Compact Kahler manifolds: generalizations, classificationclassification: 17: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)classification: 18: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)classification: 19: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)classification: 20: 32Q57 Classification theoremsclassification: 21: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantsclassification: 22: 34M55 Painleve and other special equations; classification, hierarchies;classification: 23: 37A35 Entropy and other invariants, isomorphism, classificationclassification: 24: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationclassification: 25: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)classification: 26: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)classification: 27: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)classification: 28: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)classification: 29: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)classification: 30: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsclassification: 31: 46H20 Structure, classification of topological algebrasclassification: 32: 46J40 Structure, classification of commutative topological algebrasclassification: 33: 46L36 Classification of factorsclassification: 34: 46L37 Subfactors and their classificationclassification: 35: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)classification: 36: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)classification: 37: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)classification: 38: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)classification: 39: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)classification: 40: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)
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classification: 41: 55P15 Classification of homotopy typeclassification: 42: 55R15 Classificationclassification: 43: 55S37 Classification of mappingsclassification: 44: 57Q25 Comparison of PL-structures: classification, Hauptvermutungclassification: 45: 58K40 Classification; finite determinacy of map germsclassification: 46: 62H30 Classification and discrimination; cluster analysis [See also]68T10, 91C20classification: 47: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)classification: 48: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)classification: 49: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)classifications: 1: 46L35 Classifications of C∗-algebras
classifying: 1: 55R35 Classifying spaces of groups and H-spacesclassifying: 2: 55R37 Maps between classifying spacesclassifying: 3: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R20classifying: 4: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10classifying: 5: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,etc.) [See also]57R32classroom: 1: 97D40 Teaching methods and classroom techniquesclassroom: 2: 97E50 Reasoning and proving in the mathematics classroomclassroom: 3: 97Q60 Teaching methods and classroom techniques
clifford: 1: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A66clifford: 2: 15A66 Clifford algebras, spinorsclifford: 3: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66cliques: 1: 05C69 Dominating sets, independent sets, cliquescloning: 1: 81P50 Quantum state estimation, approximate cloning
close-to-elliptic: 1: 35Hxx Close-to-elliptic equations and systemsclosed: 1: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)closed: 2: 14G27 Other nonalgebraically closed ground fieldsclosed: 3: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)closed: 4: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)closed: 5: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)closed: 6: 18D20 Enriched categories (over closed or monoidal categories)closed: 7: 35C05 Solutions in closed formclosed: 8: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)closed: 9: 47L45 Dual algebras; weakly closed singly generated operator algebrasclosed: 10: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)closed: 11: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsclosure: 1: 06A15 Galois correspondences, closure operatorsclosure: 2: 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p;
tight closure [See also]13B22closure: 3: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)closure: 4: 30B60 Completeness problems, closure of a system of functionsclosure: 5: 51Dxx Geometric closure systemsclosure: 6: 54A05 Topological spaces and generalizations (closure spaces, etc.)cluster: 1: 13F60 Cluster algebrascluster: 2: 30D40 Cluster sets, prime ends, boundary behaviorcluster: 3: 62H30 Classification and discrimination; cluster analysis [See also]68T10, 91C20cluster: 4: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30
clustering: 1: 91C20 Clustering [See also]62H30co-saks: 1: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
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Saks spaces, etc.)coadjoint: 1: 17B08 Coadjoint orbits; nilpotent varieties
coalgebras: 1: 16T15 Coalgebras and comodules; coringscoalgebras: 2: 17B62 Lie bialgebras; Lie coalgebras
coarse: 1: 14D22 Fine and coarse moduli spacescobar: 1: 57T30 Bar and cobar constructions [See also]18G55, 55Uxx
cobordism: 1: 19L41 Connective K-theory, cobordism [See also]55N22cobordism: 2: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,57R77, 57R85, 57R90cobordism: 3: 57N70 Cobordism and concordancecobordism: 4: 57Q20 Cobordismcobordism: 5: 57Q60 Cobordism and concordancecobordism: 6: 57R77 Complex cobordism (U- and SU-cobordism) [See also]55N22cobordism: 7: 57R85 Equivariant cobordismcobordism: 8: 57R90 Other types of cobordism [See also]55N22
cocycles: 1: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationscocycles: 2: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axx
codes: 1: 51E22 Linear codes and caps in Galois spaces [See also]94B05codes: 2: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q45codes: 3: 94Bxx Theory of error-correcting codes and error-detecting codescodes: 4: 94Bxx Theory of error-correcting codes and error-detecting codescodes: 5: 94B05 Linear codes, generalcodes: 6: 94B10 Convolutional codescodes: 7: 94B12 Combined modulation schemes (including trellis codes)codes: 8: 94B15 Cyclic codescodes: 9: 94B20 Burst-correcting codescodes: 10: 94B25 Combinatorial codescodes: 11: 94B30 Majority codescodes: 12: 94B40 Arithmetic codes [See also]11T71, 14G50codes: 13: 94B50 Synchronization error-correcting codescodes: 14: 94B60 Other types of codescodes: 15: 94B65 Bounds on codes
codimension: 1: 14M07 Low codimension problemscoding: 1: 11Hxx Geometry of numbers For applications in coding theory, see 94B75coding: 2: 11H71 Relations with coding theorycoding: 3: 11T71 Algebraic coding theory; cryptographycoding: 4: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B40coding: 5: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxcoding: 6: 81P70 Quantum coding (general)coding: 7: 94A24 Coding theorems (Shannon theory)coding: 8: 94A29 Source coding [See also]68P30
coefficient: 1: 30C50 Coefficient problems for univalent and multivalent functionscoefficient: 2: 55U20 Universal coefficient theorems, Bockstein operator
coefficients: 1: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxxcoefficients: 2: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A30coefficients: 3: 11F30 Fourier coefficients of automorphic formscoefficients: 4: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27coefficients: 5: 35Exx Equations and systems with constant coefficients [See also]35N05coefficients: 6: 35N05 Overdetermined systems with constant coefficientscoefficients: 7: 35N10 Overdetermined systems with variable coefficientscoefficients: 8: 35R05 Partial differential equations with discontinuous coefficients or datacoefficients: 9: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30coefficients: 10: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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coefficients: 11: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)coefficients: 12: 42B05 Fourier series and coefficientscoefficients: 13: 55N25 Homology with local coefficients, equivariant cohomology
coends: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)coexistent: 1: 74A50 Structured surfaces and interfaces, coexistent phases
cofibrations: 1: 55P05 Homotopy extension properties, cofibrationscofinalities: 1: 03E04 Ordered sets and their cofinalities; pcf theory
cognitive: 1: 91E10 Cognitive psychologycognitive: 2: 97C30 Cognitive processes, learning theoriescognitive: 3: 97Q30 Cognitive processes
cohen-macaulay: 1: 13C14 Cohen-Macaulay modules [See also]13H10cohen-macaulay: 2: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05cohen-macaulay: 3: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H10cohen-macaulay: 4: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)cohen-macaulay: 5: 16G50 Cohen-Macaulay modules
coherence: 1: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherencecoherence: 2: 81P40 Quantum coherence, entanglement, quantum correlationscoherent: 1: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V80
cohomological: 1: 12G10 Cohomological dimensioncohomological: 2: 32S20 Global theory of singularities; cohomological properties [See also]14E15cohomological: 3: 81T70 Quantization in field theory; cohomological methods [See also]58D29cohomologies: 1: 14F20 Etale and other Grothendieck topologies and (co)homologiescohomologies: 2: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne
(co)homologies)cohomologies: 3: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne
(co)homologies)cohomology: 1: 11E72 Galois cohomology of linear algebraic groups [See also]20G10cohomology: 2: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modularsymbols
cohomology: 3: 11F75 Cohomology of arithmetic groupscohomology: 4: 11R34 Galois cohomology [See also]12Gxx, 19A31cohomology: 5: 11S25 Galois cohomology [See also]12Gxx, 16H05cohomology: 6: 12G05 Galois cohomology [See also]14F22, 16Hxx, 16K50cohomology: 7: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,cyclic, dihedral, etc.)
cohomology: 8: 13D45 Local cohomology [See also]14B15cohomology: 9: 14B15 Local cohomology [See also]13D45, 32C36cohomology: 10: 14Fxx (Co)homology theory [See also]13Dxxcohomology: 11: 14F25 Classical real and complex (co)homologycohomology: 12: 14F30 p-adic cohomology, crystalline cohomologycohomology: 13: 14F30 p-adic cohomology, crystalline cohomologycohomology: 14: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L10cohomology: 15: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E15cohomology: 16: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,Donaldson-Thomas invariants [See also]53D45
cohomology: 17: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)cohomology: 18: 17B56 Cohomology of Lie (super)algebrascohomology: 19: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J22cohomology: 20: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G60cohomology: 21: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F42cohomology: 22: 19E20 Relations with cohomology theories [See also]14Fxxcohomology: 23: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,11S40, 14F20, 14G10
cohomology: 24: 20G10 Cohomology theory
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cohomology: 25: 20J06 Cohomology of groupscohomology: 26: 22E41 Continuous cohomology [See also]57R32, 57Txx, 58H10cohomology: 27: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N30cohomology: 28: 32C36 Local cohomology of analytic spacescohomology: 29: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results[See also]14F05, 18F20, 55N30
cohomology: 30: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxxcohomology: 31: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,32S60, 58J15
cohomology: 32: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx
cohomology: 33: 53D40 Floer homology and cohomology, symplectic aspectscohomology: 34: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35cohomology: 35: 55Nxx Homology and cohomology theories [See also]57Txxcohomology: 36: 55N20 Generalized (extraordinary) homology and cohomology theoriescohomology: 37: 55N25 Homology with local coefficients, equivariant cohomologycohomology: 38: 55N30 Sheaf cohomology [See also]18F20, 32C35, 32L10cohomology: 39: 55N32 Orbifold cohomologycohomology: 40: 55N33 Intersection homology and cohomologycohomology: 41: 55N34 Elliptic cohomologycohomology: 42: 55N91 Equivariant homology and cohomology [See also]19L47cohomology: 43: 55S05 Primary cohomology operationscohomology: 44: 55S20 Secondary and higher cohomology operationscohomology: 45: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxxcohomology: 46: 55T25 Generalized cohomologycohomology: 47: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10cohomology: 48: 57T10 Homology and cohomology of Lie groupscohomology: 49: 57T15 Homology and cohomology of homogeneous spaces of Lie groupscohomology: 50: 57T25 Homology and cohomology of H-spacescohomology: 51: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,etc.) [See also]57R32
cohomotopy: 1: 55Q55 Cohomotopy groupscoincidence: 1: 54H25 Fixed-point and coincidence theorems [See also]47H10, 55M20
coincidences: 1: 55M20 Fixed points and coincidences [See also]54H25colimits: 1: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30colimits: 2: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)collected: 1: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60
collections: 1: 00Bxx Conference proceedings and collections of paperscollections: 2: 00B05 Collections of abstracts of lecturescollections: 3: 00B10 Collections of articles of general interestcollections: 4: 00B15 Collections of articles of miscellaneous specific contentcollections: 5: 00B60 Collections of reprinted articles [See also]01A75collections: 6: 97R10 Comprehensive works, collections of programs
collectionwise: 1: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwisenormal, etc.)colligations: 1: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,realizations, etc.
collision: 1: 70F35 Collision of rigid or pseudo-rigid bodiescollisions: 1: 70F16 Collisions in celestial mechanics, regularization
collocation: 1: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodscollocation: 2: 65M70 Spectral, collocation and related methodscollocation: 3: 65N35 Spectral, collocation and related methodscolombeau: 1: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
color: 1: 17B75 Color Lie (super)algebrascoloring: 1: 05C15 Coloring of graphs and hypergraphscolumns: 1: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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combinatorial: 1: 03E05 Other combinatorial set theorycombinatorial: 2: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxxcombinatorial: 3: 05A19 Combinatorial identities, bijective combinatoricscombinatorial: 4: 05A20 Combinatorial inequalitiescombinatorial: 5: 05E10 Combinatorial aspects of representation theory [See also]20C30combinatorial: 6: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C80combinatorial: 7: 05E18 Group actions on combinatorial structurescombinatorial: 8: 05E40 Combinatorial aspects of commutative algebracombinatorial: 9: 05E45 Combinatorial aspects of simplicial complexescombinatorial: 10: 11B75 Other combinatorial number theorycombinatorial: 11: 14N10 Enumerative problems (combinatorial problems)combinatorial: 12: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXcombinatorial: 13: 20D60 Arithmetic and combinatorial problemscombinatorial: 14: 37E15 Combinatorial dynamics (types of periodic orbits)combinatorial: 15: 51D20 Combinatorial geometries [See also]05B25, 05B35combinatorial: 16: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxcombinatorial: 17: 52A37 Other problems of combinatorial convexitycombinatorial: 18: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxxcombinatorial: 19: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxcombinatorial: 20: 52C45 Combinatorial complexity of geometric structures [See also]68U05combinatorial: 21: 60Cxx Combinatorial probabilitycombinatorial: 22: 60C05 Combinatorial probabilitycombinatorial: 23: 90C27 Combinatorial optimizationcombinatorial: 24: 91A46 Combinatorial gamescombinatorial: 25: 94B25 Combinatorial codescombinatorics: 1: 05-XX Combinatorics For finite fields, see 11Txxcombinatorics: 2: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30combinatorics: 3: 05A19 Combinatorial identities, bijective combinatoricscombinatorics: 4: 05Dxx Extremal combinatoricscombinatorics: 5: 05Exx Algebraic combinatoricscombinatorics: 6: 06A07 Combinatorics of partially ordered setscombinatorics: 7: 11B30 Arithmetic combinatorics; higher degree uniformitycombinatorics: 8: 16T30 Connections with combinatoricscombinatorics: 9: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
combinatorics: 10: 37F20 Combinatorics and topologycombinatorics: 11: 68R05 Combinatoricscombinatorics: 12: 68R15 Combinatorics on wordscombinatorics: 13: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxcombinatorics: 14: 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cutcombinatorics: 15: 97Kxx Combinatorics, graph theory, probability theory, statisticscombinatorics: 16: 97K20 Combinatorics
combinatory: 1: 03B40 Combinatory logic and lambda-calculus [See also]68N18combined: 1: 03B62 Combined logicscombined: 2: 94B12 Combined modulation schemes (including trellis codes)
combustion: 1: 80A25 Combustioncoming: 1: 33E30 Other functions coming from differential, difference and integral equationscomma: 1: 18A25 Functor categories, comma categories
comma-free: 1: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q45common: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
communication: 1: 35Q94 PDEs in connection with information and communicationcommunication: 2: 68M10 Network design and communication [See also]68R10, 90B18communication: 3: 68P30 Coding and information theory (compaction, compression, models of communication,
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encoding schemes, etc.) [See also]94Axxcommunication: 4: 81P45 Quantum information, communication, networks [See also]94A15, 94A17communication: 5: 90B18 Communication networks [See also]68M10, 94A05communication: 6: 91A28 Signaling, communicationcommunication: 7: 94-XX Information and communication, circuitscommunication: 8: 94Axx Communication, informationcommunication: 9: 94A05 Communication theory [See also]60G35, 90B18
communities: 1: 97C50 Language and verbal communitiescommutation: 1: 81S05 Canonical quantization, commutation relations and statisticscommutative: 1: 05E40 Combinatorial aspects of commutative algebracommutative: 2: 11Txx Finite fields and commutative rings (number-theoretic aspects)commutative: 3: 13-XX Commutative algebracommutative: 4: 13Axx General commutative ring theorycommutative: 5: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24commutative: 6: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M10commutative: 7: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)commutative: 8: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxxcommutative: 9: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxxcommutative: 10: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxcommutative: 11: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)commutative: 12: 14A05 Relevant commutative algebra [See also]13-XXcommutative: 13: 16-XX Associative rings and algebras For the commutative case, see 13-XXcommutative: 14: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxcommutative: 15: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxxcommutative: 16: 16H15 Commutative orderscommutative: 17: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxcommutative: 18: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringscommutative: 19: 16R40 Identities other than those of matrices over commutative ringscommutative: 20: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
commutative: 21: 20M14 Commutative semigroupscommutative: 22: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25commutative: 23: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25commutative: 24: 46J05 General theory of commutative topological algebrascommutative: 25: 46J25 Representations of commutative topological algebrascommutative: 26: 46J40 Structure, classification of commutative topological algebrascommutative: 27: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxcommutativity: 1: 15A27 Commutativitycommutativity: 2: 16U80 Generalizations of commutativity
commutator: 1: 20F12 Commutator calculuscommutators: 1: 47B47 Commutators, derivations, elementary operators, etc.
comodules: 1: 16T15 Coalgebras and comodules; coringscompact: 1: 22Bxx Locally compact abelian groups (LCA groups)compact: 2: 22Cxx Compact groupscompact: 3: 22C05 Compact groupscompact: 4: 22Dxx Locally compact groups and their algebrascompact: 5: 22D05 General properties and structure of locally compact groupscompact: 6: 22D10 Unitary representations of locally compact groupscompact: 7: 22D12 Other representations of locally compact groupscompact: 8: 22D15 Group algebras of locally compact groupscompact: 9: 22D45 Automorphism groups of locally compact groups
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compact: 10: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G15compact: 11: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxcompact: 12: 32J15 Compact surfacescompact: 13: 32J17 Compact 3-foldscompact: 14: 32J18 Compact n-foldscompact: 15: 32J27 Compact Kahler manifolds: generalizations, classificationcompact: 16: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupscompact: 17: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05compact: 18: 43A75 Analysis on specific compact groupscompact: 19: 43A77 Analysis on general compact groupscompact: 20: 54E45 Compact (locally compact) metric spacescompact: 21: 54E45 Compact (locally compact) metric spacescompact: 22: 57S10 Compact groups of homeomorphismscompact: 23: 57S15 Compact Lie groups of differentiable transformations
compactification: 1: 32J05 Compactification of analytic spacescompactifications: 1: 14M27 Compactifications; symmetric and spherical varietiescompactifications: 2: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
compaction: 1: 68P30 Coding and information theory (compaction, compression, models of communication,encoding schemes, etc.) [See also]94Axx
compactness: 1: 08A45 Equational compactnesscompactness: 2: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)compactness: 3: 46A50 Compactness in topological linear spaces; angelic spaces, etc.compactness: 4: 46B50 Compactness in Banach (or normed) spacescompactness: 5: 47B07 Operators defined by compactness propertiescompactness: 6: 54D30 Compactnesscompactness: 7: 54D45 Local compactness, σ-compactnesscomparative: 1: 97D10 Comprehensive works, comparative studiescomparison: 1: 34C10 Oscillation theory, zeros, disconjugacy and comparison theorycomparison: 2: 34K12 Growth, boundedness, comparison of solutionscomparison: 3: 35B51 Comparison principlescomparison: 4: 39A22 Growth, boundedness, comparison of solutionscomparison: 5: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices oftopologies)
comparison: 6: 57Q25 Comparison of PL-structures: classification, Hauptvermutungcomparisons: 1: 62J15 Paired and multiple comparisonscompetitions: 1: 97U40 Problem books. Competitions. Examinations
compilers: 1: 68N20 Compilers and interpreterscomplementarity: 1: 90C33 Complementarity and equilibrium problems and variational inequalities (finite
dimensions)complementation: 1: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35complemented: 1: 06Cxx Modular lattices, complemented latticescomplemented: 2: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P10complemented: 3: 06C20 Complemented modular lattices, continuous geometries
complete: 1: 06B23 Complete lattices, completionscomplete: 2: 06D10 Complete distributivitycomplete: 3: 06E10 Chain conditions, complete algebrascomplete: 4: 11L10 Jacobsthal and Brewer sums; other complete character sumscomplete: 5: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,
14M12complete: 6: 13J10 Complete rings, completion [See also]13B35complete: 7: 14M10 Complete intersections [See also]13C40complete: 8: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionscomplete: 9: 54E50 Complete metric spaces
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complete: 10: 62C07 Complete class resultscompletely: 1: 37J35 Completely integrable systems, topological structure of phase space, integrationmethodscompletely: 2: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)completely: 3: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodscompletely: 4: 46L07 Operator spaces and completely bounded maps [See also]47L25completely: 5: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwisenormal, etc.)completely: 6: 70H06 Completely integrable systems and methods of integration
completeness: 1: 03C10 Quantifier elimination, model completeness and related topicscompleteness: 2: 03C35 Categoricity and completeness of theoriescompleteness: 3: 30B60 Completeness problems, closure of a system of functionscompleteness: 4: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctionscompleteness: 5: 35P10 Completeness of eigenfunctions, eigenfunction expansionscompleteness: 6: 42A65 Completeness of sets of functionscompleteness: 7: 42C30 Completeness of sets of functionscompleteness: 8: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)completeness: 9: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15completion: 1: 13B35 Completion [See also]13J10completion: 2: 13J10 Complete rings, completion [See also]13B35completion: 3: 15A83 Matrix completion problemscompletion: 4: 55P60 Localization and completion
completions: 1: 06B23 Complete lattices, completionscompletions: 2: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxcompletions: 3: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-tions
completions: 4: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)complex: 1: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D30complex: 2: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriescomplex: 3: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K22complex: 4: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15complex: 5: 12Dxx Real and complex fieldscomplex: 6: 14F25 Classical real and complex (co)homologycomplex: 7: 14K22 Complex multiplication [See also]11G15complex: 8: 22E10 General properties and structure of complex Lie groups [See also]32M05complex: 9: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXcomplex: 10: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXcomplex: 11: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic
functions)complex: 12: 30A10 Inequalities in the complex domaincomplex: 13: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15complex: 14: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXcomplex: 15: 30Exx Miscellaneous topics of analysis in the complex domaincomplex: 16: 30E10 Approximation in the complex domaincomplex: 17: 30E15 Asymptotic representations in the complex domaincomplex: 18: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12complex: 19: 32Axx Holomorphic functions of several complex variablescomplex: 20: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35complex: 21: 32A50 Harmonic analysis of several complex variables [See mainly]43-XXcomplex: 22: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P20
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complex: 23: 32C11 Complex supergeometry [See also]14A22, 14M30, 58A50complex: 24: 32C15 Complex spacescomplex: 25: 32C55 The Levi problem in complex spaces; generalizationscomplex: 26: 32E05 Holomorphically convex complex spaces, reduction theorycomplex: 27: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H15complex: 28: 32K07 Formal and graded complex spaces [See also]58C50complex: 29: 32Mxx Complex spaces with a group of automorphismscomplex: 30: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10complex: 31: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10complex: 32: 32M10 Homogeneous complex manifolds [See also]14M17, 57T15complex: 33: 32M25 Complex vector fieldscomplex: 34: 32N05 General theory of automorphic functions of several complex variablescomplex: 35: 32Qxx Complex manifoldscomplex: 36: 32Q35 Complex manifolds as subdomains of Euclidean spacecomplex: 37: 32Q55 Topological aspects of complex manifoldscomplex: 38: 32Q60 Almost complex manifoldscomplex: 39: 32V40 Real submanifolds in complex manifoldscomplex: 40: 32W20 Complex Monge-Ampere operatorscomplex: 41: 32W25 Pseudodifferential operators in several complex variablescomplex: 42: 32W30 Heat kernels in several complex variablescomplex: 43: 32W50 Other partial differential equations of complex analysiscomplex: 44: 34C28 Complex behavior, chaotic systems [See also]37Dxxcomplex: 45: 34K23 Complex (chaotic) behavior of solutionscomplex: 46: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G34complex: 47: 34M45 Differential equations on complex manifoldscomplex: 48: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20complex: 49: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20complex: 50: 37Fxx Complex dynamical systems [See also]30D05, 32H50complex: 51: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70complex: 52: 39A33 Complex (chaotic) behavior of solutionscomplex: 53: 39A45 Equations in the complex domaincomplex: 54: 39B32 Equations for complex functions [See also]30D05complex: 55: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
complex: 56: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
complex: 57: 51Mxx Real and complex geometrycomplex: 58: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)complex: 59: 53C56 Other complex differential geometry [See also]32Cxxcomplex: 60: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxcomplex: 61: 57R77 Complex cobordism (U- and SU-cobordism) [See also]55N22complex: 62: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30complex: 63: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30complex: 64: 74S70 Complex variable methodscomplex: 65: 97F50 Real numbers, complex numberscomplex: 66: 97I80 Complex analysis
complex-valued: 1: 28A10 Real- or complex-valued set functionscomplex-variables: 1: 76M40 Complex-variables methods
complexes: 1: 05E45 Combinatorial aspects of simplicial complexescomplexes: 2: 13D02 Syzygies, resolutions, complexes
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complexes: 3: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U10complexes: 4: 16E05 Syzygies, resolutions, complexescomplexes: 5: 18G35 Chain complexes [See also]18E30, 55U15complexes: 6: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionscomplexes: 7: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,58J10complexes: 8: 55U05 Abstract complexescomplexes: 9: 55U10 Simplicial sets and complexescomplexes: 10: 55U15 Chain complexescomplexes: 11: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxcomplexes: 12: 57M20 Two-dimensional complexescomplexes: 13: 57Q05 General topology of complexescomplexes: 14: 58J10 Differential complexes [See also]35Nxx; elliptic complexescomplexes: 15: 58J10 Differential complexes [See also]35Nxx; elliptic complexes
complexity: 1: 03D15 Complexity of computation (including implicit computational complexity)[See also]68Q15, 68Q17complexity: 2: 03D15 Complexity of computation (including implicit computational complexity)[See also]68Q15, 68Q17complexity: 3: 03F20 Complexity of proofscomplexity: 4: 11Y16 Algorithms; complexity [See also]68Q25complexity: 5: 14Q20 Effectivity, complexitycomplexity: 6: 52C45 Combinatorial complexity of geometric structures [See also]68U05complexity: 7: 65Y20 Complexity and performance of numerical algorithms [See also]68Q25complexity: 8: 68Q12 Quantum algorithms and complexity [See also]68Q05, 81P68complexity: 9: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)[See also]03D15, 68Q17, 68Q19complexity: 10: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)[See also]03D15, 68Q17, 68Q19complexity: 11: 68Q19 Descriptive complexity and finite models [See also]03C13complexity: 12: 68Q25 Analysis of algorithms and problem complexity [See also]68W40complexity: 13: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32complexity: 14: 90C60 Abstract computational complexity for mathematical programming problems[See also]68Q25compliance: 1: 74P05 Compliance or weight optimizationcomponent: 1: 76T30 Three or more component flows
components: 1: 62H25 Factor analysis and principal components; correspondence analysiscomposite: 1: 35Mxx Equations and systems of special type (mixed, composite, etc.)composite: 2: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XXcomposite: 3: 74A40 Random materials and composite materialscomposite: 4: 74E30 Composite and mixture propertiescomposite: 5: 78A48 Composite media; random media
composition: 1: 08A02 Relational systems, laws of compositioncomposition: 2: 17A75 Composition algebrascomposition: 3: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXcomposition: 4: 47B33 Composition operators
compositional: 1: 30K20 Compositional universalitycompositions: 1: 17A40 Ternary compositionscompositions: 2: 20E22 Extensions, wreath products, and other compositions [See also]20J05
compound: 1: 62C25 Compound decision problemscomprehensive: 1: 97A10 Comprehensive works, reference bookscomprehensive: 2: 97C10 Comprehensive workscomprehensive: 3: 97D10 Comprehensive works, comparative studiescomprehensive: 4: 97E10 Comprehensive workscomprehensive: 5: 97F10 Comprehensive workscomprehensive: 6: 97G10 Comprehensive workscomprehensive: 7: 97H10 Comprehensive works
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comprehensive: 8: 97I10 Comprehensive workscomprehensive: 9: 97K10 Comprehensive workscomprehensive: 10: 97N10 Comprehensive workscomprehensive: 11: 97P10 Comprehensive workscomprehensive: 12: 97Q10 Comprehensive workscomprehensive: 13: 97R10 Comprehensive works, collections of programscomprehensive: 14: 97U10 Comprehensive workscompressibility: 1: 76E19 Compressibility effectscompressibility: 2: 76F50 Compressibility effects
compressible: 1: 76Nxx Compressible fluids and gas dynamics, generalcompression: 1: 55S36 Extension and compression of mappingscompression: 2: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxcompression: 3: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U10
compressions: 1: 47A20 Dilations, extensions, compressionscomputability: 1: 03Dxx Computability and recursion theorycomputability: 2: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.computability: 3: 03D75 Abstract and axiomatic computability and recursion theorycomputability: 4: 03D80 Applications of computability and recursion theory
computably: 1: 03D25 Recursively (computably) enumerable sets and degreescomputation: 1: 03D15 Complexity of computation (including implicit computational complexity)
[See also]68Q15, 68Q17computation: 2: 03D78 Computation over the reals For constructive aspects, see 03F60computation: 3: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30computation: 4: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)computation: 5: 65D20 Computation of special functions, construction of tables [See also]33F05computation: 6: 65Y05 Parallel computationcomputation: 7: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P68computation: 8: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85computation: 9: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F10computation: 10: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F10computation: 11: 81P68 Quantum computation [See also]68Q05, 68Q12
computational: 1: 03D15 Complexity of computation (including implicit computational complexity)[See also]68Q15, 68Q17
computational: 2: 11Yxx Computational number theory [See also]11-04computational: 3: 12Yxx Computational aspects of field theory and polynomialscomputational: 4: 12Y05 Computational aspects of field theory and polynomialscomputational: 5: 13Pxx Computational aspects and applications [See also]14Qxx, 68W30computational: 6: 13P20 Computational homological algebra [See also]13Dxxcomputational: 7: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W30computational: 8: 16Zxx Computational aspects of associative ringscomputational: 9: 16Z05 Computational aspects of associative rings [See also]68W30computational: 10: 20B40 Computational methodscomputational: 11: 20C40 Computational methodscomputational: 12: 33Fxx Computational aspectscomputational: 13: 37M20 Computational methods for bifurcation problemscomputational: 14: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)computational: 15: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxcomputational: 16: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxcomputational: 17: 60H35 Computational methods for stochastic equations [See also]65C30
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computational: 18: 60J22 Computational methods in Markov chains [See also]65C40computational: 19: 65C40 Computational Markov chainscomputational: 20: 65C50 Other computational problems in probabilitycomputational: 21: 65C60 Computational problems in statisticscomputational: 22: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxcomputational: 23: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05computational: 24: 65D19 Computational issues in computer and robotic visioncomputational: 25: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15computational: 26: 68Q32 Computational learning theory [See also]68T05computational: 27: 68U05 Computer graphics; computational geometry [See also]65D18computational: 28: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q25computational: 29: 93B40 Computational methodscomputational: 30: 93E25 Other computational methodscomputations: 1: 11Y35 Analytic computationscomputations: 2: 11Y40 Algebraic number theory computationscomputations: 3: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E20computations: 4: 19L64 Computations, geometric applicationscomputations: 5: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areacomputer: 1: 03B70 Logic in computer science [See also]68-XXcomputer: 2: 08A70 Applications of universal algebra in computer sciencecomputer: 3: 11Y50 Computer solution of Diophantine equationscomputer: 4: 35Q68 PDEs in connection with computer sciencecomputer: 5: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxcomputer: 6: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07computer: 7: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05computer: 8: 65D19 Computational issues in computer and robotic visioncomputer: 9: 65Yxx Computer aspects of numerical algorithmscomputer: 10: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M07computer: 11: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areacomputer: 12: 68Mxx Computer system organizationcomputer: 13: 68M07 Mathematical problems of computer architecturecomputer: 14: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40computer: 15: 68Rxx Discrete mathematics in relation to computer sciencecomputer: 16: 68U05 Computer graphics; computational geometry [See also]65D18computer: 17: 97N80 Mathematical software, computer programscomputer: 18: 97Pxx Computer sciencecomputer: 19: 97P20 Theory of computer sciencecomputer: 20: 97P70 Computer science and societycomputer: 21: 97Qxx Computer science educationcomputer: 22: 97Q20 Affective aspects in teaching computer sciencecomputer: 23: 97Rxx Computer science applicationscomputer: 24: 97R60 Computer graphicscomputer: 25: 97U50 Computer assisted instruction; e-learning
computer-aided: 1: 68U07 Computer-aided design [See also]65D17computer-aided: 2: 93B51 Design techniques (robust design, computer-aided design, etc.)
computers: 1: 93C83 Control problems involving computers (process control, etc.)computing: 1: 68Qxx Theory of computingcomputing: 2: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
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bisimulation, transition nets, etc.)computing: 3: 68Uxx Computing methodologies and applicationscomputing: 4: 97R80 Recreational computing
concentrations: 1: 74G70 Stress concentrations, singularitiesconcentrations: 2: 74H35 Singularities, blowup, stress concentrations
concept: 1: 97F20 Pre-numerical stage, concept of numbersconcepts: 1: 03C45 Classification theory, stability and related concepts [See also]03C48concepts: 2: 34D30 Structural stability and analogous concepts [See also]37C20concepts: 3: 81P16 Quantum state spaces, operational and probabilistic concepts
concordance: 1: 57N70 Cobordism and concordanceconcordance: 2: 57Q60 Cobordism and concordance
concurrent: 1: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,etc.)concurrent: 2: 68Q85 Models and methods for concurrent and distributed computing (process algebras,bisimulation, transition nets, etc.)condensing: 1: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.conditional: 1: 39B55 Orthogonal additivity and other conditional equations
conditioning: 1: 15A12 Conditioning of matrices [See also]65F35conditioning: 2: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A60
conditions: 1: 06E10 Chain conditions, complete algebrasconditions: 2: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionsconditions: 3: 13Exx Chain conditions, finiteness conditionsconditions: 4: 13Exx Chain conditions, finiteness conditionsconditions: 5: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)[See also]13F15, 13F45, 13H10conditions: 6: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)conditions: 7: 16Pxx Chain conditions, growth conditions, and other forms of finitenessconditions: 8: 16Pxx Chain conditions, growth conditions, and other forms of finitenessconditions: 9: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimensionconditions: 10: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimensionconditions: 11: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceconditions: 12: 16Uxx Conditions on elementsconditions: 13: 19B10 Stable range conditionsconditions: 14: 20F45 Engel conditionsconditions: 15: 26B35 Special properties of functions of several variables, Holder conditions, etc.conditions: 16: 32F18 Finite-type conditionsconditions: 17: 32V35 Finite type conditions on CR manifoldsconditions: 18: 49Kxx Optimality conditionsconditions: 19: 49M05 Methods based on necessary conditionsconditions: 20: 90C46 Optimality conditions, duality [See also]49N15
cones: 1: 15B48 Positive matrices and their generalizations; cones of matricescones: 2: 47L07 Convex sets and cones of operators [See also]46A55
conference: 1: 00Bxx Conference proceedings and collections of papersconferences: 1: 00B20 Proceedings of conferences of general interestconferences: 2: 00B25 Proceedings of conferences of miscellaneous specific interestconfidence: 1: 62F25 Tolerance and confidence regionsconfidence: 2: 62G15 Tolerance and confidence regions
configuration: 1: 51A20 Configuration theoremsconfiguration: 2: 55R80 Discriminantal varieties, configuration spacesconfiguration: 3: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space
configurations: 1: 05Bxx Designs and configurations For applications of design theory, see 94C30configurations: 2: 05B30 Other designs, configurations [See also]51E30configurations: 3: 14N20 Configurations and arrangements of linear subspaces
confluent: 1: 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
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conformal: 1: 30C20 Conformal mappings of special domainsconformal: 2: 30C25 Covering theorems in conformal mapping theoryconformal: 3: 30C30 Numerical methods in conformal mapping theory [See also]65E05conformal: 4: 30C35 General theory of conformal mappingsconformal: 5: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsconformal: 6: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsconformal: 7: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)conformal: 8: 37F35 Conformal densities and Hausdorff dimensionconformal: 9: 52C26 Circle packings and discrete conformal geometryconformal: 10: 53A30 Conformal differential geometryconformal: 11: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30conformal: 12: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30conformal: 13: 81T40 Two-dimensional field theories, conformal field theories, etc.congestion: 1: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxx
congruence: 1: 06B10 Ideals, congruence relationscongruence: 2: 08A30 Subalgebras, congruence relationscongruence: 3: 08B10 Congruence modularity, congruence distributivitycongruence: 4: 08B10 Congruence modularity, congruence distributivitycongruence: 5: 19B37 Congruence subgroup problems [See also]20H05congruence: 6: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F20congruence: 7: 51F20 Congruence and orthogonality [See also]20H05
congruences: 1: 11A07 Congruences; primitive roots; residue systemscongruences: 2: 11D79 Congruences in many variablescongruences: 3: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50congruences: 4: 11P83 Partitions; congruences and congruential restrictionscongruences: 5: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamscongruential: 1: 11P83 Partitions; congruences and congruential restrictions
conjecture: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraphembedding, etc.)conjecture: 2: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture[See also]14G10conjecture: 3: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodgeconjectureconjecture: 4: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyerconjecture)conjecture: 5: 57M40 Characterizations of E3 and S3 (Poincare conjecture) [See also]57N12conjecture: 6: 57R60 Homotopy spheres, Poincare conjecture
conjectures: 1: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55conjectures: 2: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50conjectures: 3: 13D22 Homological conjectures (intersection theorems)
conjugacy: 1: 20E45 Conjugacy classesconjugacy: 2: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationconjugate: 1: 42A50 Conjugate functions, conjugate series, singular integralsconjugate: 2: 42A50 Conjugate functions, conjugate series, singular integrals
conjugates: 1: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)connected: 1: 14M22 Rationally connected varietiesconnected: 2: 37G25 Bifurcations connected with nontransversal intersectionconnected: 3: 54D05 Connected and locally connected spaces (general aspects)connected: 4: 54D05 Connected and locally connected spaces (general aspects)
connectedness: 1: 54F35 Higher-dimensional local connectedness [See also]55Mxx, 55Nxxconnection: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,68Q70, 68R15connection: 2: 34M40 Stokes phenomena and connection problems (linear and nonlinear)connection: 3: 35Q35 PDEs in connection with fluid mechanicsconnection: 4: 35Q40 PDEs in connection with quantum mechanics
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connection: 5: 35Q60 PDEs in connection with optics and electromagnetic theoryconnection: 6: 35Q62 PDEs in connection with statisticsconnection: 7: 35Q68 PDEs in connection with computer scienceconnection: 8: 35Q70 PDEs in connection with mechanics of particles and systemsconnection: 9: 35Q74 PDEs in connection with mechanics of deformable solidsconnection: 10: 35Q75 PDEs in connection with relativity and gravitational theoryconnection: 11: 35Q79 PDEs in connection with classical thermodynamics and heat transferconnection: 12: 35Q82 PDEs in connection with statistical mechanicsconnection: 13: 35Q85 PDEs in connection with astronomy and astrophysicsconnection: 14: 35Q86 PDEs in connection with geophysicsconnection: 15: 35Q90 PDEs in connection with mathematical programmingconnection: 16: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencesconnection: 17: 35Q92 PDEs in connection with biology and other natural sciencesconnection: 18: 35Q93 PDEs in connection with control and optimizationconnection: 19: 35Q94 PDEs in connection with information and communicationconnection: 20: 62E86 Fuzziness in connection with the topics on distributions in this sectionconnection: 21: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,28E10connection: 22: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,28E10
connections: 1: 11Uxx Connections with logicconnections: 2: 12Lxx Connections with logicconnections: 3: 16T30 Connections with combinatoricsconnections: 4: 20F10 Word problems, other decision problems, connections with logic and automata[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70
connections: 5: 20Jxx Connections with homological algebra and category theoryconnections: 6: 20M50 Connections of semigroups with homological algebra and category theoryconnections: 7: 28E15 Other connections with logic and set theoryconnections: 8: 31A35 Connections with differential equationsconnections: 9: 31B35 Connections with differential equationsconnections: 10: 33C80 Connections with groups and algebras, and related topicsconnections: 11: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, andrelated topics
connections: 12: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros ofAbelian integrals, etc.)
connections: 13: 53B05 Linear and affine connectionsconnections: 14: 53B10 Projective connectionsconnections: 15: 53B15 Other connectionsconnections: 16: 53C05 Connections, general theoryconnections: 17: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)[See also]32Q20
connections: 18: 54Hxx Connections with other structures, applicationsconnections: 19: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxconnective: 1: 19L41 Connective K-theory, cobordism [See also]55N22
connectivity: 1: 05C40 Connectivityconnes: 1: 58B34 Noncommutative geometry (a la Connes)
consequences: 1: 32F27 Topological consequences of geometric convexityconsequences: 2: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)conservation: 1: 35L65 Conservation lawsconservation: 2: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawsconservation: 3: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductionconservation: 4: 70S10 Symmetries and conservation lawsconservation: 5: 83C40 Gravitational energy and conservation laws; groups of motions
considerations: 1: 20A10 Metamathematical considerations For word problems, see 20F10considerations: 2: 62C05 General considerations
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consistency: 1: 03E35 Consistency and independence resultsconsistency: 2: 03F25 Relative consistency and interpretationsconsistency: 3: 54A35 Consistency and independence results [See also]03E35
constant: 1: 35Exx Equations and systems with constant coefficients [See also]35N05constant: 2: 35N05 Overdetermined systems with constant coefficients
constants: 1: 11Y60 Evaluation of constantsconstants: 2: 40D10 Tauberian constants and oscillation limitsconstants: 3: 40E20 Tauberian constantsconstants: 4: 41A44 Best constants
constitutive: 1: 74A20 Theory of constitutive functionsconstitutive: 2: 74D05 Linear constitutive equationsconstitutive: 3: 74D10 Nonlinear constitutive equationsconstitutive: 4: 74Q15 Effective constitutive equationsconstitutive: 5: 76Axx Foundations, constitutive equations, rheologyconstrained: 1: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxxconstraints: 1: 11N25 Distribution of integers with specified multiplicative constraintsconstraints: 2: 41A29 Approximation with constraintsconstraints: 3: 62F30 Inference under constraintsconstraints: 4: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxx
constructed: 1: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)constructibility: 1: 03E45 Inner models, including constructibility, ordinal definability, and core models
constructible: 1: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxxconstruction: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxconstruction: 2: 65D20 Computation of special functions, construction of tables [See also]33F05
constructions: 1: 03C20 Ultraproducts and related constructionsconstructions: 2: 03C30 Other model constructionsconstructions: 3: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M20constructions: 4: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D35constructions: 5: 16Sxx Rings and algebras arising under various constructionsconstructions: 6: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxconstructions: 7: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)constructions: 8: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05constructions: 9: 51M15 Geometric constructionsconstructions: 10: 54Bxx Basic constructionsconstructions: 11: 54B17 Adjunction spaces and similar constructionsconstructions: 12: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)constructions: 13: 57T30 Bar and cobar constructions [See also]18G55, 55Uxxconstructive: 1: 03D78 Computation over the reals For constructive aspects, see 03F60constructive: 2: 03Fxx Proof theory and constructive mathematicsconstructive: 3: 03F50 Metamathematics of constructive systemsconstructive: 4: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30,
47S30constructive: 5: 03F65 Other constructive mathematics [See also]03D45constructive: 6: 26E40 Constructive real analysis [See also]03F60constructive: 7: 46S30 Constructive functional analysis [See also]03F60constructive: 8: 47S30 Constructive operator theory [See also]03F60constructive: 9: 81T08 Constructive quantum field theory
consumer: 1: 91B42 Consumer behavior, demand theorycontact: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxxcontact: 2: 37J55 Contact systems [See also]53D10contact: 3: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxxcontact: 4: 53D10 Contact manifolds, generalcontact: 5: 53D15 Almost contact and almost symplectic manifoldscontact: 6: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxx
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contact: 7: 53D42 Symplectic field theory; contact homologycontact: 8: 57R17 Symplectic and contact topologycontact: 9: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25contact: 10: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxcontact: 11: 74M15 Contact
contemporary: 1: 01A65 Contemporarycontent: 1: 00B15 Collections of articles of miscellaneous specific content
contents: 1: 28A12 Contents, measures, outer measures, capacitiescontext: 1: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitycontext: 2: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxcontextuality: 1: 81P13 Contextualitycontingency: 1: 62H17 Contingency tables
continua: 1: 37B45 Continua theory in dynamicscontinua: 2: 54F15 Continua and generalizationscontinua: 3: 80A17 Thermodynamics of continua [See also]74A15
continuation: 1: 30B40 Analytic continuationcontinuation: 2: 32Dxx Analytic continuationcontinuation: 3: 32D15 Continuation of analytic objectscontinuation: 4: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation
of solutionscontinuation: 5: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxx
continued: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,40A15continued: 2: 11J70 Continued fractions and generalizations [See also]11A55, 11K50continued: 3: 11K50 Metric theory of continued fractions [See also]11A55, 11J70continued: 4: 11Y65 Continued fraction calculationscontinued: 5: 30B70 Continued fractions [See also]11A55, 40A15continued: 6: 40A15 Convergence and divergence of continued fractions [See also]30B70continuity: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27continuity: 2: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27continuity: 3: 26B05 Continuity and differentiation questionscontinuity: 4: 46H40 Automatic continuitycontinuity: 5: 54C08 Weak and generalized continuitycontinuity: 6: 58C07 Continuity properties of mappingscontinuity: 7: 60G30 Continuity and singularity of induced measures
continuous: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,22A26, 68Q55continuous: 2: 06C20 Complemented modular lattices, continuous geometriescontinuous: 3: 11K41 Continuous, p-adic and abstract analoguescontinuous: 4: 18B30 Categories of topological spaces and continuous mappings [See also]54-XXcontinuous: 5: 22E41 Continuous cohomology [See also]57R32, 57Txx, 58H10continuous: 6: 26A46 Absolutely continuous functionscontinuous: 7: 26B30 Absolutely continuous functions, functions of bounded variationcontinuous: 8: 28D10 One-parameter continuous families of measure-preserving transformationscontinuous: 9: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuationof solutionscontinuous: 10: 37A10 One-parameter continuous families of measure-preserving transformationscontinuous: 11: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)continuous: 12: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)continuous: 13: 46E05 Lattices of continuous, differentiable or analytic functions
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Mathematics Subject Classification 2010
continuous: 14: 46E10 Topological linear spaces of continuous, differentiable or analytic functionscontinuous: 15: 46E15 Banach spaces of continuous, differentiable or analytic functionscontinuous: 16: 46E20 Hilbert spaces of continuous, differentiable or analytic functionscontinuous: 17: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banachfunction algebras, see 46J10, 46J15continuous: 18: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25continuous: 19: 46T20 Continuous and differentiable maps [See also]46G05continuous: 20: 51D30 Continuous geometries and related topics [See also]06Cxxcontinuous: 21: 54C05 Continuous mapscontinuous: 22: 60G44 Martingales with continuous parametercontinuous: 23: 90B85 Continuous location
continuous-time: 1: 60J25 Continuous-time Markov processes on general state spacescontinuous-time: 2: 60J27 Continuous-time Markov processes on discrete state spacescontinuous-time: 3: 60J28 Applications of continuous-time Markov processes on discrete state spaces
continuum: 1: 03E17 Cardinal characteristics of the continuumcontinuum: 2: 03E50 Continuum hypothesis and Martin’s axiom [See also]03E57continuum: 3: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solidscontinuum: 4: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXcontinuum: 5: 81T27 Continuum limitscontinuum: 6: 82B21 Continuum models (systems of particles, etc.)continuum: 7: 82C21 Dynamic continuum models (systems of particles, etc.)
contraction: 1: 65N45 Method of contraction of the boundarycontraction-type: 1: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
contractions: 1: 47A45 Canonical models for contractions and nonselfadjoint operatorscontractions: 2: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.
contracts: 1: 91B40 Labor market, contractscontributions: 1: 97D20 Philosophical and theoretical contributions (maths didactics)
control: 1: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,etc.)
control: 2: 34Hxx Control problems [See also]49J15, 49K15, 93C15control: 3: 34H05 Control problems [See also]49J15, 49K15, 93C15control: 4: 34H10 Chaos controlcontrol: 5: 34H20 Bifurcation controlcontrol: 6: 34K35 Control problems [See also]49J21, 49K21, 93C23control: 7: 35Q93 PDEs in connection with control and optimizationcontrol: 8: 37N35 Dynamical systems in controlcontrol: 9: 47N70 Applications in systems theory, circuits, and control theorycontrol: 10: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XXcontrol: 11: 49J15 Optimal control problems involving ordinary differential equationscontrol: 12: 49J20 Optimal control problems involving partial differential equationscontrol: 13: 49J21 Optimal control problems involving relations other than differential equationscontrol: 14: 49N05 Linear optimal control problems [See also]93C05control: 15: 49N25 Impulsive optimal control problemscontrol: 16: 49N90 Applications of optimal control and differential games [See also]90C90, 93C95control: 17: 58E25 Applications to control theory [See also]49-XX, 93-XXcontrol: 18: 70E60 Robot dynamics and control [See also]68T40, 70Q05, 93C85control: 19: 70Qxx Control of mechanical systems [See also]60Gxx, 60Jxxcontrol: 20: 70Q05 Control of mechanical systemscontrol: 21: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxxcontrol: 22: 76B75 Flow control and optimization [See also]49Q10, 93C20, 93C95control: 23: 76D55 Flow control and optimization [See also]49Q10, 93C20, 93C95control: 24: 76F70 Control of turbulent flowscontrol: 25: 76N25 Flow control and optimizationcontrol: 26: 81Q93 Quantum controlcontrol: 27: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)
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control: 28: 93-XX Systems theory; control For optimal control, see 49-XXcontrol: 29: 93-XX Systems theory; control For optimal control, see 49-XXcontrol: 30: 93B52 Feedback controlcontrol: 31: 93Cxx Control systemscontrol: 32: 93C40 Adaptive controlcontrol: 33: 93C42 Fuzzy control systemscontrol: 34: 93C83 Control problems involving computers (process control, etc.)control: 35: 93C83 Control problems involving computers (process control, etc.)control: 36: 93Exx Stochastic systems and controlcontrol: 37: 93E20 Optimal stochastic controlcontrol: 38: 93E35 Stochastic learning and adaptive controlcontrol: 39: 97D60 Student assessment, achievement control and rating
controllability: 1: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,37C10, 93B05
controllability: 2: 93Bxx Controllability, observability, and system structurecontrollability: 3: 93B05 Controllability
controls: 1: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bangcontrols, etc.)
controls: 2: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bangcontrols, etc.)convection: 1: 76E06 Convectionconvection: 2: 76Rxx Diffusion and convectionconvection: 3: 76R05 Forced convectionconvection: 4: 76R10 Free convectionconvective: 1: 76E15 Absolute and convective instability and stabilityconvective: 2: 76F35 Convective turbulence [See also]76E15, 76Rxx
convergence: 1: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes ofconvergence
convergence: 2: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxxconvergence: 3: 40Axx Convergence and divergence of infinite limiting processesconvergence: 4: 40A05 Convergence and divergence of series and sequencesconvergence: 5: 40A10 Convergence and divergence of integralsconvergence: 6: 40A15 Convergence and divergence of continued fractions [See also]30B70convergence: 7: 40A20 Convergence and divergence of infinite productsconvergence: 8: 40A30 Convergence and divergence of series and sequences of functionsconvergence: 9: 40A35 Ideal and statistical convergence [See also]40G15convergence: 10: 40D15 Convergence factors and summability factorsconvergence: 11: 40G15 Summability methods using statistical convergence [See also]40A35convergence: 12: 41A25 Rate of convergence, degree of approximationconvergence: 13: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriesconvergence: 14: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriesconvergence: 15: 43A50 Convergence of Fourier series and of inverse transformsconvergence: 16: 46A17 Bornologies and related structures; Mackey convergence, etc.convergence: 17: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)convergence: 18: 49J45 Methods involving semicontinuity and convergence; relaxationconvergence: 19: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)convergence: 20: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)convergence: 21: 60B10 Convergence of probability measuresconvergence: 22: 65Bxx Acceleration of convergenceconvergence: 23: 65L20 Stability and convergence of numerical methodsconvergence: 24: 65M12 Stability and convergence of numerical methodsconvergence: 25: 65N12 Stability and convergence of numerical methods
convex: 1: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C07convex: 2: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)convex: 3: 32E05 Holomorphically convex complex spaces, reduction theory
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convex: 4: 46A03 General theory of locally convex spacesconvex: 5: 46A04 Locally convex Frechet spaces and (DF)-spacesconvex: 6: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)convex: 7: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07convex: 8: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsconvex: 9: 47L07 Convex sets and cones of operators [See also]46A55convex: 10: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsconvex: 11: 51M16 Inequalities and extremum problems For convex problems, see 52A40convex: 12: 52-XX Convex and discrete geometryconvex: 13: 52A05 Convex sets without dimension restrictionsconvex: 14: 52A07 Convex sets in topological vector spaces [See also]46A55convex: 15: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04convex: 16: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04convex: 17: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45convex: 18: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45convex: 19: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45convex: 20: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45convex: 21: 52A22 Random convex sets and integral geometry [See also]53C65, 60D05convex: 22: 52A23 Asymptotic theory of convex bodies [See also]46B06convex: 23: 52A27 Approximation by convex setsconvex: 24: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)convex: 25: 52A41 Convex functions and convex programs [See also]26B25, 90C25convex: 26: 52A41 Convex functions and convex programs [See also]26B25, 90C25convex: 27: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxconvex: 28: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P21convex: 29: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P21convex: 30: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)convex: 31: 90C25 Convex programmingconvex: 32: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71convexity: 1: 26A51 Convexity, generalizationsconvexity: 2: 26B25 Convexity, generalizationsconvexity: 3: 32Exx Holomorphic convexityconvexity: 4: 32E20 Polynomial convexityconvexity: 5: 32Fxx Geometric convexityconvexity: 6: 32F17 Other notions of convexityconvexity: 7: 32F27 Topological consequences of geometric convexityconvexity: 8: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)convexity: 9: 32L15 Bundle convexity [See also]32F10convexity: 10: 35E10 Convexity propertiesconvexity: 11: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxxconvexity: 12: 52Axx General convexityconvexity: 13: 52A01 Axiomatic and generalized convexityconvexity: 14: 52A37 Other problems of combinatorial convexityconvexity: 15: 52A55 Spherical and hyperbolic convexityconvexity: 16: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxconvexity: 17: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxconvolution: 1: 42A85 Convolution, factorizationconvolution: 2: 44A35 Convolutionconvolution: 3: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopftype) [See also]47B35
convolution: 4: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
81 Run: December 14, 2009
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convolution algebras and measure algebras, see 43A10, 43A20convolutional: 1: 94B10 Convolutional codes
cooperative: 1: 91A12 Cooperative gamescoordinates: 1: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spacecoproducts: 1: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction ofinverses, etc.)
core: 1: 03E45 Inner models, including constructibility, ordinal definability, and core modelscorings: 1: 16T15 Coalgebras and comodules; coringscorona: 1: 30H80 Corona theorems
corporate: 1: 91G50 Corporate financecorrections: 1: 65B05 Extrapolation to the limit, deferred correctionscorrelation: 1: 62H20 Measures of association (correlation, canonical correlation, etc.)correlation: 2: 62H20 Measures of association (correlation, canonical correlation, etc.)
correlations: 1: 81P40 Quantum coherence, entanglement, quantum correlationscorrespondence: 1: 14E16 McKay correspondencecorrespondence: 2: 62H25 Factor analysis and principal components; correspondence analysis
correspondences: 1: 06A15 Galois correspondences, closure operatorscorrespondences: 2: 11F27 Theta series; Weil representation; theta correspondencescorrespondences: 3: 11F32 Modular correspondences, etc.correspondences: 4: 32Hxx Holomorphic mappings and correspondencescorrespondences: 5: 37F05 Relations and correspondencescorrespondences: 6: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22
cosine: 1: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10cosmic: 1: 54E20 Stratifiable spaces, cosmic spaces, etc.cosmic: 2: 83C75 Space-time singularities, cosmic censorship, etc.
cosmology: 1: 83Fxx Cosmologycosmology: 2: 83F05 Cosmologycosmology: 3: 85A40 Cosmology For relativistic cosmology, see 83F05cosmology: 4: 85A40 Cosmology For relativistic cosmology, see 83F05
cost: 1: 91B32 Resource and cost allocationcounterexamples: 1: 54G20 Counterexamples
counting: 1: 11D45 Counting solutions of Diophantine equationscounting: 2: 11N45 Asymptotic results on counting functions for algebraic and topological structurescoupled: 1: 34C15 Nonlinear oscillations, coupled oscillators
coupling: 1: 74Fxx Coupling of solid mechanics with other effectscovariance: 1: 62J10 Analysis of variance and covariancecovariant: 1: 81R20 Covariant wave equationscovering: 1: 05B40 Packing and covering [See also]11H31, 52C15, 52C17covering: 2: 05C70 Factorization, matching, partitioning, covering and packingcovering: 3: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C17covering: 4: 30C25 Covering theorems in conformal mapping theorycovering: 5: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H31covering: 6: 52C17 Packing and covering in n dimensions [See also]05B40, 11H31covering: 7: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)covering: 8: 57M10 Covering spacescovering: 9: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71coverings: 1: 14E20 Coverings [See also]14H30coverings: 2: 14H30 Coverings, fundamental group [See also]14E20, 14F35coverings: 3: 57M12 Special coverings, e.g. branched
coxeter: 1: 20F55 Reflection and Coxeter groups [See also]22E40, 51F15coxeter: 2: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55cr: 1: 32G07 Deformations of special (e.g. CR) structurescr: 2: 32Vxx CR manifoldscr: 3: 32V05 CR structures, CR operators, and generalizationscr: 4: 32V05 CR structures, CR operators, and generalizations
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cr: 5: 32V10 CR functionscr: 6: 32V15 CR manifolds as boundaries of domainscr: 7: 32V20 Analysis on CR manifoldscr: 8: 32V25 Extension of functions and other analytic objects from CR manifoldscr: 9: 32V30 Embeddings of CR manifoldscr: 10: 32V35 Finite type conditions on CR manifolds
credit: 1: 91G40 Credit riskcremona: 1: 14E07 Birational automorphisms, Cremona group and generalizationscriteria: 1: 37J30 Obstructions to integrability (nonintegrability criteria)critical: 1: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30critical: 2: 35B33 Critical exponentscritical: 3: 35B38 Critical pointscritical: 4: 57R70 Critical points and critical submanifoldscritical: 5: 57R70 Critical points and critical submanifoldscritical: 6: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)critical: 7: 58E11 Critical metricscritical: 8: 58K05 Critical points of functions and mappingscritical: 9: 82B27 Critical phenomenacritical: 10: 82C27 Dynamic critical phenomenacrossed: 1: 16K20 Finite-dimensional For crossed products, see 16S35crossed: 2: 16S35 Twisted and skew group rings, crossed productscrossed: 3: 47L65 Crossed product algebras (analytic crossed products)crossed: 4: 47L65 Crossed product algebras (analytic crossed products)
cryptography: 1: 11T71 Algebraic coding theory; cryptographycryptography: 2: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B40cryptography: 3: 81P94 Quantum cryptography [See also]94A60cryptography: 4: 94A60 Cryptography [See also]11T71, 14G50, 68P25, 81P94
crystalline: 1: 14F30 p-adic cohomology, crystalline cohomologycrystalline: 2: 74E15 Crystalline structure
crystallographic: 1: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially51F15, and 82D25
crystallographic: 2: 82D25 Crystals For crystallographic group theory, see 20H15crystals: 1: 74N05 Crystalscrystals: 2: 76A15 Liquid crystals [See also]82D30crystals: 3: 82D25 Crystals For crystallographic group theory, see 20H15crystals: 4: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
csl: 1: 47L35 Nest algebras, CSL algebrascubature: 1: 65D32 Quadrature and cubature formulas
cubic: 1: 11D25 Cubic and quartic equationscubic: 2: 11R16 Cubic and quartic extensions
cultures: 1: 01A12 Indigenous cultures of the Americascultures: 2: 01A13 Other indigenous cultures (non-European)cultures: 3: 01A15 Indigenous European cultures (pre-Greek, etc.)current: 1: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
currents: 1: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27currents: 2: 32U40 Currentscurrents: 3: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C35currents: 4: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axxcurrents: 5: 58A25 Currents [See also]32C30, 53C65
curvature: 1: 32Q05 Negative curvature manifoldscurvature: 2: 32Q10 Positive curvature manifoldscurvature: 3: 35J93 Quasilinear elliptic equations with mean curvature operator
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curvature: 4: 35K93 Quasilinear parabolic equations with mean curvature operatorcurvature: 5: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42curvature: 6: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60curvature: 7: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R42curvature: 8: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
curve: 1: 65D10 Smoothing, curve fittingcurved: 1: 20F67 Hyperbolic groups and nonpositively curved groupscurved: 2: 81T20 Quantum field theory on curved space backgroundscurves: 1: 11G05 Elliptic curves over global fields [See also]14H52curves: 2: 11G07 Elliptic curves over local fields [See also]14G20, 14H52curves: 3: 11G20 Curves over finite and local fields [See also]14H25curves: 4: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25curves: 5: 14Hxx Curvescurves: 6: 14H45 Special curves and curves of low genuscurves: 7: 14H45 Special curves and curves of low genuscurves: 8: 14H50 Plane and space curvescurves: 9: 14H52 Elliptic curves [See also]11G05, 11G07, 14Kxxcurves: 10: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05curves: 11: 14Q05 Curvescurves: 12: 32Q65 Pseudoholomorphic curvescurves: 13: 34C05 Location of integral curves, singular points, limit cyclescurves: 14: 51L05 Geometry of orders of nondifferentiable curvescurves: 15: 51L10 Directly differentiable curvescurves: 16: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04curves: 17: 53A04 Curves in Euclidean spacecurves: 18: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A03curves: 19: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07
cut-elimination: 1: 03F05 Cut-elimination and normal-form theoremscw-complexes: 1: 57Q12 Wall finiteness obstruction for CW-complexes
cycles: 1: 05C38 Paths and cycles [See also]90B10cycles: 2: 14Cxx Cycles and subschemescycles: 3: 14C25 Algebraic cyclescycles: 4: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F42cycles: 5: 32S30 Deformations of singularities; vanishing cycles [See also]14B07cycles: 6: 34C05 Location of integral curves, singular points, limit cyclescycles: 7: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)cycles: 8: 37G15 Bifurcations of limit cycles and periodic orbitscycles: 9: 57R95 Realizing cycles by submanifoldscycles: 10: 70K05 Phase plane analysis, limit cyclescyclic: 1: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)cyclic: 2: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)cyclic: 3: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G60cyclic: 4: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22cyclic: 5: 47A16 Cyclic vectors, hypercyclic and chaotic operatorscyclic: 6: 55S15 Symmetric products, cyclic productscyclic: 7: 94B15 Cyclic codes
cyclotomic: 1: 11R18 Cyclotomic extensionscyclotomic: 2: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)cyclotomy: 1: 11T22 Cyclotomy
cylinder: 1: 33C10 Bessel and Airy functions, cylinder functions, 0F1
cylindric: 1: 03G15 Cylindric and polyadic algebras; relation algebras
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cylindrical: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) onmanifolds [See also]28Cxx, 46G12, 60-XXcylindrical: 2: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12
d: 1: 11F52 Modular forms associated to Drinfel′d modulesd: 2: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05d: 3: 11J93 Transcendence theory of Drinfel′d and t-modulesd: 4: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusiond: 5: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)
d’enfants: 1: 11G32 Dessins d’enfants, Belyı theoryd’enfants: 2: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32
d-modules: 1: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-als [See also]13Nxx, 32C38
damage: 1: 74A45 Theories of fracture and damagedamage: 2: 74Rxx Fracture and damagedamage: 3: 74R05 Brittle damagedamage: 4: 74R20 Anelastic fracture and damage
damping: 1: 74Dxx Materials of strain-rate type and history type, other materials with memory (includingelastic materials with viscous damping, various viscoelastic materials)
daniell: 1: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),representing set functions and measures
data: 1: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxdata: 2: 35R05 Partial differential equations with discontinuous coefficients or datadata: 3: 62H11 Directional data; spatial statisticsdata: 4: 62Nxx Survival analysis and censored datadata: 5: 62N01 Censored data modelsdata: 6: 62N86 Fuzziness, and survival analysis and censored datadata: 7: 68Pxx Theory of datadata: 8: 68P05 Data structuresdata: 9: 68P25 Data encryption [See also]94A60, 81P94data: 10: 68Q65 Abstract data types; algebraic specification [See also]18C50data: 11: 93B15 Realizations from input-output datadata: 12: 93E14 Data smoothingdata: 13: 97R50 Data bases, information systems
database: 1: 68P15 Database theoryde: 1: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G20de: 2: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L10de: 3: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35de: 4: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32de: 5: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22de: 6: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22de: 7: 58A12 de Rham theory [See also]14Fxx
deals: 1: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
decentralized: 1: 93A14 Decentralized systemsdecidability: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F10decidability: 2: 11U05 Decidability [See also]03B25decidability: 3: 12L05 Decidability [See also]03B25
decision: 1: 20F10 Word problems, other decision problems, connections with logic and automata[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70
decision: 2: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35decision: 3: 62C12 Empirical decision procedures; empirical Bayes proceduresdecision: 4: 62C25 Compound decision problems
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Mathematics Subject Classification 2010
decision: 5: 62C86 Decision theory and fuzzinessdecision: 6: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)
[See also]68M11decision: 7: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B06decision: 8: 90C40 Markov and semi-Markov decision processesdecision: 9: 91A35 Decision theory for games [See also]62Cxx, 91B06, 90B50decision: 10: 91B06 Decision theory [See also]62Cxx, 90B50, 91A35
decoding: 1: 94B35 Decodingdecoherence: 1: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31
decomposable: 1: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.decomposition: 1: 05C51 Graph designs and isomomorphic decomposition [See also]05B30decomposition: 2: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tiondecomposition: 3: 46L45 Decomposition theory for C∗-algebrasdecomposition: 4: 49M27 Decomposition methodsdecomposition: 5: 65M55 Multigrid methods; domain decompositiondecomposition: 6: 65N55 Multigrid methods; domain decomposition
decompositions: 1: 17C27 Idempotents, Peirce decompositionsdecompositions: 2: 54B15 Quotient spaces, decompositions
dedekind: 1: 11F20 Dedekind eta function, Dedekind sumsdedekind: 2: 11F20 Dedekind eta function, Dedekind sumsdedekind: 3: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizations
deduction: 1: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B35deductive: 1: 03B22 Abstract deductive systemsdeductive: 2: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXdeferred: 1: 65B05 Extrapolation to the limit, deferred corrections
definability: 1: 03C40 Interpolation, preservation, definabilitydefinability: 2: 03D70 Inductive definabilitydefinability: 3: 03E45 Inner models, including constructibility, ordinal definability, and core modelsdefinability: 4: 03E47 Other notions of set-theoretic definability
defined: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)[See also]13A05, 14M05
defined: 2: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)[See also]13F15, 13F45, 13H10
defined: 3: 20F22 Other classes of groups defined by subgroup chainsdefined: 4: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)defined: 5: 33D60 Basic hypergeometric integrals and functions defined by themdefined: 6: 33E20 Other functions defined by series and integralsdefined: 7: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40defined: 8: 47B07 Operators defined by compactness propertiesdefined: 9: 54Cxx Maps and general types of spaces defined by mapsdefined: 10: 54C50 Special sets defined by functions [See also]26A21definite: 1: 42A82 Positive definite functionsdefinite: 2: 43A35 Positive definite functions on groups, semigroups, etc.
definitions: 1: 18A05 Definitions, generalizationsdeformable: 1: 35Q74 PDEs in connection with mechanics of deformable solidsdeformable: 2: 74-XX Mechanics of deformable solids
deformation: 1: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10deformation: 2: 53D55 Deformation quantization, star productsdeformation: 3: 58K60 Deformation of singularitiesdeformation: 4: 74A05 Kinematics of deformation
deformations: 1: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxxdeformations: 2: 14B07 Deformations of singularities [See also]14D15, 32S30deformations: 3: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxxdeformations: 4: 16S80 Deformations of rings [See also]13D10, 14D15deformations: 5: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
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[See also]16T20, 20G42, 81R50, 82B23deformations: 6: 32Gxx Deformations of analytic structuresdeformations: 7: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H15deformations: 8: 32G07 Deformations of special (e.g. CR) structuresdeformations: 9: 32G08 Deformations of fiber bundlesdeformations: 10: 32G10 Deformations of submanifolds and subspacesdeformations: 11: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxdeformations: 12: 32S30 Deformations of singularities; vanishing cycles [See also]14B07deformations: 13: 34M56 Isomonodromic deformationsdeformations: 14: 46L65 Quantizations, deformationsdeformations: 15: 58H15 Deformations of structures [See also]32Gxx, 58J10deformations: 16: 74B15 Equations linearized about a deformed state (small deformations superposed on large)
deformed: 1: 74B15 Equations linearized about a deformed state (small deformations superposed on large)degenerate: 1: 35J70 Degenerate elliptic equationsdegenerate: 2: 35K65 Degenerate parabolic equationsdegenerate: 3: 35L80 Degenerate hyperbolic equations
degenerations: 1: 14D06 Fibrations, degenerationsdegenerations: 2: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K30degree: 1: 03D28 Other Turing degree structuresdegree: 2: 11B30 Arithmetic combinatorics; higher degree uniformitydegree: 3: 11D41 Higher degree equations; Fermat’s equationdegree: 4: 11E76 Forms of degree higher than twodegree: 5: 14N25 Varieties of low degreedegree: 6: 41A25 Rate of convergence, degree of approximationdegree: 7: 47H11 Degree theory [See also]55M25, 58C30degree: 8: 55M25 Degree, winding number
degree-theoretic: 1: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoreticmethods
degrees: 1: 03D25 Recursively (computably) enumerable sets and degreesdegrees: 2: 03D30 Other degrees and reducibilitiesdegrees: 3: 03D35 Undecidability and degrees of sets of sentencesdegrees: 4: 05C07 Vertex degrees [See also]05E30dehn’s: 1: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity
deligne: 1: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne(co)homologies)
demand: 1: 60K10 Applications (reliability, demand theory, etc.)demand: 2: 91B42 Consumer behavior, demand theory
demodulation: 1: 94A14 Modulation and demodulationdemography: 1: 91D20 Mathematical geography and demography
dendrites: 1: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A03denjoy: 1: 26A39 Denjoy and Perron integrals, other special integrals
densities: 1: 37F35 Conformal densities and Hausdorff dimensiondensity: 1: 05C42 Density (toughness, etc.)density: 2: 11B05 Density, gaps, topologydensity: 3: 11R45 Density theoremsdensity: 4: 62G07 Density estimation
denumerable: 1: 03C15 Denumerable structuresdependence: 1: 13B21 Integral dependence; going up, going downdependence: 2: 15A03 Vector spaces, linear dependence, rankdependence: 3: 32J10 Algebraic dependence theoremsdependence: 4: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuationof solutions
dependence: 5: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterdependence: 6: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxdependent: 1: 34B08 Parameter dependent boundary value problems
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Mathematics Subject Classification 2010
depth: 1: 13C15 Dimension theory, depth, related rings (catenary, etc.)derivations: 1: 13N15 Derivationsderivations: 2: 16W25 Derivations, actions of Lie algebrasderivations: 3: 17A36 Automorphisms, derivations, other operatorsderivations: 4: 17B40 Automorphisms, derivations, other operatorsderivations: 5: 46L57 Derivations, dissipations and positive semigroups in C∗-algebrasderivations: 6: 47B47 Commutators, derivations, elementary operators, etc.derivative: 1: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txxderivative: 2: 91G20 Derivative securities
derivative-free: 1: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52derivatives: 1: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also]28A15derivatives: 2: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),discontinuous derivativesderivatives: 3: 26A33 Fractional derivatives and integralsderivatives: 4: 26D10 Inequalities involving derivatives and differential and integral operatorsderivatives: 5: 34K37 Functional-differential equations with fractional derivativesderivatives: 6: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities forintegralsderivatives: 7: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10derivatives: 8: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10derivatives: 9: 46G05 Derivatives [See also]46T20, 58C20, 58C25derivatives: 10: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52
derived: 1: 13D09 Derived categoriesderived: 2: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M20derived: 3: 16E35 Derived categoriesderived: 4: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxderived: 5: 18E25 Derived functors and satellitesderived: 6: 18E30 Derived categories, triangulated categoriesderived: 7: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E25derived: 8: 20F14 Derived series, central series, and generalizations
desarguesian: 1: 06C05 Modular lattices, Desarguesian latticesdesarguesian: 2: 51A30 Desarguesian and Pappian geometries
descent: 1: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,steepest descent) [See also]34E20
descent: 2: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)[See also]30E15describing: 1: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)describing: 2: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)describing: 3: 32P05 Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)descriptive: 1: 03E15 Descriptive set theory [See also]28A05, 54H05descriptive: 2: 51Nxx Analytic and descriptive geometrydescriptive: 3: 51N05 Descriptive geometry [See also]65D17, 68U07descriptive: 4: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)[See also]03E15, 26A21, 28A05descriptive: 5: 68Q19 Descriptive complexity and finite models [See also]03C13descriptive: 6: 97G80 Descriptive geometry
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descriptive: 7: 97K40 Descriptive statisticsdesign: 1: 05Bxx Designs and configurations For applications of design theory, see 94C30design: 2: 62Kxx Design of experiments [See also]05Bxxdesign: 3: 62K86 Fuzziness and design of experimentsdesign: 4: 62L05 Sequential designdesign: 5: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07design: 6: 68M10 Network design and communication [See also]68R10, 90B18design: 7: 68U07 Computer-aided design [See also]65D17design: 8: 93B51 Design techniques (robust design, computer-aided design, etc.)design: 9: 93B51 Design techniques (robust design, computer-aided design, etc.)design: 10: 93B51 Design techniques (robust design, computer-aided design, etc.)design: 11: 94C30 Applications of design theory [See also]05Bxx
designs: 1: 05Bxx Designs and configurations For applications of design theory, see 94C30designs: 2: 05B05 Block designs [See also]51E05, 62K10designs: 3: 05B30 Other designs, configurations [See also]51E30designs: 4: 05C51 Graph designs and isomomorphic decomposition [See also]05B30designs: 5: 51E05 General block designs [See also]05B05designs: 6: 62K05 Optimal designsdesigns: 7: 62K10 Block designsdesigns: 8: 62K15 Factorial designsdesigns: 9: 62K20 Response surface designsdesigns: 10: 62K25 Robust parameter designs
desingularization: 1: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros ofAbelian integrals, etc.)
dessins: 1: 11G32 Dessins d’enfants, Belyı theorydessins: 2: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32
detection: 1: 60G35 Signal detection and filtering [See also]62M20, 93E10, 93E11, 94Axxdetection: 2: 93E10 Estimation and detection [See also]60G35detection: 3: 94A13 Detection theorydetection: 4: 94C12 Fault detection; testing
determinacy: 1: 03E60 Determinacy principlesdeterminacy: 2: 58K40 Classification; finite determinacy of map germsdeterminant: 1: 58J52 Determinants and determinant bundles, analytic torsion
determinantal: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,14M12
determinantal: 2: 14M12 Determinantal varieties [See also]13C40determinants: 1: 11C20 Matrices, determinants [See also]15B36determinants: 2: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasdeterminants: 3: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14determinants: 4: 58J52 Determinants and determinant bundles, analytic torsiondeterminants: 5: 65F40 Determinants
determination: 1: 74Qxx Homogenization, determination of effective propertiesdetermined: 1: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction ofinverses, etc.)
determined: 2: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
determined: 3: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
determined: 4: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartzspaces, Montel spaces, etc.)
deterministic: 1: 90B10 Network models, deterministicdeterministic: 2: 90B35 Scheduling theory, deterministic [See also]68M20
developmental: 1: 92C15 Developmental biology, pattern formationdeviations: 1: 60F10 Large deviations
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Mathematics Subject Classification 2010
devices: 1: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxxdf-spaces: 1: 46A04 Locally convex Frechet spaces and (DF)-spaces
diagnostics: 1: 62J20 Diagnosticsdiagonalizable: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E25diagonalizable: 2: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45diagram: 1: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]
diagrams: 1: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05diagrams: 2: 51E24 Buildings and the geometry of diagramsdiagrams: 3: 52B35 Gale and other diagramsdiagrams: 4: 81T18 Feynman diagramsdiamond: 1: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
dichotomy: 1: 34D09 Dichotomy, trichotomydictionaries: 1: 00A20 Dictionaries and other general reference works
didactics: 1: 00A35 Methodology of mathematics, didactics [See also]97Cxx, 97Dxxdidactics: 2: 97D20 Philosophical and theoretical contributions (maths didactics)
diffeomorphisms: 1: 37C05 Smooth mappings and diffeomorphismsdiffeomorphisms: 2: 37C55 Periodic and quasiperiodic flows and diffeomorphismsdiffeomorphisms: 3: 37E30 Homeomorphisms and diffeomorphisms of planes and surfacesdiffeomorphisms: 4: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricsdiffeomorphisms: 5: 57R50 Diffeomorphismsdiffeomorphisms: 6: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismsdiffeomorphisms: 7: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S05
difference: 1: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B13difference: 2: 12Hxx Differential and difference algebradifference: 3: 12H10 Difference algebra [See also]39Axxdifference: 4: 33E30 Other functions coming from differential, difference and integral equationsdifference: 5: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H15difference: 6: 39-XX Difference and functional equationsdifference: 7: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05difference: 8: 39A10 Difference equations, additivedifference: 9: 39A13 Difference equations, scaling (q-differences) [See also]33Dxxdifference: 10: 39A14 Partial difference equationsdifference: 11: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typedifference: 12: 39A50 Stochastic difference equationsdifference: 13: 39A70 Difference operators [See also]47B39difference: 14: 47B39 Difference operators [See also]39A70difference: 15: 65L12 Finite difference methodsdifference: 16: 65M06 Finite difference methodsdifference: 17: 65N06 Finite difference methodsdifference: 18: 65Qxx Difference and functional equations, recurrence relationsdifference: 19: 65Q10 Difference equationsdifference: 20: 74S20 Finite difference methodsdifference: 21: 76M20 Finite difference methodsdifference: 22: 78M20 Finite difference methodsdifference: 23: 80M20 Finite difference methods
differentiability: 1: 49J50 Frechet and Gateaux differentiability [See also]46G05, 58C20differentiability: 2: 58B10 Differentiability questions
differentiable: 1: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see12Jxx, 13Jxx, 16W80
differentiable: 2: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05differentiable: 3: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25differentiable: 4: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25
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Mathematics Subject Classification 2010
differentiable: 5: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationdifferentiable: 6: 46E05 Lattices of continuous, differentiable or analytic functionsdifferentiable: 7: 46E10 Topological linear spaces of continuous, differentiable or analytic functionsdifferentiable: 8: 46E15 Banach spaces of continuous, differentiable or analytic functionsdifferentiable: 9: 46E20 Hilbert spaces of continuous, differentiable or analytic functionsdifferentiable: 10: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15differentiable: 11: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60differentiable: 12: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30differentiable: 13: 46T20 Continuous and differentiable maps [See also]46G05differentiable: 14: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C70differentiable: 15: 51L10 Directly differentiable curvesdifferentiable: 16: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxdifferentiable: 17: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxdifferentiable: 18: 57R35 Differentiable mappingsdifferentiable: 19: 57R45 Singularities of differentiable mappingsdifferentiable: 20: 57R55 Differentiable structuresdifferentiable: 21: 57S15 Compact Lie groups of differentiable transformationsdifferentiable: 22: 58Axx General theory of differentiable manifolds [See also]32Cxxdifferentiable: 23: 58A03 Topos-theoretic approach to differentiable manifoldsdifferentiable: 24: 58A05 Differentiable manifolds, foundationsdifferentiable: 25: 58C25 Differentiable mapsdifferentiable: 26: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldsdifferentiable: 27: 58H05 Pseudogroups and differentiable groupoids [See also]22A22, 22E65
differential: 1: 11F25 Hecke-Petersson operators, differential operators (one variable)differential: 2: 11F60 Hecke-Petersson operators, differential operators (several variables)differential: 3: 12Hxx Differential and difference algebradifferential: 4: 12H05 Differential algebra [See also]13Nxxdifferential: 5: 12H20 Abstract differential equations [See also]34Mxxdifferential: 6: 12H25 p-adic differential equations [See also]11S80, 14G20differential: 7: 13Nxx Differential algebra [See also]12H05, 14F10differential: 8: 13N10 Rings of differential operators and their modules [See also]16S32, 32C38differential: 9: 16E45 Differential graded algebras and applicationsdifferential: 10: 16S32 Rings of differential operators [See also]13N10, 32C38differential: 11: 26D10 Inequalities involving derivatives and differential and integral operatorsdifferential: 12: 31A35 Connections with differential equationsdifferential: 13: 31B35 Connections with differential equationsdifferential: 14: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,35A27, 58J15differential: 15: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation) [See also]34Mxxdifferential: 16: 32S40 Monodromy; relations with differential equations and D-modulesdifferential: 17: 32Wxx Differential operators in several variablesdifferential: 18: 32W50 Other partial differential equations of complex analysisdifferential: 19: 33E30 Other functions coming from differential, difference and integral equationsdifferential: 20: 34-XX Ordinary differential equationsdifferential: 21: 34A07 Fuzzy differential equationsdifferential: 22: 34A08 Fractional differential equationsdifferential: 23: 34A26 Geometric methods in differential equationsdifferential: 24: 34A33 Lattice differential equationsdifferential: 25: 34A35 Differential equations of infinite orderdifferential: 26: 34A37 Differential equations with impulsesdifferential: 27: 34A40 Differential inequalities [See also]26D20
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Mathematics Subject Classification 2010
differential: 28: 34A60 Differential inclusions [See also]49J21, 49K21differential: 29: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxdifferential: 30: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,58D25differential: 31: 34Lxx Ordinary differential operators [See also]47E05differential: 32: 34L30 Nonlinear ordinary differential operatorsdifferential: 33: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G34differential: 34: 34M45 Differential equations on complex manifoldsdifferential: 35: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)differential: 36: 35-XX Partial differential equationsdifferential: 37: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities forintegralsdifferential: 38: 35A24 Methods of ordinary differential equationsdifferential: 39: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxxdifferential: 40: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)differential: 41: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.differential: 42: 35R05 Partial differential equations with discontinuous coefficients or datadifferential: 43: 35R06 Partial differential equations with measuredifferential: 44: 35R09 Integro-partial differential equations [See also]45Kxxdifferential: 45: 35R11 Fractional partial differential equationsdifferential: 46: 35R12 Impulsive partial differential equationsdifferential: 47: 35R13 Fuzzy partial differential equationsdifferential: 48: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE ininfinitely many variables) [See also]46Gxx, 58D25differential: 49: 35R45 Partial differential inequalitiesdifferential: 50: 35R50 Partial differential equations of infinite orderdifferential: 51: 35R60 Partial differential equations with randomness, stochastic partial differential equations[See also]60H15differential: 52: 35R60 Partial differential equations with randomness, stochastic partial differential equations[See also]60H15differential: 53: 35R70 Partial differential equations with multivalued right-hand sidesdifferential: 54: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators[See also]47G30, 58J40differential: 55: 37C10 Vector fields, flows, ordinary differential equationsdifferential: 56: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,34K50, 60H10, 60H15differential: 57: 37K25 Relations with differential geometrydifferential: 58: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G20differential: 59: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G20differential: 60: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20differential: 61: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20differential: 62: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J22differential: 63: 46N20 Applications to differential and integral equationsdifferential: 64: 47Exx Ordinary differential operators [See also]34Bxx, 34Lxxdifferential: 65: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)differential: 66: 47Fxx Partial differential operators [See also]35Pxx, 58Jxxdifferential: 67: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)differential: 68: 47N20 Applications to differential and integral equationsdifferential: 69: 49J15 Optimal control problems involving ordinary differential equationsdifferential: 70: 49J20 Optimal control problems involving partial differential equationsdifferential: 71: 49J21 Optimal control problems involving relations other than differential equationsdifferential: 72: 49K15 Problems involving ordinary differential equationsdifferential: 73: 49K20 Problems involving partial differential equationsdifferential: 74: 49K21 Problems involving relations other than differential equationsdifferential: 75: 49N70 Differential games
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differential: 76: 49N90 Applications of optimal control and differential games [See also]90C90, 93C95differential: 77: 51K10 Synthetic differential geometrydifferential: 78: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questionsof differentiable manifolds, see 58Axxdifferential: 79: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questionsof differentiable manifolds, see 58Axxdifferential: 80: 53Axx Classical differential geometrydifferential: 81: 53A15 Affine differential geometrydifferential: 82: 53A20 Projective differential geometrydifferential: 83: 53A25 Differential line geometrydifferential: 84: 53A30 Conformal differential geometrydifferential: 85: 53A35 Non-Euclidean differential geometrydifferential: 86: 53A40 Other special differential geometriesdifferential: 87: 53A55 Differential invariants (local theory), geometric objectsdifferential: 88: 53Bxx Local differential geometrydifferential: 89: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see55Rxx, 57Rxxdifferential: 90: 53C08 Gerbes, differential characters: differential geometric aspectsdifferential: 91: 53C08 Gerbes, differential characters: differential geometric aspectsdifferential: 92: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R32differential: 93: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysison metric spacesdifferential: 94: 53C43 Differential geometric aspects of harmonic maps [See also]58E20differential: 95: 53C56 Other complex differential geometry [See also]32Cxxdifferential: 96: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.[See mainly]58Axxdifferential: 97: 57M05 Fundamental group, presentations, free differential calculusdifferential: 98: 57Rxx Differential topology For foundational questions of differentiable manifolds, see58Axx; for infinite-dimensional manifolds, see 58Bxxdifferential: 99: 58A10 Differential formsdifferential: 100: 58A15 Exterior differential systems (Cartan theory)differential: 101: 58A40 Differential spacesdifferential: 102: 58D27 Moduli problems for differential geometric structuresdifferential: 103: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-XX, 53Cxxdifferential: 104: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-XX, 53Cxxdifferential: 105: 58J10 Differential complexes [See also]35Nxx; elliptic complexesdifferential: 106: 60H10 Stochastic ordinary differential equations [See also]34F05differential: 107: 60H15 Stochastic partial differential equations [See also]35R60differential: 108: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoreticalaspects, see 68U20 and 60H35differential: 109: 65C30 Stochastic differential and integral equationsdifferential: 110: 65Lxx Ordinary differential equationsdifferential: 111: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary valueproblemsdifferential: 112: 65Nxx Partial differential equations, boundary value problemsdifferential: 113: 81Q15 Perturbation theories for operators and differential equationsdifferential: 114: 91A23 Differential games [See also]49N70differential: 115: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)differential: 116: 93C15 Systems governed by ordinary differential equations [See also]34H05differential: 117: 93C20 Systems governed by partial differential equationsdifferential: 118: 93C30 Systems governed by functional relations other than differential equations (such ashybrid and switching systems)differential: 119: 97I40 Differential calculus
differential-algebraic: 1: 34A09 Implicit equations, differential-algebraic equations [See also]65L80differential-algebraic: 2: 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
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differential-algebraic: 3: 65L80 Methods for differential-algebraic equationsdifferential-difference: 1: 34Kxx Functional-differential and differential-difference equations [See also]37-XXdifferential-geometric: 1: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxdifferential-geometric: 2: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
differential-topological: 1: 70G40 Topological and differential-topological methodsdifferentials: 1: 13N05 Modules of differentialsdifferentials: 2: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals andpolynomials [See also]13Nxx, 32C38
differentials: 3: 14K20 Analytic theory; abelian integrals and differentialsdifferentials: 4: 30F30 Differentials on Riemann surfaces
differentiation: 1: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also]28A15
differentiation: 2: 26B05 Continuity and differentiation questionsdifferentiation: 3: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24differentiation: 4: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24differentiation: 5: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G05differentiation: 6: 65D25 Numerical differentiation
difficulties: 1: 97D70 Learning difficulties and student errorsdifficulty: 1: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15difficulty: 2: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15diffraction: 1: 78A45 Diffraction, scattering [See also]34E20 for WKB methods
diffusion: 1: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusiondiffusion: 2: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxdiffusion: 3: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60diffusion: 4: 60J60 Diffusion processes [See also]58J65diffusion: 5: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxdiffusion: 6: 74N25 Transformations involving diffusiondiffusion: 7: 76Rxx Diffusion and convectiondiffusion: 8: 76R50 Diffusion [See also]60J60
diffusion-limited: 1: 82B24 Interface problems; diffusion-limited aggregationdiffusion-limited: 2: 82C24 Interface problems; diffusion-limited aggregation
digital: 1: 11A63 Radix representation; digital problems For metric results, see 11K16digital: 2: 93C62 Digital systems
digraphs: 1: 05C20 Directed graphs (digraphs), tournamentsdihedral: 1: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)dihedral: 2: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)dilations: 1: 47A20 Dilations, extensions, compressions
dimension: 1: 03D32 Algorithmic randomness and dimension [See also]68Q30dimension: 2: 11G10 Abelian varieties of dimension > 1 [See also]14Kxxdimension: 3: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension[See also]11N99, 28Dxxdimension: 4: 12G10 Cohomological dimensiondimension: 5: 13C15 Dimension theory, depth, related rings (catenary, etc.)dimension: 6: 13D05 Homological dimensiondimension: 7: 16E10 Homological dimensiondimension: 8: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimensiondimension: 9: 16P90 Growth rate, Gelfand-Kirillov dimensiondimension: 10: 18G20 Homological dimension [See also]13D05, 16E10dimension: 11: 37C45 Dimension theory of dynamical systemsdimension: 12: 37F35 Conformal densities and Hausdorff dimension
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dimension: 13: 52A05 Convex sets without dimension restrictionsdimension: 14: 54F45 Dimension theory [See also]55M10dimension: 15: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A03dimension: 16: 55M10 Dimension theory [See also]54F45
dimensional: 1: 00A73 Dimensional analysisdimensional: 2: 76M55 Dimensional analysis and similaritydimensions: 1: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see32A22dimensions: 2: 37L30 Attractors and their dimensions, Lyapunov exponentsdimensions: 3: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04dimensions: 4: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45dimensions: 5: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45dimensions: 6: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P21dimensions: 7: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P21dimensions: 8: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H31dimensions: 9: 52C17 Packing and covering in n dimensions [See also]05B40, 11H31dimensions: 10: 52C20 Tilings in 2 dimensions [See also]05B45, 51M20dimensions: 11: 52C22 Tilings in n dimensions [See also]05B45, 51M20dimensions: 12: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxdimensions: 13: 57M25 Knots and links in S3 For higher dimensions, see 57Q45dimensions: 14: 57M60 Group actions in low dimensionsdimensions: 15: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25dimensions: 16: 83C80 Analogues in lower dimensionsdimensions: 17: 90C33 Complementarity and equilibrium problems and variational inequalities (finitedimensions)
dimer: 1: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphsdinatural: 1: 18A23 Natural morphisms, dinatural morphisms
diophantine: 1: 11Dxx Diophantine equations [See also]11Gxx, 14Gxxdiophantine: 2: 11D45 Counting solutions of Diophantine equationsdiophantine: 3: 11D75 Diophantine inequalities [See also]11J25diophantine: 4: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxxdiophantine: 5: 11Jxx Diophantine approximation, transcendental number theory [See also]11K60diophantine: 6: 11J25 Diophantine inequalities [See also]11D75diophantine: 7: 11K60 Diophantine approximation [See also]11Jxxdiophantine: 8: 11Y50 Computer solution of Diophantine equationsdiophantine: 9: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxx
dirac: 1: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)dirac: 2: 35Q41 Time-dependent Schrodinger equations, Dirac equationsdirac: 3: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsdirac’s: 1: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxxdirect: 1: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tiondirect: 2: 20K25 Direct sums, direct products, etc.direct: 3: 20K25 Direct sums, direct products, etc.direct: 4: 40Dxx Direct theorems on summabilitydirect: 5: 51L15 n-vertex theorems via direct methodsdirect: 6: 53C70 Direct methods (G-spaces of Busemann, etc.)direct: 7: 65F05 Direct methods for linear systems and matrix inversiondirect: 8: 76F65 Direct numerical and large eddy simulation of turbulence
directed: 1: 05C20 Directed graphs (digraphs), tournamentsdirected: 2: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)directional: 1: 62H11 Directional data; spatial statistics
directly: 1: 51L10 Directly differentiable curvesdirichlet: 1: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsdirichlet: 2: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
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group multiple Dirichlet seriesdirichlet: 3: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesdirichlet: 4: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesdirichlet: 5: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasdirichlet: 6: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72dirichlet: 7: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXdirichlet: 8: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10dirichlet: 9: 30K10 Universal Dirichlet seriesdirichlet: 10: 31C25 Dirichlet spaces
disc: 1: 30Jxx Function theory on the discdisconjugacy: 1: 34C10 Oscillation theory, zeros, disconjugacy and comparison theorydisconnected: 1: 54G05 Extremally disconnected spaces, F -spaces, etc.
discontinuities: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
discontinuities: 2: 74J40 Shocks and related discontinuitiesdiscontinuous: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45discontinuous: 2: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativesdiscontinuous: 3: 34A36 Discontinuous equationsdiscontinuous: 4: 35R05 Partial differential equations with discontinuous coefficients or datadiscontinuous: 5: 57S30 Discontinuous groups of transformations
discrepancy: 1: 11K38 Irregularities of distribution, discrepancy [See also]11Nxxdiscrete: 1: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxxdiscrete: 2: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40discrete: 3: 30G25 Discrete analytic functionsdiscrete: 4: 31C20 Discrete potential theory and numerical methodsdiscrete: 5: 39A12 Discrete version of topics in analysisdiscrete: 6: 44A55 Discrete operational calculusdiscrete: 7: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxdiscrete: 8: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesdiscrete: 9: 49M25 Discrete approximationsdiscrete: 10: 52-XX Convex and discrete geometrydiscrete: 11: 52Cxx Discrete geometrydiscrete: 12: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxdiscrete: 13: 52C26 Circle packings and discrete conformal geometrydiscrete: 14: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80discrete: 15: 60G42 Martingales with discrete parameterdiscrete: 16: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)discrete: 17: 60J27 Continuous-time Markov processes on discrete state spacesdiscrete: 18: 60J28 Applications of continuous-time Markov processes on discrete state spacesdiscrete: 19: 65T50 Discrete and fast Fourier transformsdiscrete: 20: 68Rxx Discrete mathematics in relation to computer sciencediscrete: 21: 83C27 Lattice gravity, Regge calculus and other discrete methodsdiscrete: 22: 90B80 Discrete location and assignment [See also]90C10discrete: 23: 93C65 Discrete event systemsdiscrete: 24: 97N70 Discrete mathematics
discrete-time: 1: 60J05 Discrete-time Markov processes on general state spacesdiscrete-time: 2: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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discrete-time: 3: 60J20 Applications of Markov chains and discrete-time Markov processes on general statespaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40
discrete-time: 4: 91A50 Discrete-time gamesdiscrete-time: 5: 93C55 Discrete-time systemsdiscretization: 1: 70J50 Systems arising from the discretization of structural vibration problems
discretized: 1: 65M22 Solution of discretized equations [See also]65Fxx, 65Hxxdiscretized: 2: 65N22 Solution of discretized equations [See also]65Fxx, 65Hxx
discriminantal: 1: 55R80 Discriminantal varieties, configuration spacesdiscriminants: 1: 11R29 Class numbers, class groups, discriminants
discrimination: 1: 62H30 Classification and discrimination; cluster analysis [See also]68T10, 91C20disintegration: 1: 28A50 Integration and disintegration of measures
disordered: 1: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)disordered: 2: 82C44 Dynamics of disordered systems (random Ising systems, etc.)disordered: 3: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)dispersion: 1: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction[See also]35Q30dispersion: 2: 81U30 Dispersion theory, dispersion relationsdispersion: 3: 81U30 Dispersion theory, dispersion relationsdispersive: 1: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemsdisplacive: 1: 74N10 Displacive transformations
dissections: 1: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)dissipations: 1: 46L57 Derivations, dissipations and positive semigroups in C∗-algebrasdissipative: 1: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxxdissipative: 2: 47B44 Accretive operators, dissipative operators, etc.dissipative: 3: 47H06 Accretive operators, dissipative operators, etc.
distal: 1: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrentfunctions, distal functions, etc.); almost automorphic functions
distality: 1: 37B05 Transformations and group actions with special properties (minimality, distality,proximality, etc.)
distance: 1: 05C12 Distance in graphsdistance: 2: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)distance: 3: 51Kxx Distance geometry
distributed: 1: 68M14 Distributed systemsdistributed: 2: 68Q85 Models and methods for concurrent and distributed computing (process algebras,bisimulation, transition nets, etc.)distributed: 3: 68W15 Distributed algorithms
distribution: 1: 11J71 Distribution modulo one [See also]11K06distribution: 2: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmsdistribution: 3: 11K06 General theory of distribution modulo 1 [See also]11J71distribution: 4: 11K38 Irregularities of distribution, discrepancy [See also]11Nxxdistribution: 5: 11N05 Distribution of primesdistribution: 6: 11N25 Distribution of integers with specified multiplicative constraintsdistribution: 7: 11N60 Distribution functions associated with additive and positive multiplicative functionsdistribution: 8: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsdistribution: 9: 11N69 Distribution of integers in special residue classesdistribution: 10: 11R44 Distribution of prime ideals [See also]11N05distribution: 11: 30D35 Distribution of values, Nevanlinna theorydistribution: 12: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see32A22
distribution: 13: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionsdistribution: 14: 35P20 Asymptotic distribution of eigenvalues and eigenfunctionsdistribution: 15: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
distribution: 16: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
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Mathematics Subject Classification 2010
distribution: 17: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T30distribution: 18: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XXdistribution: 19: 60Exx Distribution theory [See also]62Exx, 62Hxxdistribution: 20: 62Exx Distribution theory [See also]60Exxdistribution: 21: 62E15 Exact distribution theorydistribution: 22: 62E20 Asymptotic distribution theorydistribution: 23: 62G30 Order statistics; empirical distribution functionsdistribution: 24: 62H10 Distribution of statistics
distributions: 1: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T30distributions: 2: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E35distributions: 3: 46F10 Operations with distributionsdistributions: 4: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40distributions: 5: 46F25 Distributions on infinite-dimensional spaces [See also]58C35distributions: 6: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxdistributions: 7: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsdistributions: 8: 58A30 Vector distributions (subbundles of the tangent bundles)distributions: 9: 60E05 Distributions: general theorydistributions: 10: 60E07 Infinitely divisible distributions; stable distributionsdistributions: 11: 60E07 Infinitely divisible distributions; stable distributionsdistributions: 12: 62E17 Approximations to distributions (nonasymptotic)distributions: 13: 62E86 Fuzziness in connection with the topics on distributions in this sectiondistributions: 14: 81S30 Phase-space methods including Wigner distributions, etc.distributions: 15: 97K60 Distributions and stochastic processesdistributive: 1: 06Dxx Distributive latticesdistributive: 2: 06D75 Other generalizations of distributive lattices
distributivity: 1: 06D10 Complete distributivitydistributivity: 2: 08B10 Congruence modularity, congruence distributivity
ditkin: 1: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)divergence: 1: 40Axx Convergence and divergence of infinite limiting processesdivergence: 2: 40A05 Convergence and divergence of series and sequencesdivergence: 3: 40A10 Convergence and divergence of integralsdivergence: 4: 40A15 Convergence and divergence of continued fractions [See also]30B70divergence: 5: 40A20 Convergence and divergence of infinite productsdivergence: 6: 40A30 Convergence and divergence of series and sequences of functionsdivisibility: 1: 13A05 Divisibility; factorizations [See also]13F15divisibility: 2: 16U30 Divisibility, noncommutative UFDs
divisible: 1: 60E07 Infinitely divisible distributions; stable distributionsdivision: 1: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsdivision: 2: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxxdivision: 3: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A30division: 4: 17A35 Division algebrasdivision: 5: 17C60 Division algebrasdivision: 6: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15divisors: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsdivisors: 2: 14C20 Divisors, linear systems, invertible sheavesdivisors: 3: 14H51 Special divisors (gonality, Brill-Noether theory)divisors: 4: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setsdivisors: 5: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusion
dn: 1: 46A63 Topological invariants ((DN), (Ω), etc.)dna: 1: 92D20 Protein sequences, DNA sequencesdo: 1: 65J10 Equations with linear operators (do not use 65Fxx)do: 2: 65J15 Equations with nonlinear operators (do not use 65Hxx)
domain: 1: 30A10 Inequalities in the complex domaindomain: 2: 30D05 Functional equations in the complex domain, iteration and composition of analytic
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functions [See also]34Mxx, 37Fxx, 39-XXdomain: 3: 30Exx Miscellaneous topics of analysis in the complex domaindomain: 4: 30E10 Approximation in the complex domaindomain: 5: 30E15 Asymptotic representations in the complex domaindomain: 6: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G34domain: 7: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20domain: 8: 39A45 Equations in the complex domaindomain: 9: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
domain: 10: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
domain: 11: 65M55 Multigrid methods; domain decompositiondomain: 12: 65M85 Fictitious domain methodsdomain: 13: 65N55 Multigrid methods; domain decompositiondomain: 14: 65N85 Fictitious domain methods
domains: 1: 13Gxx Integral domainsdomains: 2: 13G05 Integral domainsdomains: 3: 16U10 Integral domainsdomains: 4: 30C20 Conformal mappings of special domainsdomains: 5: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)domains: 6: 32D05 Domains of holomorphydomains: 7: 32D26 Riemann domainsdomains: 8: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15domains: 9: 32N15 Automorphic functions in symmetric domainsdomains: 10: 32Txx Pseudoconvex domainsdomains: 11: 32T05 Domains of holomorphydomains: 12: 32T15 Strongly pseudoconvex domainsdomains: 13: 32T20 Worm domainsdomains: 14: 32T25 Finite type domainsdomains: 15: 32V15 CR manifolds as boundaries of domainsdomains: 16: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setsdomains: 17: 39B52 Equations for functions with more general domains and/or rangesdomains: 18: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
dominated: 1: 37D30 Partially hyperbolic systems and dominated splittingsdominating: 1: 05C69 Dominating sets, independent sets, cliquesdonaldson: 1: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)donaldson: 2: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also]58-XX
donaldson-thomas: 1: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,Donaldson-Thomas invariants [See also]53D45
dots: 1: 81Q37 Quantum dots, waveguides, ratchets, etc.dots: 2: 81V65 Quantum dots [See also]82D20
double: 1: 18D05 Double categories, 2-categories, bicategories and generalizationsdouble: 2: 32L25 Twistor theory, double fibrations [See also]53C28
down: 1: 13B21 Integral dependence; going up, going downdraft: 1: 97D80 Teaching units and draft lessons
drawing: 1: 05C62 Graph representations (geometric and intersection representations, etc.) For graphdrawing, see also 68R10
drawing: 2: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C35drinfel′: 1: 11F52 Modular forms associated to Drinfel′d modulesdrinfel′: 2: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05drinfel′: 3: 11J93 Transcendence theory of Drinfel′d and t-modules
dual: 1: 43A40 Character groups and dual objects
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dual: 2: 45F10 Dual, triple, etc., integral and series equationsdual: 3: 47L45 Dual algebras; weakly closed singly generated operator algebrasdual: 4: 47L50 Dual spaces of operator algebras
dualities: 1: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A30dualities: 2: 51A10 Homomorphism, automorphism and dualities
duality: 1: 06D50 Lattices and dualityduality: 2: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualityduality: 3: 22D35 Duality theoremsduality: 4: 32C37 Duality theoremsduality: 5: 46A20 Duality theoryduality: 6: 46B10 Duality and reflexivity [See also]46A25duality: 7: 49M29 Methods involving dualityduality: 8: 49N15 Duality theoryduality: 9: 55M05 Dualityduality: 10: 55P25 Spanier-Whitehead dualityduality: 11: 55P30 Eckmann-Hilton dualityduality: 12: 55U30 Dualityduality: 13: 57P10 Poincare duality spacesduality: 14: 90C46 Optimality conditions, duality [See also]49N15
duals: 1: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
duals: 2: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For functionalgebras, see 46J10
duals: 3: 55P45 H-spaces and dualsdusty-gas: 1: 76T15 Dusty-gas two-phase flows
dyer-lashof: 1: 55S12 Dyer-Lashof operationsdynamic: 1: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05dynamic: 2: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70dynamic: 3: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70dynamic: 4: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05dynamic: 5: 49Lxx Hamilton-Jacobi theories, including dynamic programmingdynamic: 6: 49L20 Dynamic programming methoddynamic: 7: 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)dynamic: 8: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)dynamic: 9: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphsdynamic: 10: 82C21 Dynamic continuum models (systems of particles, etc.)dynamic: 11: 82C23 Exactly solvable dynamic models [See also]37K60dynamic: 12: 82C26 Dynamic and nonequilibrium phase transitions (general)dynamic: 13: 82C27 Dynamic critical phenomenadynamic: 14: 82C28 Dynamic renormalization group methods [See also]81T17dynamic: 15: 90C39 Dynamic programming [See also]49L20dynamic: 16: 91A25 Dynamic gamesdynamic: 17: 91B51 Dynamic stochastic general equilibrium theory
dynamical: 1: 11S82 Non-Archimedean dynamical systems [See mainly]37Pxxdynamical: 2: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,46Lxx, 58Jxx, 70-XXdynamical: 3: 37A60 Dynamical systems in statistical mechanics [See also]82Cxxdynamical: 4: 37B55 Nonautonomous dynamical systemsdynamical: 5: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxxdynamical: 6: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytictechniques in dynamical systemsdynamical: 7: 37C45 Dimension theory of dynamical systems
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dynamical: 8: 37C60 Nonautonomous smooth dynamical systems [See also]37B55dynamical: 9: 37C80 Symmetries, equivariant dynamical systemsdynamical: 10: 37Dxx Dynamical systems with hyperbolic behaviordynamical: 11: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,etc.)dynamical: 12: 37Exx Low-dimensional dynamical systemsdynamical: 13: 37Fxx Complex dynamical systems [See also]30D05, 32H50dynamical: 14: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups asdynamical systemsdynamical: 15: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationsdynamical: 16: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,93Exxdynamical: 17: 37J60 Nonholonomic dynamical systems [See also]70F25dynamical: 18: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxxdynamical: 19: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,60H10, 60H15dynamical: 20: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxdynamical: 21: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,70Kxxdynamical: 22: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-XX, especially 76D05, 76F20, 86A05, 86A10dynamical: 23: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxxdynamical: 24: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,laser physics)dynamical: 25: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXdynamical: 26: 37N30 Dynamical systems in numerical analysisdynamical: 27: 37N35 Dynamical systems in controldynamical: 28: 37N40 Dynamical systems in optimization and economicsdynamical: 29: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A45dynamical: 30: 37P50 Dynamical systems on Berkovich spacesdynamical: 31: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations ontime scales, see 34N05dynamical: 32: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H20dynamical: 33: 65Pxx Numerical problems in dynamical systems [See also]37Mxxdynamical: 34: 70G60 Dynamical systems methodsdynamical: 35: 74Hxx Dynamical problemsdynamical: 36: 74H60 Dynamical bifurcationdynamical: 37: 74Q10 Homogenization and oscillations in dynamical problemsdynamical: 38: 76F20 Dynamical systems approach to turbulence [See also]37-XXdynamical: 39: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,SPDE, dynamical systems)
dynamics: 1: 37Bxx Topological dynamics [See also]54H20dynamics: 2: 37B10 Symbolic dynamics [See also]37Cxx, 37Dxxdynamics: 3: 37B45 Continua theory in dynamicsdynamics: 4: 37B50 Multi-dimensional shifts of finite type, tiling dynamicsdynamics: 5: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxdynamics: 6: 37D45 Strange attractors, chaotic dynamicsdynamics: 7: 37E15 Combinatorial dynamics (types of periodic orbits)dynamics: 8: 37K60 Lattice dynamics [See also]37L60dynamics: 9: 37L60 Lattice dynamics [See also]37K60dynamics: 10: 37P55 Arithmetic dynamics on general algebraic varietiesdynamics: 11: 54H20 Topological dynamics [See also]28Dxx, 37Bxxdynamics: 12: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)dynamics: 13: 70Exx Dynamics of a rigid body and of multibody systemsdynamics: 14: 70E20 Perturbation methods for rigid body dynamics
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dynamics: 15: 70E55 Dynamics of multibody systemsdynamics: 16: 70E60 Robot dynamics and control [See also]68T40, 70Q05, 93C85dynamics: 17: 70Fxx Dynamics of a system of particles, including celestial mechanicsdynamics: 18: 70H40 Relativistic dynamicsdynamics: 19: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxxdynamics: 20: 70Kxx Nonlinear dynamics [See also]34Cxx, 37-XXdynamics: 21: 74N20 Dynamics of phase boundariesdynamics: 22: 76Nxx Compressible fluids and gas dynamics, generaldynamics: 23: 76N15 Gas dynamics, generaldynamics: 24: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31dynamics: 25: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)dynamics: 26: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50dynamics: 27: 82C44 Dynamics of disordered systems (random Ising systems, etc.)dynamics: 28: 85A05 Galactic and stellar dynamicsdynamics: 29: 86A17 Global dynamics, earthquake problemsdynamics: 30: 91B55 Economic dynamicsdynamics: 31: 92Dxx Genetics and population dynamicsdynamics: 32: 92D25 Population dynamics (general)e-learning: 1: 97U50 Computer assisted instruction; e-learning
earthquake: 1: 86A17 Global dynamics, earthquake problemseckmann-hilton: 1: 55P30 Eckmann-Hilton duality
ecology: 1: 92D40 Ecologyeconometrics: 1: 91Bxx Mathematical economics For econometrics, see 62P20econometrics: 2: 91G70 Statistical methods, econometrics
economic: 1: 91B55 Economic dynamicseconomic: 2: 91B82 Statistical methods; economic indices and measureseconomic: 3: 91B84 Economic time series analysis [See also]62M10
economics: 1: 03H10 Other applications of nonstandard models (economics, physics, etc.)economics: 2: 35Q91 PDEs in connection with game theory, economics, social and behavioral scienceseconomics: 3: 37N40 Dynamical systems in optimization and economicseconomics: 4: 46N10 Applications in optimization, convex analysis, mathematical programming, economicseconomics: 5: 47N10 Applications in optimization, convex analysis, mathematical programming, economicseconomics: 6: 58E17 Pareto optimality, etc., applications to economics [See also]90C29economics: 7: 62P20 Applications to economics [See also]91Bxxeconomics: 8: 91-XX Game theory, economics, social and behavioral scienceseconomics: 9: 91Bxx Mathematical economics For econometrics, see 62P20economics: 10: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics ingeneral)economics: 11: 91B15 Welfare economicseconomics: 12: 91B44 Informational economicseconomics: 13: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)economics: 14: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)economics: 15: 97M40 Operations research, economicseconomies: 1: 91B54 Special types of economies
econophysics: 1: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)eddy: 1: 76F65 Direct numerical and large eddy simulation of turbulence
education: 1: 97-XX Mathematics educationeducation: 2: 97Axx General, mathematics and educationeducation: 3: 97A30 History of mathematics and mathematics education [See also]01-XXeducation: 4: 97B20 General educationeducation: 5: 97B30 Vocational educationeducation: 6: 97B40 Higher educationeducation: 7: 97B50 Teacher education For research aspects, see 97C70education: 8: 97B60 Adult and further educationeducation: 9: 97Cxx Psychology of mathematics education, research in mathematics educationeducation: 10: 97Cxx Psychology of mathematics education, research in mathematics educationeducation: 11: 97Dxx Education and instruction in mathematics
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education: 12: 97M20 Mathematics in vocational training and career educationeducation: 13: 97Qxx Computer science education
educational: 1: 97Bxx Educational policy and systemseducational: 2: 97B10 Educational research and planningeducational: 3: 97B70 Syllabuses, educational standardseducational: 4: 97Uxx Educational material and media, educational technologyeducational: 5: 97Uxx Educational material and media, educational technology
effect: 1: 81T55 Casimir effecteffect: 2: 81V70 Many-body theory; quantum Hall effect
effective: 1: 03C57 Effective and recursion-theoretic model theory [See also]03D45effective: 2: 74Qxx Homogenization, determination of effective propertieseffective: 3: 74Q15 Effective constitutive equationseffective: 4: 74Q20 Bounds on effective properties
effectively: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-tic and similar approaches see 03F55effectivity: 1: 14Q20 Effectivity, complexity
effects: 1: 74Fxx Coupling of solid mechanics with other effectseffects: 2: 74F05 Thermal effectseffects: 3: 74F15 Electromagnetic effectseffects: 4: 74F20 Mixture effectseffects: 5: 74F25 Chemical and reactive effectseffects: 6: 76B70 Stratification effects in inviscid fluidseffects: 7: 76D10 Boundary-layer theory, separation and reattachment, higher-order effectseffects: 8: 76D50 Stratification effects in viscous fluidseffects: 9: 76E19 Compressibility effectseffects: 10: 76E30 Nonlinear effectseffects: 11: 76F45 Stratification effectseffects: 12: 76F50 Compressibility effectseffects: 13: 76Vxx Reaction effects in flows [See also]80A32effects: 14: 76V05 Reaction effects in flows [See also]80A32
efficient: 1: 19A15 Efficient generationegyptian: 1: 01A16 Egyptian
eigenfunction: 1: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctionseigenfunction: 2: 35P10 Completeness of eigenfunctions, eigenfunction expansionseigenfunction: 3: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
eigenfunctions: 1: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctionseigenfunctions: 2: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctionseigenfunctions: 3: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionseigenfunctions: 4: 35P10 Completeness of eigenfunctions, eigenfunction expansionseigenfunctions: 5: 35P20 Asymptotic distribution of eigenvalues and eigenfunctions
eigenvalue: 1: 34B09 Boundary eigenvalue problemseigenvalue: 2: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F05eigenvalue: 3: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theoryeigenvalue: 4: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A75eigenvalue: 5: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A75eigenvalue: 6: 47A75 Eigenvalue problems [See also]47J10, 49R05eigenvalue: 7: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,Kolmogorov numbers, entropy numbers, etc. of operatorseigenvalue: 8: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05eigenvalue: 9: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E07eigenvalue: 10: 65F18 Inverse eigenvalue problemseigenvalue: 11: 65L15 Eigenvalue problemseigenvalue: 12: 65N25 Eigenvalue problemseigenvalue: 13: 93B60 Eigenvalue problems
eigenvalues: 1: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)eigenvalues: 2: 15A18 Eigenvalues, singular values, and eigenvectorseigenvalues: 3: 15A42 Inequalities involving eigenvalues and eigenvectors
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eigenvalues: 4: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundseigenvalues: 5: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundseigenvalues: 6: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumeigenvalues: 7: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionseigenvalues: 8: 35P15 Estimation of eigenvalues, upper and lower boundseigenvalues: 9: 35P20 Asymptotic distribution of eigenvalues and eigenfunctionseigenvalues: 10: 49Rxx Variational methods for eigenvalues of operators [See also]47A75eigenvalues: 11: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)eigenvalues: 12: 65F15 Eigenvalues, eigenvectorseigenvalues: 13: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C30
eigenvectors: 1: 15A18 Eigenvalues, singular values, and eigenvectorseigenvectors: 2: 15A42 Inequalities involving eigenvalues and eigenvectorseigenvectors: 3: 65F15 Eigenvalues, eigenvectorseigenvectors: 4: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C30
eilenberg-mac: 1: 55P20 Eilenberg-Mac Lane spaceseilenberg-moore: 1: 55T20 Eilenberg-Moore spectral sequences [See also]57T35eilenberg-moore: 2: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T20
einstein: 1: 35Q76 Einstein equationseinstein: 2: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
einstein’s: 1: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)einstein’s: 2: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theorieseinstein’s: 3: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theorieseinstein-maxwell: 1: 83C22 Einstein-Maxwell equations
eisenstein: 1: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,Dirichlet series, Eisenstein series, etc. Explicit formulas
elastic: 1: 74Bxx Elastic materialselastic: 2: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)elasticity: 1: 74B05 Classical linear elasticityelasticity: 2: 74B10 Linear elasticity with initial stresseselasticity: 3: 74B20 Nonlinear elasticity
elasto-plastic: 1: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plasticmaterials)
electro-: 1: 78A30 Electro- and magnetostaticselectrochemistry: 1: 78A57 Electrochemistryelectrodynamics: 1: 81P20 Stochastic mechanics (including stochastic electrodynamics)electrodynamics: 2: 81V10 Electromagnetic interaction; quantum electrodynamics
electrohydrodynamic: 1: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flowselectrohydrodynamics: 1: 76Wxx Magnetohydrodynamics and electrohydrodynamicselectrohydrodynamics: 2: 76W05 Magnetohydrodynamics and electrohydrodynamics
electromagnetic: 1: 35Q60 PDEs in connection with optics and electromagnetic theoryelectromagnetic: 2: 74F15 Electromagnetic effectselectromagnetic: 3: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10electromagnetic: 4: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10electromagnetic: 5: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80electromagnetic: 6: 78A25 Electromagnetic theory, generalelectromagnetic: 7: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)electromagnetic: 8: 81V10 Electromagnetic interaction; quantum electrodynamicselectromagnetic: 9: 83C50 Electromagnetic fields
electron: 1: 78A15 Electron opticselement: 1: 65M38 Boundary element methodselement: 2: 65N38 Boundary element methodselement: 3: 74S05 Finite element methods
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element: 4: 74S15 Boundary element methodselement: 5: 76M10 Finite element methodselement: 6: 76M15 Boundary element methodselement: 7: 78M10 Finite element methodselement: 8: 78M15 Boundary element methodselement: 9: 80M10 Finite element methodselement: 10: 80M15 Boundary element methods
elementary: 1: 03C48 Abstract elementary classes and related topics [See also]03C45elementary: 2: 11Axx Elementary number theory For analogues in number fields, see 11R04elementary: 3: 11P81 Elementary theory of partitions [See also]05A17elementary: 4: 14A25 Elementary questionselementary: 5: 20A05 Axiomatics and elementary propertieselementary: 6: 26A03 Foundations: limits and generalizations, elementary topology of the lineelementary: 7: 26A09 Elementary functionselementary: 8: 33Bxx Elementary classical functionselementary: 9: 47B47 Commutators, derivations, elementary operators, etc.elementary: 10: 51M04 Elementary problems in Euclidean geometrieselementary: 11: 51M09 Elementary problems in hyperbolic and elliptic geometrieselementary: 12: 81V25 Other elementary particle theoryelementary: 13: 97H20 Elementary algebra
elements: 1: 16Uxx Conditions on elementselements: 2: 16U70 Center, normalizer (invariant elements)elements: 3: 47Cxx Individual linear operators as elements of algebraic systemselements: 4: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodselements: 5: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodselements: 6: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
elimination: 1: 03C10 Quantifier elimination, model completeness and related topicselliptic: 1: 11G05 Elliptic curves over global fields [See also]14H52elliptic: 2: 11G07 Elliptic curves over local fields [See also]14G20, 14H52elliptic: 3: 11G16 Elliptic and modular units [See also]11R27elliptic: 4: 11J89 Transcendence theory of elliptic and abelian functionselliptic: 5: 14H52 Elliptic curves [See also]11G05, 11G07, 14Kxxelliptic: 6: 14J27 Elliptic surfaceselliptic: 7: 33C75 Elliptic integrals as hypergeometric functionselliptic: 8: 33E05 Elliptic functions and integralselliptic: 9: 35Jxx Elliptic equations and systems [See also]58J10, 58J20elliptic: 10: 35J15 Second-order elliptic equationselliptic: 11: 35J20 Variational methods for second-order elliptic equationselliptic: 12: 35J25 Boundary value problems for second-order elliptic equationselliptic: 13: 35J30 Higher-order elliptic equations [See also]31A30, 31B30elliptic: 14: 35J35 Variational methods for higher-order elliptic equationselliptic: 15: 35J40 Boundary value problems for higher-order elliptic equationselliptic: 16: 35J46 First-order elliptic systemselliptic: 17: 35J47 Second-order elliptic systemselliptic: 18: 35J48 Higher-order elliptic systemselliptic: 19: 35J50 Variational methods for elliptic systemselliptic: 20: 35J56 Boundary value problems for first-order elliptic systemselliptic: 21: 35J57 Boundary value problems for second-order elliptic systemselliptic: 22: 35J58 Boundary value problems for higher-order elliptic systemselliptic: 23: 35J60 Nonlinear elliptic equationselliptic: 24: 35J61 Semilinear elliptic equationselliptic: 25: 35J62 Quasilinear elliptic equationselliptic: 26: 35J65 Nonlinear boundary value problems for linear elliptic equationselliptic: 27: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationselliptic: 28: 35J67 Boundary values of solutions to elliptic equationselliptic: 29: 35J70 Degenerate elliptic equationselliptic: 30: 35J75 Singular elliptic equations
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elliptic: 31: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities[See also]35R35, 49J40
elliptic: 32: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities[See also]35R35, 49J40
elliptic: 33: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities[See also]35R35, 49J40
elliptic: 34: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities[See also]35R35, 49J40
elliptic: 35: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J40elliptic: 36: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianelliptic: 37: 35J92 Quasilinear elliptic equations with p-Laplacianelliptic: 38: 35J93 Quasilinear elliptic equations with mean curvature operatorelliptic: 39: 35J96 Elliptic Monge-Ampere equationselliptic: 40: 51M09 Elementary problems in hyperbolic and elliptic geometrieselliptic: 41: 51M10 Hyperbolic and elliptic geometries (general) and generalizationselliptic: 42: 55N34 Elliptic cohomologyelliptic: 43: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXelliptic: 44: 58J10 Differential complexes [See also]35Nxx; elliptic complexeselliptic: 45: 58J26 Elliptic genera
embeddable: 1: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsembedding: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraphembedding, etc.)embedding: 2: 18B15 Embedding theorems, universal categories [See also]18E20embedding: 3: 18E20 Embedding theorems [See also]18B15embedding: 4: 32C09 Embedding of real analytic manifoldsembedding: 5: 32C22 Embedding of analytic spacesembedding: 6: 32Q40 Embedding theoremsembedding: 7: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, tracetheoremsembedding: 8: 54C25 Embedding
embeddings: 1: 14E25 Embeddingsembeddings: 2: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)embeddings: 3: 30L05 Geometric embeddings of metric spacesembeddings: 4: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsembeddings: 5: 32V30 Embeddings of CR manifoldsembeddings: 6: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology andcomputer science [See also]05C12, 68Rxx
embeddings: 7: 57M30 Wild knots and surfaces, etc., wild embeddingsembeddings: 8: 57N35 Embeddings and immersionsembeddings: 9: 57Q35 Embeddings and immersionsembeddings: 10: 57R40 Embeddings
empirical: 1: 62C12 Empirical decision procedures; empirical Bayes proceduresempirical: 2: 62C12 Empirical decision procedures; empirical Bayes proceduresempirical: 3: 62G30 Order statistics; empirical distribution functionsencoding: 1: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxencryption: 1: 68P25 Data encryption [See also]94A60, 81P94
endomorphism: 1: 16S50 Endomorphism rings; matrix rings [See also]15-XXendomorphisms: 1: 08A35 Automorphisms, endomorphismsendomorphisms: 2: 16W20 Automorphisms and endomorphismsendomorphisms: 3: 20K30 Automorphisms, homomorphisms, endomorphisms, etc.
ends: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
ends: 2: 30D40 Cluster sets, prime ends, boundary behaviorenergy: 1: 74G65 Energy minimizationenergy: 2: 83C40 Gravitational energy and conservation laws; groups of motions
engel: 1: 20F45 Engel conditions
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engineering: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)engineering: 2: 62P30 Applications in engineering and industryengineering: 3: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,requirements, etc.)
engineering: 4: 97M50 Physics, astronomy, technology, engineeringengulfing: 1: 57N30 Engulfingengulfing: 2: 57Q30 Engulfingenriched: 1: 18D20 Enriched categories (over closed or monoidal categories)enriques: 1: 14J28 K3 surfaces and Enriques surfaces
entailment: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
entanglement: 1: 81P40 Quantum coherence, entanglement, quantum correlationsentire: 1: 30Dxx Entire and meromorphic functions, and related topicsentire: 2: 30D10 Representations of entire functions by series and integralsentire: 3: 30D15 Special classes of entire functions and growth estimatesentire: 4: 30D20 Entire functions, general theoryentire: 5: 32A15 Entire functionsentire: 6: 34M05 Entire and meromorphic solutionsentire: 7: 35B08 Entire solutionsentire: 8: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04entries: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
entropy: 1: 28D20 Entropy and other invariantsentropy: 2: 37A35 Entropy and other invariants, isomorphism, classificationentropy: 3: 37B40 Topological entropyentropy: 4: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)entropy: 5: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropyentropy: 6: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsentropy: 7: 54C70 Entropyentropy: 8: 94A17 Measures of information, entropy
enumerable: 1: 03D25 Recursively (computably) enumerable sets and degreesenumeration: 1: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30enumeration: 2: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxxenumeration: 3: 05A16 Asymptotic enumerationenumeration: 4: 05C30 Enumeration in graph theoryenumerative: 1: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30enumerative: 2: 14Nxx Projective and enumerative geometry [See also]51-XXenumerative: 3: 14N10 Enumerative problems (combinatorial problems)
envelopes: 1: 32D10 Envelopes of holomorphyenveloping: 1: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B35enveloping: 2: 17B35 Universal enveloping (super)algebras [See also]16S30enveloping: 3: 17B37 Quantum groups (quantized enveloping algebras) and related deformations[See also]16T20, 20G42, 81R50, 82B23
environmental: 1: 62P12 Applications to environmental and related topicsenvironmental: 2: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)environments: 1: 60K37 Processes in random environments
enzyme: 1: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)[See also]80A30
epidemiology: 1: 92C60 Medical epidemiologyepidemiology: 2: 92D30 Epidemiology
epimorphisms: 1: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsepstein: 1: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)equalizers: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)
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equation: 1: 11D41 Higher degree equations; Fermat’s equationequation: 2: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationequation: 3: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxequation: 4: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxequation: 5: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxequation: 6: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxequation: 7: 35K05 Heat equationequation: 8: 35L05 Wave equationequation: 9: 58J35 Heat and other parabolic equation methodsequation: 10: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05equation: 11: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05
equational: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C05equational: 2: 08A45 Equational compactnessequational: 3: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionsequational: 4: 18C05 Equational categories [See also]03C05, 08C05equations: 1: 11Dxx Diophantine equations [See also]11Gxx, 14Gxxequations: 2: 11D04 Linear equationsequations: 3: 11D09 Quadratic and bilinear equationsequations: 4: 11D25 Cubic and quartic equationsequations: 5: 11D41 Higher degree equations; Fermat’s equationequations: 6: 11D45 Counting solutions of Diophantine equationsequations: 7: 11D57 Multiplicative and norm form equationsequations: 8: 11D59 Thue-Mahler equationsequations: 9: 11D61 Exponential equationsequations: 10: 11D72 Equations in many variables [See also]11P55equations: 11: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsequations: 12: 11Y50 Computer solution of Diophantine equationsequations: 13: 12E12 Equationsequations: 14: 12H20 Abstract differential equations [See also]34Mxxequations: 15: 12H25 p-adic differential equations [See also]11S80, 14G20equations: 16: 15A06 Linear equationsequations: 17: 15A24 Matrix equations and identitiesequations: 18: 16T25 Yang-Baxter equationsequations: 19: 20F70 Algebraic geometry over groups; equations over groupsequations: 20: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05equations: 21: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXequations: 22: 31A10 Integral representations, integral operators, integral equations methodsequations: 23: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationequations: 24: 31A35 Connections with differential equationsequations: 25: 31B10 Integral representations, integral operators, integral equations methodsequations: 26: 31B30 Biharmonic and polyharmonic equations and functionsequations: 27: 31B35 Connections with differential equationsequations: 28: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxequations: 29: 32S40 Monodromy; relations with differential equations and D-modulesequations: 30: 32W50 Other partial differential equations of complex analysisequations: 31: 33E30 Other functions coming from differential, difference and integral equationsequations: 32: 34-XX Ordinary differential equationsequations: 33: 34A07 Fuzzy differential equationsequations: 34: 34A08 Fractional differential equationsequations: 35: 34A09 Implicit equations, differential-algebraic equations [See also]65L80
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equations: 36: 34A09 Implicit equations, differential-algebraic equations [See also]65L80equations: 37: 34A26 Geometric methods in differential equationsequations: 38: 34A30 Linear equations and systems, generalequations: 39: 34A33 Lattice differential equationsequations: 40: 34A34 Nonlinear equations and systems, generalequations: 41: 34A35 Differential equations of infinite orderequations: 42: 34A36 Discontinuous equationsequations: 43: 34A37 Differential equations with impulsesequations: 44: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)equations: 45: 34C20 Transformation and reduction of equations and systems, normal formsequations: 46: 34C40 Equations and systems on manifoldsequations: 47: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E03equations: 48: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E03equations: 49: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D25equations: 50: 34G10 Linear equations [See also]47D06, 47D09equations: 51: 34G20 Nonlinear equations [See also]47Hxx, 47Jxxequations: 52: 34Kxx Functional-differential and differential-difference equations [See also]37-XXequations: 53: 34K06 Linear functional-differential equationsequations: 54: 34K17 Transformation and reduction of equations and systems, normal formsequations: 55: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxxequations: 56: 34K31 Lattice functional-differential equationsequations: 57: 34K32 Implicit equationsequations: 58: 34K36 Fuzzy functional-differential equationsequations: 59: 34K37 Functional-differential equations with fractional derivativesequations: 60: 34K40 Neutral equationsequations: 61: 34K45 Equations with impulsesequations: 62: 34K50 Stochastic functional-differential equations [See also]60Hxxequations: 63: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G34equations: 64: 34M03 Linear equations and systemsequations: 65: 34M45 Differential equations on complex manifoldsequations: 66: 34M55 Painleve and other special equations; classification, hierarchies;equations: 67: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70equations: 68: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70equations: 69: 35-XX Partial differential equationsequations: 70: 35A24 Methods of ordinary differential equationsequations: 71: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50equations: 72: 35Exx Equations and systems with constant coefficients [See also]35N05equations: 73: 35Fxx General first-order equations and systemsequations: 74: 35F05 Linear first-order equationsequations: 75: 35F10 Initial value problems for linear first-order equationsequations: 76: 35F15 Boundary value problems for linear first-order equationsequations: 77: 35F16 Initial-boundary value problems for linear first-order equationsequations: 78: 35F20 Nonlinear first-order equationsequations: 79: 35F21 Hamilton-Jacobi equationsequations: 80: 35F25 Initial value problems for nonlinear first-order equationsequations: 81: 35F30 Boundary value problems for nonlinear first-order equationsequations: 82: 35F31 Initial-boundary value problems for nonlinear first-order equationsequations: 83: 35Gxx General higher-order equations and systemsequations: 84: 35G05 Linear higher-order equationsequations: 85: 35G10 Initial value problems for linear higher-order equationsequations: 86: 35G15 Boundary value problems for linear higher-order equationsequations: 87: 35G16 Initial-boundary value problems for linear higher-order equationsequations: 88: 35G20 Nonlinear higher-order equationsequations: 89: 35G25 Initial value problems for nonlinear higher-order equations
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equations: 90: 35G30 Boundary value problems for nonlinear higher-order equationsequations: 91: 35G31 Initial-boundary value problems for nonlinear higher-order equationsequations: 92: 35Hxx Close-to-elliptic equations and systemsequations: 93: 35H10 Hypoelliptic equationsequations: 94: 35H20 Subelliptic equationsequations: 95: 35H30 Quasi-elliptic equationsequations: 96: 35Jxx Elliptic equations and systems [See also]58J10, 58J20equations: 97: 35J15 Second-order elliptic equationsequations: 98: 35J20 Variational methods for second-order elliptic equationsequations: 99: 35J25 Boundary value problems for second-order elliptic equationsequations: 100: 35J30 Higher-order elliptic equations [See also]31A30, 31B30equations: 101: 35J35 Variational methods for higher-order elliptic equationsequations: 102: 35J40 Boundary value problems for higher-order elliptic equationsequations: 103: 35J60 Nonlinear elliptic equationsequations: 104: 35J61 Semilinear elliptic equationsequations: 105: 35J62 Quasilinear elliptic equationsequations: 106: 35J65 Nonlinear boundary value problems for linear elliptic equationsequations: 107: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsequations: 108: 35J67 Boundary values of solutions to elliptic equationsequations: 109: 35J70 Degenerate elliptic equationsequations: 110: 35J75 Singular elliptic equationsequations: 111: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianequations: 112: 35J92 Quasilinear elliptic equations with p-Laplacianequations: 113: 35J93 Quasilinear elliptic equations with mean curvature operatorequations: 114: 35J96 Elliptic Monge-Ampere equationsequations: 115: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J35equations: 116: 35K10 Second-order parabolic equationsequations: 117: 35K15 Initial value problems for second-order parabolic equationsequations: 118: 35K20 Initial-boundary value problems for second-order parabolic equationsequations: 119: 35K25 Higher-order parabolic equationsequations: 120: 35K30 Initial value problems for higher-order parabolic equationsequations: 121: 35K35 Initial-boundary value problems for higher-order parabolic equationsequations: 122: 35K55 Nonlinear parabolic equationsequations: 123: 35K57 Reaction-diffusion equationsequations: 124: 35K58 Semilinear parabolic equationsequations: 125: 35K59 Quasilinear parabolic equationsequations: 126: 35K60 Nonlinear initial value problems for linear parabolic equationsequations: 127: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsequations: 128: 35K65 Degenerate parabolic equationsequations: 129: 35K67 Singular parabolic equationsequations: 130: 35K70 Ultraparabolic equations, pseudoparabolic equations, etc.equations: 131: 35K70 Ultraparabolic equations, pseudoparabolic equations, etc.equations: 132: 35K90 Abstract parabolic equationsequations: 133: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacianequations: 134: 35K92 Quasilinear parabolic equations with p-Laplacianequations: 135: 35K93 Quasilinear parabolic equations with mean curvature operatorequations: 136: 35K96 Parabolic Monge-Ampere equationsequations: 137: 35Lxx Hyperbolic equations and systems [See also]58J45equations: 138: 35L02 First-order hyperbolic equationsequations: 139: 35L03 Initial value problems for first-order hyperbolic equationsequations: 140: 35L04 Initial-boundary value problems for first-order hyperbolic equationsequations: 141: 35L10 Second-order hyperbolic equationsequations: 142: 35L15 Initial value problems for second-order hyperbolic equationsequations: 143: 35L20 Initial-boundary value problems for second-order hyperbolic equationsequations: 144: 35L25 Higher-order hyperbolic equationsequations: 145: 35L30 Initial value problems for higher-order hyperbolic equationsequations: 146: 35L35 Initial-boundary value problems for higher-order hyperbolic equations
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equations: 147: 35L60 Nonlinear first-order hyperbolic equationsequations: 148: 35L70 Nonlinear second-order hyperbolic equationsequations: 149: 35L71 Semilinear second-order hyperbolic equationsequations: 150: 35L72 Quasilinear second-order hyperbolic equationsequations: 151: 35L75 Nonlinear higher-order hyperbolic equationsequations: 152: 35L76 Semilinear higher-order hyperbolic equationsequations: 153: 35L77 Quasilinear higher-order hyperbolic equationsequations: 154: 35L80 Degenerate hyperbolic equationsequations: 155: 35L81 Singular hyperbolic equationsequations: 156: 35L82 Pseudohyperbolic equationsequations: 157: 35L90 Abstract hyperbolic equationsequations: 158: 35Mxx Equations and systems of special type (mixed, composite, etc.)equations: 159: 35M10 Equations of mixed typeequations: 160: 35M11 Initial value problems for equations of mixed typeequations: 161: 35M12 Boundary value problems for equations of mixed typeequations: 162: 35M13 Initial-boundary value problems for equations of mixed typeequations: 163: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L05equations: 164: 35Q05 Euler-Poisson-Darboux equationsequations: 165: 35Q20 Boltzmann equationsequations: 166: 35Q30 Navier-Stokes equations [See also]76D05, 76D07, 76N10equations: 167: 35Q31 Euler equations [See also]76D05, 76D07, 76N10equations: 168: 35Q41 Time-dependent Schrodinger equations, Dirac equationsequations: 169: 35Q41 Time-dependent Schrodinger equations, Dirac equationsequations: 170: 35Q51 Soliton-like equations [See also]37K40equations: 171: 35Q53 KdV-like equations (Korteweg-de Vries) [See also]37K10equations: 172: 35Q55 NLS-like equations (nonlinear Schrodinger) [See also]37K10equations: 173: 35Q56 Ginzburg-Landau equationsequations: 174: 35Q61 Maxwell equationsequations: 175: 35Q76 Einstein equationsequations: 176: 35Q83 Vlasov-like equationsequations: 177: 35Q84 Fokker-Planck equationsequations: 178: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15equations: 179: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxxequations: 180: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)equations: 181: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.equations: 182: 35R05 Partial differential equations with discontinuous coefficients or dataequations: 183: 35R06 Partial differential equations with measureequations: 184: 35R09 Integro-partial differential equations [See also]45Kxxequations: 185: 35R10 Partial functional-differential equationsequations: 186: 35R11 Fractional partial differential equationsequations: 187: 35R12 Impulsive partial differential equationsequations: 188: 35R13 Fuzzy partial differential equationsequations: 189: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25equations: 190: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxequations: 191: 35R50 Partial differential equations of infinite orderequations: 192: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15equations: 193: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15equations: 194: 35R70 Partial differential equations with multivalued right-hand sidesequations: 195: 37C10 Vector fields, flows, ordinary differential equationsequations: 196: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H15
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equations: 197: 37L05 General theory, nonlinear semigroups, evolution equationsequations: 198: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemsequations: 199: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H15equations: 200: 39-XX Difference and functional equationsequations: 201: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05equations: 202: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05equations: 203: 39A06 Linear equationsequations: 204: 39A10 Difference equations, additiveequations: 205: 39A13 Difference equations, scaling (q-differences) [See also]33Dxxequations: 206: 39A14 Partial difference equationsequations: 207: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typeequations: 208: 39A45 Equations in the complex domainequations: 209: 39A50 Stochastic difference equationsequations: 210: 39Bxx Functional equations and inequalities [See also]30D05equations: 211: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XXequations: 212: 39B22 Equations for real functions [See also]26A51, 26B25equations: 213: 39B32 Equations for complex functions [See also]30D05equations: 214: 39B42 Matrix and operator equations [See also]47Jxxequations: 215: 39B52 Equations for functions with more general domains and/or rangesequations: 216: 39B55 Orthogonal additivity and other conditional equationsequations: 217: 39B72 Systems of functional equations and inequalitiesequations: 218: 45-XX Integral equationsequations: 219: 45Axx Linear integral equationsequations: 220: 45A05 Linear integral equationsequations: 221: 45Bxx Fredholm integral equationsequations: 222: 45B05 Fredholm integral equationsequations: 223: 45Dxx Volterra integral equations [See also]34A12equations: 224: 45D05 Volterra integral equations [See also]34A12equations: 225: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A35equations: 226: 45E05 Integral equations with kernels of Cauchy type [See also]35J15equations: 227: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35equations: 228: 45Fxx Systems of linear integral equationsequations: 229: 45F05 Systems of nonsingular linear integral equationsequations: 230: 45F10 Dual, triple, etc., integral and series equationsequations: 231: 45F15 Systems of singular linear integral equationsequations: 232: 45Gxx Nonlinear integral equations [See also]47H30, 47Jxxequations: 233: 45G05 Singular nonlinear integral equationsequations: 234: 45G10 Other nonlinear integral equationsequations: 235: 45G15 Systems of nonlinear integral equationsequations: 236: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G20equations: 237: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G20equations: 238: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20equations: 239: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20equations: 240: 45Nxx Abstract integral equations, integral equations in abstract spacesequations: 241: 45Nxx Abstract integral equations, integral equations in abstract spacesequations: 242: 45N05 Abstract integral equations, integral equations in abstract spacesequations: 243: 45N05 Abstract integral equations, integral equations in abstract spacesequations: 244: 45Rxx Random integral equations [See also]60H20equations: 245: 45R05 Random integral equations [See also]60H20equations: 246: 46N20 Applications to differential and integral equationsequations: 247: 47A50 Equations and inequalities involving linear operators, with vector unknownsequations: 248: 47A62 Equations involving linear operators, with operator unknownsequations: 249: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K30
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equations: 250: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For globaland geometric aspects, see 58-XXequations: 251: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J25equations: 252: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D25equations: 253: 47J40 Equations with hysteresis operators [See also]34C55, 74N30equations: 254: 47N20 Applications to differential and integral equationsequations: 255: 49J15 Optimal control problems involving ordinary differential equationsequations: 256: 49J20 Optimal control problems involving partial differential equationsequations: 257: 49J21 Optimal control problems involving relations other than differential equationsequations: 258: 49K15 Problems involving ordinary differential equationsequations: 259: 49K20 Problems involving partial differential equationsequations: 260: 49K21 Problems involving relations other than differential equationsequations: 261: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)equations: 262: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxequations: 263: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxequations: 264: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxxequations: 265: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXequations: 266: 58J45 Hyperbolic equations [See also]35Lxxequations: 267: 60H10 Stochastic ordinary differential equations [See also]34F05equations: 268: 60H15 Stochastic partial differential equations [See also]35R60equations: 269: 60H20 Stochastic integral equationsequations: 270: 60H25 Random operators and equations [See also]47B80equations: 271: 60H35 Computational methods for stochastic equations [See also]65C30equations: 272: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35equations: 273: 65C30 Stochastic differential and integral equationsequations: 274: 65Hxx Nonlinear algebraic or transcendental equationsequations: 275: 65H04 Roots of polynomial equationsequations: 276: 65H05 Single equationsequations: 277: 65H10 Systems of equationsequations: 278: 65J08 Abstract evolution equationsequations: 279: 65J10 Equations with linear operators (do not use 65Fxx)equations: 280: 65J15 Equations with nonlinear operators (do not use 65Hxx)equations: 281: 65Lxx Ordinary differential equationsequations: 282: 65L03 Functional-differential equationsequations: 283: 65L04 Stiff equationsequations: 284: 65L80 Methods for differential-algebraic equationsequations: 285: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsequations: 286: 65M22 Solution of discretized equations [See also]65Fxx, 65Hxxequations: 287: 65Nxx Partial differential equations, boundary value problemsequations: 288: 65N22 Solution of discretized equations [See also]65Fxx, 65Hxxequations: 289: 65Qxx Difference and functional equations, recurrence relationsequations: 290: 65Q10 Difference equationsequations: 291: 65Q20 Functional equationsequations: 292: 65Rxx Integral equations, integral transformsequations: 293: 65R20 Integral equationsequations: 294: 70H03 Lagrange’s equationsequations: 295: 70H05 Hamilton’s equationsequations: 296: 70H20 Hamilton-Jacobi equationsequations: 297: 74B15 Equations linearized about a deformed state (small deformations superposed on large)equations: 298: 74D05 Linear constitutive equationsequations: 299: 74D10 Nonlinear constitutive equations
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equations: 300: 74Q15 Effective constitutive equationsequations: 301: 76Axx Foundations, constitutive equations, rheologyequations: 302: 76D05 Navier-Stokes equations [See also]35Q30equations: 303: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M35equations: 304: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsequations: 305: 81Q15 Perturbation theories for operators and differential equationsequations: 306: 81Q40 Bethe-Salpeter and other integral equationsequations: 307: 81R20 Covariant wave equationsequations: 308: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31equations: 309: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)equations: 310: 83C10 Equations of motionequations: 311: 83C22 Einstein-Maxwell equationsequations: 312: 93C15 Systems governed by ordinary differential equations [See also]34H05equations: 313: 93C20 Systems governed by partial differential equationsequations: 314: 93C23 Systems governed by functional-differential equations [See also]34K35equations: 315: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)equations: 316: 97H30 Equations and inequalitiesequations: 317: 97I70 Functional equationsequilibria: 1: 70K42 Equilibria and periodic trajectoriesequilibria: 2: 91B52 Special types of equilibria
equilibrium: 1: 37D35 Thermodynamic formalism, variational principles, equilibrium statesequilibrium: 2: 74Gxx Equilibrium (steady-state) problemsequilibrium: 3: 74Q05 Homogenization in equilibrium problemsequilibrium: 4: 82Bxx Equilibrium statistical mechanicsequilibrium: 5: 82B05 Classical equilibrium statistical mechanics (general)equilibrium: 6: 82B10 Quantum equilibrium statistical mechanics (general)equilibrium: 7: 90C33 Complementarity and equilibrium problems and variational inequalities (finitedimensions)
equilibrium: 8: 91B50 General equilibrium theoryequilibrium: 9: 91B51 Dynamic stochastic general equilibrium theory
equisingularity: 1: 32S15 Equisingularity (topological and analytic) [See also]14E15equivalence: 1: 03D50 Recursive equivalence types of sets and structures, isolsequivalence: 2: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoreticcontext; Morita equivalence and duality
equivalence: 3: 34C41 Equivalence, asymptotic equivalenceequivalence: 4: 34C41 Equivalence, asymptotic equivalenceequivalence: 5: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationsequivalence: 6: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationsequivalence: 7: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationequivalence: 8: 40D25 Inclusion and equivalence theorems
equivalences: 1: 55P10 Homotopy equivalencesequivariance: 1: 58K70 Symmetries, equivarianceequivariant: 1: 14C15 (Equivariant) Chow groups and rings; motivesequivariant: 2: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne(co)homologies)equivariant: 3: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S91equivariant: 4: 37C80 Symmetries, equivariant dynamical systemsequivariant: 5: 37G40 Symmetries, equivariant bifurcation theoryequivariant: 6: 55N25 Homology with local coefficients, equivariant cohomologyequivariant: 7: 55N91 Equivariant homology and cohomology [See also]19L47equivariant: 8: 55P91 Equivariant homotopy theory [See also]19L47equivariant: 9: 55P92 Relations between equivariant and nonequivariant homotopy theoryequivariant: 10: 55Q91 Equivariant homotopy groups [See also]19L47equivariant: 11: 55R91 Equivariant fiber spaces and bundles [See also]19L47equivariant: 12: 55S91 Equivariant operations and obstructions [See also]19L47
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equivariant: 13: 57Q91 Equivariant PL-topologyequivariant: 14: 57R85 Equivariant cobordismequivariant: 15: 57R91 Equivariant algebraic topology of manifolds
erdos: 1: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxergodic: 1: 22D40 Ergodic theory on groups [See also]28Dxxergodic: 2: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G10ergodic: 3: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XXergodic: 4: 37Axx Ergodic theory [See also]28Dxxergodic: 5: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationsergodic: 6: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35ergodic: 7: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35ergodic: 8: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxxergodic: 9: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxergodic: 10: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxxergodic: 11: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)ergodic: 12: 47A35 Ergodic theory [See also]28Dxx, 37Axxergodic: 13: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A35ergodic: 14: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicityergodic: 15: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxx
ergodicity: 1: 37A25 Ergodicity, mixing, rates of mixingergodicity: 2: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
error: 1: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnelintegrals)
error: 2: 65Gxx Error analysis and interval analysiserror: 3: 65G50 Roundoff errorerror: 4: 65L70 Error boundserror: 5: 65M15 Error boundserror: 6: 65N15 Error boundserror: 7: 94B70 Error probability
error-correcting: 1: 94Bxx Theory of error-correcting codes and error-detecting codeserror-correcting: 2: 94B50 Synchronization error-correcting codeserror-detecting: 1: 94Bxx Theory of error-correcting codes and error-detecting codes
errors: 1: 97D70 Learning difficulties and student errorserrors: 2: 97N20 Rounding, estimation, theory of errors
esp: 1: 58D17 Manifolds of metrics (esp. Riemannian)especially: 1: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]especially: 2: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25especially: 3: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40especially: 4: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A10especially: 5: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxestimates: 1: 11L07 Estimates on exponential sumsestimates: 2: 11L40 Estimates on character sumsestimates: 3: 30D15 Special classes of entire functions and growth estimatesestimates: 4: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30estimates: 5: 35B45 A priori estimatesestimates: 6: 40E10 Growth estimates
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estimation: 1: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundsestimation: 2: 35P15 Estimation of eigenvalues, upper and lower boundsestimation: 3: 62F10 Point estimationestimation: 4: 62G05 Estimationestimation: 5: 62G07 Density estimationestimation: 6: 62H12 Estimationestimation: 7: 62L12 Sequential estimationestimation: 8: 62M05 Markov processes: estimationestimation: 9: 62M09 Non-Markovian processes: estimationestimation: 10: 62N02 Estimationestimation: 11: 81P50 Quantum state estimation, approximate cloningestimation: 12: 93E10 Estimation and detection [See also]60G35estimation: 13: 97N20 Rounding, estimation, theory of errorsestimators: 1: 62F12 Asymptotic properties of estimatorsestimators: 2: 62J07 Ridge regression; shrinkage estimators
et: 1: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)eta: 1: 11F20 Dedekind eta function, Dedekind sums
eta-invariants: 1: 58J28 Eta-invariants, Chern-Simons invariantsethnomathematics: 1: 01A07 Ethnomathematics, general
euclidean: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorseuclidean: 2: 13F07 Euclidean rings and generalizationseuclidean: 3: 32Q35 Complex manifolds as subdomains of Euclidean spaceeuclidean: 4: 42-XX Harmonic analysis on Euclidean spaceseuclidean: 5: 51M04 Elementary problems in Euclidean geometrieseuclidean: 6: 51M05 Euclidean geometries (general) and generalizationseuclidean: 7: 51N20 Euclidean analytic geometryeuclidean: 8: 53A04 Curves in Euclidean spaceeuclidean: 9: 53A05 Surfaces in Euclidean spaceeuclidean: 10: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-spaceeuclidean: 11: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxx
euler: 1: 11B68 Bernoulli and Euler numbers and polynomialseuler: 2: 35Q31 Euler equations [See also]76D05, 76D07, 76N10euler: 3: 40G05 Cesaro, Euler, Norlund and Hausdorff methods
euler-maclaurin: 1: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurinsummation formula, see 65B15
euler-maclaurin: 2: 65B15 Euler-Maclaurin formulaeuler-poisson-darboux: 1: 35Q05 Euler-Poisson-Darboux equations
eulerian: 1: 05C45 Eulerian and Hamiltonian graphseuropean: 1: 01A15 Indigenous European cultures (pre-Greek, etc.)
evaluation: 1: 11Y60 Evaluation of constantsevaluation: 2: 33F05 Numerical approximation and evaluation [See also]65D20evaluation: 3: 68M20 Performance evaluation; queueing; scheduling [See also]60K25, 90Bxx
evasion: 1: 49N75 Pursuit and evasion gamesevasion: 2: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N75
event: 1: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spaceevent: 2: 93C65 Discrete event systems
evolution: 1: 34G25 Evolution inclusionsevolution: 2: 37L05 General theory, nonlinear semigroups, evolution equationsevolution: 3: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K30evolution: 4: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D25evolution: 5: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)evolution: 6: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxevolution: 7: 60J67 Stochastic (Schramm-)Loewner evolution (SLE)evolution: 8: 65J08 Abstract evolution equationsevolution: 9: 91D10 Models of societies, social and urban evolution
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evolution: 10: 92D15 Problems related to evolutionevolutionary: 1: 91A22 Evolutionary games
exact: 1: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxxexact: 2: 18E10 Exact categories, abelian categoriesexact: 3: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)exact: 4: 62E15 Exact distribution theoryexact: 5: 83C15 Exact solutions
exactly: 1: 81U15 Exactly and quasi-solvable systemsexactly: 2: 82B23 Exactly solvable models; Bethe ansatzexactly: 3: 82C23 Exactly solvable dynamic models [See also]37K60
examinations: 1: 97U40 Problem books. Competitions. Examinationsexcellent: 1: 13F40 Excellent rings
except: 1: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXexcept: 2: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)except: 3: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionexceptional: 1: 17B25 Exceptional (super)algebrasexceptional: 2: 17C40 Exceptional Jordan structuresexceptional: 3: 20G41 Exceptional groups
exchange: 1: 51D10 Abstract geometries with exchange axiomexchangeability: 1: 60G09 Exchangeability
excision: 1: 19C40 Excision for K2
exhaustion: 1: 32T35 Exhaustion functionsexhaustion: 2: 32U10 Plurisubharmonic exhaustion functions
existence: 1: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuationof solutions
existence: 2: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)
existence: 3: 35A01 Existence problems: global existence, local existence, non-existenceexistence: 4: 35A01 Existence problems: global existence, local existence, non-existenceexistence: 5: 35A01 Existence problems: global existence, local existence, non-existenceexistence: 6: 49Jxx Existence theoriesexistence: 7: 74G20 Local existence of solutions (near a given solution)existence: 8: 74G25 Global existence of solutionsexistence: 9: 74H20 Existence of solutionsexistence: 10: 76B03 Existence, uniqueness, and regularity theory [See also]35Q35existence: 11: 76D03 Existence, uniqueness, and regularity theory [See also]35Q30existence: 12: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q30
exotic: 1: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)exotic: 2: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M20
expanding: 1: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)expanding: 2: 37F15 Expanding maps; hyperbolicity; structural stabilityexpansions: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63expansions: 2: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension[See also]11N99, 28Dxxexpansions: 3: 30Bxx Series expansionsexpansions: 4: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXexpansions: 5: 34E05 Asymptotic expansionsexpansions: 6: 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctionsexpansions: 7: 35C20 Asymptotic expansionsexpansions: 8: 35P10 Completeness of eigenfunctions, eigenfunction expansionsexpansions: 9: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxxexpansions: 10: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical
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approximation, see 65Dxxexpansions: 11: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)expansions: 12: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)[See also]30E15expansions: 13: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localizationexpansions: 14: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localizationexpansions: 15: 42C15 General harmonic expansions, framesexpansions: 16: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
experimental: 1: 83Bxx Observational and experimental questionsexperimental: 2: 83B05 Observational and experimental questionsexperimental: 3: 91A90 Experimental studiesexperiments: 1: 62B15 Theory of statistical experimentsexperiments: 2: 62Kxx Design of experiments [See also]05Bxxexperiments: 3: 62K86 Fuzziness and design of experiments
expert: 1: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)explicit: 1: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasexplicit: 2: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10explicit: 3: 34A05 Explicit solutions and reductionsexplicit: 4: 74G05 Explicit solutionsexplicit: 5: 74H05 Explicit solutions
exponential: 1: 11D61 Exponential equationsexponential: 2: 11Lxx Exponential sums and character sums For finite fields, see 11Txxexponential: 3: 11L03 Trigonometric and exponential sums, generalexponential: 4: 11L07 Estimates on exponential sumsexponential: 5: 11T23 Exponential sumsexponential: 6: 15A16 Matrix exponential and similar functions of matricesexponential: 7: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXexponential: 8: 33B10 Exponential and trigonometric functionsexponential: 9: 65F60 Matrix exponential and similar matrix functions
exponents: 1: 34D08 Characteristic and Lyapunov exponentsexponents: 2: 35B33 Critical exponentsexponents: 3: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)exponents: 4: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,37Dxxexponents: 5: 37L30 Attractors and their dimensions, Lyapunov exponentsexponents: 6: 37M25 Computational methods for ergodic theory (approximation of invariant measures,computation of Lyapunov exponents, entropy)expressible: 1: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of specialfunctions in one variableexpressible: 2: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
expressions: 1: 41A45 Approximation by arbitrary linear expressionsexpressions: 2: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
ext: 1: 13D07 Homological functors on modules (Tor, Ext, etc.)ext: 2: 16E30 Homological functors on modules (Tor, Ext, etc.)ext: 3: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U25ext: 4: 19K33 EXT and K-homology [See also]55N22ext: 5: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20
extended: 1: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrasextended: 2: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30extension: 1: 11S15 Ramification and extension theoryextension: 2: 13B02 Extension theoryextension: 3: 32V25 Extension of functions and other analytic objects from CR manifoldsextension: 4: 39B82 Stability, separation, extension, and related topics [See also]46A22
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extension: 5: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators[See also]46M10extension: 6: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60extension: 7: 54C20 Extension of mapsextension: 8: 55P05 Homotopy extension properties, cofibrationsextension: 9: 55S36 Extension and compression of mappings
extensions: 1: 11R11 Quadratic extensionsextensions: 2: 11R16 Cubic and quartic extensionsextensions: 3: 11R18 Cyclotomic extensionsextensions: 4: 11R20 Other abelian and metabelian extensionsextensions: 5: 12Fxx Field extensionsextensions: 6: 12F05 Algebraic extensionsextensions: 7: 12F10 Separable extensions, Galois theoryextensions: 8: 12F15 Inseparable extensionsextensions: 9: 12F20 Transcendental extensionsextensions: 10: 13Bxx Ring extensions and related topicsextensions: 11: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,14B25extensions: 12: 16S20 Centralizing and normalizing extensionsextensions: 13: 16S70 Extensions of rings by idealsextensions: 14: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)extensions: 15: 19C09 Central extensions and Schur multipliersextensions: 16: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumannextensions, and generalizationsextensions: 17: 20E22 Extensions, wreath products, and other compositions [See also]20J05extensions: 18: 20K35 Extensionsextensions: 19: 47A20 Dilations, extensions, compressionsextensions: 20: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)extensive: 1: 91A18 Games in extensive formextensor: 1: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15extensor: 2: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15exterior: 1: 15A75 Exterior algebra, Grassmann algebrasexterior: 2: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66exterior: 3: 58A15 Exterior differential systems (Cartan theory)external: 1: 00A17 External book reviews
extra: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B48extraordinary: 1: 55N20 Generalized (extraordinary) homology and cohomology theoriesextrapolation: 1: 65B05 Extrapolation to the limit, deferred correctionsextrapolation: 2: 65L06 Multistep, Runge-Kutta and extrapolation methods
extremal: 1: 05C35 Extremal problems [See also]90C35extremal: 2: 05Dxx Extremal combinatoricsextremal: 3: 05D05 Extremal set theoryextremal: 4: 14E30 Minimal model program (Mori theory, extremal rays)extremal: 5: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsextremal: 6: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsextremal: 7: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85extremal: 8: 31B15 Potentials and capacities, extremal lengthextremal: 9: 42A05 Trigonometric polynomials, inequalities, extremal problemsextremal: 10: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.extremal: 11: 60G70 Extreme value theory; extremal processes
extremally: 1: 54G05 Extremally disconnected spaces, F -spaces, etc.extreme: 1: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)
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extreme: 2: 60G70 Extreme value theory; extremal processesextreme: 3: 62G32 Statistics of extreme values; tail inference
extreme-point: 1: 90C49 Extreme-point and pivoting methodsextremum: 1: 51M16 Inequalities and extremum problems For convex problems, see 52A40extremum: 2: 52A40 Inequalities and extremum problems
face: 1: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U10faces: 1: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxx
factor: 1: 62H25 Factor analysis and principal components; correspondence analysisfactorial: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M05factorial: 2: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H10factorial: 3: 62K15 Factorial designs
factorials: 1: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxxfactorials: 2: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A30
factorization: 1: 05C70 Factorization, matching, partitioning, covering and packingfactorization: 2: 11A51 Factorization; primalityfactorization: 3: 11R27 Units and factorizationfactorization: 4: 11Y05 Factorizationfactorization: 5: 12D05 Polynomials: factorizationfactorization: 6: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M05factorization: 7: 13P05 Polynomials, factorization [See also]12Y05factorization: 8: 15A23 Factorization of matricesfactorization: 9: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamsfactorization: 10: 42A85 Convolution, factorizationfactorization: 11: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)factorization: 12: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
factorizations: 1: 13A05 Divisibility; factorizations [See also]13F15factorizations: 2: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)
factors: 1: 40D15 Convergence factors and summability factorsfactors: 2: 40D15 Convergence factors and summability factorsfactors: 3: 46L36 Classification of factors
fairly: 1: 54Dxx Fairly general propertiesfaithful: 1: 18A22 Special properties of functors (faithful, full, etc.)families: 1: 05C75 Structural characterization of families of graphsfamilies: 2: 14Dxx Families, fibrationsfamilies: 3: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)families: 4: 14H10 Families, moduli (algebraic)families: 5: 14H15 Families, moduli (analytic) [See also]30F10, 32G15families: 6: 14J10 Families, moduli, classification: algebraic theoryfamilies: 7: 28D10 One-parameter continuous families of measure-preserving transformationsfamilies: 8: 30D45 Bloch functions, normal functions, normal familiesfamilies: 9: 32A17 Special families of functionsfamilies: 10: 32A19 Normal families of functions, mappingsfamilies: 11: 37A10 One-parameter continuous families of measure-preserving transformationsfamilies: 12: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationsfamilies: 13: 37P45 Families and moduli spaces
fano: 1: 14J45 Fano varietiesfantappie-type: 1: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)
farey: 1: 11B57 Farey sequences; the sequences 1k, 2k, · · ·fast: 1: 65T50 Discrete and fast Fourier transformsfast: 2: 70K70 Systems with slow and fast motions
fatou: 1: 31A20 Boundary behavior (theorems of Fatou type, etc.)fatou: 2: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setsfatou: 3: 37P40 Non-Archimedean Fatou and Julia setsfault: 1: 68M15 Reliability, testing and fault tolerance [See also]94C12
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fault: 2: 94C12 Fault detection; testingfc-groups: 1: 20F24 FC-groups and their generalizationsfeedback: 1: 49N35 Optimal feedback synthesis [See also]93B52feedback: 2: 93B52 Feedback controlfeedback: 3: 93D10 Popov-type stability of feedback systemsfeedback: 4: 93D15 Stabilization of systems by feedbackfermat’s: 1: 11D41 Higher degree equations; Fermat’s equation
ferroelectrics: 1: 82D45 Ferroelectricsfestschriften: 1: 00B30 Festschriftenfewnomials: 1: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros ofAbelian integrals, etc.)
feynman: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) onmanifolds [See also]28Cxx, 46G12, 60-XX
feynman: 2: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluiddynamics, etc.)
feynman: 3: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraicgeometry [See also]14D05, 32S40
feynman: 4: 81T18 Feynman diagramsfeynman-kac: 1: 47D08 Schrodinger and Feynman-Kac semigroups
fiber: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
fiber: 2: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxxfiber: 3: 32G08 Deformations of fiber bundlesfiber: 4: 32Lxx Holomorphic fiber spaces [See also]55Rxxfiber: 5: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25fiber: 6: 55R05 Fiber spacesfiber: 7: 55R10 Fiber bundlesfiber: 8: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txxfiber: 9: 55R65 Generalizations of fiber spaces and bundlesfiber: 10: 55R91 Equivariant fiber spaces and bundles [See also]19L47fiber: 11: 55S40 Sectioning fiber spaces and bundlesfiber: 12: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxx
fibered: 1: 18D30 Fibered categoriesfiberings: 1: 55R55 Fiberings with singularitiesfibonacci: 1: 11B39 Fibonacci and Lucas numbers and polynomials and generalizationsfibration: 1: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45
fibrations: 1: 14Dxx Families, fibrationsfibrations: 2: 14D06 Fibrations, degenerationsfibrations: 3: 14R25 Affine fibrations [See also]14D06fibrations: 4: 32L25 Twistor theory, double fibrations [See also]53C28fibrewise: 1: 55R70 Fibrewise topologyfictitious: 1: 65M85 Fictitious domain methodsfictitious: 2: 65N85 Fictitious domain methods
field: 1: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F05field: 2: 11J17 Approximation by numbers from a fixed fieldfield: 3: 11J72 Irrationality; linear independence over a fieldfield: 4: 11R37 Class field theoryfield: 5: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55field: 6: 11S31 Class field theory; p-adic formal groups [See also]14L05field: 7: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50field: 8: 12-XX Field theory and polynomialsfield: 9: 12Exx General field theoryfield: 10: 12E30 Field arithmeticfield: 11: 12Fxx Field extensionsfield: 12: 12Gxx Homological methods (field theory)field: 13: 12Yxx Computational aspects of field theory and polynomialsfield: 14: 12Y05 Computational aspects of field theory and polynomials
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Mathematics Subject Classification 2010
field: 15: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistortheory, instantons, quantum field theory) [See also]32L25, 81Txx
field: 16: 19F05 Generalized class field theory [See also]11G45field: 17: 53D42 Symplectic field theory; contact homologyfield: 18: 57R56 Topological quantum field theoriesfield: 19: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XXfield: 20: 70S20 More general nonquantum field theoriesfield: 21: 81Txx Quantum field theory; related classical field theories [See also]70Sxxfield: 22: 81Txx Quantum field theory; related classical field theories [See also]70Sxxfield: 23: 81T05 Axiomatic quantum field theory; operator algebrasfield: 24: 81T08 Constructive quantum field theoryfield: 25: 81T10 Model quantum field theoriesfield: 26: 81T20 Quantum field theory on curved space backgroundsfield: 27: 81T25 Quantum field theory on latticesfield: 28: 81T28 Thermal quantum field theory [See also]82B30field: 29: 81T40 Two-dimensional field theories, conformal field theories, etc.field: 30: 81T40 Two-dimensional field theories, conformal field theories, etc.field: 31: 81T45 Topological field theories [See also]57R56, 58Dxxfield: 32: 81T60 Supersymmetric field theoriesfield: 33: 81T70 Quantization in field theory; cohomological methods [See also]58D29field: 34: 83C45 Quantization of the gravitational fieldfield: 35: 83C47 Methods of quantum field theory [See also]81T20field: 36: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)field: 37: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesfield: 38: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesfield: 39: 83Exx Unified, higher-dimensional and super field theories
field-theoretic: 1: 12E20 Finite fields (field-theoretic aspects)field-theoretical: 1: 76F30 Renormalization and other field-theoretical methods [See also]81T99
fields: 1: 05-XX Combinatorics For finite fields, see 11Txxfields: 2: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65fields: 3: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80fields: 4: 11Axx Elementary number theory For analogues in number fields, see 11R04fields: 5: 11D88 p-adic and power series fieldsfields: 6: 11E04 Quadratic forms over general fieldsfields: 7: 11E08 Quadratic forms over local rings and fieldsfields: 8: 11E10 Forms over real fieldsfields: 9: 11E12 Quadratic forms over global rings and fieldsfields: 10: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsfields: 11: 11F85 p-adic theory, local fields [See also]14G20, 22E50fields: 12: 11G05 Elliptic curves over global fields [See also]14H52fields: 13: 11G07 Elliptic curves over local fields [See also]14G20, 14H52fields: 14: 11G20 Curves over finite and local fields [See also]14H25fields: 15: 11G25 Varieties over finite and local fields [See also]14G15, 14G20fields: 16: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25fields: 17: 11G35 Varieties over global fields [See also]14G25fields: 18: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10fields: 19: 11Lxx Exponential sums and character sums For finite fields, see 11Txxfields: 20: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72fields: 21: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15fields: 22: 11R21 Other number fieldsfields: 23: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F27fields: 24: 11R58 Arithmetic theory of algebraic function fields [See also]14-XX
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fields: 25: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)fields: 26: 11R70 K-theory of global fields [See also]19Fxxfields: 27: 11R80 Totally real fields [See also]12J15fields: 28: 11Sxx Algebraic number theory: local and p-adic fieldsfields: 29: 11S70 K-theory of local fields [See also]19Fxxfields: 30: 11Txx Finite fields and commutative rings (number-theoretic aspects)fields: 31: 11T55 Arithmetic theory of polynomial rings over finite fieldsfields: 32: 12Dxx Real and complex fieldsfields: 33: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxfields: 34: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxfields: 35: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxfields: 36: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxxfields: 37: 12E20 Finite fields (field-theoretic aspects)fields: 38: 12E25 Hilbertian fields; Hilbert’s irreducibility theoremfields: 39: 12Jxx Topological fieldsfields: 40: 12J05 Normed fieldsfields: 41: 12J10 Valued fieldsfields: 42: 12J12 Formally p-adic fieldsfields: 43: 12J15 Ordered fieldsfields: 44: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S10fields: 45: 12Kxx Generalizations of fieldsfields: 46: 14D10 Arithmetic ground fields (finite, local, global)fields: 47: 14G15 Finite ground fieldsfields: 48: 14G17 Positive characteristic ground fieldsfields: 49: 14G20 Local ground fieldsfields: 50: 14G25 Global ground fieldsfields: 51: 14G27 Other nonalgebraically closed ground fieldsfields: 52: 14H05 Algebraic functions; function fields [See also]11R58fields: 53: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxxfields: 54: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxxfields: 55: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxxfields: 56: 15B33 Matrices over special rings (quaternions, finite fields, etc.)fields: 57: 17B66 Lie algebras of vector fields and related (super) algebrasfields: 58: 20G15 Linear algebraic groups over arbitrary fieldsfields: 59: 20G25 Linear algebraic groups over local fields and their integersfields: 60: 20G30 Linear algebraic groups over global fields and their integersfields: 61: 20G40 Linear algebraic groups over finite fieldsfields: 62: 20H20 Other matrix groups over fieldsfields: 63: 20H30 Other matrix groups over finite fieldsfields: 64: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W80fields: 65: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05fields: 66: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05fields: 67: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05fields: 68: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H05fields: 69: 32M25 Complex vector fieldsfields: 70: 32S65 Singularities of holomorphic vector fields and foliationsfields: 71: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)fields: 72: 37C10 Vector fields, flows, ordinary differential equationsfields: 73: 37C27 Periodic orbits of vector fields and flows
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fields: 74: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxxfields: 75: 37P15 Global ground fieldsfields: 76: 37P20 Non-Archimedean local ground fieldsfields: 77: 37P25 Finite ground fieldsfields: 78: 40D09 Structure of summability fieldsfields: 79: 40D20 Summability and bounded fields of methodsfields: 80: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05fields: 81: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theoryfields: 82: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80fields: 83: 57R25 Vector fields, frame fieldsfields: 84: 57R25 Vector fields, frame fieldsfields: 85: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B05fields: 86: 58K45 Singularities of vector fields, topological aspectsfields: 87: 60G60 Random fieldsfields: 88: 62B05 Sufficient statistics and fieldsfields: 89: 62M40 Random fields; image analysisfields: 90: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10fields: 91: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10fields: 92: 83C25 Approximation procedures, weak fieldsfields: 93: 83C50 Electromagnetic fieldsfields: 94: 97H40 Groups, rings, fields
figures: 1: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15films: 1: 74K35 Thin filmsfilms: 2: 76A20 Thin fluid films
filtered: 1: 16W70 Filtered rings; filtrational and graded techniquesfiltering: 1: 60G35 Signal detection and filtering [See also]62M20, 93E10, 93E11, 94Axxfiltering: 2: 62M20 Prediction [See also]60G25; filtering [See also]60G35, 93E10, 93E11filtering: 3: 93E11 Filtering [See also]60G35filtering: 4: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
filters: 1: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)filtration: 1: 76Sxx Flows in porous media; filtration; seepagefiltration: 2: 76S05 Flows in porous media; filtration; seepage
filtrational: 1: 16W70 Filtered rings; filtrational and graded techniquesfinance: 1: 91Gxx Mathematical financefinance: 2: 91G50 Corporate finance
financial: 1: 62P05 Applications to actuarial sciences and financial mathematicsfinancial: 2: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)financial: 3: 97M30 Financial and insurance mathematics
fine: 1: 14D22 Fine and coarse moduli spacesfine: 2: 31C40 Fine potential theory
finely: 1: 30G12 Finely holomorphic functions and topological function theoryfinitary: 1: 08A62 Finitary algebras
finite: 1: 03C13 Finite structures [See also]68Q15, 68Q19finite: 2: 05-XX Combinatorics For finite fields, see 11Txxfinite: 3: 05B25 Finite geometries [See also]51D20, 51Exxfinite: 4: 11F22 Relationship to Lie algebras and finite simple groupsfinite: 5: 11G20 Curves over finite and local fields [See also]14H25finite: 6: 11G25 Varieties over finite and local fields [See also]14G15, 14G20finite: 7: 11Lxx Exponential sums and character sums For finite fields, see 11Txxfinite: 8: 11Txx Finite fields and commutative rings (number-theoretic aspects)finite: 9: 11T55 Arithmetic theory of polynomial rings over finite fieldsfinite: 10: 11T60 Finite upper half-planesfinite: 11: 12E20 Finite fields (field-theoretic aspects)
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finite: 12: 13E15 Rings and modules of finite generation or presentation; number of generatorsfinite: 13: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxfinite: 14: 14D10 Arithmetic ground fields (finite, local, global)finite: 15: 14G15 Finite ground fieldsfinite: 16: 15B33 Matrices over special rings (quaternions, finite fields, etc.)finite: 17: 16G60 Representation type (finite, tame, wild, etc.)finite: 18: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxfinite: 19: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)finite: 20: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)finite: 21: 20B05 General theory for finite groupsfinite: 22: 20B20 Multiply transitive finite groupsfinite: 23: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXfinite: 24: 20C05 Group rings of finite groups and their modules [See also]16S34finite: 25: 20C10 Integral representations of finite groupsfinite: 26: 20C11 p-adic representations of finite groupsfinite: 27: 20C30 Representations of finite symmetric groupsfinite: 28: 20C33 Representations of finite groups of Lie typefinite: 29: 20Dxx Abstract finite groupsfinite: 30: 20D05 Finite simple groups and their classificationfinite: 31: 20Exx Structure and classification of infinite or finite groupsfinite: 32: 20E26 Residual properties and generalizations; residually finite groupsfinite: 33: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]finite: 34: 20Fxx Special aspects of infinite or finite groupsfinite: 35: 20F11 Groups of finite Morley rank [See also]03C45, 03C60finite: 36: 20F50 Periodic groups; locally finite groupsfinite: 37: 20G40 Linear algebraic groups over finite fieldsfinite: 38: 20H30 Other matrix groups over finite fieldsfinite: 39: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]finite: 40: 20K15 Torsion-free groups, finite rankfinite: 41: 32T25 Finite type domainsfinite: 42: 32V35 Finite type conditions on CR manifoldsfinite: 43: 37B50 Multi-dimensional shifts of finite type, tiling dynamicsfinite: 44: 37P25 Finite ground fieldsfinite: 45: 51Exx Finite geometry and special incidence structuresfinite: 46: 51E14 Finite partial geometries (general), nets, partial spreadsfinite: 47: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxfinite: 48: 51E25 Other finite nonlinear geometriesfinite: 49: 51E26 Other finite linear geometriesfinite: 50: 51E30 Other finite incidence structures [See also]05B30finite: 51: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17finite: 52: 57S17 Finite transformation groupsfinite: 53: 58K40 Classification; finite determinacy of map germsfinite: 54: 65G30 Interval and finite arithmeticfinite: 55: 65L12 Finite difference methodsfinite: 56: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodsfinite: 57: 65M06 Finite difference methodsfinite: 58: 65M08 Finite volume methodsfinite: 59: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsfinite: 60: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsfinite: 61: 65N06 Finite difference methodsfinite: 62: 65N08 Finite volume methodsfinite: 63: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsfinite: 64: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsfinite: 65: 68Q19 Descriptive complexity and finite models [See also]03C13finite: 66: 74S05 Finite element methods
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finite: 67: 74S10 Finite volume methodsfinite: 68: 74S20 Finite difference methodsfinite: 69: 76M10 Finite element methodsfinite: 70: 76M12 Finite volume methodsfinite: 71: 76M20 Finite difference methodsfinite: 72: 78M10 Finite element methodsfinite: 73: 78M12 Finite volume methods, finite integration techniquesfinite: 74: 78M12 Finite volume methods, finite integration techniquesfinite: 75: 78M20 Finite difference methodsfinite: 76: 80M10 Finite element methodsfinite: 77: 80M12 Finite volume methodsfinite: 78: 80M20 Finite difference methodsfinite: 79: 90C33 Complementarity and equilibrium problems and variational inequalities (finite
dimensions)finite: 80: 94A55 Shift register sequences and sequences over finite alphabets
finite-dimensional: 1: 13E10 Artinian rings and modules, finite-dimensional algebrasfinite-dimensional: 2: 16K20 Finite-dimensional For crossed products, see 16S35finite-dimensional: 3: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxfinite-dimensional: 4: 17C55 Finite-dimensional structuresfinite-dimensional: 5: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxfinite-dimensional: 6: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxxfinite-dimensional: 7: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxfinite-dimensional: 8: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70finite-type: 1: 32F18 Finite-type conditionsfiniteness: 1: 13Exx Chain conditions, finiteness conditionsfiniteness: 2: 16Pxx Chain conditions, growth conditions, and other forms of finitenessfiniteness: 3: 19J05 Finiteness and other obstructions in K0
finiteness: 4: 32H35 Proper mappings, finiteness theoremsfiniteness: 5: 57Q12 Wall finiteness obstruction for CW-complexes
finsler: 1: 53B40 Finsler spaces and generalizations (areal metrics)finsler: 2: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B20finsler: 3: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C60finsler: 4: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)
firm: 1: 91B38 Production theory, theory of the firmfirst-order: 1: 03B10 Classical first-order logicfirst-order: 2: 03C07 Basic properties of first-order languages and structuresfirst-order: 3: 03C68 Other classical first-order model theoryfirst-order: 4: 03F30 First-order arithmetic and fragmentsfirst-order: 5: 35Fxx General first-order equations and systemsfirst-order: 6: 35F05 Linear first-order equationsfirst-order: 7: 35F10 Initial value problems for linear first-order equationsfirst-order: 8: 35F15 Boundary value problems for linear first-order equationsfirst-order: 9: 35F16 Initial-boundary value problems for linear first-order equationsfirst-order: 10: 35F20 Nonlinear first-order equationsfirst-order: 11: 35F25 Initial value problems for nonlinear first-order equationsfirst-order: 12: 35F30 Boundary value problems for nonlinear first-order equationsfirst-order: 13: 35F31 Initial-boundary value problems for nonlinear first-order equationsfirst-order: 14: 35F35 Linear first-order systemsfirst-order: 15: 35F40 Initial value problems for linear first-order systemsfirst-order: 16: 35F45 Boundary value problems for linear first-order systemsfirst-order: 17: 35F46 Initial-boundary value problems for linear first-order systemsfirst-order: 18: 35F50 Nonlinear first-order systems
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first-order: 19: 35F55 Initial value problems for nonlinear first-order systemsfirst-order: 20: 35F60 Boundary value problems for nonlinear first-order systemsfirst-order: 21: 35F61 Initial-boundary value problems for nonlinear first-order systemsfirst-order: 22: 35J46 First-order elliptic systemsfirst-order: 23: 35J56 Boundary value problems for first-order elliptic systemsfirst-order: 24: 35L02 First-order hyperbolic equationsfirst-order: 25: 35L03 Initial value problems for first-order hyperbolic equationsfirst-order: 26: 35L04 Initial-boundary value problems for first-order hyperbolic equationsfirst-order: 27: 35L40 First-order hyperbolic systemsfirst-order: 28: 35L45 Initial value problems for first-order hyperbolic systemsfirst-order: 29: 35L50 Initial-boundary value problems for first-order hyperbolic systemsfirst-order: 30: 35L60 Nonlinear first-order hyperbolic equations
fitting: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks[See also]20F17
fitting: 2: 20D25 Special subgroups (Frattini, Fitting, etc.)fitting: 3: 20F17 Formations of groups, Fitting classes [See also]20D10fitting: 4: 65D10 Smoothing, curve fitting
fixed: 1: 11J17 Approximation by numbers from a fixed fieldfixed: 2: 37C25 Fixed points, periodic points, fixed-point index theoryfixed: 3: 37J10 Symplectic mappings, fixed pointsfixed: 4: 55M20 Fixed points and coincidences [See also]54H25fixed: 5: 58C30 Fixed point theorems on manifolds [See also]47H10fixed: 6: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80fixed: 7: 70E17 Motion of a rigid body with a fixed point
fixed-point: 1: 37C25 Fixed points, periodic points, fixed-point index theoryfixed-point: 2: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C30fixed-point: 3: 54H25 Fixed-point and coincidence theorems [See also]47H10, 55M20
flag: 1: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M35flat: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
14B25flat: 2: 13C11 Injective and flat modules and idealsflat: 3: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B40flat: 4: 16D40 Free, projective, and flat modules and ideals [See also]19A13
flatness: 1: 57N45 Flatness and tamenessflats: 1: 52C35 Arrangements of points, flats, hyperplanes [See also]32S22
flexibility: 1: 52C25 Rigidity and flexibility of structures [See also]70B15flexible: 1: 17A20 Flexible algebras
floer: 1: 53D40 Floer homology and cohomology, symplectic aspectsfloer: 2: 57R58 Floer homologyflow: 1: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)flow: 2: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)flow: 3: 76B75 Flow control and optimization [See also]49Q10, 93C20, 93C95flow: 4: 76D55 Flow control and optimization [See also]49Q10, 93C20, 93C95flow: 5: 76N25 Flow control and optimizationflow: 6: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10flow: 7: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10flow: 8: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10flow: 9: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10flow: 10: 80A20 Heat and mass transfer, heat flowflow: 11: 92C35 Physiological flow [See also]76Z05
flows: 1: 05C21 Flows in graphsflows: 2: 37A17 Homogeneous flows [See also]22Fxxflows: 3: 37C10 Vector fields, flows, ordinary differential equationsflows: 4: 37C27 Periodic orbits of vector fields and flowsflows: 5: 37C55 Periodic and quasiperiodic flows and diffeomorphismsflows: 6: 37C65 Monotone flowsflows: 7: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
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etc.)flows: 8: 37E35 Flows on surfacesflows: 9: 53D25 Geodesic flowsflows: 10: 58J30 Spectral flowsflows: 11: 76B07 Free-surface potential flowsflows: 12: 76B47 Vortex flowsflows: 13: 76D07 Stokes and related (Oseen, etc.) flowsflows: 14: 76D17 Viscous vortex flowsflows: 15: 76D27 Other free-boundary flows; Hele-Shaw flowsflows: 16: 76D27 Other free-boundary flows; Hele-Shaw flowsflows: 17: 76E05 Parallel shear flowsflows: 18: 76E09 Stability and instability of nonparallel flowsflows: 19: 76E20 Stability and instability of geophysical and astrophysical flowsflows: 20: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flowsflows: 21: 76F10 Shear flowsflows: 22: 76F70 Control of turbulent flowsflows: 23: 76Gxx General aerodynamics and subsonic flowsflows: 24: 76G25 General aerodynamics and subsonic flowsflows: 25: 76Hxx Transonic flowsflows: 26: 76H05 Transonic flowsflows: 27: 76Jxx Supersonic flowsflows: 28: 76J20 Supersonic flowsflows: 29: 76Kxx Hypersonic flowsflows: 30: 76K05 Hypersonic flowsflows: 31: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05flows: 32: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05flows: 33: 76Sxx Flows in porous media; filtration; seepageflows: 34: 76S05 Flows in porous media; filtration; seepageflows: 35: 76Txx Two-phase and multiphase flowsflows: 36: 76T10 Liquid-gas two-phase flows, bubbly flowsflows: 37: 76T10 Liquid-gas two-phase flows, bubbly flowsflows: 38: 76T15 Dusty-gas two-phase flowsflows: 39: 76T25 Granular flows [See also]74C99, 74E20flows: 40: 76T30 Three or more component flowsflows: 41: 76Vxx Reaction effects in flows [See also]80A32flows: 42: 76V05 Reaction effects in flows [See also]80A32flows: 43: 76Z05 Physiological flows [See also]92C35flows: 44: 80A32 Chemically reacting flows [See also]92C45, 92E20flows: 45: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A32fluid: 1: 35Q35 PDEs in connection with fluid mechanicsfluid: 2: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A10fluid: 3: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)fluid: 4: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXfluid: 5: 76A02 Foundations of fluid mechanicsfluid: 6: 76A20 Thin fluid filmsfluid: 7: 76Mxx Basic methods in fluid mechanics [See also]65-XXfluid: 8: 76Zxx Biological fluid mechanics [See also]74F10, 74L15, 92Cxx
fluid-solid: 1: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)fluids: 1: 76A05 Non-Newtonian fluidsfluids: 2: 76A10 Viscoelastic fluidsfluids: 3: 76Bxx Incompressible inviscid fluidsfluids: 4: 76B70 Stratification effects in inviscid fluidsfluids: 5: 76Dxx Incompressible viscous fluidsfluids: 6: 76D50 Stratification effects in viscous fluidsfluids: 7: 76Nxx Compressible fluids and gas dynamics, general
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fluids: 8: 76Uxx Rotating fluidsfluids: 9: 76U05 Rotating fluids
fock: 1: 30H20 Bergman spaces, Fock spacesfokker-planck: 1: 35Q84 Fokker-Planck equationsfokker-planck: 2: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H10
foliations: 1: 32S65 Singularities of holomorphic vector fields and foliationsfoliations: 2: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxfoliations: 3: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxxfoliations: 4: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R32foliations: 5: 57R30 Foliations; geometric theoryfoliations: 6: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10
fond’s: 1: 11J85 Algebraic independence; Gel′fond’s methodfor: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)for: 2: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45for: 3: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45for: 4: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-
tic and similar approaches see 03F55for: 5: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A26for: 6: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A30for: 7: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50for: 8: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72for: 9: 11N45 Asymptotic results on counting functions for algebraic and topological structuresfor: 10: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxfor: 11: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)for: 12: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45for: 13: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxfor: 14: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30for: 15: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxfor: 16: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66for: 17: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
for: 18: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
for: 19: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
for: 20: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
for: 21: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology andderived functors for triples [See also]18Gxx
for: 22: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology andderived functors for triples [See also]18Gxx
for: 23: 19A13 Stability for projective modules [See also]13C10for: 24: 19B14 Stability for linear groupsfor: 25: 19C40 Excision for K2
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for: 26: 19G05 Stability for quadratic modulesfor: 27: 20B05 General theory for finite groupsfor: 28: 20B07 General theory for infinite groupsfor: 29: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)for: 30: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]for: 31: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
for: 32: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
for: 33: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]for: 34: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05for: 35: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05for: 36: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXfor: 37: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90for: 38: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40for: 39: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
for: 40: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
for: 41: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
for: 42: 26D05 Inequalities for trigonometric functions and polynomialsfor: 43: 26D15 Inequalities for sums, series and integralsfor: 44: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10for: 45: 30C50 Coefficient problems for univalent and multivalent functionsfor: 46: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsfor: 47: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsfor: 48: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14for: 49: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxfor: 50: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxfor: 51: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
for: 52: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
for: 53: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
for: 54: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
for: 55: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities forintegrals
for: 56: 35F10 Initial value problems for linear first-order equationsfor: 57: 35F15 Boundary value problems for linear first-order equations
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for: 58: 35F16 Initial-boundary value problems for linear first-order equationsfor: 59: 35F25 Initial value problems for nonlinear first-order equationsfor: 60: 35F30 Boundary value problems for nonlinear first-order equationsfor: 61: 35F31 Initial-boundary value problems for nonlinear first-order equationsfor: 62: 35F40 Initial value problems for linear first-order systemsfor: 63: 35F45 Boundary value problems for linear first-order systemsfor: 64: 35F46 Initial-boundary value problems for linear first-order systemsfor: 65: 35F55 Initial value problems for nonlinear first-order systemsfor: 66: 35F60 Boundary value problems for nonlinear first-order systemsfor: 67: 35F61 Initial-boundary value problems for nonlinear first-order systemsfor: 68: 35G10 Initial value problems for linear higher-order equationsfor: 69: 35G15 Boundary value problems for linear higher-order equationsfor: 70: 35G16 Initial-boundary value problems for linear higher-order equationsfor: 71: 35G25 Initial value problems for nonlinear higher-order equationsfor: 72: 35G30 Boundary value problems for nonlinear higher-order equationsfor: 73: 35G31 Initial-boundary value problems for nonlinear higher-order equationsfor: 74: 35G40 Initial value problems for linear higher-order systemsfor: 75: 35G45 Boundary value problems for linear higher-order systemsfor: 76: 35G46 Initial-boundary value problems for linear higher-order systemsfor: 77: 35G55 Initial value problems for nonlinear higher-order systemsfor: 78: 35G60 Boundary value problems for nonlinear higher-order systemsfor: 79: 35G61 Initial-boundary value problems for nonlinear higher-order systemsfor: 80: 35J20 Variational methods for second-order elliptic equationsfor: 81: 35J25 Boundary value problems for second-order elliptic equationsfor: 82: 35J35 Variational methods for higher-order elliptic equationsfor: 83: 35J40 Boundary value problems for higher-order elliptic equationsfor: 84: 35J50 Variational methods for elliptic systemsfor: 85: 35J56 Boundary value problems for first-order elliptic systemsfor: 86: 35J57 Boundary value problems for second-order elliptic systemsfor: 87: 35J58 Boundary value problems for higher-order elliptic systemsfor: 88: 35J65 Nonlinear boundary value problems for linear elliptic equationsfor: 89: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsfor: 90: 35K15 Initial value problems for second-order parabolic equationsfor: 91: 35K20 Initial-boundary value problems for second-order parabolic equationsfor: 92: 35K30 Initial value problems for higher-order parabolic equationsfor: 93: 35K35 Initial-boundary value problems for higher-order parabolic equationsfor: 94: 35K45 Initial value problems for second-order parabolic systemsfor: 95: 35K46 Initial value problems for higher-order parabolic systemsfor: 96: 35K51 Initial-boundary value problems for second-order parabolic systemsfor: 97: 35K52 Initial-boundary value problems for higher-order parabolic systemsfor: 98: 35K60 Nonlinear initial value problems for linear parabolic equationsfor: 99: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsfor: 100: 35L03 Initial value problems for first-order hyperbolic equationsfor: 101: 35L04 Initial-boundary value problems for first-order hyperbolic equationsfor: 102: 35L15 Initial value problems for second-order hyperbolic equationsfor: 103: 35L20 Initial-boundary value problems for second-order hyperbolic equationsfor: 104: 35L30 Initial value problems for higher-order hyperbolic equationsfor: 105: 35L35 Initial-boundary value problems for higher-order hyperbolic equationsfor: 106: 35L45 Initial value problems for first-order hyperbolic systemsfor: 107: 35L50 Initial-boundary value problems for first-order hyperbolic systemsfor: 108: 35L52 Initial value problems for second-order hyperbolic systemsfor: 109: 35L53 Initial-boundary value problems for second-order hyperbolic systemsfor: 110: 35L56 Initial value problems for higher-order hyperbolic systemsfor: 111: 35L57 Initial-boundary value problems for higher-order hyperbolic systemsfor: 112: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J40for: 113: 35M11 Initial value problems for equations of mixed type
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for: 114: 35M12 Boundary value problems for equations of mixed typefor: 115: 35M13 Initial-boundary value problems for equations of mixed typefor: 116: 35M31 Initial value problems for systems of mixed typefor: 117: 35M32 Boundary value problems for systems of mixed typefor: 118: 35M33 Initial-boundary value problems for systems of mixed typefor: 119: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15for: 120: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15for: 121: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxfor: 122: 35S10 Initial value problems for pseudodifferential operatorsfor: 123: 35S11 Initial-boundary value problems for pseudodifferential operatorsfor: 124: 35S15 Boundary value problems for pseudodifferential operatorsfor: 125: 37K55 Perturbations, KAM for infinite-dimensional systemsfor: 126: 37M20 Computational methods for bifurcation problemsfor: 127: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)for: 128: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05for: 129: 39B22 Equations for real functions [See also]26A51, 26B25for: 130: 39B32 Equations for complex functions [See also]30D05for: 131: 39B52 Equations for functions with more general domains and/or rangesfor: 132: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 133: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 134: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 135: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
for: 136: 42C25 Uniqueness and localization for orthogonal seriesfor: 137: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 138: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 139: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 140: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 141: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 142: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
for: 143: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)for: 144: 46L45 Decomposition theory for C∗-algebrasfor: 145: 47A45 Canonical models for contractions and nonselfadjoint operators
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for: 146: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 forother integral operators; see also 32A25, 32M15
for: 147: 49Rxx Variational methods for eigenvalues of operators [See also]47A75for: 148: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)for: 149: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55for: 150: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxfor: 151: 52B60 Isoperimetric problems for polytopesfor: 152: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxfor: 153: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxfor: 154: 55N40 Axioms for homology theory and uniqueness theoremsfor: 155: 57Q12 Wall finiteness obstruction for CW-complexesfor: 156: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxfor: 157: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10for: 158: 58D27 Moduli problems for differential geometric structuresfor: 159: 58D29 Moduli problems for topological structuresfor: 160: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32for: 161: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)for: 162: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)for: 163: 60H35 Computational methods for stochastic equations [See also]65C30for: 164: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35for: 165: 65D15 Algorithms for functional approximationfor: 166: 65F05 Direct methods for linear systems and matrix inversionfor: 167: 65F08 Preconditioners for iterative methodsfor: 168: 65F10 Iterative methods for linear systems [See also]65N22for: 169: 65K15 Numerical methods for variational inequalities and related problemsfor: 170: 65L80 Methods for differential-algebraic equationsfor: 171: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M07for: 172: 65Y10 Algorithms for specific classes of architecturesfor: 173: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)for: 174: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxfor: 175: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXfor: 176: 70E20 Perturbation methods for rigid body dynamicsfor: 177: 74G45 Bounds for solutionsfor: 178: 78A45 Diffraction, scattering [See also]34E20 for WKB methodsfor: 179: 81Q15 Perturbation theories for operators and differential equationsfor: 180: 81U05 2-body potential scattering theory [See also]34E20 for WKB methodsfor: 181: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q25for: 182: 91A30 Utility theory for games [See also]91B16for: 183: 91A35 Decision theory for games [See also]62Cxx, 91B06, 90B50
forced: 1: 70J35 Forced motionsforced: 2: 70K40 Forced motionsforced: 3: 76R05 Forced convection
forcing: 1: 03C25 Model-theoretic forcingforcing: 2: 03E40 Other aspects of forcing and Boolean-valued modelsforcing: 3: 03E57 Generic absoluteness and forcing axioms [See also]03E50
form: 1: 11D57 Multiplicative and norm form equations
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form: 2: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and relatedtopics
form: 3: 35C05 Solutions in closed formform: 4: 91A18 Games in extensive form
formal: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,68Q70, 68R15
formal: 2: 11S31 Class field theory; p-adic formal groups [See also]14L05formal: 3: 13F25 Formal power series rings [See also]13J05formal: 4: 14B20 Formal neighborhoodsformal: 5: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxxformal: 6: 14L05 Formal groups, p-divisible groups [See also]55N22formal: 7: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxformal: 8: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q65formal: 9: 32K07 Formal and graded complex spaces [See also]58C50formal: 10: 34M25 Formal solutions, transform techniquesformal: 11: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J10formal: 12: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R90formal: 13: 68Q45 Formal languages and automata [See also]03D05, 68Q70, 94A45
formalism: 1: 37D35 Thermodynamic formalism, variational principles, equilibrium statesformalism: 2: 70S05 Lagrangian formalism and Hamiltonian formalismformalism: 3: 70S05 Lagrangian formalism and Hamiltonian formalismformalism: 4: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)formalism: 5: 83C60 Spinor and twistor methods; Newman-Penrose formalism
formally: 1: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)[See also]11Exx
formally: 2: 12J12 Formally p-adic fieldsformation: 1: 35B36 Pattern formationformation: 2: 92C15 Developmental biology, pattern formation
formations: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks[See also]20F17formations: 2: 20F17 Formations of groups, Fitting classes [See also]20D10
forms: 1: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linearalgebra, see 15A63
forms: 2: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linearalgebra, see 15A63
forms: 3: 11E04 Quadratic forms over general fieldsforms: 4: 11E08 Quadratic forms over local rings and fieldsforms: 5: 11E10 Forms over real fieldsforms: 6: 11E12 Quadratic forms over global rings and fieldsforms: 7: 11E16 General binary quadratic formsforms: 8: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesforms: 9: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesforms: 10: 11E25 Sums of squares and representations by other particular quadratic formsforms: 11: 11E39 Bilinear and Hermitian formsforms: 12: 11E41 Class numbers of quadratic and Hermitian formsforms: 13: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)forms: 14: 11E70 K-theory of quadratic and Hermitian formsforms: 15: 11E76 Forms of degree higher than twoforms: 16: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24forms: 17: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45forms: 18: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45forms: 19: 11F11 Holomorphic modular forms of integral weight
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forms: 20: 11F12 Automorphic forms, one variableforms: 21: 11F30 Fourier coefficients of automorphic formsforms: 22: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50forms: 23: 11F37 Forms of half-integer weight; nonholomorphic modular formsforms: 24: 11F37 Forms of half-integer weight; nonholomorphic modular formsforms: 25: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20forms: 26: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20forms: 27: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formsforms: 28: 11F50 Jacobi formsforms: 29: 11F52 Modular forms associated to Drinfel′d modulesforms: 30: 11F55 Other groups and their modular and automorphic forms (several variables)forms: 31: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsforms: 32: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesforms: 33: 11H46 Products of linear formsforms: 34: 11H50 Minima of formsforms: 35: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)forms: 36: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)forms: 37: 11J13 Simultaneous homogeneous approximation, linear formsforms: 38: 11J20 Inhomogeneous linear formsforms: 39: 11J86 Linear forms in logarithms; Baker’s methodforms: 40: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxforms: 41: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13forms: 42: 15A21 Canonical forms, reductions, classificationforms: 43: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exxforms: 44: 16Pxx Chain conditions, growth conditions, and other forms of finitenessforms: 45: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)forms: 46: 19Gxx K-theory of forms [See also]11Exxforms: 47: 32N10 Automorphic formsforms: 48: 34C20 Transformation and reduction of equations and systems, normal formsforms: 49: 34K17 Transformation and reduction of equations and systems, normal formsforms: 50: 34M35 Singularities, monodromy, local behavior of solutions, normal formsforms: 51: 37G05 Normal formsforms: 52: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionforms: 53: 37L10 Normal forms, center manifold theory, bifurcation theoryforms: 54: 47A07 Forms (bilinear, sesquilinear, multilinear)forms: 55: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axxforms: 56: 58A10 Differential formsforms: 57: 58K50 Normal formsforms: 58: 70K45 Normal forms
formula: 1: 11F72 Spectral theory; Selberg trace formulaformula: 2: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U25formula: 3: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15formula: 4: 55U25 Homology of a product, Kunneth formulaformula: 5: 65B15 Euler-Maclaurin formula
formularies: 1: 00A22 Formulariesformulas: 1: 11A25 Arithmetic functions; related numbers; inversion formulasformulas: 2: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasformulas: 3: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)formulas: 4: 41A80 Remainders in approximation formulas
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formulas: 5: 65D32 Quadrature and cubature formulasfoundational: 1: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxfoundational: 2: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxfoundational: 3: 62Axx Foundational and philosophical topicsfoundations: 1: 03-XX Mathematical logic and foundationsfoundations: 2: 03Axx Philosophical aspects of logic and foundationsfoundations: 3: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35foundations: 4: 14Axx Foundationsfoundations: 5: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXfoundations: 6: 20Axx Foundationsfoundations: 7: 26A03 Foundations: limits and generalizations, elementary topology of the linefoundations: 8: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxfoundations: 9: 55U40 Topological categories, foundations of homotopy theoryfoundations: 10: 58A05 Differentiable manifolds, foundationsfoundations: 11: 60Axx Foundations of probability theoryfoundations: 12: 60G05 Foundations of stochastic processesfoundations: 13: 62A01 Foundations and philosophical topicsfoundations: 14: 70Axx Axiomatics, foundationsfoundations: 15: 70A05 Axiomatics, foundationsfoundations: 16: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solidsfoundations: 17: 76Axx Foundations, constitutive equations, rheologyfoundations: 18: 76A02 Foundations of fluid mechanicsfoundations: 19: 78A02 Foundationsfoundations: 20: 80A05 Foundationsfoundations: 21: 81Pxx Axiomatics, foundations, philosophyfoundations: 22: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15foundations: 23: 82B03 Foundationsfoundations: 24: 82C03 Foundationsfoundations: 25: 97Exx Foundations of mathematicsfoundations: 26: 97K70 Foundations and methodology of statistics
fourier: 1: 11F30 Fourier coefficients of automorphic formsfourier: 2: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
fourier: 3: 35S30 Fourier integral operatorsfourier: 4: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)fourier: 5: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30fourier: 6: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30fourier: 7: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30fourier: 8: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriesfourier: 9: 42A24 Summability and absolute summability of Fourier and trigonometric seriesfourier: 10: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier: 11: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier: 12: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann
theory, localizationfourier: 13: 42B05 Fourier series and coefficientsfourier: 14: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier: 15: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier: 16: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)fourier: 17: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupsfourier: 18: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
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fourier: 19: 43A32 Other transforms and operators of Fourier typefourier: 20: 43A50 Convergence of Fourier series and of inverse transformsfourier: 21: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
fourier: 22: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
fourier: 23: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxxfourier: 24: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationfourier: 25: 65Txx Numerical methods in Fourier analysisfourier: 26: 65T50 Discrete and fast Fourier transforms
fourier-stieltjes: 1: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier-stieltjes: 2: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typefourier-stieltjes: 3: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupsfourier-stieltjes: 4: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
frechet: 1: 46A04 Locally convex Frechet spaces and (DF)-spacesfrechet: 2: 46A61 Graded Frechet spaces and tame operatorsfrechet: 3: 49J50 Frechet and Gateaux differentiability [See also]46G05, 58C20frechet: 4: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G05fractals: 1: 28A80 Fractals [See also]37Fxxfractals: 2: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.fraction: 1: 11Y65 Continued fraction calculations
fractional: 1: 05C72 Fractional graph theory, fuzzy graph theoryfractional: 2: 11J54 Small fractional parts of polynomials and generalizationsfractional: 3: 26A33 Fractional derivatives and integralsfractional: 4: 34A08 Fractional differential equationsfractional: 5: 34K37 Functional-differential equations with fractional derivativesfractional: 6: 35R11 Fractional partial differential equationsfractional: 7: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10fractional: 8: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10fractional: 9: 60G22 Fractional processes, including fractional Brownian motionfractional: 10: 60G22 Fractional processes, including fractional Brownian motionfractional: 11: 90C32 Fractional programmingfractions: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A15fractions: 2: 11D68 Rational numbers as sums of fractionsfractions: 3: 11J70 Continued fractions and generalizations [See also]11A55, 11K50fractions: 4: 11K50 Metric theory of continued fractions [See also]11A55, 11J70fractions: 5: 13B30 Rings of fractions and localization [See also]16S85fractions: 6: 16S85 Rings of fractions and localizations [See also]13B30fractions: 7: 30B70 Continued fractions [See also]11A55, 40A15fractions: 8: 40A15 Convergence and divergence of continued fractions [See also]30B70fracture: 1: 74A45 Theories of fracture and damagefracture: 2: 74Rxx Fracture and damagefracture: 3: 74R10 Brittle fracturefracture: 4: 74R15 High-velocity fracturefracture: 5: 74R20 Anelastic fracture and damage
fragments: 1: 03E30 Axiomatics of classical set theory and its fragmentsfragments: 2: 03F30 First-order arithmetic and fragmentsfragments: 3: 03F35 Second- and higher-order arithmetic and fragments [See also]03B30
frame: 1: 57R25 Vector fields, frame fieldsframed: 1: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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frames: 1: 06D22 Frames, locales For topological questions see 54-XXframes: 2: 42C15 General harmonic expansions, framesfrattini: 1: 20D25 Special subgroups (Frattini, Fitting, etc.)
fredholm: 1: 45Bxx Fredholm integral equationsfredholm: 2: 45B05 Fredholm integral equationsfredholm: 3: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)fredholm: 4: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J20fredholm: 5: 58B15 Fredholm structures [See also]47A53
free: 1: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10free: 2: 08B20 Free algebrasfree: 3: 13C10 Projective and free modules and ideals [See also]19A13free: 4: 16D40 Free, projective, and flat modules and ideals [See also]19A13free: 5: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.free: 6: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)free: 7: 17A50 Free algebrasfree: 8: 17B01 Identities, free Lie (super)algebrasfree: 9: 17C05 Identities and free Jordan structuresfree: 10: 20E05 Free nonabelian groupsfree: 11: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsfree: 12: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsfree: 13: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F10free: 14: 35R35 Free boundary problemsfree: 15: 46L09 Free products of C∗-algebrasfree: 16: 46L54 Free probability and free operator algebrasfree: 17: 46L54 Free probability and free operator algebrasfree: 18: 49J05 Free problems in one independent variablefree: 19: 49J10 Free problems in two or more independent variablesfree: 20: 49K05 Free problems in one independent variablefree: 21: 49K10 Free problems in two or more independent variablesfree: 22: 57M05 Fundamental group, presentations, free differential calculusfree: 23: 70E15 Free motion of a rigid body [See also]70M20free: 24: 70J30 Free motionsfree: 25: 70K25 Free motionsfree: 26: 76R10 Free convection
free-boundary: 1: 76D27 Other free-boundary flows; Hele-Shaw flowsfree-streamline: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingfree-surface: 1: 76B07 Free-surface potential flows
frequency-response: 1: 93C80 Frequency-response methodsfresnel: 1: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)fresnel: 2: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXfriction: 1: 70F40 Problems with frictionfriction: 2: 74A55 Theories of friction (tribology)friction: 3: 74M10 Friction
frobenius: 1: 11D07 The Frobenius problemfrobenius: 2: 19A22 Frobenius induction, Burnside and representation ringsfrobenius: 3: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35
from: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)from: 2: 11J17 Approximation by numbers from a fixed fieldfrom: 3: 15A78 Other algebras built from modulesfrom: 4: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22
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from: 5: 19Jxx Obstructions from topologyfrom: 6: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35from: 7: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)from: 8: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)from: 9: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)from: 10: 32V25 Extension of functions and other analytic objects from CR manifoldsfrom: 11: 33E30 Other functions coming from differential, difference and integral equationsfrom: 12: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)from: 13: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)from: 14: 62Mxx Inference from stochastic processesfrom: 15: 62M86 Inference from stochastic processes and fuzzinessfrom: 16: 70J50 Systems arising from the discretization of structural vibration problemsfrom: 17: 93B15 Realizations from input-output datafront: 1: 35A18 Wave front sets
fuchsian: 1: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxxfuchsian: 2: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxxfuchsian: 3: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemsfukaya: 1: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J33full: 1: 18A22 Special properties of functors (faithful, full, etc.)
function: 1: 11F20 Dedekind eta function, Dedekind sumsfunction: 2: 11R58 Arithmetic theory of algebraic function fields [See also]14-XXfunction: 3: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)function: 4: 14H05 Algebraic functions; function fields [See also]11R58function: 5: 15A54 Matrices over function rings in one or more variablesfunction: 6: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50function: 7: 26B10 Implicit function theorems, Jacobians, transformations with several variablesfunction: 8: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E15function: 9: 30Cxx Geometric function theoryfunction: 10: 30Gxx Generalized function theoryfunction: 11: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05function: 12: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05function: 13: 30G12 Finely holomorphic functions and topological function theoryfunction: 14: 30Jxx Function theory on the discfunction: 15: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35function: 16: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25function: 17: 41A30 Approximation by other special function classesfunction: 18: 42B35 Function spaces arising in harmonic analysisfunction: 19: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.function: 20: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.function: 21: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxfunction: 22: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exx
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function: 23: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see46Exx
function: 24: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For functionalgebras, see 46J10
function: 25: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For functionalgebras, see 46J10
function: 26: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banachfunction algebras, see 46J10, 46J15
function: 27: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
function: 28: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25function: 29: 46L52 Noncommutative function spacesfunction: 30: 47B38 Operators on function spaces (general)function: 31: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15function: 32: 54C35 Function spaces [See also]46Exx, 58D15function: 33: 54C40 Algebraic properties of function spaces [See also]46J10function: 34: 58C15 Implicit function theorems; global Newton methodsfunction: 35: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxfunction: 36: 65M80 Fundamental solutions, Green’s function methods, etc.function: 37: 65N80 Fundamental solutions, Green’s function methods, etc.
function-space: 1: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C60function-theoretic: 1: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see
32A22function-theoretic: 2: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22function-theoretic: 3: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)functional: 1: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsfunctional: 2: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05functional: 3: 16R60 Functional identitiesfunctional: 4: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E15functional: 5: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXfunctional: 6: 32A70 Functional analysis techniques [See mainly]46Exxfunctional: 7: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemsfunctional: 8: 39-XX Difference and functional equationsfunctional: 9: 39Bxx Functional equations and inequalities [See also]30D05functional: 10: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxxfunctional: 11: 39B72 Systems of functional equations and inequalitiesfunctional: 12: 40Hxx Functional analytic methods in summabilityfunctional: 13: 40H05 Functional analytic methods in summabilityfunctional: 14: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxfunctional: 15: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32functional: 16: 46G15 Functional analytic lifting theory [See also]28A51functional: 17: 46H30 Functional calculus in topological algebras [See also]47A60functional: 18: 46Mxx Methods of category theory in functional analysis [See also]18-XXfunctional: 19: 46Nxx Miscellaneous applications of functional analysis [See also]47Nxxfunctional: 20: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxxfunctional: 21: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05
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functional: 22: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedeanfunctional analysis [See also]12J25, 32P05functional: 23: 46S20 Nonstandard functional analysis [See also]03H05functional: 24: 46S30 Constructive functional analysis [See also]03F60functional: 25: 46S40 Fuzzy functional analysis [See also]03E72functional: 26: 46S50 Functional analysis in probabilistic metric linear spacesfunctional: 27: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50functional: 28: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxxfunctional: 29: 47A60 Functional calculusfunctional: 30: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)functional: 31: 60F17 Functional limit theorems; invariance principlesfunctional: 32: 65D15 Algorithms for functional approximationfunctional: 33: 65Qxx Difference and functional equations, recurrence relationsfunctional: 34: 65Q20 Functional equationsfunctional: 35: 68N18 Functional programming and lambda calculus [See also]03B40functional: 36: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)functional: 37: 97I70 Functional equations
functional-analytic: 1: 70G70 Functional-analytic methodsfunctional-differential: 1: 34Kxx Functional-differential and differential-difference equations [See also]37-XXfunctional-differential: 2: 34K06 Linear functional-differential equationsfunctional-differential: 3: 34K08 Spectral theory of functional-differential operatorsfunctional-differential: 4: 34K09 Functional-differential inclusionsfunctional-differential: 5: 34K31 Lattice functional-differential equationsfunctional-differential: 6: 34K36 Fuzzy functional-differential equationsfunctional-differential: 7: 34K37 Functional-differential equations with fractional derivativesfunctional-differential: 8: 34K38 Functional-differential inequalitiesfunctional-differential: 9: 34K50 Stochastic functional-differential equations [See also]60Hxxfunctional-differential: 10: 35R10 Partial functional-differential equationsfunctional-differential: 11: 65L03 Functional-differential equationsfunctional-differential: 12: 93C23 Systems governed by functional-differential equations [See also]34K35
functionals: 1: 03F10 Functionals in proof theoryfunctionals: 2: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),representing set functions and measuresfunctionals: 3: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators[See also]46M10functionals: 4: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J15functionals: 5: 58E15 Application to extremal problems in several variables; Yang-Mills functionals[See also]81T13, etc.functionals: 6: 60J55 Local time and additive functionalsfunctionals: 7: 60J57 Multiplicative functionals
functions: 1: 03D20 Recursive functions and relations, subrecursive hierarchiesfunctions: 2: 03E20 Other classical set theory (including functions, relations, and set algebra)functions: 3: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxxfunctions: 4: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxxfunctions: 5: 05E05 Symmetric functions and generalizationsfunctions: 6: 06E30 Boolean functions [See also]94C10functions: 7: 11A25 Arithmetic functions; related numbers; inversion formulasfunctions: 8: 11B34 Representation functionsfunctions: 9: 11B37 Recurrences For applications to special functions, see 33-XXfunctions: 10: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)functions: 11: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)functions: 12: 11F03 Modular and automorphic functionsfunctions: 13: 11J89 Transcendence theory of elliptic and abelian functions
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functions: 14: 11J91 Transcendence theory of other special functionsfunctions: 15: 11K65 Arithmetic functions [See also]11Nxxfunctions: 16: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesfunctions: 17: 11M35 Hurwitz and Lerch zeta functionsfunctions: 18: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasfunctions: 19: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72functions: 20: 11N37 Asymptotic results on arithmetic functionsfunctions: 21: 11N45 Asymptotic results on counting functions for algebraic and topological structuresfunctions: 22: 11N56 Rate of growth of arithmetic functionsfunctions: 23: 11N60 Distribution functions associated with additive and positive multiplicative functionsfunctions: 24: 11N60 Distribution functions associated with additive and positive multiplicative functionsfunctions: 25: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsfunctions: 26: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxfunctions: 27: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F27functions: 28: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsfunctions: 29: 11S40 Zeta functions and L-functions [See also]11M41, 19F27functions: 30: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxxfunctions: 31: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)functions: 32: 11Y70 Values of arithmetic functions; tablesfunctions: 33: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincare seriesfunctions: 34: 14H05 Algebraic functions; function fields [See also]11R58functions: 35: 14H42 Theta functions; Schottky problem [See also]14K25, 32G20functions: 36: 14K25 Theta functions [See also]14H42functions: 37: 14P20 Nash functions and manifolds [See also]32C07, 58A07functions: 38: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14functions: 39: 15A16 Matrix exponential and similar functions of matricesfunctions: 40: 16S60 Rings of functions, subdirect products, sheaves of ringsfunctions: 41: 26-XX Real functions [See also]54C30functions: 42: 26Axx Functions of one variablefunctions: 43: 26A09 Elementary functionsfunctions: 44: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48functions: 45: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48functions: 46: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05functions: 47: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05functions: 48: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15functions: 49: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativesfunctions: 50: 26A30 Singular functions, Cantor functions, functions with other special propertiesfunctions: 51: 26A30 Singular functions, Cantor functions, functions with other special propertiesfunctions: 52: 26A30 Singular functions, Cantor functions, functions with other special propertiesfunctions: 53: 26A45 Functions of bounded variation, generalizationsfunctions: 54: 26A46 Absolutely continuous functionsfunctions: 55: 26A48 Monotonic functions, generalizationsfunctions: 56: 26Bxx Functions of several variablesfunctions: 57: 26B12 Calculus of vector functionsfunctions: 58: 26B30 Absolutely continuous functions, functions of bounded variationfunctions: 59: 26B30 Absolutely continuous functions, functions of bounded variationfunctions: 60: 26B35 Special properties of functions of several variables, Holder conditions, etc.functions: 61: 26B40 Representation and superposition of functionsfunctions: 62: 26Cxx Polynomials, rational functionsfunctions: 63: 26C15 Rational functions [See also]14Pxx
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functions: 64: 26D05 Inequalities for trigonometric functions and polynomialsfunctions: 65: 26D07 Inequalities involving other types of functionsfunctions: 66: 26E05 Real-analytic functions [See also]32B05, 32C05functions: 67: 26E10 C∞-functions, quasi-analytic functions [See also]58C25functions: 68: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxxfunctions: 69: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxfunctions: 70: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxxfunctions: 71: 28A10 Real- or complex-valued set functionsfunctions: 72: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24functions: 73: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of
convergencefunctions: 74: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of
convergencefunctions: 75: 28A25 Integration with respect to measures and other set functionsfunctions: 76: 28Bxx Set functions, measures and integrals with values in abstract spacesfunctions: 77: 28B05 Vector-valued set functions, measures and integrals [See also]46G10functions: 78: 28B10 Group- or semigroup-valued set functions, measures and integralsfunctions: 79: 28B15 Set functions, measures and integrals with values in ordered spacesfunctions: 80: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B14functions: 81: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B14functions: 82: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20functions: 83: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresfunctions: 84: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05functions: 85: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)functions: 86: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11functions: 87: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXfunctions: 88: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic
functions)functions: 89: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic
functions)functions: 90: 30B60 Completeness problems, closure of a system of functionsfunctions: 91: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10functions: 92: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10functions: 93: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10functions: 94: 30C40 Kernel functions and applicationsfunctions: 95: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)functions: 96: 30C50 Coefficient problems for univalent and multivalent functionsfunctions: 97: 30C55 General theory of univalent and multivalent functionsfunctions: 98: 30Dxx Entire and meromorphic functions, and related topicsfunctions: 99: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXfunctions: 100: 30D10 Representations of entire functions by series and integralsfunctions: 101: 30D15 Special classes of entire functions and growth estimatesfunctions: 102: 30D20 Entire functions, general theoryfunctions: 103: 30D30 Meromorphic functions, general theory
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functions: 104: 30D45 Bloch functions, normal functions, normal familiesfunctions: 105: 30D45 Bloch functions, normal functions, normal familiesfunctions: 106: 30D60 Quasi-analytic and other classes of functionsfunctions: 107: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxfunctions: 108: 30F15 Harmonic functions on Riemann surfacesfunctions: 109: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxxfunctions: 110: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)functions: 111: 30G12 Finely holomorphic functions and topological function theoryfunctions: 112: 30G25 Discrete analytic functionsfunctions: 113: 30G30 Other generalizations of analytic functions (including abstract-valued functions)functions: 114: 30G30 Other generalizations of analytic functions (including abstract-valued functions)functions: 115: 30G35 Functions of hypercomplex variables and generalized variablesfunctions: 116: 30Hxx Spaces and algebras of analytic functionsfunctions: 117: 30H05 Bounded analytic functionsfunctions: 118: 30H50 Algebras of analytic functionsfunctions: 119: 30J05 Inner functionsfunctions: 120: 30J15 Singular inner functionsfunctions: 121: 30Kxx Universal holomorphic functionsfunctions: 122: 30K15 Bounded universal functionsfunctions: 123: 31A05 Harmonic, subharmonic, superharmonic functionsfunctions: 124: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationfunctions: 125: 31B05 Harmonic, subharmonic, superharmonic functionsfunctions: 126: 31B30 Biharmonic and polyharmonic equations and functionsfunctions: 127: 31C05 Harmonic, subharmonic, superharmonic functionsfunctions: 128: 31C10 Pluriharmonic and plurisubharmonic functions [See also]32U05functions: 129: 32Axx Holomorphic functions of several complex variablesfunctions: 130: 32A05 Power series, series of functionsfunctions: 131: 32A10 Holomorphic functionsfunctions: 132: 32A15 Entire functionsfunctions: 133: 32A17 Special families of functionsfunctions: 134: 32A18 Bloch functions, normal functionsfunctions: 135: 32A18 Bloch functions, normal functionsfunctions: 136: 32A19 Normal families of functions, mappingsfunctions: 137: 32A20 Meromorphic functionsfunctions: 138: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35functions: 139: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxfunctions: 140: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J15functions: 141: 32A40 Boundary behavior of holomorphic functionsfunctions: 142: 32A60 Zero sets of holomorphic functionsfunctions: 143: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P20functions: 144: 32E35 Global boundary behavior of holomorphic functionsfunctions: 145: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25functions: 146: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F35functions: 147: 32N05 General theory of automorphic functions of several complex variablesfunctions: 148: 32N15 Automorphic functions in symmetric domainsfunctions: 149: 32T35 Exhaustion functionsfunctions: 150: 32T40 Peak functionsfunctions: 151: 32U05 Plurisubharmonic functions and generalizations [See also]31C10functions: 152: 32U10 Plurisubharmonic exhaustion functionsfunctions: 153: 32U35 Pluricomplex Green functionsfunctions: 154: 32V10 CR functionsfunctions: 155: 32V25 Extension of functions and other analytic objects from CR manifoldsfunctions: 156: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
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orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
functions: 157: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
functions: 158: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
functions: 159: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
functions: 160: 33Bxx Elementary classical functionsfunctions: 161: 33B10 Exponential and trigonometric functionsfunctions: 162: 33B15 Gamma, beta and polygamma functionsfunctions: 163: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)functions: 164: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)functions: 165: 33B30 Higher logarithm functionsfunctions: 166: 33Cxx Hypergeometric functionsfunctions: 167: 33C05 Classical hypergeometric functions, 2F1
functions: 168: 33C10 Bessel and Airy functions, cylinder functions, 0F1
functions: 169: 33C10 Bessel and Airy functions, cylinder functions, 0F1
functions: 170: 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
functions: 171: 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
functions: 172: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
functions: 173: 33C47 Other special orthogonal polynomials and functionsfunctions: 174: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablefunctions: 175: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablefunctions: 176: 33C52 Orthogonal polynomials and functions associated with root systemsfunctions: 177: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)functions: 178: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)functions: 179: 33C65 Appell, Horn and Lauricella functionsfunctions: 180: 33C67 Hypergeometric functions associated with root systemsfunctions: 181: 33C70 Other hypergeometric functions and integrals in several variablesfunctions: 182: 33C75 Elliptic integrals as hypergeometric functionsfunctions: 183: 33Dxx Basic hypergeometric functionsfunctions: 184: 33D05 q-gamma functions, q-beta functions and integralsfunctions: 185: 33D15 Basic hypergeometric functions in one variable, rϕs
functions: 186: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)functions: 187: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variablefunctions: 188: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variablefunctions: 189: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)functions: 190: 33D60 Basic hypergeometric integrals and functions defined by themfunctions: 191: 33D65 Bibasic functions and multiple basesfunctions: 192: 33D67 Basic hypergeometric functions associated with root systemsfunctions: 193: 33D70 Other basic hypergeometric functions and integrals in several variablesfunctions: 194: 33Exx Other special functionsfunctions: 195: 33E05 Elliptic functions and integralsfunctions: 196: 33E10 Lame, Mathieu, and spheroidal wave functionsfunctions: 197: 33E12 Mittag-Leffler functions and generalizations
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functions: 198: 33E15 Other wave functionsfunctions: 199: 33E17 Painleve-type functionsfunctions: 200: 33E20 Other functions defined by series and integralsfunctions: 201: 33E30 Other functions coming from differential, difference and integral equationsfunctions: 202: 33E50 Special functions in characteristic p (gamma functions, etc.)functions: 203: 33E50 Special functions in characteristic p (gamma functions, etc.)functions: 204: 34B27 Green functionsfunctions: 205: 35J08 Green’s functionsfunctions: 206: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxfunctions: 207: 37B25 Lyapunov functions and stability; attractors, repellersfunctions: 208: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemsfunctions: 209: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04functions: 210: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70functions: 211: 37L45 Hyperbolicity; Lyapunov functionsfunctions: 212: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40functions: 213: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40functions: 214: 39B22 Equations for real functions [See also]26A51, 26B25functions: 215: 39B32 Equations for complex functions [See also]30D05functions: 216: 39B52 Equations for functions with more general domains and/or rangesfunctions: 217: 40A30 Convergence and divergence of series and sequences of functionsfunctions: 218: 41A20 Approximation by rational functionsfunctions: 219: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30functions: 220: 42A50 Conjugate functions, conjugate series, singular integralsfunctions: 221: 42A55 Lacunary series of trigonometric and other functions; Riesz productsfunctions: 222: 42A65 Completeness of sets of functionsfunctions: 223: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60functions: 224: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60functions: 225: 42A82 Positive definite functionsfunctions: 226: 42B25 Maximal functions, Littlewood-Paley theoryfunctions: 227: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45functions: 228: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)functions: 229: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)functions: 230: 42C30 Completeness of sets of functionsfunctions: 231: 43A35 Positive definite functions on groups, semigroups, etc.functions: 232: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsfunctions: 233: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsfunctions: 234: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsfunctions: 235: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsfunctions: 236: 43A90 Spherical functions [See also]22E45, 22E46, 33C55functions: 237: 44A20 Transforms of special functionsfunctions: 238: 46E05 Lattices of continuous, differentiable or analytic functionsfunctions: 239: 46E10 Topological linear spaces of continuous, differentiable or analytic functionsfunctions: 240: 46E15 Banach spaces of continuous, differentiable or analytic functionsfunctions: 241: 46E20 Hilbert spaces of continuous, differentiable or analytic functionsfunctions: 242: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15functions: 243: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
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Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)functions: 244: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremsfunctions: 245: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesfunctions: 246: 46E40 Spaces of vector- and operator-valued functionsfunctions: 247: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60functions: 248: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T30functions: 249: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E35functions: 250: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40functions: 251: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)functions: 252: 46J10 Banach algebras of continuous functions, function algebras [See also]46E25functions: 253: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30functions: 254: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxfunctions: 255: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.functions: 256: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)functions: 257: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)functions: 258: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10functions: 259: 52A41 Convex functions and convex programs [See also]26B25, 90C25functions: 260: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80functions: 261: 54C30 Real-valued functions [See also]26-XXfunctions: 262: 54C50 Special sets defined by functions [See also]26A21functions: 263: 58C05 Real-valued functionsfunctions: 264: 58K05 Critical points of functions and mappingsfunctions: 265: 60E10 Characteristic functions; other transformsfunctions: 266: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D07functions: 267: 62G30 Order statistics; empirical distribution functionsfunctions: 268: 65D20 Computation of special functions, construction of tables [See also]33F05functions: 269: 65F60 Matrix exponential and similar matrix functionsfunctions: 270: 74A20 Theory of constitutive functionsfunctions: 271: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)functions: 272: 93D30 Scalar and vector Lyapunov functionsfunctions: 273: 94A11 Application of orthogonal and other special functionsfunctions: 274: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30functions: 275: 97I20 Mappings and functionsfunctions: 276: 97I60 Functions of several variablesfunctions: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsfunctor: 1: 18A25 Functor categories, comma categories
functors: 1: 13D07 Homological functors on modules (Tor, Ext, etc.)functors: 2: 16E30 Homological functors on modules (Tor, Ext, etc.)functors: 3: 18Axx General theory of categories and functorsfunctors: 4: 18A22 Special properties of functors (faithful, full, etc.)functors: 5: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionsfunctors: 6: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)functors: 7: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxfunctors: 8: 18D25 Strong functors, strong adjunctionsfunctors: 9: 18E25 Derived functors and satellites
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functors: 10: 18F05 Local categories and functorsfunctors: 11: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E25functors: 12: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20functors: 13: 55P65 Homotopy functors
fundamental: 1: 14F35 Homotopy theory; fundamental groups [See also]14H30fundamental: 2: 14H30 Coverings, fundamental group [See also]14E20, 14F35fundamental: 3: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxxfundamental: 4: 35A08 Fundamental solutionsfundamental: 5: 35E05 Fundamental solutionsfundamental: 6: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15fundamental: 7: 57M05 Fundamental group, presentations, free differential calculusfundamental: 8: 65M80 Fundamental solutions, Green’s function methods, etc.fundamental: 9: 65N80 Fundamental solutions, Green’s function methods, etc.fundamental: 10: 81V19 Other fundamental interactionsfundamental: 11: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)fundamentals: 1: 76F02 Fundamentals
further: 1: 97B60 Adult and further educationfuture: 1: 01A67 Future prospectives
fuzziness: 1: 62B86 Fuzziness, sufficiency, and informationfuzziness: 2: 62C86 Decision theory and fuzzinessfuzziness: 3: 62E86 Fuzziness in connection with the topics on distributions in this sectionfuzziness: 4: 62F86 Parametric inference and fuzzinessfuzziness: 5: 62G86 Nonparametric inference and fuzzinessfuzziness: 6: 62H86 Multivariate analysis and fuzzinessfuzziness: 7: 62J86 Fuzziness, and linear inference and regressionfuzziness: 8: 62K86 Fuzziness and design of experimentsfuzziness: 9: 62L86 Fuzziness and sequential methodsfuzziness: 10: 62M86 Inference from stochastic processes and fuzzinessfuzziness: 11: 62N86 Fuzziness, and survival analysis and censored data
fuzzy: 1: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D05fuzzy: 2: 03E72 Fuzzy set theoryfuzzy: 3: 05C72 Fractional graph theory, fuzzy graph theoryfuzzy: 4: 06D72 Fuzzy lattices (soft algebras) and related topicsfuzzy: 5: 08A72 Fuzzy algebraic structuresfuzzy: 6: 15B15 Fuzzy matricesfuzzy: 7: 20N25 Fuzzy groups [See also]03E72fuzzy: 8: 26E50 Fuzzy real analysis [See also]03E72, 28E10fuzzy: 9: 28E10 Fuzzy measure theory [See also]03E72, 26E50, 94D05fuzzy: 10: 34A07 Fuzzy differential equationsfuzzy: 11: 34K36 Fuzzy functional-differential equationsfuzzy: 12: 35R13 Fuzzy partial differential equationsfuzzy: 13: 46S40 Fuzzy functional analysis [See also]03E72fuzzy: 14: 47S40 Fuzzy operator theory [See also]03E72fuzzy: 15: 54A40 Fuzzy topology [See also]03E72fuzzy: 16: 60A86 Fuzzy probabilityfuzzy: 17: 62A86 Fuzzy analysis in statisticsfuzzy: 18: 90C70 Fuzzy programmingfuzzy: 19: 93C42 Fuzzy control systemsfuzzy: 20: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10fuzzy: 21: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10godel: 1: 03F40 Godel numberings and issues of incompleteness
galactic: 1: 85A05 Galactic and stellar dynamicsgalactic: 2: 85A15 Galactic and stellar structure
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gale: 1: 52B35 Gale and other diagramsgalerkin: 1: 37L65 Special approximation methods (nonlinear Galerkin, etc.)galerkin: 2: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodsgalerkin: 3: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsgalerkin: 4: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
galois: 1: 06A15 Galois correspondences, closure operatorsgalois: 2: 11E72 Galois cohomology of linear algebraic groups [See also]20G10galois: 3: 11F80 Galois representationsgalois: 4: 11R32 Galois theorygalois: 5: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10galois: 6: 11R34 Galois cohomology [See also]12Gxx, 19A31galois: 7: 11S20 Galois theorygalois: 8: 11S25 Galois cohomology [See also]12Gxx, 16H05galois: 9: 12F10 Separable extensions, Galois theorygalois: 10: 12F12 Inverse Galois theorygalois: 11: 12G05 Galois cohomology [See also]14F22, 16Hxx, 16K50galois: 12: 13B05 Galois theorygalois: 13: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)galois: 14: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)galois: 15: 51E22 Linear codes and caps in Galois spaces [See also]94B05
galton-watson: 1: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)gambling: 1: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60gambling: 2: 91A60 Probabilistic games; gambling [See also]60G40
game: 1: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencesgame: 2: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35game: 3: 91-XX Game theory, economics, social and behavioral sciencesgame: 4: 91Axx Game theorygame: 5: 91A80 Applications of game theory
game-theoretic: 1: 91A40 Game-theoretic modelsgames: 1: 05C57 Games on graphs [See also]91A43, 91A46games: 2: 49N70 Differential gamesgames: 3: 49N75 Pursuit and evasion gamesgames: 4: 49N90 Applications of optimal control and differential games [See also]90C90, 93C95games: 5: 91A05 2-person gamesgames: 6: 91A10 Noncooperative gamesgames: 7: 91A12 Cooperative gamesgames: 8: 91A13 Games with infinitely many playersgames: 9: 91A15 Stochastic gamesgames: 10: 91A18 Games in extensive formgames: 11: 91A20 Multistage and repeated gamesgames: 12: 91A22 Evolutionary gamesgames: 13: 91A23 Differential games [See also]49N70games: 14: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N75games: 15: 91A25 Dynamic gamesgames: 16: 91A30 Utility theory for games [See also]91B16games: 17: 91A35 Decision theory for games [See also]62Cxx, 91B06, 90B50games: 18: 91A43 Games involving graphs [See also]05C57games: 19: 91A44 Games involving topology or set theorygames: 20: 91A46 Combinatorial gamesgames: 21: 91A50 Discrete-time gamesgames: 22: 91A55 Games of timinggames: 23: 91A60 Probabilistic games; gambling [See also]60G40games: 24: 91A65 Hierarchical gamesgames: 25: 91A70 Spaces of gamesgames: 26: 97A20 Recreational mathematics, games [See also]00A08
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gamma: 1: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)gamma: 2: 33B15 Gamma, beta and polygamma functionsgamma: 3: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)gamma: 4: 33E50 Special functions in characteristic p (gamma functions, etc.)
gap: 1: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxxgaps: 1: 11B05 Density, gaps, topologygas: 1: 76Nxx Compressible fluids and gas dynamics, generalgas: 2: 76N15 Gas dynamics, generalgas: 3: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05gas: 4: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05gas: 5: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10gas: 6: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10
gases: 1: 82B40 Kinetic theory of gasesgases: 2: 82C40 Kinetic theory of gasesgases: 3: 82D05 Gases
gateaux: 1: 49J50 Frechet and Gateaux differentiability [See also]46G05, 58C20gateaux: 2: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G05
gauge: 1: 70S15 Yang-Mills and other gauge theoriesgauge: 2: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E15gauss: 1: 11L05 Gauss and Kloosterman sums; generalizationsgauss: 2: 11T24 Other character sums and Gauss sumsgauss: 3: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)
gaussian: 1: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wienermeasure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11
gaussian: 2: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) onmanifolds [See also]28Cxx, 46G12, 60-XX
gaussian: 3: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12gaussian: 4: 60G15 Gaussian processes
gel′: 1: 11J85 Algebraic independence; Gel′fond’s methodgelfand-fuks: 1: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10gelfand-fuks: 2: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32gelfand-kirillov: 1: 16P90 Growth rate, Gelfand-Kirillov dimension
genera: 1: 58J26 Elliptic generageneral: 1: 00-XX Generalgeneral: 2: 00Axx General and miscellaneous specific topicsgeneral: 3: 00A05 General mathematicsgeneral: 4: 00A20 Dictionaries and other general reference worksgeneral: 5: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86general: 6: 00A72 General methods of simulationgeneral: 7: 00B10 Collections of articles of general interestgeneral: 8: 00B20 Proceedings of conferences of general interestgeneral: 9: 01A05 General histories, source booksgeneral: 10: 01A07 Ethnomathematics, generalgeneral: 11: 03Bxx General logicgeneral: 12: 03F03 Proof theory, generalgeneral: 13: 06A06 Partial order, generalgeneral: 14: 08-XX General algebraic systemsgeneral: 15: 11E04 Quadratic forms over general fieldsgeneral: 16: 11E16 General binary quadratic formsgeneral: 17: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesgeneral: 18: 11J81 Transcendence (general theory)general: 19: 11K06 General theory of distribution modulo 1 [See also]11J71general: 20: 11L03 Trigonometric and exponential sums, generalgeneral: 21: 12Exx General field theorygeneral: 22: 12J20 General valuation theory [See also]13A18
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general: 23: 13Axx General commutative ring theorygeneral: 24: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxgeneral: 25: 14J29 Surfaces of general typegeneral: 26: 16Bxx General and miscellaneousgeneral: 27: 16D10 General module theorygeneral: 28: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxgeneral: 29: 16K40 Infinite-dimensional and generalgeneral: 30: 16N80 General radicals and rings For radicals in module categories, see 16S90general: 31: 16S40 Smash products of general Hopf actions [See also]16T05general: 32: 17Axx General nonassociative ringsgeneral: 33: 17A01 General theorygeneral: 34: 18Axx General theory of categories and functorsgeneral: 35: 20B05 General theory for finite groupsgeneral: 36: 20B07 General theory for infinite groupsgeneral: 37: 20E34 General structure theoremsgeneral: 38: 20M10 General structure theorygeneral: 39: 22A05 Structure of general topological groupsgeneral: 40: 22A10 Analysis on general topological groupsgeneral: 41: 22A25 Representations of general topological groups and semigroupsgeneral: 42: 22B05 General properties and structure of LCA groupsgeneral: 43: 22D05 General properties and structure of locally compact groupsgeneral: 44: 22E10 General properties and structure of complex Lie groups [See also]32M05general: 45: 22E15 General properties and structure of real Lie groupsgeneral: 46: 22E20 General properties and structure of other Lie groupsgeneral: 47: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05general: 48: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20general: 49: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40general: 50: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15general: 51: 28D15 General groups of measure-preserving transformationsgeneral: 52: 30Axx General propertiesgeneral: 53: 30C35 General theory of conformal mappingsgeneral: 54: 30C55 General theory of univalent and multivalent functionsgeneral: 55: 30D20 Entire functions, general theorygeneral: 56: 30D30 Meromorphic functions, general theorygeneral: 57: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30general: 58: 32N05 General theory of automorphic functions of several complex variablesgeneral: 59: 32U15 General pluripotential theorygeneral: 60: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsgeneral: 61: 34Axx General theorygeneral: 62: 34A30 Linear equations and systems, generalgeneral: 63: 34A34 Nonlinear equations and systems, generalgeneral: 64: 34E15 Singular perturbations, general theorygeneral: 65: 34K05 General theorygeneral: 66: 34L05 General spectral theorygeneral: 67: 35Axx General topicsgeneral: 68: 35E20 General theorygeneral: 69: 35Fxx General first-order equations and systemsgeneral: 70: 35Gxx General higher-order equations and systemsgeneral: 71: 35P05 General topics in linear spectral theory
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general: 72: 37A15 General groups of measure-preserving transformations [See mainly]22Fxxgeneral: 73: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxxgeneral: 74: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxgeneral: 75: 37J05 General theory, relations with symplectic geometry and topologygeneral: 76: 37L05 General theory, nonlinear semigroups, evolution equationsgeneral: 77: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)general: 78: 37P55 Arithmetic dynamics on general algebraic varietiesgeneral: 79: 39A05 General theorygeneral: 80: 39B05 Generalgeneral: 81: 39B52 Equations for functions with more general domains and/or rangesgeneral: 82: 40Cxx General summability methodsgeneral: 83: 40D05 General theoremsgeneral: 84: 40E05 Tauberian theorems, generalgeneral: 85: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45general: 86: 42C15 General harmonic expansions, framesgeneral: 87: 43A77 Analysis on general compact groupsgeneral: 88: 44A05 General transforms [See also]42A38general: 89: 46A03 General theory of locally convex spacesgeneral: 90: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)general: 91: 46B25 Classical Banach spaces in the general theorygeneral: 92: 46H05 General theory of topological algebrasgeneral: 93: 46J05 General theory of commutative topological algebrasgeneral: 94: 46K05 General theory of topological algebras with involutiongeneral: 95: 46L05 General theory of C∗-algebrasgeneral: 96: 46L10 General theory of von Neumann algebrasgeneral: 97: 47Axx General theory of linear operatorsgeneral: 98: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)general: 99: 47B38 Operators on function spaces (general)general: 100: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J25general: 101: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J40general: 102: 51A05 General theory and projective geometriesgeneral: 103: 51B05 General theorygeneral: 104: 51E05 General block designs [See also]05B05general: 105: 51E14 Finite partial geometries (general), nets, partial spreadsgeneral: 106: 51H05 General theorygeneral: 107: 51J05 General theorygeneral: 108: 51K05 General theorygeneral: 109: 51M05 Euclidean geometries (general) and generalizationsgeneral: 110: 51M10 Hyperbolic and elliptic geometries (general) and generalizationsgeneral: 111: 52Axx General convexitygeneral: 112: 53C05 Connections, general theorygeneral: 113: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)general: 114: 53D05 Symplectic manifolds, generalgeneral: 115: 53D10 Contact manifolds, generalgeneral: 116: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxgeneral: 117: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)general: 118: 54Cxx Maps and general types of spaces defined by mapsgeneral: 119: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15general: 120: 54Dxx Fairly general propertiesgeneral: 121: 54D05 Connected and locally connected spaces (general aspects)general: 122: 55Q05 Homotopy groups, general; sets of homotopy classesgeneral: 123: 55T05 General
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general: 124: 57N10 Topology of general 3-manifolds [See also]57Mxxgeneral: 125: 57N75 General position and transversalitygeneral: 126: 57Q05 General topology of complexesgeneral: 127: 57Q65 General position and transversalitygeneral: 128: 58Axx General theory of differentiable manifolds [See also]32Cxxgeneral: 129: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldsgeneral: 130: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXgeneral: 131: 60A05 Axioms; other general questionsgeneral: 132: 60E05 Distributions: general theorygeneral: 133: 60G07 General theory of processesgeneral: 134: 60G12 General second-order processesgeneral: 135: 60J05 Discrete-time Markov processes on general state spacesgeneral: 136: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40general: 137: 60J25 Continuous-time Markov processes on general state spacesgeneral: 138: 62C05 General considerationsgeneral: 139: 62J02 General nonlinear regressiongeneral: 140: 65G40 General methods in interval analysisgeneral: 141: 65J05 General theorygeneral: 142: 68M01 Generalgeneral: 143: 68N01 Generalgeneral: 144: 68P01 Generalgeneral: 145: 68Q01 Generalgeneral: 146: 68R01 Generalgeneral: 147: 68T01 Generalgeneral: 148: 68U01 Generalgeneral: 149: 68W01 Generalgeneral: 150: 70Gxx General models, approaches, and methods [See also]37-XXgeneral: 151: 70K60 General perturbation schemesgeneral: 152: 70S20 More general nonquantum field theoriesgeneral: 153: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXgeneral: 154: 76Gxx General aerodynamics and subsonic flowsgeneral: 155: 76G25 General aerodynamics and subsonic flowsgeneral: 156: 76Nxx Compressible fluids and gas dynamics, generalgeneral: 157: 76N15 Gas dynamics, generalgeneral: 158: 78Axx Generalgeneral: 159: 78A25 Electromagnetic theory, generalgeneral: 160: 80A50 Chemistry (general) [See mainly]92Exxgeneral: 161: 81P05 General and philosophicalgeneral: 162: 81P70 Quantum coding (general)general: 163: 81Qxx General mathematical topics and methods in quantum theorygeneral: 164: 81Sxx General quantum mechanics and problems of quantizationgeneral: 165: 82B05 Classical equilibrium statistical mechanics (general)general: 166: 82B10 Quantum equilibrium statistical mechanics (general)general: 167: 82B26 Phase transitions (general)general: 168: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)general: 169: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)general: 170: 82C26 Dynamic and nonequilibrium phase transitions (general)general: 171: 83Cxx General relativitygeneral: 172: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)general: 173: 85A04 Generalgeneral: 174: 86A04 Generalgeneral: 175: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)general: 176: 91B50 General equilibrium theorygeneral: 177: 91B51 Dynamic stochastic general equilibrium theorygeneral: 178: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XX
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general: 179: 92Bxx Mathematical biology in generalgeneral: 180: 92B05 General biology and biomathematicsgeneral: 181: 92B15 General biostatistics [See also]62P10general: 182: 92C30 Physiology (general)general: 183: 92C50 Medical applications (general)general: 184: 92D25 Population dynamics (general)general: 185: 93Axx Generalgeneral: 186: 93A10 General systemsgeneral: 187: 93E03 Stochastic systems, generalgeneral: 188: 94A15 Information theory, general [See also]62B10, 81P45general: 189: 94B05 Linear codes, generalgeneral: 190: 97Axx General, mathematics and educationgeneral: 191: 97B20 General education
generalities: 1: 54Axx Generalitiesgeneralities: 2: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
generalizations: 1: 05E05 Symmetric functions and generalizationsgeneralizations: 2: 06A75 Generalizations of ordered setsgeneralizations: 3: 06B75 Generalizations of latticesgeneralizations: 4: 06D75 Other generalizations of distributive latticesgeneralizations: 5: 06E75 Generalizations of Boolean algebrasgeneralizations: 6: 11B39 Fibonacci and Lucas numbers and polynomials and generalizationsgeneralizations: 7: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E40generalizations: 8: 11J06 Markov and Lagrange spectra and generalizationsgeneralizations: 9: 11J54 Small fractional parts of polynomials and generalizationsgeneralizations: 10: 11J70 Continued fractions and generalizations [See also]11A55, 11K50generalizations: 11: 11L05 Gauss and Kloosterman sums; generalizationsgeneralizations: 12: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measuregeneralizations: 13: 12Kxx Generalizations of fieldsgeneralizations: 14: 13A18 Valuations and their generalizations [See also]12J20generalizations: 15: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizationsgeneralizations: 16: 13F07 Euclidean rings and generalizationsgeneralizations: 17: 14A20 Generalizations (algebraic spaces, stacks)generalizations: 18: 14E07 Birational automorphisms, Cremona group and generalizationsgeneralizations: 19: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T15generalizations: 20: 15B48 Positive matrices and their generalizations; cones of matricesgeneralizations: 21: 16E50 von Neumann regular rings and generalizationsgeneralizations: 22: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)generalizations: 23: 16Lxx Local rings and generalizationsgeneralizations: 24: 16U80 Generalizations of commutativitygeneralizations: 25: 16Yxx Generalizations For nonassociative rings, see 17-XXgeneralizations: 26: 18A05 Definitions, generalizationsgeneralizations: 27: 18C30 Sketches and generalizationsgeneralizations: 28: 18D05 Double categories, 2-categories, bicategories and generalizationsgeneralizations: 29: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U25generalizations: 30: 20-XX Group theory and generalizationsgeneralizations: 31: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsgeneralizations: 32: 20E26 Residual properties and generalizations; residually finite groupsgeneralizations: 33: 20F14 Derived series, central series, and generalizationsgeneralizations: 34: 20F19 Generalizations of solvable and nilpotent groupsgeneralizations: 35: 20F24 FC-groups and their generalizationsgeneralizations: 36: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxxgeneralizations: 37: 20Nxx Other generalizations of groupsgeneralizations: 38: 26A03 Foundations: limits and generalizations, elementary topology of the linegeneralizations: 39: 26A45 Functions of bounded variation, generalizations
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generalizations: 40: 26A48 Monotonic functions, generalizationsgeneralizations: 41: 26A51 Convexity, generalizationsgeneralizations: 42: 26B25 Convexity, generalizationsgeneralizations: 43: 30C65 Quasiconformal mappings in Rn, other generalizationsgeneralizations: 44: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
subordinationgeneralizations: 45: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)generalizations: 46: 30G30 Other generalizations of analytic functions (including abstract-valued functions)generalizations: 47: 31Cxx Other generalizationsgeneralizations: 48: 31C45 Other generalizations (nonlinear potential theory, etc.)generalizations: 49: 32A30 Other generalizations of function theory of one complex variable (should also be
assigned at least one classification number from Section 30) For functions of several hypercomplex variables, see30G35
generalizations: 50: 32B05 Analytic algebras and generalizations, preparation theoremsgeneralizations: 51: 32C55 The Levi problem in complex spaces; generalizationsgeneralizations: 52: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see 32A22generalizations: 53: 32J27 Compact Kahler manifolds: generalizations, classificationgeneralizations: 54: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)generalizations: 55: 32L05 Holomorphic bundles and generalizationsgeneralizations: 56: 32U05 Plurisubharmonic functions and generalizations [See also]31C10generalizations: 57: 32U20 Capacity theory and generalizationsgeneralizations: 58: 32V05 CR structures, CR operators, and generalizationsgeneralizations: 59: 33E12 Mittag-Leffler functions and generalizationsgeneralizations: 60: 34B20 Weyl theory and its generalizationsgeneralizations: 61: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J10generalizations: 62: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40generalizations: 63: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsgeneralizations: 64: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxgeneralizations: 65: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)generalizations: 66: 47B36 Jacobi (tridiagonal) operators (matrices) and generalizationsgeneralizations: 67: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationsgeneralizations: 68: 47H05 Monotone operators and generalizationsgeneralizations: 69: 51M05 Euclidean geometries (general) and generalizationsgeneralizations: 70: 51M10 Hyperbolic and elliptic geometries (general) and generalizationsgeneralizations: 71: 51M30 Line geometries and their generalizations [See also]53A25generalizations: 72: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15generalizations: 73: 53B40 Finsler spaces and generalizations (areal metrics)generalizations: 74: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B20generalizations: 75: 54A05 Topological spaces and generalizations (closure spaces, etc.)generalizations: 76: 54E05 Proximity structures and generalizationsgeneralizations: 77: 54E15 Uniform structures and generalizationsgeneralizations: 78: 54F15 Continua and generalizationsgeneralizations: 79: 55Q15 Whitehead products and generalizationsgeneralizations: 80: 55R65 Generalizations of fiber spaces and bundlesgeneralizations: 81: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D05generalizations: 82: 60G48 Generalizations of martingalesgeneralizations: 83: 70E45 Higher-dimensional generalizations
generalized: 1: 05C55 Generalized Ramsey theory [See also]05D10generalized: 2: 11N80 Generalized primes and integersgeneralized: 3: 15A09 Matrix inversion, generalized inverses
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Mathematics Subject Classification 2010
generalized: 4: 16R50 Other kinds of identities (generalized polynomial, rational, involution)generalized: 5: 19F05 Generalized class field theory [See also]11G45generalized: 6: 20K10 Torsion groups, primary groups and generalized primary groupsgeneralized: 7: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also]28A15
generalized: 8: 30Gxx Generalized function theorygeneralized: 9: 30G35 Functions of hypercomplex variables and generalized variablesgeneralized: 10: 33C20 Generalized hypergeometric series, pFq
generalized: 11: 35Dxx Generalized solutionsgeneralized: 12: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typegeneralized: 13: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T30generalized: 14: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)generalized: 15: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxgeneralized: 16: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spacesgeneralized: 17: 51E12 Generalized quadrangles, generalized polygonsgeneralized: 18: 51E12 Generalized quadrangles, generalized polygonsgeneralized: 19: 52A01 Axiomatic and generalized convexitygeneralized: 20: 53D18 Generalized geometries (a la Hitchin)generalized: 21: 54C08 Weak and generalized continuitygeneralized: 22: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially orderedspaces [See also]06B30, 06F30
generalized: 23: 55N20 Generalized (extraordinary) homology and cohomology theoriesgeneralized: 24: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxxgeneralized: 25: 55T25 Generalized cohomologygeneralized: 26: 57Pxx Generalized manifolds [See also]18F15generalized: 27: 57P05 Local properties of generalized manifoldsgeneralized: 28: 60G20 Generalized stochastic processesgeneralized: 29: 62J12 Generalized linear modelsgeneralized: 30: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spacegeneralized: 31: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52
generated: 1: 47L45 Dual algebras; weakly closed singly generated operator algebrasgenerating: 1: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxxgeneration: 1: 13E15 Rings and modules of finite generation or presentation; number of generatorsgeneration: 2: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)generation: 3: 19A15 Efficient generationgeneration: 4: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,34K50, 60H10, 60H15generation: 5: 65C10 Random number generationgeneration: 6: 65L50 Mesh generation and refinementgeneration: 7: 65M50 Mesh generation and refinementgeneration: 8: 65N50 Mesh generation and refinementgenerators: 1: 13E15 Rings and modules of finite generation or presentation; number of generatorsgenerators: 2: 20F05 Generators, relations, and presentationsgenerators: 3: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,20F10generators: 4: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D07
generic: 1: 03E57 Generic absoluteness and forcing axioms [See also]03E50generic: 2: 37C20 Generic properties, structural stabilitygenetic: 1: 17D92 Genetic algebrasgenetic: 2: 92D10 Genetics For genetic algebras, see 17D92
genetics: 1: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorptionproblems, etc.) [See also]92Dxx
genetics: 2: 92Dxx Genetics and population dynamicsgenetics: 3: 92D10 Genetics For genetic algebras, see 17D92
genus: 1: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25genus: 2: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25genus: 3: 14H45 Special curves and curves of low genus
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Mathematics Subject Classification 2010
geo-electricity: 1: 86A25 Geo-electricity and geomagnetism [See also]76W05, 78A25geodesic: 1: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
etc.)geodesic: 2: 53D25 Geodesic flows
geodesics: 1: 53C22 Geodesics [See also]58E10geodesics: 2: 58E10 Applications to the theory of geodesics (problems in one independent variable)
geodesy: 1: 86A30 Geodesy, mapping problemsgeography: 1: 91D20 Mathematical geography and demographygeological: 1: 86A60 Geological problems
geomagnetism: 1: 86A25 Geo-electricity and geomagnetism [See also]76W05, 78A25geometric: 1: 05B35 Matroids, geometric lattices [See also]52B40, 90C27geometric: 2: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
57M25geometric: 3: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10geometric: 4: 06C10 Semimodular lattices, geometric latticesgeometric: 5: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F05geometric: 6: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E57geometric: 7: 14L24 Geometric invariant theory [See also]13A50geometric: 8: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N30geometric: 9: 14L40 Other algebraic groups (geometric aspects)geometric: 10: 19L64 Computations, geometric applicationsgeometric: 11: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXgeometric: 12: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxxgeometric: 13: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55geometric: 14: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25geometric: 15: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D24geometric: 16: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15geometric: 17: 30Cxx Geometric function theorygeometric: 18: 30L05 Geometric embeddings of metric spacesgeometric: 19: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30geometric: 20: 32Fxx Geometric convexitygeometric: 21: 32F27 Topological consequences of geometric convexitygeometric: 22: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)geometric: 23: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundariesgeometric: 24: 34A26 Geometric methods in differential equationsgeometric: 25: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J72geometric: 26: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
etc.)geometric: 27: 37F40 Geometric limitsgeometric: 28: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxgeometric: 29: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXgeometric: 30: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C35geometric: 31: 49Q20 Variational problems in a geometric measure-theoretic settinggeometric: 32: 51Dxx Geometric closure systemsgeometric: 33: 51Lxx Geometric order structures [See also]53C75geometric: 34: 51M15 Geometric constructionsgeometric: 35: 52A35 Helly-type theorems and geometric transversal theorygeometric: 36: 52C45 Combinatorial complexity of geometric structures [See also]68U05
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geometric: 37: 53A55 Differential invariants (local theory), geometric objectsgeometric: 38: 53C08 Gerbes, differential characters: differential geometric aspectsgeometric: 39: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R32geometric: 40: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)geometric: 41: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesgeometric: 42: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesgeometric: 43: 53C43 Differential geometric aspects of harmonic maps [See also]58E20geometric: 44: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)geometric: 45: 53C75 Geometric orders, order geometry [See also]51Lxxgeometric: 46: 53D50 Geometric quantizationgeometric: 47: 57M50 Geometric structures on low-dimensional manifoldsgeometric: 48: 57N16 Geometric structures on manifolds [See also]57M50geometric: 49: 57R30 Foliations; geometric theorygeometric: 50: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15geometric: 51: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C60geometric: 52: 58D27 Moduli problems for differential geometric structuresgeometric: 53: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C65geometric: 54: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C65geometric: 55: 78A05 Geometric opticsgeometric: 56: 93B27 Geometric methodsgeometric: 57: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50geometrical: 1: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometricalstructures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40
geometrical: 2: 74P20 Geometrical methodsgeometries: 1: 05B25 Finite geometries [See also]51D20, 51Exxgeometries: 2: 06C20 Complemented modular lattices, continuous geometriesgeometries: 3: 17C37 Associated geometriesgeometries: 4: 51A05 General theory and projective geometriesgeometries: 5: 51A30 Desarguesian and Pappian geometriesgeometries: 6: 51A45 Incidence structures imbeddable into projective geometriesgeometries: 7: 51B10 Mobius geometriesgeometries: 8: 51B15 Laguerre geometriesgeometries: 9: 51B20 Minkowski geometriesgeometries: 10: 51B25 Lie geometriesgeometries: 11: 51D05 Abstract (Maeda) geometriesgeometries: 12: 51D10 Abstract geometries with exchange axiomgeometries: 13: 51D15 Abstract geometries with parallelismgeometries: 14: 51D20 Combinatorial geometries [See also]05B25, 05B35geometries: 15: 51D30 Continuous geometries and related topics [See also]06Cxxgeometries: 16: 51E14 Finite partial geometries (general), nets, partial spreadsgeometries: 17: 51E25 Other finite nonlinear geometriesgeometries: 18: 51E26 Other finite linear geometriesgeometries: 19: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see20F55geometries: 20: 51Gxx Ordered geometries (ordered incidence structures, etc.)geometries: 21: 51G05 Ordered geometries (ordered incidence structures, etc.)geometries: 22: 51H20 Topological geometries on manifolds [See also]57-XXgeometries: 23: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C70geometries: 24: 51H30 Geometries with algebraic manifold structure [See also]14-XXgeometries: 25: 51M04 Elementary problems in Euclidean geometriesgeometries: 26: 51M05 Euclidean geometries (general) and generalizationsgeometries: 27: 51M09 Elementary problems in hyperbolic and elliptic geometries
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Mathematics Subject Classification 2010
geometries: 28: 51M10 Hyperbolic and elliptic geometries (general) and generalizationsgeometries: 29: 51M30 Line geometries and their generalizations [See also]53A25geometries: 30: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,Veronesians and their generalizations) [See also]14M15geometries: 31: 53A40 Other special differential geometriesgeometries: 32: 53C38 Calibrations and calibrated geometriesgeometries: 33: 53D18 Generalized geometries (a la Hitchin)
geometrodynamics: 1: 83E05 Geometrodynamicsgeometry: 1: 11F23 Relations with algebraic geometry and topologygeometry: 2: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxxgeometry: 3: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxxgeometry: 4: 11Hxx Geometry of numbers For applications in coding theory, see 94B75geometry: 5: 11M55 Relations with noncommutative geometrygeometry: 6: 14-XX Algebraic geometrygeometry: 7: 14A22 Noncommutative algebraic geometry [See also]16S38geometry: 8: 14Exx Birational geometrygeometry: 9: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxxgeometry: 10: 14G22 Rigid analytic geometrygeometry: 11: 14Nxx Projective and enumerative geometry [See also]51-XXgeometry: 12: 14Pxx Real algebraic and real analytic geometrygeometry: 13: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W30geometry: 14: 14Rxx Affine geometrygeometry: 15: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B20geometry: 16: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B20geometry: 17: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22geometry: 18: 18Fxx Categories and geometrygeometry: 19: 19Exx K-theory in geometrygeometry: 20: 20F70 Algebraic geometry over groups; equations over groupsgeometry: 21: 32Bxx Local analytic geometry [See also]13-XX and 14-XXgeometry: 22: 32J25 Transcendental methods of algebraic geometry [See also]14C30geometry: 23: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)geometry: 24: 37J05 General theory, relations with symplectic geometry and topologygeometry: 25: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70geometry: 26: 37K25 Relations with differential geometrygeometry: 27: 46B20 Geometry and structure of normed linear spacesgeometry: 28: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)geometry: 29: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J22geometry: 30: 51-XX Geometry For algebraic geometry, see 14-XXgeometry: 31: 51-XX Geometry For algebraic geometry, see 14-XXgeometry: 32: 51Axx Linear incidence geometrygeometry: 33: 51A50 Polar geometry, symplectic spaces, orthogonal spacesgeometry: 34: 51Bxx Nonlinear incidence geometrygeometry: 35: 51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)geometry: 36: 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)geometry: 37: 51Exx Finite geometry and special incidence structuresgeometry: 38: 51E24 Buildings and the geometry of diagramsgeometry: 39: 51Fxx Metric geometrygeometry: 40: 51Hxx Topological geometrygeometry: 41: 51Kxx Distance geometrygeometry: 42: 51K10 Synthetic differential geometrygeometry: 43: 51L05 Geometry of orders of nondifferentiable curvesgeometry: 44: 51L20 Geometry of orders of surfacesgeometry: 45: 51Mxx Real and complex geometrygeometry: 46: 51Nxx Analytic and descriptive geometrygeometry: 47: 51N05 Descriptive geometry [See also]65D17, 68U07
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Mathematics Subject Classification 2010
geometry: 48: 51N10 Affine analytic geometrygeometry: 49: 51N15 Projective analytic geometrygeometry: 50: 51N20 Euclidean analytic geometrygeometry: 51: 51N25 Analytic geometry with other transformation groupsgeometry: 52: 51N30 Geometry of classical groups [See also]20Gxx, 14L35geometry: 53: 51N35 Questions of classical algebraic geometry [See also]14Nxxgeometry: 54: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)geometry: 55: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)geometry: 56: 52-XX Convex and discrete geometrygeometry: 57: 52A22 Random convex sets and integral geometry [See also]53C65, 60D05geometry: 58: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxgeometry: 59: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxgeometry: 60: 52Cxx Discrete geometrygeometry: 61: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxgeometry: 62: 52C26 Circle packings and discrete conformal geometrygeometry: 63: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxgeometry: 64: 53Axx Classical differential geometrygeometry: 65: 53A15 Affine differential geometrygeometry: 66: 53A20 Projective differential geometrygeometry: 67: 53A25 Differential line geometrygeometry: 68: 53A30 Conformal differential geometrygeometry: 69: 53A35 Non-Euclidean differential geometrygeometry: 70: 53A60 Geometry of webs [See also]14C21, 20N05geometry: 71: 53Bxx Local differential geometrygeometry: 72: 53B20 Local Riemannian geometrygeometry: 73: 53B21 Methods of Riemannian geometrygeometry: 74: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxgeometry: 75: 53C17 Sub-Riemannian geometrygeometry: 76: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B20geometry: 77: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60geometry: 78: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometrygeometry: 79: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometrygeometry: 80: 53C27 Spin and Spinc geometrygeometry: 81: 53C56 Other complex differential geometry [See also]32Cxxgeometry: 82: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axxgeometry: 83: 53C75 Geometric orders, order geometry [See also]51Lxxgeometry: 84: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxxgeometry: 85: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxxgeometry: 86: 57R18 Topology and geometry of orbifoldsgeometry: 87: 58B32 Geometry of quantum groupsgeometry: 88: 58B34 Noncommutative geometry (a la Connes)geometry: 89: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxxgeometry: 90: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C65geometry: 91: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C65geometry: 92: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxgeometry: 93: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05geometry: 94: 68U05 Computer graphics; computational geometry [See also]65D18
160 Run: December 14, 2009
Mathematics Subject Classification 2010
geometry: 95: 70G55 Algebraic geometry methodsgeometry: 96: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40geometry: 97: 81R60 Noncommutative geometrygeometry: 98: 81S10 Geometry and quantization, symplectic methods [See also]53D50geometry: 99: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B34geometry: 100: 83C65 Methods of noncommutative geometry [See also]58B34geometry: 101: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50geometry: 102: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71geometry: 103: 97Gxx Geometrygeometry: 104: 97G20 Informal geometrygeometry: 105: 97G40 Plane and solid geometrygeometry: 106: 97G50 Transformation geometrygeometry: 107: 97G70 Analytic geometry. Vector algebrageometry: 108: 97G80 Descriptive geometry
geophysical: 1: 74L05 Geophysical solid mechanics [See also]86-XXgeophysical: 2: 76E20 Stability and instability of geophysical and astrophysical flowsgeophysics: 1: 35Q86 PDEs in connection with geophysicsgeophysics: 2: 86-XX Geophysics [See also]76U05, 76V05geophysics: 3: 86Axx Geophysics [See also]76U05, 76V05
geostatistics: 1: 86A32 Geostatisticsgerbes: 1: 53C08 Gerbes, differential characters: differential geometric aspectsgerms: 1: 32B10 Germs of analytic sets, local parametrizationgerms: 2: 58K40 Classification; finite determinacy of map germs
ginzburg-landau: 1: 35Q56 Ginzburg-Landau equationsgiven: 1: 74Exx Material properties given special treatmentgiven: 2: 74G20 Local existence of solutions (near a given solution)
glaciology: 1: 86A40 Glaciologyglasses: 1: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)global: 1: 11E12 Quadratic forms over global rings and fieldsglobal: 2: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsglobal: 3: 11G05 Elliptic curves over global fields [See also]14H52global: 4: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25global: 5: 11G35 Varieties over global fields [See also]14G25global: 6: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10global: 7: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72global: 8: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15global: 9: 11R70 K-theory of global fields [See also]19Fxxglobal: 10: 13J20 Global topological ringsglobal: 11: 14D10 Arithmetic ground fields (finite, local, global)global: 12: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S45global: 13: 14G25 Global ground fieldsglobal: 14: 20G30 Linear algebraic groups over global fields and their integersglobal: 15: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05global: 16: 32E35 Global boundary behavior of holomorphic functionsglobal: 17: 32S20 Global theory of singularities; cohomological properties [See also]14E15global: 18: 34D23 Global stabilityglobal: 19: 35A01 Existence problems: global existence, local existence, non-existenceglobal: 20: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenessglobal: 21: 37P15 Global ground fieldsglobal: 22: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
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58-XX, especially 58Cxxglobal: 23: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXglobal: 24: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxglobal: 25: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B20global: 26: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesglobal: 27: 53C40 Global submanifolds [See also]53B25global: 28: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)global: 29: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxxglobal: 30: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXglobal: 31: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15global: 32: 58C15 Implicit function theorems; global Newton methodsglobal: 33: 58E35 Variational inequalities (global problems)global: 34: 58J42 Noncommutative global analysis, noncommutative residuesglobal: 35: 58K30 Global theoryglobal: 36: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C30global: 37: 74G25 Global existence of solutionsglobal: 38: 86A17 Global dynamics, earthquake problemsglobal: 39: 90C26 Nonconvex programming, global optimization
goal: 1: 90C29 Multi-objective and goal programminggoals: 1: 97D30 Objectives and goalsgoing: 1: 13B21 Integral dependence; going up, going downgoing: 2: 13B21 Integral dependence; going up, going down
goldbach-type: 1: 11P32 Goldbach-type theorems; other additive questions involving primesgoldie-type: 1: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimension
gonality: 1: 14H51 Special divisors (gonality, Brill-Noether theory)good: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,
etc. [See also]11A63goods: 1: 91B18 Public goods
gopakumar-vafa: 1: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,Donaldson-Thomas invariants [See also]53D45gorenstein: 1: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05gorenstein: 2: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
gosper: 1: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30governed: 1: 93C15 Systems governed by ordinary differential equations [See also]34H05governed: 2: 93C20 Systems governed by partial differential equationsgoverned: 3: 93C23 Systems governed by functional-differential equations [See also]34K35governed: 4: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)grobner: 1: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)graceful: 1: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)graded: 1: 13A02 Graded rings [See also]16W50graded: 2: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsgraded: 3: 16E45 Differential graded algebras and applicationsgraded: 4: 16W50 Graded rings and modulesgraded: 5: 16W70 Filtered rings; filtrational and graded techniquesgraded: 6: 17B70 Graded Lie (super)algebrasgraded: 7: 32K07 Formal and graded complex spaces [See also]58C50graded: 8: 46A61 Graded Frechet spaces and tame operatorsgraded: 9: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
162 Run: December 14, 2009
Mathematics Subject Classification 2010
and 58C50graded: 10: 58A50 Supermanifolds and graded manifolds [See also]14A22, 32C11graded: 11: 58C50 Analysis on supermanifolds or graded manifolds
gradient: 1: 90C52 Methods of reduced gradient typegradient-like: 1: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets
grammars: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,68Q70, 68R15grammars: 2: 68Q42 Grammars and rewriting systems
granular: 1: 76T25 Granular flows [See also]74C99, 74E20granularity: 1: 74E20 Granularity
graph: 1: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30graph: 2: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C15graph: 3: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
57M25graph: 4: 05C30 Enumeration in graph theorygraph: 5: 05C31 Graph polynomialsgraph: 6: 05C51 Graph designs and isomomorphic decomposition [See also]05B30graph: 7: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10graph: 8: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10graph: 9: 05C72 Fractional graph theory, fuzzy graph theorygraph: 10: 05C72 Fractional graph theory, fuzzy graph theorygraph: 11: 05C76 Graph operations (line graphs, products, etc.)graph: 12: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)graph: 13: 05C83 Graph minorsgraph: 14: 05C85 Graph algorithms [See also]68R10, 68W05graph: 15: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)graph: 16: 57M15 Relations with graph theory [See also]05Cxxgraph: 17: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C35graph: 18: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C35graph: 19: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxgraph: 20: 94C15 Applications of graph theory [See also]05Cxx, 68R10graph: 21: 97Kxx Combinatorics, graph theory, probability theory, statisticsgraph: 22: 97K30 Graph theory
graph-theoretic: 1: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)graphical: 1: 65Sxx Graphical methodsgraphical: 2: 65S05 Graphical methodsgraphics: 1: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05graphics: 2: 68U05 Computer graphics; computational geometry [See also]65D18graphics: 3: 97R60 Computer graphics
graphs: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,90C35, 92E10, 94C15
graphs: 2: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,57M25
graphs: 3: 05C12 Distance in graphsgraphs: 4: 05C15 Coloring of graphs and hypergraphsgraphs: 5: 05C17 Perfect graphsgraphs: 6: 05C20 Directed graphs (digraphs), tournamentsgraphs: 7: 05C21 Flows in graphsgraphs: 8: 05C22 Signed and weighted graphsgraphs: 9: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65graphs: 10: 05C45 Eulerian and Hamiltonian graphs
163 Run: December 14, 2009
Mathematics Subject Classification 2010
graphs: 11: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)graphs: 12: 05C57 Games on graphs [See also]91A43, 91A46graphs: 13: 05C63 Infinite graphsgraphs: 14: 05C75 Structural characterization of families of graphsgraphs: 15: 05C76 Graph operations (line graphs, products, etc.)graphs: 16: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)graphs: 17: 05C80 Random graphs [See also]60B20graphs: 18: 05C81 Random walks on graphsgraphs: 19: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D30graphs: 20: 05E30 Association schemes, strongly regular graphsgraphs: 21: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]graphs: 22: 34B45 Boundary value problems on graphs and networksgraphs: 23: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)graphs: 24: 37E25 Maps of trees and graphsgraphs: 25: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40graphs: 26: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.graphs: 27: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphsgraphs: 28: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphsgraphs: 29: 90C35 Programming involving graphs or networks [See also]90C27graphs: 30: 91A43 Games involving graphs [See also]05C57
grassmann: 1: 15A75 Exterior algebra, Grassmann algebrasgrassmannians: 1: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M35grassmannians: 2: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15gravitational: 1: 35Q75 PDEs in connection with relativity and gravitational theorygravitational: 2: 81V17 Gravitational interaction [See also]83Cxx and 83Exxgravitational: 3: 83-XX Relativity and gravitational theorygravitational: 4: 83C35 Gravitational wavesgravitational: 5: 83C40 Gravitational energy and conservation laws; groups of motionsgravitational: 6: 83C45 Quantization of the gravitational fieldgravitational: 7: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)gravitational: 8: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesgravitational: 9: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesgravity: 1: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30gravity: 2: 83C27 Lattice gravity, Regge calculus and other discrete methods
greatest: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsgreek: 1: 01A20 Greek, Romangreen: 1: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)green: 2: 32U35 Pluricomplex Green functionsgreen: 3: 34B27 Green functionsgreen: 4: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40
green’s: 1: 35J08 Green’s functionsgreen’s: 2: 65M80 Fundamental solutions, Green’s function methods, etc.green’s: 3: 65N80 Fundamental solutions, Green’s function methods, etc.gromov: 1: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesgromov-witten: 1: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D45gromov-witten: 2: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35
grothendieck: 1: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D50grothendieck: 2: 14F20 Etale and other Grothendieck topologies and (co)homologiesgrothendieck: 3: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D50grothendieck: 4: 18E15 Grothendieck categories
164 Run: December 14, 2009
Mathematics Subject Classification 2010
grothendieck: 5: 18F10 Grothendieck topologies [See also]14F20grothendieck: 6: 18F30 Grothendieck groups [See also]13D15, 16E20, 19Axxgrothendieck: 7: 19Axx Grothendieck groups and K0 [See also]13D15, 18F30
ground: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72
ground: 2: 14D10 Arithmetic ground fields (finite, local, global)ground: 3: 14G15 Finite ground fieldsground: 4: 14G17 Positive characteristic ground fieldsground: 5: 14G20 Local ground fieldsground: 6: 14G25 Global ground fieldsground: 7: 14G27 Other nonalgebraically closed ground fieldsground: 8: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxxground: 9: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxxground: 10: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxxground: 11: 37P15 Global ground fieldsground: 12: 37P20 Non-Archimedean local ground fieldsground: 13: 37P25 Finite ground fieldsgroup: 1: 05E18 Group actions on combinatorial structuresgroup: 2: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesgroup: 3: 14E07 Birational automorphisms, Cremona group and generalizationsgroup: 4: 14H30 Coverings, fundamental group [See also]14E20, 14F35group: 5: 14L10 Group varietiesgroup: 6: 14L15 Group schemesgroup: 7: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17group: 8: 14R20 Group actions on affine varieties [See also]13A50, 14L30group: 9: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial ringsgroup: 10: 16S35 Twisted and skew group rings, crossed productsgroup: 11: 18D35 Structured objects in a category (group objects, etc.)group: 12: 19A31 K0 of group rings and ordersgroup: 13: 19B28 K1 of group rings and orders [See also]57Q10group: 14: 19C30 K2 and the Brauer groupgroup: 15: 19G24 L-theory of group rings [See also]11E81group: 16: 19J35 Obstructions to group actionsgroup: 17: 19K14 K0 as an ordered group, tracesgroup: 18: 20-XX Group theory and generalizationsgroup: 19: 20A15 Applications of logic to group theorygroup: 20: 20C05 Group rings of finite groups and their modules [See also]16S34group: 21: 20C07 Group rings of infinite groups and their modules [See also]16S34group: 22: 20C35 Applications of group representations to physicsgroup: 23: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxxgroup: 24: 20J05 Homological methods in group theorygroup: 25: 20Pxx Probabilistic methods in group theory [See also]60Bxxgroup: 26: 20P05 Probabilistic methods in group theory [See also]60Bxxgroup: 27: 22B10 Structure of group algebras of LCA groupsgroup: 28: 22D15 Group algebras of locally compact groupsgroup: 29: 22D20 Representations of group algebrasgroup: 30: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxxgroup: 31: 22E43 Structure and representation of the Lorentz groupgroup: 32: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20group: 33: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axxgroup: 34: 32Mxx Complex spaces with a group of automorphismsgroup: 35: 37B05 Transformations and group actions with special properties (minimality, distality,
proximality, etc.)group: 36: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxx
165 Run: December 14, 2009
Mathematics Subject Classification 2010
group: 37: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,convolution algebras and measure algebras, see 43A10, 43A20
group: 38: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,57R77, 57R85, 57R90
group: 39: 57M05 Fundamental group, presentations, free differential calculusgroup: 40: 57M07 Topological methods in group theorygroup: 41: 57M60 Group actions in low dimensionsgroup: 42: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D05group: 43: 58D19 Group actions and symmetry propertiesgroup: 44: 58E40 Group actionsgroup: 45: 76M60 Symmetry analysis, Lie group and algebra methodsgroup: 46: 81T17 Renormalization group methodsgroup: 47: 82B28 Renormalization group methods [See also]81T17group: 48: 82C28 Dynamic renormalization group methods [See also]81T17group: 49: 82D25 Crystals For crystallographic group theory, see 20H15group: 50: 91B10 Group preferences
group-: 1: 28B10 Group- or semigroup-valued set functions, measures and integralsgroup-invariant: 1: 58E09 Group-invariant bifurcation theorygroup-theoretic: 1: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B13group-theoretic: 2: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05
group-theoretical: 1: 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)groupoids: 1: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
20L05, 20Mxxgroupoids: 2: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05groupoids: 3: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05groupoids: 4: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05groupoids: 5: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05groupoids: 6: 20N02 Sets with a single binary operation (groupoids)groupoids: 7: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05groupoids: 8: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05groupoids: 9: 53D17 Poisson manifolds; Poisson groupoids and algebroidsgroupoids: 10: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldsgroupoids: 11: 58H05 Pseudogroups and differentiable groupoids [See also]22A22, 22E65
groups: 1: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65groups: 2: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C80groups: 3: 06F15 Ordered groups [See also]20F60groups: 4: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40groups: 5: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40groups: 6: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63groups: 7: 11E57 Classical groups [See also]14Lxx, 20Gxxgroups: 8: 11E72 Galois cohomology of linear algebraic groups [See also]20G10groups: 9: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24groups: 10: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45groups: 11: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E40groups: 12: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E40groups: 13: 11F22 Relationship to Lie algebras and finite simple groupsgroups: 14: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20
166 Run: December 14, 2009
Mathematics Subject Classification 2010
groups: 15: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formsgroups: 16: 11F55 Other groups and their modular and automorphic forms (several variables)groups: 17: 11F75 Cohomology of arithmetic groupsgroups: 18: 11H56 Automorphism groups of latticesgroups: 19: 11R29 Class numbers, class groups, discriminantsgroups: 20: 11R56 Adele rings and groupsgroups: 21: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)groups: 22: 11R65 Class groups and Picard groups of ordersgroups: 23: 11R65 Class groups and Picard groups of ordersgroups: 24: 11S31 Class field theory; p-adic formal groups [See also]14L05groups: 25: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24groups: 26: 13C20 Class groups [See also]11R29groups: 27: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D50groups: 28: 14C15 (Equivariant) Chow groups and rings; motivesgroups: 29: 14C22 Picard groupsgroups: 30: 14F22 Brauer groups of schemes [See also]12G05, 16K50groups: 31: 14F35 Homotopy theory; fundamental groups [See also]14H30groups: 32: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)groups: 33: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45groups: 34: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45groups: 35: 14L05 Formal groups, p-divisible groups [See also]55N22groups: 36: 14L05 Formal groups, p-divisible groups [See also]55N22groups: 37: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D35groups: 38: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N30groups: 39: 14L40 Other algebraic groups (geometric aspects)groups: 40: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D50groups: 41: 16K50 Brauer groups [See also]12G05, 14F22groups: 42: 16Txx Hopf algebras, quantum groups and related topicsgroups: 43: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R50groups: 44: 16U60 Units, groups of unitsgroups: 45: 16W22 Actions of groups and semigroups; invariant theorygroups: 46: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxgroups: 47: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B23groups: 48: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxxgroups: 49: 17C30 Associated groups, automorphismsgroups: 50: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
groups: 51: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
groups: 52: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,20L05, 20Mxx
groups: 53: 18F30 Grothendieck groups [See also]13D15, 16E20, 19Axxgroups: 54: 19Axx Grothendieck groups and K0 [See also]13D15, 18F30groups: 55: 19Bxx Whitehead groups and K1
groups: 56: 19B14 Stability for linear groupsgroups: 57: 19Cxx Steinberg groups and K2
groups: 58: 19G12 Witt groups of rings [See also]11E81groups: 59: 20Bxx Permutation groupsgroups: 60: 20B05 General theory for finite groupsgroups: 61: 20B07 General theory for infinite groupsgroups: 62: 20B15 Primitive groupsgroups: 63: 20B20 Multiply transitive finite groupsgroups: 64: 20B22 Multiply transitive infinite groups
167 Run: December 14, 2009
Mathematics Subject Classification 2010
groups: 65: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX
groups: 66: 20B27 Infinite automorphism groups [See also]12F10groups: 67: 20B30 Symmetric groupsgroups: 68: 20B35 Subgroups of symmetric groupsgroups: 69: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)groups: 70: 20C05 Group rings of finite groups and their modules [See also]16S34groups: 71: 20C07 Group rings of infinite groups and their modules [See also]16S34groups: 72: 20C10 Integral representations of finite groupsgroups: 73: 20C11 p-adic representations of finite groupsgroups: 74: 20C12 Integral representations of infinite groupsgroups: 75: 20C30 Representations of finite symmetric groupsgroups: 76: 20C32 Representations of infinite symmetric groupsgroups: 77: 20C33 Representations of finite groups of Lie typegroups: 78: 20C34 Representations of sporadic groupsgroups: 79: 20Dxx Abstract finite groupsgroups: 80: 20D05 Finite simple groups and their classificationgroups: 81: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxgroups: 82: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxgroups: 83: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxgroups: 84: 20D08 Simple groups: sporadic groupsgroups: 85: 20D08 Simple groups: sporadic groupsgroups: 86: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17groups: 87: 20D15 Nilpotent groups, p-groupsgroups: 88: 20Exx Structure and classification of infinite or finite groupsgroups: 89: 20E05 Free nonabelian groupsgroups: 90: 20E08 Groups acting on trees [See also]20F65groups: 91: 20E10 Quasivarieties and varieties of groupsgroups: 92: 20E18 Limits, profinite groupsgroups: 93: 20E26 Residual properties and generalizations; residually finite groupsgroups: 94: 20E32 Simple groups [See also]20D05groups: 95: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]groups: 96: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]groups: 97: 20E42 Groups with a BN -pair; buildings [See also]51E24groups: 98: 20Fxx Special aspects of infinite or finite groupsgroups: 99: 20F11 Groups of finite Morley rank [See also]03C45, 03C60groups: 100: 20F16 Solvable groups, supersolvable groups [See also]20D10groups: 101: 20F16 Solvable groups, supersolvable groups [See also]20D10groups: 102: 20F17 Formations of groups, Fitting classes [See also]20D10groups: 103: 20F18 Nilpotent groups [See also]20D15groups: 104: 20F19 Generalizations of solvable and nilpotent groupsgroups: 105: 20F22 Other classes of groups defined by subgroup chainsgroups: 106: 20F28 Automorphism groups of groups [See also]20E36groups: 107: 20F28 Automorphism groups of groups [See also]20E36groups: 108: 20F29 Representations of groups as automorphism groups of algebraic systemsgroups: 109: 20F29 Representations of groups as automorphism groups of algebraic systemsgroups: 110: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxxgroups: 111: 20F36 Braid groups; Artin groupsgroups: 112: 20F36 Braid groups; Artin groupsgroups: 113: 20F38 Other groups related to topology or analysisgroups: 114: 20F50 Periodic groups; locally finite groupsgroups: 115: 20F50 Periodic groups; locally finite groupsgroups: 116: 20F55 Reflection and Coxeter groups [See also]22E40, 51F15groups: 117: 20F60 Ordered groups [See mainly]06F15groups: 118: 20F67 Hyperbolic groups and nonpositively curved groups
168 Run: December 14, 2009
Mathematics Subject Classification 2010
groups: 119: 20F67 Hyperbolic groups and nonpositively curved groupsgroups: 120: 20F69 Asymptotic properties of groupsgroups: 121: 20F70 Algebraic geometry over groups; equations over groupsgroups: 122: 20F70 Algebraic geometry over groups; equations over groupsgroups: 123: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
groups: 124: 20G15 Linear algebraic groups over arbitrary fieldsgroups: 125: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionsgroups: 126: 20G25 Linear algebraic groups over local fields and their integersgroups: 127: 20G30 Linear algebraic groups over global fields and their integersgroups: 128: 20G35 Linear algebraic groups over adeles and other rings and schemesgroups: 129: 20G40 Linear algebraic groups over finite fieldsgroups: 130: 20G41 Exceptional groupsgroups: 131: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50groups: 132: 20G44 Kac-Moody groupsgroups: 133: 20Hxx Other groups of matrices [See also]15A30groups: 134: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F20groups: 135: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxxgroups: 136: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25groups: 137: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25groups: 138: 20H20 Other matrix groups over fieldsgroups: 139: 20H25 Other matrix groups over ringsgroups: 140: 20H30 Other matrix groups over finite fieldsgroups: 141: 20J06 Cohomology of groupsgroups: 142: 20J15 Category of groupsgroups: 143: 20Kxx Abelian groupsgroups: 144: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]groups: 145: 20K10 Torsion groups, primary groups and generalized primary groupsgroups: 146: 20K10 Torsion groups, primary groups and generalized primary groupsgroups: 147: 20K10 Torsion groups, primary groups and generalized primary groupsgroups: 148: 20K15 Torsion-free groups, finite rankgroups: 149: 20K20 Torsion-free groups, infinite rankgroups: 150: 20K21 Mixed groupsgroups: 151: 20Nxx Other generalizations of groupsgroups: 152: 20N25 Fuzzy groups [See also]03E72groups: 153: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXgroups: 154: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXgroups: 155: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXgroups: 156: 22A05 Structure of general topological groupsgroups: 157: 22A10 Analysis on general topological groupsgroups: 158: 22A25 Representations of general topological groups and semigroupsgroups: 159: 22Bxx Locally compact abelian groups (LCA groups)groups: 160: 22Bxx Locally compact abelian groups (LCA groups)groups: 161: 22B05 General properties and structure of LCA groupsgroups: 162: 22B10 Structure of group algebras of LCA groupsgroups: 163: 22Cxx Compact groupsgroups: 164: 22C05 Compact groupsgroups: 165: 22Dxx Locally compact groups and their algebrasgroups: 166: 22D05 General properties and structure of locally compact groupsgroups: 167: 22D10 Unitary representations of locally compact groups
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groups: 168: 22D12 Other representations of locally compact groupsgroups: 169: 22D15 Group algebras of locally compact groupsgroups: 170: 22D40 Ergodic theory on groups [See also]28Dxxgroups: 171: 22D45 Automorphism groups of locally compact groupsgroups: 172: 22D45 Automorphism groups of locally compact groupsgroups: 173: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90groups: 174: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90groups: 175: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H05groups: 176: 22E10 General properties and structure of complex Lie groups [See also]32M05groups: 177: 22E15 General properties and structure of real Lie groupsgroups: 178: 22E20 General properties and structure of other Lie groupsgroups: 179: 22E25 Nilpotent and solvable Lie groupsgroups: 180: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)groups: 181: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXgroups: 182: 22E35 Analysis on p-adic Lie groupsgroups: 183: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxxgroups: 184: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05groups: 185: 22E46 Semisimple Lie groups and their representationsgroups: 186: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10groups: 187: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05groups: 188: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05groups: 189: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxgroups: 190: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05groups: 191: 22E66 Analysis on and representations of infinite-dimensional Lie groupsgroups: 192: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05groups: 193: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10groups: 194: 22Fxx Noncompact transformation groupsgroups: 195: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40groups: 196: 22F50 Groups as automorphisms of other structuresgroups: 197: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05groups: 198: 28D15 General groups of measure-preserving transformationsgroups: 199: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxxgroups: 200: 30F40 Kleinian groups [See also]20H10groups: 201: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N30groups: 202: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10groups: 203: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10groups: 204: 32M17 Automorphism groups of Cn and affine manifoldsgroups: 205: 33C80 Connections with groups and algebras, and related topicsgroups: 206: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras,
and related topicsgroups: 207: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras,
and related topicsgroups: 208: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras,
and related topicsgroups: 209: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.groups: 210: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.groups: 211: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
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groups: 212: 37A15 General groups of measure-preserving transformations [See mainly]22Fxxgroups: 213: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemsgroups: 214: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricsgroups: 215: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxgroups: 216: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxgroups: 217: 43A05 Measures on groups and semigroups, etc.groups: 218: 43A07 Means on groups, semigroups, etc.; amenable groupsgroups: 219: 43A07 Means on groups, semigroups, etc.; amenable groupsgroups: 220: 43A10 Measure algebras on groups, semigroups, etc.groups: 221: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.groups: 222: 43A17 Analysis on ordered groups, Hp-theorygroups: 223: 43A20 L1-algebras on groups, semigroups, etc.groups: 224: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.groups: 225: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupsgroups: 226: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.groups: 227: 43A35 Positive definite functions on groups, semigroups, etc.groups: 228: 43A40 Character groups and dual objectsgroups: 229: 43A45 Spectral synthesis on groups, semigroups, etc.groups: 230: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05groups: 231: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsgroups: 232: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E45groups: 233: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05groups: 234: 43A75 Analysis on specific compact groupsgroups: 235: 43A77 Analysis on general compact groupsgroups: 236: 43A80 Analysis on other specific Lie groups [See also]22Exxgroups: 237: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationsgroups: 238: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20groups: 239: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55groups: 240: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55groups: 241: 51F25 Orthogonal and unitary groups [See also]20H05groups: 242: 51Jxx Incidence groupsgroups: 243: 51J10 Projective incidence groupsgroups: 244: 51N25 Analytic geometry with other transformation groupsgroups: 245: 51N30 Geometry of classical groups [See also]20Gxx, 14L35groups: 246: 54H11 Topological groups [See also]22A05groups: 247: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxxgroups: 248: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17groups: 249: 55Qxx Homotopy groupsgroups: 250: 55Q05 Homotopy groups, general; sets of homotopy classesgroups: 251: 55Q07 Shape groupsgroups: 252: 55Q10 Stable homotopy groupsgroups: 253: 55Q20 Homotopy groups of wedges, joins, and simple spacesgroups: 254: 55Q35 Operations in homotopy groupsgroups: 255: 55Q40 Homotopy groups of spheresgroups: 256: 55Q52 Homotopy groups of special spacesgroups: 257: 55Q55 Cohomotopy groupsgroups: 258: 55Q70 Homotopy groups of special types [See also]55N05, 55N07groups: 259: 55Q91 Equivariant homotopy groups [See also]19L47groups: 260: 55R35 Classifying spaces of groups and H-spaces
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groups: 261: 57R67 Surgery obstructions, Wall groups [See also]19J25groups: 262: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D05groups: 263: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismsgroups: 264: 57S10 Compact groups of homeomorphismsgroups: 265: 57S15 Compact Lie groups of differentiable transformationsgroups: 266: 57S17 Finite transformation groupsgroups: 267: 57S20 Noncompact Lie groups of transformationsgroups: 268: 57S25 Groups acting on specific manifoldsgroups: 269: 57S30 Discontinuous groups of transformationsgroups: 270: 57Txx Homology and homotopy of topological groups and related structuresgroups: 271: 57T10 Homology and cohomology of Lie groupsgroups: 272: 57T15 Homology and cohomology of homogeneous spaces of Lie groupsgroups: 273: 57T20 Homotopy groups of topological groups and homogeneous spacesgroups: 274: 57T20 Homotopy groups of topological groups and homogeneous spacesgroups: 275: 58B32 Geometry of quantum groupsgroups: 276: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S05groups: 277: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H20groups: 278: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationgroups: 279: 81Rxx Groups and algebras in quantum theorygroups: 280: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70groups: 281: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
groups: 282: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B37groups: 283: 83C40 Gravitational energy and conservation laws; groups of motionsgroups: 284: 97H40 Groups, rings, fieldsgrowth: 1: 11N56 Rate of growth of arithmetic functionsgrowth: 2: 16Pxx Chain conditions, growth conditions, and other forms of finitenessgrowth: 3: 16P90 Growth rate, Gelfand-Kirillov dimensiongrowth: 4: 20E07 Subgroup theorems; subgroup growthgrowth: 5: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48growth: 6: 30D15 Special classes of entire functions and growth estimatesgrowth: 7: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30growth: 8: 34C11 Growth, boundednessgrowth: 9: 34K12 Growth, boundedness, comparison of solutionsgrowth: 10: 34M10 Oscillation, growth of solutionsgrowth: 11: 37C35 Orbit growthgrowth: 12: 39A22 Growth, boundedness, comparison of solutionsgrowth: 13: 40E10 Growth estimatesgrowth: 14: 91B62 Growth modelsguides: 1: 82D77 Quantum wave guides, quantum wires [See also]78A50
gyroscope: 1: 70E05 Motion of the gyroscopeholder: 1: 26A16 Lipschitz (Holder) classesholder: 2: 26B35 Special properties of functions of several variables, Holder conditions, etc.
haar: 1: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,invariant measures [See also]22Axx, 43A05hadamard: 1: 05B20 Matrices (incidence, Hadamard, etc.)hadamard: 2: 15B34 Boolean and Hadamard matrices
hahn-banach: 1: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators[See also]46M10
half-factorial: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)[See also]13A05, 14M05
half-integer: 1: 11F37 Forms of half-integer weight; nonholomorphic modular formshalf-planes: 1: 11T60 Finite upper half-planes
hall: 1: 81V70 Many-body theory; quantum Hall effect
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hamilton’s: 1: 70H05 Hamilton’s equationshamilton’s: 2: 70H25 Hamilton’s principle
hamilton-jacobi: 1: 35F21 Hamilton-Jacobi equationshamilton-jacobi: 2: 49Lxx Hamilton-Jacobi theories, including dynamic programminghamilton-jacobi: 3: 70H20 Hamilton-Jacobi equations
hamiltonian: 1: 05C45 Eulerian and Hamiltonian graphshamiltonian: 2: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems[See also]53Dxx, 70Fxx, 70Hxx
hamiltonian: 3: 37Kxx Infinite-dimensional Hamiltonian systems [See also]35Axx, 35Qxxhamiltonian: 4: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawshamiltonian: 5: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings andmetrics
hamiltonian: 6: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemshamiltonian: 7: 65P10 Hamiltonian systems including symplectic integratorshamiltonian: 8: 70Hxx Hamiltonian and Lagrangian mechanics [See also]37Jxxhamiltonian: 9: 70H08 Nearly integrable Hamiltonian systems, KAM theoryhamiltonian: 10: 70S05 Lagrangian formalism and Hamiltonian formalism
hammerstein: 1: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)[See also]45Gxx, 45P05
handlebodies: 1: 57R65 Surgery and handlebodieshankel: 1: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15hannay: 1: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
hardware: 1: 97P60 Hardwarehardy: 1: 30H10 Hardy spaces
hardy-littlewood: 1: 11P55 Applications of the Hardy-Littlewood method [See also]11D85harmonic: 1: 11K70 Harmonic analysis and almost periodicityharmonic: 2: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXharmonic: 3: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15harmonic: 4: 30F15 Harmonic functions on Riemann surfacesharmonic: 5: 31A05 Harmonic, subharmonic, superharmonic functionsharmonic: 6: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85harmonic: 7: 31B05 Harmonic, subharmonic, superharmonic functionsharmonic: 8: 31C05 Harmonic, subharmonic, superharmonic functionsharmonic: 9: 32A50 Harmonic analysis of several complex variables [See mainly]43-XXharmonic: 10: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxharmonic: 11: 42-XX Harmonic analysis on Euclidean spacesharmonic: 12: 42Axx Harmonic analysis in one variableharmonic: 13: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30harmonic: 14: 42B35 Function spaces arising in harmonic analysisharmonic: 15: 42B37 Harmonic analysis and PDE [See also]35-XXharmonic: 16: 42Cxx Nontrigonometric harmonic analysisharmonic: 17: 42C15 General harmonic expansions, framesharmonic: 18: 42C20 Other transformations of harmonic typeharmonic: 19: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxharmonic: 20: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxharmonic: 21: 53C43 Differential geometric aspects of harmonic maps [See also]58E20harmonic: 22: 58E20 Harmonic maps [See also]53C43, etc.
harmonics: 1: 33C55 Spherical harmonicshartogs: 1: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)
harvesting: 1: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)hauptvermutung: 1: 57Q25 Comparison of PL-structures: classification, Hauptvermutung
hausdorff: 1: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension[See also]11N99, 28Dxx
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hausdorff: 2: 28A78 Hausdorff and packing measureshausdorff: 3: 37F35 Conformal densities and Hausdorff dimensionhausdorff: 4: 40G05 Cesaro, Euler, Norlund and Hausdorff methodsheapoids: 1: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
heaps: 1: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)heat: 1: 32W30 Heat kernels in several complex variablesheat: 2: 35K05 Heat equationheat: 3: 35K08 Heat kernelheat: 4: 35Q79 PDEs in connection with classical thermodynamics and heat transferheat: 5: 58J35 Heat and other parabolic equation methodsheat: 6: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15heat: 7: 80Axx Thermodynamics and heat transferheat: 8: 80A20 Heat and mass transfer, heat flowheat: 9: 80A20 Heat and mass transfer, heat flow
hecke: 1: 20C08 Hecke algebras and their representationshecke: 2: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras,
and related topicshecke-petersson: 1: 11F25 Hecke-Petersson operators, differential operators (one variable)hecke-petersson: 2: 11F60 Hecke-Petersson operators, differential operators (several variables)
height: 1: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40heights: 1: 11G50 Heights [See also]14G40, 37P30heights: 2: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30
heisenberg: 1: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.hele-shaw: 1: 76D27 Other free-boundary flows; Hele-Shaw flowshelly-type: 1: 52A35 Helly-type theorems and geometric transversal theoryhelmholtz: 1: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxhelson: 1: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
henselian: 1: 13J15 Henselian rings [See also]13B40henselization: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
14B25hereditary: 1: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
hermite: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
hermite-einstein-yang-mills: 1: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)[See also]32Q20hermitian: 1: 11E39 Bilinear and Hermitian formshermitian: 2: 11E41 Class numbers of quadratic and Hermitian formshermitian: 3: 11E70 K-theory of quadratic and Hermitian formshermitian: 4: 15B57 Hermitian, skew-Hermitian, and related matriceshermitian: 5: 19G38 Hermitian K-theory, relations with K-theory of ringshermitian: 6: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15hermitian: 7: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)hermitian: 8: 53B35 Hermitian and Kahlerian structures [See also]32Cxxhermitian: 9: 53C55 Hermitian and Kahlerian manifolds [See also]32Cxx
heteroclinic: 1: 34C37 Homoclinic and heteroclinic solutionsheteroclinic: 2: 37C29 Homoclinic and heteroclinic orbitsheteroclinic: 3: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoreticmethods
heteroclinic: 4: 70K44 Homoclinic and heteroclinic trajectoriesheterogeneous: 1: 08A68 Heterogeneous algebrasheterogeneous: 2: 91B69 Heterogeneous agent models
heuristic: 1: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned atleast one other classification number in this section)
heuristic: 2: 78M32 Neural and heuristic methodsheuristic: 3: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxx
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heuristics: 1: 68T20 Problem solving (heuristics, search strategies, etc.)heuristics: 2: 90C59 Approximation methods and heuristics
heyting: 1: 06D20 Heyting algebras [See also]03G25hierarchical: 1: 91A65 Hierarchical gameshierarchical: 2: 93A13 Hierarchical systemshierarchies: 1: 03D20 Recursive functions and relations, subrecursive hierarchieshierarchies: 2: 03D55 Hierarchieshierarchies: 3: 34M55 Painleve and other special equations; classification, hierarchies;hierarchies: 4: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)hierarchies: 5: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)[See also]03D15, 68Q17, 68Q19
high: 1: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25high-velocity: 1: 74R15 High-velocity fracture
higher: 1: 11B30 Arithmetic combinatorics; higher degree uniformityhigher: 2: 11D41 Higher degree equations; Fermat’s equationhigher: 3: 11E76 Forms of degree higher than twohigher: 4: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G20higher: 5: 19Dxx Higher algebraic K-theoryhigher: 6: 19D45 Higher symbols, Milnor K-theoryhigher: 7: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E20higher: 8: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G10higher: 9: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22higher: 10: 33B30 Higher logarithm functionshigher: 11: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)higher: 12: 55S20 Secondary and higher cohomology operationshigher: 13: 57M25 Knots and links in S3 For higher dimensions, see 57Q45higher: 14: 97B40 Higher education
higher-dimensional: 1: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05higher-dimensional: 2: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxhigher-dimensional: 3: 14J50 Automorphisms of surfaces and higher-dimensional varietieshigher-dimensional: 4: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxhigher-dimensional: 5: 14Q15 Higher-dimensional varietieshigher-dimensional: 6: 31Bxx Higher-dimensional theoryhigher-dimensional: 7: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-spacehigher-dimensional: 8: 54F35 Higher-dimensional local connectedness [See also]55Mxx, 55Nxxhigher-dimensional: 9: 70E45 Higher-dimensional generalizationshigher-dimensional: 10: 83Exx Unified, higher-dimensional and super field theorieshigher-dimensional: 11: 83E15 Kaluza-Klein and other higher-dimensional theories
higher-order: 1: 03B15 Higher-order logic and type theoryhigher-order: 2: 03C85 Second- and higher-order model theoryhigher-order: 3: 03F35 Second- and higher-order arithmetic and fragments [See also]03B30higher-order: 4: 35Gxx General higher-order equations and systemshigher-order: 5: 35G05 Linear higher-order equationshigher-order: 6: 35G10 Initial value problems for linear higher-order equationshigher-order: 7: 35G15 Boundary value problems for linear higher-order equationshigher-order: 8: 35G16 Initial-boundary value problems for linear higher-order equationshigher-order: 9: 35G20 Nonlinear higher-order equationshigher-order: 10: 35G25 Initial value problems for nonlinear higher-order equationshigher-order: 11: 35G30 Boundary value problems for nonlinear higher-order equationshigher-order: 12: 35G31 Initial-boundary value problems for nonlinear higher-order equationshigher-order: 13: 35G35 Linear higher-order systemshigher-order: 14: 35G40 Initial value problems for linear higher-order systems
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higher-order: 15: 35G45 Boundary value problems for linear higher-order systemshigher-order: 16: 35G46 Initial-boundary value problems for linear higher-order systemshigher-order: 17: 35G50 Nonlinear higher-order systemshigher-order: 18: 35G55 Initial value problems for nonlinear higher-order systemshigher-order: 19: 35G60 Boundary value problems for nonlinear higher-order systemshigher-order: 20: 35G61 Initial-boundary value problems for nonlinear higher-order systemshigher-order: 21: 35J30 Higher-order elliptic equations [See also]31A30, 31B30higher-order: 22: 35J35 Variational methods for higher-order elliptic equationshigher-order: 23: 35J40 Boundary value problems for higher-order elliptic equationshigher-order: 24: 35J48 Higher-order elliptic systemshigher-order: 25: 35J58 Boundary value problems for higher-order elliptic systemshigher-order: 26: 35K25 Higher-order parabolic equationshigher-order: 27: 35K30 Initial value problems for higher-order parabolic equationshigher-order: 28: 35K35 Initial-boundary value problems for higher-order parabolic equationshigher-order: 29: 35K41 Higher-order parabolic systemshigher-order: 30: 35K46 Initial value problems for higher-order parabolic systemshigher-order: 31: 35K52 Initial-boundary value problems for higher-order parabolic systemshigher-order: 32: 35L25 Higher-order hyperbolic equationshigher-order: 33: 35L30 Initial value problems for higher-order hyperbolic equationshigher-order: 34: 35L35 Initial-boundary value problems for higher-order hyperbolic equationshigher-order: 35: 35L55 Higher-order hyperbolic systemshigher-order: 36: 35L56 Initial value problems for higher-order hyperbolic systemshigher-order: 37: 35L57 Initial-boundary value problems for higher-order hyperbolic systemshigher-order: 38: 35L75 Nonlinear higher-order hyperbolic equationshigher-order: 39: 35L76 Semilinear higher-order hyperbolic equationshigher-order: 40: 35L77 Quasilinear higher-order hyperbolic equationshigher-order: 41: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10higher-order: 42: 70H50 Higher-order theorieshigher-order: 43: 76D10 Boundary-layer theory, separation and reattachment, higher-order effectshigher-type: 1: 03D65 Higher-type and set recursion theory
higman-neumann-neumann: 1: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumannextensions, and generalizations
hilbert: 1: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
hilbert: 2: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
hilbert: 3: 14C05 Parametrization (Chow and Hilbert schemes)hilbert: 4: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35hilbert: 5: 44A15 Special transforms (Legendre, Hilbert, etc.)hilbert: 6: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxhilbert: 7: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)hilbert: 8: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35hilbert: 9: 46C15 Characterizations of Hilbert spaceshilbert: 10: 46E20 Hilbert spaces of continuous, differentiable or analytic functionshilbert: 11: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32hilbert: 12: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32hilbert: 13: 46K15 Hilbert algebrashilbert: 14: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaceshilbert: 15: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22hilbert: 16: 47L30 Abstract operator algebras on Hilbert spaces
hilbert’s: 1: 12E25 Hilbertian fields; Hilbert’s irreducibility theorem
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hilbert’s: 2: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)
hilbert’s: 3: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)hilbert-kunz: 1: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincare series
hilbert-samuel: 1: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincare serieshilbert-siegel: 1: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20hilbert-siegel: 2: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
hilbertian: 1: 12E25 Hilbertian fields; Hilbert’s irreducibility theoremhill: 1: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)
histories: 1: 01A05 General histories, source bookshistoriography: 1: 01A85 Historiography
history: 1: 01-XX History and biography [See also]the classification number–03 in the other sectionshistory: 2: 01Axx History of mathematics and mathematicianshistory: 3: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)history: 4: 91F10 History, political sciencehistory: 5: 97A30 History of mathematics and mathematics education [See also]01-XXhitchin: 1: 53D18 Generalized geometries (a la Hitchin)
hjelmslev: 1: 51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)hjelmslev: 2: 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
hochschild: 1: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,cyclic, dihedral, etc.)hochschild: 2: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
hodge: 1: 13F50 Rings with straightening laws, Hodge algebrashodge: 2: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecturehodge: 3: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecturehodge: 4: 14D07 Variation of Hodge structures [See also]32G20hodge: 5: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14hodge: 6: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K30hodge: 7: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D07hodge: 8: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S35holes: 1: 83C57 Black holes
holomorphic: 1: 11F11 Holomorphic modular forms of integral weightholomorphic: 2: 30G12 Finely holomorphic functions and topological function theoryholomorphic: 3: 30Kxx Universal holomorphic functionsholomorphic: 4: 32Axx Holomorphic functions of several complex variablesholomorphic: 5: 32A10 Holomorphic functionsholomorphic: 6: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxholomorphic: 7: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J15holomorphic: 8: 32A40 Boundary behavior of holomorphic functionsholomorphic: 9: 32A60 Zero sets of holomorphic functionsholomorphic: 10: 32Exx Holomorphic convexityholomorphic: 11: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolationholomorphic: 12: 32E35 Global boundary behavior of holomorphic functionsholomorphic: 13: 32Hxx Holomorphic mappings and correspondencesholomorphic: 14: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsholomorphic: 15: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsholomorphic: 16: 32Lxx Holomorphic fiber spaces [See also]55Rxxholomorphic: 17: 32L05 Holomorphic bundles and generalizationsholomorphic: 18: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30holomorphic: 19: 32S65 Singularities of holomorphic vector fields and foliations
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holomorphic: 20: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationsholomorphic: 21: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxxholomorphic: 22: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60holomorphic: 23: 46T25 Holomorphic maps [See also]46G20holomorphic: 24: 58C10 Holomorphic maps [See also]32-XX
holomorphically: 1: 32E05 Holomorphically convex complex spaces, reduction theoryholomorphy: 1: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12holomorphy: 2: 32D05 Domains of holomorphyholomorphy: 3: 32D10 Envelopes of holomorphyholomorphy: 4: 32T05 Domains of holomorphyholomorphy: 5: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txxholomorphy: 6: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C10holomorphy: 7: 58B12 Questions of holomorphy [See also]32-XX, 46G20
holonomic: 1: 70F20 Holonomic systemsholonomy: 1: 53C29 Issues of holonomyholonomy: 2: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
homeomorphisms: 1: 37E30 Homeomorphisms and diffeomorphisms of planes and surfaceshomeomorphisms: 2: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismshomeomorphisms: 3: 57S10 Compact groups of homeomorphismshomeomorphisms: 4: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S05
homoclinic: 1: 34C37 Homoclinic and heteroclinic solutionshomoclinic: 2: 37C29 Homoclinic and heteroclinic orbitshomoclinic: 3: 37G20 Hyperbolic singular points with homoclinic trajectorieshomoclinic: 4: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoreticmethodshomoclinic: 5: 70K44 Homoclinic and heteroclinic trajectories
homogeneous: 1: 11J04 Homogeneous approximation to one numberhomogeneous: 2: 11J13 Simultaneous homogeneous approximation, linear formshomogeneous: 3: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T15homogeneous: 4: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90homogeneous: 5: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40homogeneous: 6: 32M10 Homogeneous complex manifolds [See also]14M17, 57T15homogeneous: 7: 32M12 Almost homogeneous manifolds and spaces [See also]14M17homogeneous: 8: 37A17 Homogeneous flows [See also]22Fxxhomogeneous: 9: 43A85 Analysis on homogeneous spaceshomogeneous: 10: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T15homogeneous: 11: 57T15 Homology and cohomology of homogeneous spaces of Lie groupshomogeneous: 12: 57T20 Homotopy groups of topological groups and homogeneous spaceshomogeneous: 13: 76F05 Isotropic turbulence; homogeneous turbulence
homogenization: 1: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50homogenization: 2: 74Qxx Homogenization, determination of effective propertieshomogenization: 3: 74Q05 Homogenization in equilibrium problemshomogenization: 4: 74Q10 Homogenization and oscillations in dynamical problemshomogenization: 5: 76M50 Homogenizationhomogenization: 6: 78M40 Homogenizationhomogenization: 7: 80M40 Homogenization
homological: 1: 12Gxx Homological methods (field theory)homological: 2: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,see 18Gxx
homological: 3: 13D05 Homological dimensionhomological: 4: 13D07 Homological functors on modules (Tor, Ext, etc.)homological: 5: 13D22 Homological conjectures (intersection theorems)
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homological: 6: 13P20 Computational homological algebra [See also]13Dxxhomological: 7: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see18Gxx
homological: 8: 16E10 Homological dimensionhomological: 9: 16E30 Homological functors on modules (Tor, Ext, etc.)homological: 10: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
homological: 11: 17B55 Homological methods in Lie (super)algebrashomological: 12: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
homological: 13: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txxhomological: 14: 18G20 Homological dimension [See also]13D05, 16E10homological: 15: 18G25 Relative homological algebra, projective classeshomological: 16: 18G50 Nonabelian homological algebrahomological: 17: 20Jxx Connections with homological algebra and category theoryhomological: 18: 20J05 Homological methods in group theoryhomological: 19: 20K40 Homological and categorical methodshomological: 20: 20M50 Connections of semigroups with homological algebra and category theoryhomological: 21: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE[See also]32C38, 58J15
homological: 22: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)homological: 23: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category[See also]14J33
homological: 24: 55Uxx Applied homological algebra and category theory [See also]18Gxxhomologies: 1: 55N07 Steenrod-Sitnikov homologies
homology: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology andderived functors for triples [See also]18Gxxhomology: 2: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G60homology: 3: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G60homology: 4: 53D40 Floer homology and cohomology, symplectic aspectshomology: 5: 53D42 Symplectic field theory; contact homologyhomology: 6: 55Nxx Homology and cohomology theories [See also]57Txxhomology: 7: 55N20 Generalized (extraordinary) homology and cohomology theorieshomology: 8: 55N25 Homology with local coefficients, equivariant cohomologyhomology: 9: 55N33 Intersection homology and cohomologyhomology: 10: 55N35 Other homology theorieshomology: 11: 55N40 Axioms for homology theory and uniqueness theoremshomology: 12: 55N91 Equivariant homology and cohomology [See also]19L47homology: 13: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txxhomology: 14: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R20homology: 15: 55R45 Homology and homotopy of BO and BU; Bott periodicityhomology: 16: 55U25 Homology of a product, Kunneth formulahomology: 17: 57R58 Floer homologyhomology: 18: 57Txx Homology and homotopy of topological groups and related structureshomology: 19: 57T10 Homology and cohomology of Lie groupshomology: 20: 57T15 Homology and cohomology of homogeneous spaces of Lie groupshomology: 21: 57T25 Homology and cohomology of H-spaces
homomorphism: 1: 51A10 Homomorphism, automorphism and dualitieshomomorphisms: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)homomorphisms: 2: 20K30 Automorphisms, homomorphisms, endomorphisms, etc.homomorphisms: 3: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
homotopical: 1: 18G55 Homotopical algebrahomotopy: 1: 14F35 Homotopy theory; fundamental groups [See also]14H30homotopy: 2: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E15homotopy: 3: 55Pxx Homotopy theory For simple homotopy type, see 57Q10
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homotopy: 4: 55Pxx Homotopy theory For simple homotopy type, see 57Q10homotopy: 5: 55P05 Homotopy extension properties, cofibrationshomotopy: 6: 55P10 Homotopy equivalenceshomotopy: 7: 55P15 Classification of homotopy typehomotopy: 8: 55P42 Stable homotopy theory, spectrahomotopy: 9: 55P57 Proper homotopy theoryhomotopy: 10: 55P62 Rational homotopy theoryhomotopy: 11: 55P65 Homotopy functorshomotopy: 12: 55P91 Equivariant homotopy theory [See also]19L47homotopy: 13: 55P92 Relations between equivariant and nonequivariant homotopy theoryhomotopy: 14: 55Qxx Homotopy groupshomotopy: 15: 55Q05 Homotopy groups, general; sets of homotopy classeshomotopy: 16: 55Q05 Homotopy groups, general; sets of homotopy classeshomotopy: 17: 55Q10 Stable homotopy groupshomotopy: 18: 55Q20 Homotopy groups of wedges, joins, and simple spaceshomotopy: 19: 55Q35 Operations in homotopy groupshomotopy: 20: 55Q40 Homotopy groups of sphereshomotopy: 21: 55Q45 Stable homotopy of sphereshomotopy: 22: 55Q52 Homotopy groups of special spaceshomotopy: 23: 55Q70 Homotopy groups of special types [See also]55N05, 55N07homotopy: 24: 55Q91 Equivariant homotopy groups [See also]19L47homotopy: 25: 55R45 Homology and homotopy of BO and BU; Bott periodicityhomotopy: 26: 55U35 Abstract and axiomatic homotopy theoryhomotopy: 27: 55U40 Topological categories, foundations of homotopy theoryhomotopy: 28: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28homotopy: 29: 57R60 Homotopy spheres, Poincare conjecturehomotopy: 30: 57Txx Homology and homotopy of topological groups and related structureshomotopy: 31: 57T20 Homotopy groups of topological groups and homogeneous spaceshomotopy: 32: 58B05 Homotopy and topological questionshomotopy: 33: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C30
hopf: 1: 16S40 Smash products of general Hopf actions [See also]16T05hopf: 2: 16Txx Hopf algebras, quantum groups and related topicshopf: 3: 16T05 Hopf algebras and their applications [See also]16S40, 57T05hopf: 4: 55Q25 Hopf invariantshopf: 5: 57T05 Hopf algebras [See also]16T05horn: 1: 33C65 Appell, Horn and Lauricella functions
horocycle: 1: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,etc.)
hurwitz: 1: 11M35 Hurwitz and Lerch zeta functionshybrid: 1: 34A38 Hybrid systemshybrid: 2: 34K34 Hybrid systemshybrid: 3: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)hydro-: 1: 76Qxx Hydro- and aero-acousticshydro-: 2: 76Q05 Hydro- and aero-acoustics
hydro-elasticity: 1: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)hydrodynamic: 1: 76Exx Hydrodynamic stabilityhydrodynamic: 2: 85A30 Hydrodynamic and hydromagnetic problems [See also]76Y05
hydrodynamics: 1: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30
hydrodynamics: 2: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30
hydrodynamics: 3: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30
hydrodynamics: 4: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30
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hydrodynamics: 5: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)hydrofoil: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshinghydrography: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U05
hydrology: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U05hydromagnetic: 1: 85A30 Hydrodynamic and hydromagnetic problems [See also]76Y05
hyper-kahler: 1: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometryhyperalgebra: 1: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D35
hyperbolic: 1: 20F67 Hyperbolic groups and nonpositively curved groupshyperbolic: 2: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)hyperbolic: 3: 32Q45 Hyperbolic and Kobayashi hyperbolic manifoldshyperbolic: 4: 32Q45 Hyperbolic and Kobayashi hyperbolic manifoldshyperbolic: 5: 35Lxx Hyperbolic equations and systems [See also]58J45hyperbolic: 6: 35L02 First-order hyperbolic equationshyperbolic: 7: 35L03 Initial value problems for first-order hyperbolic equationshyperbolic: 8: 35L04 Initial-boundary value problems for first-order hyperbolic equationshyperbolic: 9: 35L10 Second-order hyperbolic equationshyperbolic: 10: 35L15 Initial value problems for second-order hyperbolic equationshyperbolic: 11: 35L20 Initial-boundary value problems for second-order hyperbolic equationshyperbolic: 12: 35L25 Higher-order hyperbolic equationshyperbolic: 13: 35L30 Initial value problems for higher-order hyperbolic equationshyperbolic: 14: 35L35 Initial-boundary value problems for higher-order hyperbolic equationshyperbolic: 15: 35L40 First-order hyperbolic systemshyperbolic: 16: 35L45 Initial value problems for first-order hyperbolic systemshyperbolic: 17: 35L50 Initial-boundary value problems for first-order hyperbolic systemshyperbolic: 18: 35L51 Second-order hyperbolic systemshyperbolic: 19: 35L52 Initial value problems for second-order hyperbolic systemshyperbolic: 20: 35L53 Initial-boundary value problems for second-order hyperbolic systemshyperbolic: 21: 35L55 Higher-order hyperbolic systemshyperbolic: 22: 35L56 Initial value problems for higher-order hyperbolic systemshyperbolic: 23: 35L57 Initial-boundary value problems for higher-order hyperbolic systemshyperbolic: 24: 35L60 Nonlinear first-order hyperbolic equationshyperbolic: 25: 35L70 Nonlinear second-order hyperbolic equationshyperbolic: 26: 35L71 Semilinear second-order hyperbolic equationshyperbolic: 27: 35L72 Quasilinear second-order hyperbolic equationshyperbolic: 28: 35L75 Nonlinear higher-order hyperbolic equationshyperbolic: 29: 35L76 Semilinear higher-order hyperbolic equationshyperbolic: 30: 35L77 Quasilinear higher-order hyperbolic equationshyperbolic: 31: 35L80 Degenerate hyperbolic equationshyperbolic: 32: 35L81 Singular hyperbolic equationshyperbolic: 33: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities[See also]35R35, 49J40hyperbolic: 34: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities[See also]35R35, 49J40hyperbolic: 35: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variationalinequalities [See also]35R35, 49J40hyperbolic: 36: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variationalinequalities [See also]35R35, 49J40hyperbolic: 37: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,49J40hyperbolic: 38: 35L90 Abstract hyperbolic equationshyperbolic: 39: 37Dxx Dynamical systems with hyperbolic behaviorhyperbolic: 40: 37D05 Hyperbolic orbits and setshyperbolic: 41: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)hyperbolic: 42: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)hyperbolic: 43: 37D30 Partially hyperbolic systems and dominated splittingshyperbolic: 44: 37D50 Hyperbolic systems with singularities (billiards, etc.)
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hyperbolic: 45: 37G20 Hyperbolic singular points with homoclinic trajectorieshyperbolic: 46: 51M09 Elementary problems in hyperbolic and elliptic geometrieshyperbolic: 47: 51M10 Hyperbolic and elliptic geometries (general) and generalizationshyperbolic: 48: 52A55 Spherical and hyperbolic convexityhyperbolic: 49: 58J45 Hyperbolic equations [See also]35Lxx
hyperbolicity: 1: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,etc.)
hyperbolicity: 2: 37F15 Expanding maps; hyperbolicity; structural stabilityhyperbolicity: 3: 37L45 Hyperbolicity; Lyapunov functions
hypercohomology: 1: 18G40 Spectral sequences, hypercohomology [See also]55Txxhypercomplex: 1: 30G35 Functions of hypercomplex variables and generalized variableshypercomplex: 2: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35hypercyclic: 1: 47A16 Cyclic vectors, hypercyclic and chaotic operators
hyperfunctions: 1: 32A45 Hyperfunctions [See also]46F15hyperfunctions: 2: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J15hyperfunctions: 3: 58J15 Relations with hyperfunctions
hypergeometric: 1: 33Cxx Hypergeometric functionshypergeometric: 2: 33C05 Classical hypergeometric functions, 2F1
hypergeometric: 3: 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
hypergeometric: 4: 33C20 Generalized hypergeometric series, pFq
hypergeometric: 5: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
hypergeometric: 6: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)hypergeometric: 7: 33C67 Hypergeometric functions associated with root systemshypergeometric: 8: 33C70 Other hypergeometric functions and integrals in several variableshypergeometric: 9: 33C75 Elliptic integrals as hypergeometric functionshypergeometric: 10: 33Dxx Basic hypergeometric functionshypergeometric: 11: 33D15 Basic hypergeometric functions in one variable, rϕs
hypergeometric: 12: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
hypergeometric: 13: 33D60 Basic hypergeometric integrals and functions defined by themhypergeometric: 14: 33D67 Basic hypergeometric functions associated with root systemshypergeometric: 15: 33D70 Other basic hypergeometric functions and integrals in several variables
hypergraphs: 1: 05C15 Coloring of graphs and hypergraphshypergraphs: 2: 05C65 Hypergraphshypergroups: 1: 20N20 Hypergroupshypergroups: 2: 43A62 Hypergroupshyperplanes: 1: 32S22 Relations with arrangements of hyperplanes [See also]52C35hyperplanes: 2: 52C35 Arrangements of points, flats, hyperplanes [See also]32S22
hypersonic: 1: 76Kxx Hypersonic flowshypersonic: 2: 76K05 Hypersonic flows
hyperspaces: 1: 54B20 Hyperspaceshypersurface: 1: 32S25 Surface and hypersurface singularities [See also]14J17
hypersurfaces: 1: 14J70 Hypersurfaceshypersurfaces: 2: 14Q10 Surfaces, hypersurfaceshypersurfaces: 3: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45
hypertext: 1: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)[See also]68M11
hypertranscendence: 1: 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)hypoelliptic: 1: 35H10 Hypoelliptic equationshyponormal: 1: 47B20 Subnormal operators, hyponormal operators, etc.hypotheses: 1: 03E65 Other hypotheses and axiomshypotheses: 2: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheseshypothesis: 1: 03E50 Continuum hypothesis and Martin’s axiom [See also]03E57hypothesis: 2: 62F03 Hypothesis testinghypothesis: 3: 62G10 Hypothesis testing
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hypothesis: 4: 62H15 Hypothesis testinghypothesis: 5: 62M02 Markov processes: hypothesis testinghypothesis: 6: 62M07 Non-Markovian processes: hypothesis testinghysteresis: 1: 34C55 Hysteresishysteresis: 2: 47J40 Equations with hysteresis operators [See also]34C55, 74N30hysteresis: 3: 74N30 Problems involving hysteresis
i: 1: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-typeI representations, etc.)
ideal: 1: 13A15 Ideals; multiplicative ideal theoryideal: 2: 13F10 Principal ideal ringsideal: 3: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.ideal: 4: 20M12 Ideal theoryideal: 5: 30F25 Ideal boundary theoryideal: 6: 40A35 Ideal and statistical convergence [See also]40G15ideal: 7: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)ideals: 1: 06B10 Ideals, congruence relationsideals: 2: 11R44 Distribution of prime ideals [See also]11N05ideals: 3: 13A15 Ideals; multiplicative ideal theoryideals: 4: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsideals: 5: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)ideals: 6: 13Cxx Theory of modules and idealsideals: 7: 13C10 Projective and free modules and ideals [See also]19A13ideals: 8: 13C11 Injective and flat modules and idealsideals: 9: 13C12 Torsion modules and idealsideals: 10: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,
14M12ideals: 11: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25ideals: 12: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)ideals: 13: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C38ideals: 14: 14F18 Multiplier idealsideals: 15: 16Dxx Modules, bimodules and idealsideals: 16: 16D25 Idealsideals: 17: 16D40 Free, projective, and flat modules and ideals [See also]19A13ideals: 18: 16D60 Simple and semisimple modules, primitive rings and idealsideals: 19: 16D80 Other classes of modules and ideals [See also]16G50ideals: 20: 16N40 Nil and nilpotent radicals, sets, ideals, ringsideals: 21: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceideals: 22: 16S70 Extensions of rings by idealsideals: 23: 46H10 Ideals and subalgebrasideals: 24: 46J20 Ideals, maximal ideals, boundariesideals: 25: 46J20 Ideals, maximal ideals, boundariesideals: 26: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20ideals: 27: 47L20 Operator ideals [See also]47B10ideals: 28: 47L22 Ideals of polynomials and of multilinear mappings
idempotents: 1: 17C27 Idempotents, Peirce decompositionsidentification: 1: 93B30 System identificationidentification: 2: 93E12 System identification
identities: 1: 05A19 Combinatorial identities, bijective combinatoricsidentities: 2: 11P84 Partition identities; identities of Rogers-Ramanujan typeidentities: 3: 11P84 Partition identities; identities of Rogers-Ramanujan typeidentities: 4: 15A24 Matrix equations and identitiesidentities: 5: 16R10 T -ideals, identities, varieties of rings and algebras
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identities: 6: 16R40 Identities other than those of matrices over commutative ringsidentities: 7: 16R50 Other kinds of identities (generalized polynomial, rational, involution)identities: 8: 16R60 Functional identitiesidentities: 9: 17A30 Algebras satisfying other identitiesidentities: 10: 17B01 Identities, free Lie (super)algebrasidentities: 11: 17C05 Identities and free Jordan structures
identity: 1: 16Rxx Rings with polynomial identityif: 1: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)ill-posed: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R30ill-posed: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R30ill-posed: 3: 65N20 Ill-posed problems
ill-posedness: 1: 65F22 Ill-posedness, regularizationimage: 1: 62H35 Image analysisimage: 2: 62M40 Random fields; image analysisimage: 3: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U05image: 4: 68U10 Image processingimage: 5: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U10
imaging: 1: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A12imbeddable: 1: 51A45 Incidence structures imbeddable into projective geometriesimbeddings: 1: 58D10 Spaces of imbeddings and immersionsimmersions: 1: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,57R40, 57R42
immersions: 2: 57N35 Embeddings and immersionsimmersions: 3: 57Q35 Embeddings and immersionsimmersions: 4: 57R42 Immersionsimmersions: 5: 58D10 Spaces of imbeddings and immersions
impact: 1: 74M20 Impactimplicit: 1: 03D15 Complexity of computation (including implicit computational complexity)
[See also]68Q15, 68Q17implicit: 2: 26B10 Implicit function theorems, Jacobians, transformations with several variablesimplicit: 3: 34A09 Implicit equations, differential-algebraic equations [See also]65L80implicit: 4: 34K32 Implicit equationsimplicit: 5: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15implicit: 6: 58C15 Implicit function theorems; global Newton methods
improperly: 1: 35R25 Improperly posed problemsimproperly: 2: 65J20 Improperly posed problems; regularizationimproperly: 3: 65L08 Improperly posed problemsimproperly: 4: 65M30 Improperly posed problemsimproperly: 5: 65R30 Improperly posed problems
impulse-energy: 1: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spaceimpulses: 1: 34A37 Differential equations with impulsesimpulses: 2: 34B37 Boundary value problems with impulsesimpulses: 3: 34K45 Equations with impulses
impulsive: 1: 35R12 Impulsive partial differential equationsimpulsive: 2: 49N25 Impulsive optimal control problems
in: 1: 01-XX History and biography [See also]the classification number–03 in the other sectionsin: 2: 03A10 Logic in the philosophy of sciencein: 3: 03B70 Logic in computer science [See also]68-XXin: 4: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R15in: 5: 03F10 Functionals in proof theoryin: 6: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J05
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in: 7: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30in: 8: 05C12 Distance in graphsin: 9: 05C21 Flows in graphsin: 10: 05C30 Enumeration in graph theoryin: 11: 08A70 Applications of universal algebra in computer sciencein: 12: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C60in: 13: 11Axx Elementary number theory For analogues in number fields, see 11R04in: 14: 11D72 Equations in many variables [See also]11P55in: 15: 11D79 Congruences in many variablesin: 16: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63in: 17: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesin: 18: 11Hxx Geometry of numbers For applications in coding theory, see 94B75in: 19: 11J61 Approximation in non-Archimedean valuationsin: 20: 11J86 Linear forms in logarithms; Baker’s methodin: 21: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)in: 22: 11N13 Primes in progressions [See also]11B25in: 23: 11N69 Distribution of integers in special residue classesin: 24: 11P21 Lattice points in specified regionsin: 25: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxin: 26: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W30in: 27: 15A54 Matrices over function rings in one or more variablesin: 28: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXin: 29: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)in: 30: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionin: 31: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualityin: 32: 16H10 Orders in separable algebrasin: 33: 16N80 General radicals and rings For radicals in module categories, see 16S90in: 34: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsin: 35: 17B55 Homological methods in Lie (super)algebrasin: 36: 18D35 Structured objects in a category (group objects, etc.)in: 37: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10in: 38: 19Exx K-theory in geometryin: 39: 19Fxx K-theory in number theory [See also]11R70, 11S70in: 40: 19J05 Finiteness and other obstructions in K0
in: 41: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
in: 42: 20J05 Homological methods in group theoryin: 43: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05in: 44: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05in: 45: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50in: 46: 20Pxx Probabilistic methods in group theory [See also]60Bxxin: 47: 20P05 Probabilistic methods in group theory [See also]60Bxxin: 48: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxxin: 49: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxin: 50: 28A35 Measures and integrals in product spacesin: 51: 28Bxx Set functions, measures and integrals with values in abstract spacesin: 52: 28B15 Set functions, measures and integrals with values in ordered spacesin: 53: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
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measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11in: 54: 28Exx Miscellaneous topics in measure theoryin: 55: 30A10 Inequalities in the complex domainin: 56: 30C25 Covering theorems in conformal mapping theoryin: 57: 30C30 Numerical methods in conformal mapping theory [See also]65E05in: 58: 30C62 Quasiconformal mappings in the planein: 59: 30C65 Quasiconformal mappings in Rn, other generalizationsin: 60: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15in: 61: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXin: 62: 30Exx Miscellaneous topics of analysis in the complex domainin: 63: 30E10 Approximation in the complex domainin: 64: 30E15 Asymptotic representations in the complex domainin: 65: 30L10 Quasiconformal mappings in metric spacesin: 66: 32C55 The Levi problem in complex spaces; generalizationsin: 67: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22in: 68: 32N15 Automorphic functions in symmetric domainsin: 69: 32V40 Real submanifolds in complex manifoldsin: 70: 32Wxx Differential operators in several variablesin: 71: 32W25 Pseudodifferential operators in several complex variablesin: 72: 32W30 Heat kernels in several complex variablesin: 73: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablein: 74: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablein: 75: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablein: 76: 33C70 Other hypergeometric functions and integrals in several variablesin: 77: 33D15 Basic hypergeometric functions in one variable, rϕs
in: 78: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
in: 79: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
in: 80: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
in: 81: 33D70 Other basic hypergeometric functions and integrals in several variablesin: 82: 33E50 Special functions in characteristic p (gamma functions, etc.)in: 83: 34A26 Geometric methods in differential equationsin: 84: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D25in: 85: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxxin: 86: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G34in: 87: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20in: 88: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15in: 89: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50in: 90: 35C05 Solutions in closed formin: 91: 35P05 General topics in linear spectral theoryin: 92: 35Q35 PDEs in connection with fluid mechanicsin: 93: 35Q40 PDEs in connection with quantum mechanicsin: 94: 35Q60 PDEs in connection with optics and electromagnetic theoryin: 95: 35Q62 PDEs in connection with statisticsin: 96: 35Q68 PDEs in connection with computer sciencein: 97: 35Q70 PDEs in connection with mechanics of particles and systemsin: 98: 35Q74 PDEs in connection with mechanics of deformable solids
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in: 99: 35Q75 PDEs in connection with relativity and gravitational theoryin: 100: 35Q79 PDEs in connection with classical thermodynamics and heat transferin: 101: 35Q82 PDEs in connection with statistical mechanicsin: 102: 35Q85 PDEs in connection with astronomy and astrophysicsin: 103: 35Q86 PDEs in connection with geophysicsin: 104: 35Q90 PDEs in connection with mathematical programmingin: 105: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencesin: 106: 35Q92 PDEs in connection with biology and other natural sciencesin: 107: 35Q93 PDEs in connection with control and optimizationin: 108: 35Q94 PDEs in connection with information and communicationin: 109: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25in: 110: 37A60 Dynamical systems in statistical mechanics [See also]82Cxxin: 111: 37B45 Continua theory in dynamicsin: 112: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemsin: 113: 37G30 Infinite nonwandering sets arising in bifurcationsin: 114: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxxin: 115: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A10in: 116: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxxin: 117: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)in: 118: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXin: 119: 37N30 Dynamical systems in numerical analysisin: 120: 37N35 Dynamical systems in controlin: 121: 37N40 Dynamical systems in optimization and economicsin: 122: 39A12 Discrete version of topics in analysisin: 123: 39A45 Equations in the complex domainin: 124: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)in: 125: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)in: 126: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)in: 127: 40Hxx Functional analytic methods in summabilityin: 128: 40H05 Functional analytic methods in summabilityin: 129: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B15in: 130: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)in: 131: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)in: 132: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
in: 133: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
in: 134: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)in: 135: 41A35 Approximation by operators (in particular, by integral operators)in: 136: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)in: 137: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)in: 138: 41A80 Remainders in approximation formulasin: 139: 42Axx Harmonic analysis in one variable
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in: 140: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30in: 141: 42B35 Function spaces arising in harmonic analysisin: 142: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)in: 143: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
in: 144: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
in: 145: 45Nxx Abstract integral equations, integral equations in abstract spacesin: 146: 45N05 Abstract integral equations, integral equations in abstract spacesin: 147: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)in: 148: 46A50 Compactness in topological linear spaces; angelic spaces, etc.in: 149: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07in: 150: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07in: 151: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxin: 152: 46B25 Classical Banach spaces in the general theoryin: 153: 46B50 Compactness in Banach (or normed) spacesin: 154: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxin: 155: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XXin: 156: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)in: 157: 46H30 Functional calculus in topological algebras [See also]47A60in: 158: 46K50 Nonselfadjoint (sub)algebras in algebras with involutionin: 159: 46L57 Derivations, dissipations and positive semigroups in C∗-algebrasin: 160: 46Mxx Methods of category theory in functional analysis [See also]18-XXin: 161: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsin: 162: 46N30 Applications in probability theory and statisticsin: 163: 46N40 Applications in numerical analysis [See also]65Jxxin: 164: 46N50 Applications in quantum physicsin: 165: 46N55 Applications in statistical physicsin: 166: 46N60 Applications in biology and other sciencesin: 167: 46S50 Functional analysis in probabilistic metric linear spacesin: 168: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60in: 169: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20in: 170: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22in: 171: 47C05 Operators in algebrasin: 172: 47C10 Operators in ∗-algebrasin: 173: 47C15 Operators in C∗- or von Neumann algebrasin: 174: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)in: 175: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)in: 176: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsin: 177: 47N30 Applications in probability theory and statisticsin: 178: 47N40 Applications in numerical analysis [See also]65Jxxin: 179: 47N50 Applications in the physical sciencesin: 180: 47N60 Applications in chemistry and life sciencesin: 181: 47N70 Applications in systems theory, circuits, and control theoryin: 182: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70in: 183: 49J05 Free problems in one independent variable
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in: 184: 49J10 Free problems in two or more independent variablesin: 185: 49J27 Problems in abstract spaces [See also]90C48, 93C25in: 186: 49K05 Free problems in one independent variablein: 187: 49K10 Free problems in two or more independent variablesin: 188: 49K27 Problems in abstract spaces [See also]90C48, 93C25in: 189: 49Q20 Variational problems in a geometric measure-theoretic settingin: 190: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)in: 191: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)in: 192: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxin: 193: 51E22 Linear codes and caps in Galois spaces [See also]94B05in: 194: 51M04 Elementary problems in Euclidean geometriesin: 195: 51M09 Elementary problems in hyperbolic and elliptic geometriesin: 196: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15in: 197: 52A07 Convex sets in topological vector spaces [See also]46A55in: 198: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04in: 199: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45in: 200: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45in: 201: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxin: 202: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxin: 203: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P21in: 204: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P21in: 205: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H31in: 206: 52C17 Packing and covering in n dimensions [See also]05B40, 11H31in: 207: 52C20 Tilings in 2 dimensions [See also]05B45, 51M20in: 208: 52C22 Tilings in n dimensions [See also]05B45, 51M20in: 209: 53A04 Curves in Euclidean spacein: 210: 53A05 Surfaces in Euclidean spacein: 211: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-spacein: 212: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)in: 213: 55Q35 Operations in homotopy groupsin: 214: 57M07 Topological methods in group theoryin: 215: 57M25 Knots and links in S3 For higher dimensions, see 57Q45in: 216: 57M60 Group actions in low dimensionsin: 217: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25in: 218: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxin: 219: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)in: 220: 58Exx Variational problems in infinite-dimensional spacesin: 221: 58E10 Applications to the theory of geodesics (problems in one independent variable)in: 222: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05in: 223: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.in: 224: 60J22 Computational methods in Markov chains [See also]65C40in: 225: 60K37 Processes in random environmentsin: 226: 62A86 Fuzzy analysis in statisticsin: 227: 62E86 Fuzziness in connection with the topics on distributions in this sectionin: 228: 62E86 Fuzziness in connection with the topics on distributions in this sectionin: 229: 62P30 Applications in engineering and industryin: 230: 65C50 Other computational problems in probabilityin: 231: 65C60 Computational problems in statistics
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in: 232: 65D19 Computational issues in computer and robotic visionin: 233: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30in: 234: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30in: 235: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30in: 236: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30in: 237: 65G40 General methods in interval analysisin: 238: 65Jxx Numerical analysis in abstract spacesin: 239: 65Pxx Numerical problems in dynamical systems [See also]37Mxxin: 240: 65Txx Numerical methods in Fourier analysisin: 241: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areain: 242: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areain: 243: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40in: 244: 68Rxx Discrete mathematics in relation to computer sciencein: 245: 68T27 Logic in artificial intelligencein: 246: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25in: 247: 70F16 Collisions in celestial mechanics, regularizationin: 248: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C26in: 249: 74Q05 Homogenization in equilibrium problemsin: 250: 74Q10 Homogenization and oscillations in dynamical problemsin: 251: 76B70 Stratification effects in inviscid fluidsin: 252: 76D50 Stratification effects in viscous fluidsin: 253: 76Mxx Basic methods in fluid mechanics [See also]65-XXin: 254: 76Sxx Flows in porous media; filtration; seepagein: 255: 76S05 Flows in porous media; filtration; seepagein: 256: 76Vxx Reaction effects in flows [See also]80A32in: 257: 76V05 Reaction effects in flows [See also]80A32in: 258: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10in: 259: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10in: 260: 76Z10 Biopropulsion in water and in airin: 261: 76Z10 Biopropulsion in water and in airin: 262: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)in: 263: 81Qxx General mathematical topics and methods in quantum theoryin: 264: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysisin: 265: 81Q12 Non-selfadjoint operator theory in quantum theoryin: 266: 81Rxx Groups and algebras in quantum theoryin: 267: 81T70 Quantization in field theory; cohomological methods [See also]58D29in: 268: 83C80 Analogues in lower dimensionsin: 269: 90C48 Programming in abstract spacesin: 270: 91A18 Games in extensive formin: 271: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)in: 272: 92Bxx Mathematical biology in generalin: 273: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A30in: 274: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)in: 275: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)in: 276: 93C25 Systems in abstract spaces
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in: 277: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,28E10
in: 278: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,28E10
in: 279: 97Cxx Psychology of mathematics education, research in mathematics educationin: 280: 97Dxx Education and instruction in mathematicsin: 281: 97E50 Reasoning and proving in the mathematics classroomin: 282: 97M20 Mathematics in vocational training and career educationin: 283: 97Q20 Affective aspects in teaching computer sciencein: 284: 97R20 Applications in mathematicsin: 285: 97R30 Applications in sciences
incidence: 1: 05B20 Matrices (incidence, Hadamard, etc.)incidence: 2: 51Axx Linear incidence geometryincidence: 3: 51A45 Incidence structures imbeddable into projective geometriesincidence: 4: 51Bxx Nonlinear incidence geometryincidence: 5: 51Exx Finite geometry and special incidence structuresincidence: 6: 51E30 Other finite incidence structures [See also]05B30incidence: 7: 51Gxx Ordered geometries (ordered incidence structures, etc.)incidence: 8: 51G05 Ordered geometries (ordered incidence structures, etc.)incidence: 9: 51H10 Topological linear incidence structuresincidence: 10: 51H15 Topological nonlinear incidence structuresincidence: 11: 51Jxx Incidence groupsincidence: 12: 51J10 Projective incidence groupsincluding: 1: 03B20 Subsystems of classical logic (including intuitionistic logic)including: 2: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35including: 3: 03B42 Logics of knowledge and belief (including belief change)including: 4: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45including: 5: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52including: 6: 03D15 Complexity of computation (including implicit computational complexity)
[See also]68Q15, 68Q17including: 7: 03E20 Other classical set theory (including functions, relations, and set algebra)including: 8: 03E45 Inner models, including constructibility, ordinal definability, and core modelsincluding: 9: 11B13 Additive bases, including sumsets [See also]05B10including: 10: 11P70 Inverse problems of additive number theory, including sumsetsincluding: 11: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25including: 12: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05including: 13: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic
functions)including: 14: 30B10 Power series (including lacunary series)including: 15: 30G30 Other generalizations of analytic functions (including abstract-valued functions)including: 16: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxxincluding: 17: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)including: 18: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)including: 19: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45including: 20: 46B03 Isomorphic theory (including renorming) of Banach spacesincluding: 21: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)including: 22: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32including: 23: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22
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including: 24: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,including analytic and meromorphic ones)
including: 25: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)including: 26: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22including: 27: 49J40 Variational methods including variational inequalities [See also]47J20including: 28: 49Lxx Hamilton-Jacobi theories, including dynamic programmingincluding: 29: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04including: 30: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45including: 31: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45including: 32: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxincluding: 33: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxincluding: 34: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B20including: 35: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60including: 36: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17including: 37: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxincluding: 38: 60G22 Fractional processes, including fractional Brownian motionincluding: 39: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C30including: 40: 65P10 Hamiltonian systems including symplectic integratorsincluding: 41: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C35including: 42: 70Fxx Dynamics of a system of particles, including celestial mechanicsincluding: 43: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic
materials)including: 44: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)including: 45: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)including: 46: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)including: 47: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)including: 48: 80A10 Classical thermodynamics, including relativisticincluding: 49: 81P20 Stochastic mechanics (including stochastic electrodynamics)including: 50: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysisincluding: 51: 81Q20 Semiclassical techniques, including WKB and Maslov methodsincluding: 52: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.including: 53: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
including: 54: 81S30 Phase-space methods including Wigner distributions, etc.including: 55: 81V05 Strong interaction, including quantum chromodynamicsincluding: 56: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E20including: 57: 82C35 Irreversible thermodynamics, including Onsager-Machlup theoryincluding: 58: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)including: 59: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesincluding: 60: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesincluding: 61: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B06including: 62: 91Dxx Mathematical sociology (including anthropology)including: 63: 91G60 Numerical methods (including Monte Carlo methods)including: 64: 94A40 Channel models (including quantum)including: 65: 94B12 Combined modulation schemes (including trellis codes)including: 66: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50
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inclusion: 1: 40D25 Inclusion and equivalence theoremsinclusions: 1: 34A60 Differential inclusions [See also]49J21, 49K21inclusions: 2: 34G25 Evolution inclusionsinclusions: 3: 34K09 Functional-differential inclusionsinclusions: 4: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K21
incomplete: 1: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnelintegrals)incomplete: 2: 49N30 Problems with incomplete information [See also]93C41incomplete: 3: 93C41 Problems with incomplete information
incompleteness: 1: 03F40 Godel numberings and issues of incompletenessincompressible: 1: 76Bxx Incompressible inviscid fluidsincompressible: 2: 76Dxx Incompressible viscous fluids
increments: 1: 60G51 Processes with independent increments; Levy processesindefinite: 1: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50indefinite: 2: 47B50 Operators on spaces with an indefinite metric [See also]46C50indefinite: 3: 53B30 Lorentz metrics, indefinite metricsindefinite: 4: 53C50 Lorentz manifolds, manifolds with indefinite metrics
independence: 1: 03E35 Consistency and independence resultsindependence: 2: 11J72 Irrationality; linear independence over a fieldindependence: 3: 11J85 Algebraic independence; Gel′fond’s methodindependence: 4: 54A35 Consistency and independence results [See also]03E35independent: 1: 05C69 Dominating sets, independent sets, cliquesindependent: 2: 49J05 Free problems in one independent variableindependent: 3: 49J10 Free problems in two or more independent variablesindependent: 4: 49K05 Free problems in one independent variableindependent: 5: 49K10 Free problems in two or more independent variablesindependent: 6: 58E10 Applications to the theory of geodesics (problems in one independent variable)independent: 7: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05independent: 8: 60G50 Sums of independent random variables; random walksindependent: 9: 60G51 Processes with independent increments; Levy processes
index: 1: 19K56 Index theory [See also]58J20, 58J22index: 2: 37B30 Index theory, Morse-Conley indicesindex: 3: 37C25 Fixed points, periodic points, fixed-point index theoryindex: 4: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J20index: 5: 53D12 Lagrangian submanifolds; Maslov indexindex: 6: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80index: 7: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M20india: 1: 01A32 India
indices: 1: 37B30 Index theory, Morse-Conley indicesindices: 2: 91B82 Statistical methods; economic indices and measures
indigenous: 1: 01A12 Indigenous cultures of the Americasindigenous: 2: 01A13 Other indigenous cultures (non-European)indigenous: 3: 01A15 Indigenous European cultures (pre-Greek, etc.)individual: 1: 47Cxx Individual linear operators as elements of algebraic systemsindividual: 2: 91B08 Individual preferences
induced: 1: 22D30 Induced representationsinduced: 2: 60G30 Continuity and singularity of induced measures
induction: 1: 19A22 Frobenius induction, Burnside and representation ringsinductive: 1: 03B48 Probability and inductive logic [See also]60A05inductive: 2: 03D70 Inductive definabilityinductive: 3: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40inductive: 4: 46M40 Inductive and projective limits [See also]46A13industrial: 1: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40industry: 1: 62P30 Applications in engineering and industry
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inelastic: 1: 81U35 Inelastic and multichannel scatteringinequalities: 1: 05A20 Combinatorial inequalitiesinequalities: 2: 11D75 Diophantine inequalities [See also]11J25inequalities: 3: 11J25 Diophantine inequalities [See also]11D75inequalities: 4: 15A39 Linear inequalitiesinequalities: 5: 15A42 Inequalities involving eigenvalues and eigenvectorsinequalities: 6: 15A45 Miscellaneous inequalities involving matricesinequalities: 7: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
inequalities: 8: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
inequalities: 9: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
inequalities: 10: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
inequalities: 11: 26D05 Inequalities for trigonometric functions and polynomialsinequalities: 12: 26D07 Inequalities involving other types of functionsinequalities: 13: 26D10 Inequalities involving derivatives and differential and integral operatorsinequalities: 14: 26D15 Inequalities for sums, series and integralsinequalities: 15: 26D20 Other analytical inequalitiesinequalities: 16: 30A10 Inequalities in the complex domaininequalities: 17: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,see 32H25, 32H30
inequalities: 18: 34A40 Differential inequalities [See also]26D20inequalities: 19: 34K38 Functional-differential inequalitiesinequalities: 20: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities forintegrals
inequalities: 21: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities forintegrals
inequalities: 22: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities[See also]35R35, 49J40
inequalities: 23: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities[See also]35R35, 49J40
inequalities: 24: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J40inequalities: 25: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities[See also]35R35, 49J40
inequalities: 26: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities[See also]35R35, 49J40
inequalities: 27: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J40inequalities: 28: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities[See also]35R35, 49J40
inequalities: 29: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variationalinequalities [See also]35R35, 49J40
inequalities: 30: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,49J40
inequalities: 31: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,49J40
inequalities: 32: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type[See also]35R35, 49J40
inequalities: 33: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J40inequalities: 34: 35R45 Partial differential inequalitiesinequalities: 35: 39Bxx Functional equations and inequalities [See also]30D05inequalities: 36: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,26Dxx
inequalities: 37: 39B72 Systems of functional equations and inequalitiesinequalities: 38: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)inequalities: 39: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)
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inequalities: 40: 42A05 Trigonometric polynomials, inequalities, extremal problemsinequalities: 41: 47A30 Norms (inequalities, more than one norm, etc.)inequalities: 42: 47A50 Equations and inequalities involving linear operators, with vector unknownsinequalities: 43: 47A63 Operator inequalitiesinequalities: 44: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For globaland geometric aspects, see 58-XX
inequalities: 45: 47J20 Variational and other types of inequalities involving nonlinear operators (general)[See also]49J40
inequalities: 46: 49J40 Variational methods including variational inequalities [See also]47J20inequalities: 47: 51M16 Inequalities and extremum problems For convex problems, see 52A40inequalities: 48: 52A40 Inequalities and extremum problemsinequalities: 49: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)[See also]03Exx For ultrafilters, see 54D80
inequalities: 50: 58E35 Variational inequalities (global problems)inequalities: 51: 60E15 Inequalities; stochastic orderingsinequalities: 52: 65K15 Numerical methods for variational inequalities and related problemsinequalities: 53: 90C33 Complementarity and equilibrium problems and variational inequalities (finitedimensions)
inequalities: 54: 97H30 Equations and inequalitiesinertial: 1: 35B42 Inertial manifoldsinertial: 2: 37L25 Inertial manifolds and other invariant attracting sets
inference: 1: 62Fxx Parametric inferenceinference: 2: 62F15 Bayesian inferenceinference: 3: 62F30 Inference under constraintsinference: 4: 62F86 Parametric inference and fuzzinessinference: 5: 62Gxx Nonparametric inferenceinference: 6: 62G32 Statistics of extreme values; tail inferenceinference: 7: 62G86 Nonparametric inference and fuzzinessinference: 8: 62Jxx Linear inference, regressioninference: 9: 62J86 Fuzziness, and linear inference and regressioninference: 10: 62Mxx Inference from stochastic processesinference: 11: 62M86 Inference from stochastic processes and fuzzinessinfinitary: 1: 03C75 Other infinitary logicinfinitary: 2: 08A65 Infinitary algebras
infinite: 1: 05C63 Infinite graphsinfinite: 2: 20B07 General theory for infinite groupsinfinite: 3: 20B22 Multiply transitive infinite groupsinfinite: 4: 20B27 Infinite automorphism groups [See also]12F10infinite: 5: 20C07 Group rings of infinite groups and their modules [See also]16S34infinite: 6: 20C12 Integral representations of infinite groupsinfinite: 7: 20C32 Representations of infinite symmetric groupsinfinite: 8: 20Exx Structure and classification of infinite or finite groupsinfinite: 9: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]infinite: 10: 20Fxx Special aspects of infinite or finite groupsinfinite: 11: 20K20 Torsion-free groups, infinite rankinfinite: 12: 34A35 Differential equations of infinite orderinfinite: 13: 34B40 Boundary value problems on infinite intervalsinfinite: 14: 35R50 Partial differential equations of infinite orderinfinite: 15: 37G30 Infinite nonwandering sets arising in bifurcationsinfinite: 16: 40Axx Convergence and divergence of infinite limiting processesinfinite: 17: 40A20 Convergence and divergence of infinite productsinfinite: 18: 55P47 Infinite loop spacesinfinite: 19: 70F45 Infinite particle systems
infinite-dimensional: 1: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)infinite-dimensional: 2: 16K40 Infinite-dimensional and generalinfinite-dimensional: 3: 17B65 Infinite-dimensional Lie (super)algebras [See also]22E65infinite-dimensional: 4: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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[See also]17B65, 58B25, 58H05infinite-dimensional: 5: 22E66 Analysis on and representations of infinite-dimensional Lie groupsinfinite-dimensional: 6: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxxinfinite-dimensional: 7: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxinfinite-dimensional: 8: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11infinite-dimensional: 9: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12infinite-dimensional: 10: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25infinite-dimensional: 11: 37Kxx Infinite-dimensional Hamiltonian systems [See also]35Axx, 35Qxxinfinite-dimensional: 12: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresinfinite-dimensional: 13: 37K55 Perturbations, KAM for infinite-dimensional systemsinfinite-dimensional: 14: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxxinfinite-dimensional: 15: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H15infinite-dimensional: 16: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60infinite-dimensional: 17: 46F25 Distributions on infinite-dimensional spaces [See also]58C35infinite-dimensional: 18: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txxinfinite-dimensional: 19: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C10infinite-dimensional: 20: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxxinfinite-dimensional: 21: 57N20 Topology of infinite-dimensional manifolds [See also]58Bxxinfinite-dimensional: 22: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxinfinite-dimensional: 23: 58Bxx Infinite-dimensional manifoldsinfinite-dimensional: 24: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D05infinite-dimensional: 25: 58Exx Variational problems in infinite-dimensional spacesinfinite-dimensional: 26: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)infinite-dimensional: 27: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
infinite-measure: 1: 37A40 Nonsingular (and infinite-measure preserving) transformationsinfinitely: 1: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25infinitely: 2: 60E07 Infinitely divisible distributions; stable distributionsinfinitely: 3: 91A13 Games with infinitely many players
infinitesimal: 1: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxxinfinitesimal: 2: 14B10 Infinitesimal methods [See also]13D10
infinity: 1: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48informal: 1: 97G20 Informal geometry
information: 1: 35Q94 PDEs in connection with information and communicationinformation: 2: 49N30 Problems with incomplete information [See also]93C41information: 3: 62Bxx Sufficiency and informationinformation: 4: 62B86 Fuzziness, sufficiency, and informationinformation: 5: 68P20 Information storage and retrievalinformation: 6: 68P30 Coding and information theory (compaction, compression, models of communication,encoding schemes, etc.) [See also]94Axx
information: 7: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32information: 8: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)[See also]68M11
information: 9: 81P45 Quantum information, communication, networks [See also]94A15, 94A17information: 10: 93C41 Problems with incomplete informationinformation: 11: 94-XX Information and communication, circuits
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information: 12: 94Axx Communication, informationinformation: 13: 94A15 Information theory, general [See also]62B10, 81P45information: 14: 94A17 Measures of information, entropyinformation: 15: 97R50 Data bases, information systems
information-theoretic: 1: 62B10 Information-theoretic topics [See also]94A17informational: 1: 91B44 Informational economics
inhomogeneity: 1: 74E05 Inhomogeneityinhomogeneous: 1: 11J20 Inhomogeneous linear forms
initial: 1: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuationof solutions
initial: 2: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxinitial: 3: 35E15 Initial value problemsinitial: 4: 35F10 Initial value problems for linear first-order equationsinitial: 5: 35F25 Initial value problems for nonlinear first-order equationsinitial: 6: 35F40 Initial value problems for linear first-order systemsinitial: 7: 35F55 Initial value problems for nonlinear first-order systemsinitial: 8: 35G10 Initial value problems for linear higher-order equationsinitial: 9: 35G25 Initial value problems for nonlinear higher-order equationsinitial: 10: 35G40 Initial value problems for linear higher-order systemsinitial: 11: 35G55 Initial value problems for nonlinear higher-order systemsinitial: 12: 35K15 Initial value problems for second-order parabolic equationsinitial: 13: 35K30 Initial value problems for higher-order parabolic equationsinitial: 14: 35K45 Initial value problems for second-order parabolic systemsinitial: 15: 35K46 Initial value problems for higher-order parabolic systemsinitial: 16: 35K60 Nonlinear initial value problems for linear parabolic equationsinitial: 17: 35L03 Initial value problems for first-order hyperbolic equationsinitial: 18: 35L15 Initial value problems for second-order hyperbolic equationsinitial: 19: 35L30 Initial value problems for higher-order hyperbolic equationsinitial: 20: 35L45 Initial value problems for first-order hyperbolic systemsinitial: 21: 35L52 Initial value problems for second-order hyperbolic systemsinitial: 22: 35L56 Initial value problems for higher-order hyperbolic systemsinitial: 23: 35M11 Initial value problems for equations of mixed typeinitial: 24: 35M31 Initial value problems for systems of mixed typeinitial: 25: 35N20 Overdetermined initial value problemsinitial: 26: 35S10 Initial value problems for pseudodifferential operatorsinitial: 27: 58J47 Propagation of singularities; initial value problemsinitial: 28: 65L05 Initial value problemsinitial: 29: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsinitial: 30: 74B10 Linear elasticity with initial stresses
initial-boundary: 1: 35F16 Initial-boundary value problems for linear first-order equationsinitial-boundary: 2: 35F31 Initial-boundary value problems for nonlinear first-order equationsinitial-boundary: 3: 35F46 Initial-boundary value problems for linear first-order systemsinitial-boundary: 4: 35F61 Initial-boundary value problems for nonlinear first-order systemsinitial-boundary: 5: 35G16 Initial-boundary value problems for linear higher-order equationsinitial-boundary: 6: 35G31 Initial-boundary value problems for nonlinear higher-order equationsinitial-boundary: 7: 35G46 Initial-boundary value problems for linear higher-order systemsinitial-boundary: 8: 35G61 Initial-boundary value problems for nonlinear higher-order systemsinitial-boundary: 9: 35K20 Initial-boundary value problems for second-order parabolic equationsinitial-boundary: 10: 35K35 Initial-boundary value problems for higher-order parabolic equationsinitial-boundary: 11: 35K51 Initial-boundary value problems for second-order parabolic systemsinitial-boundary: 12: 35K52 Initial-boundary value problems for higher-order parabolic systemsinitial-boundary: 13: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsinitial-boundary: 14: 35L04 Initial-boundary value problems for first-order hyperbolic equationsinitial-boundary: 15: 35L20 Initial-boundary value problems for second-order hyperbolic equationsinitial-boundary: 16: 35L35 Initial-boundary value problems for higher-order hyperbolic equationsinitial-boundary: 17: 35L50 Initial-boundary value problems for first-order hyperbolic systems
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initial-boundary: 18: 35L53 Initial-boundary value problems for second-order hyperbolic systemsinitial-boundary: 19: 35L57 Initial-boundary value problems for higher-order hyperbolic systemsinitial-boundary: 20: 35M13 Initial-boundary value problems for equations of mixed typeinitial-boundary: 21: 35M33 Initial-boundary value problems for systems of mixed typeinitial-boundary: 22: 35N30 Overdetermined initial-boundary value problemsinitial-boundary: 23: 35S11 Initial-boundary value problems for pseudodifferential operatorsinitial-boundary: 24: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsinjective: 1: 13C11 Injective and flat modules and idealsinjective: 2: 16D50 Injective modules, self-injective rings [See also]16L60injective: 3: 46M10 Projective and injective objects [See also]46A22
injectives: 1: 08B30 Injectives, projectivesinjectives: 2: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D50
inner: 1: 03E45 Inner models, including constructibility, ordinal definability, and core modelsinner: 2: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exxinner: 3: 30J05 Inner functionsinner: 4: 30J15 Singular inner functionsinner: 5: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxinner: 6: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)inner: 7: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50inner: 8: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)inner: 9: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
input-output: 1: 93B15 Realizations from input-output datainput-output: 2: 93D25 Input-output approaches
inseparable: 1: 12F15 Inseparable extensionsinspection: 1: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N05instability: 1: 70K50 Bifurcations and instabilityinstability: 2: 76E09 Stability and instability of nonparallel flowsinstability: 3: 76E15 Absolute and convective instability and stabilityinstability: 4: 76E17 Interfacial stability and instabilityinstability: 5: 76E20 Stability and instability of geophysical and astrophysical flowsinstability: 6: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flowsinstantons: 1: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistortheory, instantons, quantum field theory) [See also]32L25, 81Txx
institutions: 1: 01A74 Other institutions and academiesinstruction: 1: 97Dxx Education and instruction in mathematicsinstruction: 2: 97U50 Computer assisted instruction; e-learning
insurance: 1: 91B30 Risk theory, insuranceinsurance: 2: 97M30 Financial and insurance mathematics
integer: 1: 11Y55 Calculation of integer sequencesinteger: 2: 90C10 Integer programminginteger: 3: 90C11 Mixed integer programming
integer-valued: 1: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25integers: 1: 05A17 Partitions of integers [See also]11P81, 11P82, 11P83integers: 2: 11N25 Distribution of integers with specified multiplicative constraintsintegers: 3: 11N69 Distribution of integers in special residue classesintegers: 4: 11N80 Generalized primes and integersintegers: 5: 11R04 Algebraic numbers; rings of algebraic integersintegers: 6: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10integers: 7: 15B36 Matrices of integers [See also]11C20integers: 8: 20G25 Linear algebraic groups over local fields and their integersintegers: 9: 20G30 Linear algebraic groups over global fields and their integersintegers: 10: 97F40 Integers, rational numbers
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integrability: 1: 37J30 Obstructions to integrability (nonintegrability criteria)integrability: 2: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,
hierarchies (KdV, KP, Toda, etc.)integrable: 1: 14H70 Relationships with integrable systemsintegrable: 2: 17B80 Applications to integrable systemsintegrable: 3: 37J35 Completely integrable systems, topological structure of phase space, integrationmethodsintegrable: 4: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)integrable: 5: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsintegrable: 6: 70E40 Integrable cases of motionintegrable: 7: 70H06 Completely integrable systems and methods of integrationintegrable: 8: 70H08 Nearly integrable Hamiltonian systems, KAM theoryintegrable: 9: 81R12 Relations with integrable systems [See also]17Bxx, 37J35
integral: 1: 11F11 Holomorphic modular forms of integral weightintegral: 2: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10integral: 3: 11S23 Integral representationsintegral: 4: 13B21 Integral dependence; going up, going downintegral: 5: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)integral: 6: 13Gxx Integral domainsintegral: 7: 13G05 Integral domainsintegral: 8: 16U10 Integral domainsintegral: 9: 20C10 Integral representations of finite groupsintegral: 10: 20C12 Integral representations of infinite groupsintegral: 11: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)integral: 12: 26D10 Inequalities involving derivatives and differential and integral operatorsintegral: 13: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10integral: 14: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxintegral: 15: 31A10 Integral representations, integral operators, integral equations methodsintegral: 16: 31A10 Integral representations, integral operators, integral equations methodsintegral: 17: 31A10 Integral representations, integral operators, integral equations methodsintegral: 18: 31B10 Integral representations, integral operators, integral equations methodsintegral: 19: 31B10 Integral representations, integral operators, integral equations methodsintegral: 20: 31B10 Integral representations, integral operators, integral equations methodsintegral: 21: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)integral: 22: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)integral: 23: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)integral: 24: 33E30 Other functions coming from differential, difference and integral equationsintegral: 25: 34C05 Location of integral curves, singular points, limit cyclesintegral: 26: 35A22 Transform methods (e.g. integral transforms)integral: 27: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities for
integralsintegral: 28: 35C15 Integral representations of solutionsintegral: 29: 35S30 Fourier integral operatorsintegral: 30: 40C10 Integral methodsintegral: 31: 41A35 Approximation by operators (in particular, by integral operators)integral: 32: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
integral: 33: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
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integral: 34: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
integral: 35: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
integral: 36: 45-XX Integral equationsintegral: 37: 45Axx Linear integral equationsintegral: 38: 45A05 Linear integral equationsintegral: 39: 45Bxx Fredholm integral equationsintegral: 40: 45B05 Fredholm integral equationsintegral: 41: 45Dxx Volterra integral equations [See also]34A12integral: 42: 45D05 Volterra integral equations [See also]34A12integral: 43: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A35integral: 44: 45E05 Integral equations with kernels of Cauchy type [See also]35J15integral: 45: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35integral: 46: 45Fxx Systems of linear integral equationsintegral: 47: 45F05 Systems of nonsingular linear integral equationsintegral: 48: 45F10 Dual, triple, etc., integral and series equationsintegral: 49: 45F15 Systems of singular linear integral equationsintegral: 50: 45Gxx Nonlinear integral equations [See also]47H30, 47Jxxintegral: 51: 45G05 Singular nonlinear integral equationsintegral: 52: 45G10 Other nonlinear integral equationsintegral: 53: 45G15 Systems of nonlinear integral equationsintegral: 54: 45Nxx Abstract integral equations, integral equations in abstract spacesintegral: 55: 45Nxx Abstract integral equations, integral equations in abstract spacesintegral: 56: 45N05 Abstract integral equations, integral equations in abstract spacesintegral: 57: 45N05 Abstract integral equations, integral equations in abstract spacesintegral: 58: 45Pxx Integral operators [See also]47B38, 47G10integral: 59: 45P05 Integral operators [See also]47B38, 47G10integral: 60: 45Rxx Random integral equations [See also]60H20integral: 61: 45R05 Random integral equations [See also]60H20integral: 62: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XXintegral: 63: 46N20 Applications to differential and integral equationsintegral: 64: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15integral: 65: 47Gxx Integral, integro-differential, and pseudodifferential operators [See also]58Jxxintegral: 66: 47G10 Integral operators [See also]45P05integral: 67: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)integral: 68: 47N20 Applications to differential and integral equationsintegral: 69: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C35integral: 70: 52A22 Random convex sets and integral geometry [See also]53C65, 60D05integral: 71: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axxintegral: 72: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxxintegral: 73: 60H20 Stochastic integral equationsintegral: 74: 65C30 Stochastic differential and integral equationsintegral: 75: 65Rxx Integral equations, integral transformsintegral: 76: 65Rxx Integral equations, integral transformsintegral: 77: 65R10 Integral transformsintegral: 78: 65R20 Integral equationsintegral: 79: 81Q40 Bethe-Salpeter and other integral equationsintegral: 80: 97I50 Integral calculus
integrally: 1: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings(Japanese, etc.)
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integrals: 1: 14K20 Analytic theory; abelian integrals and differentialsintegrals: 2: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)integrals: 3: 26A33 Fractional derivatives and integralsintegrals: 4: 26A39 Denjoy and Perron integrals, other special integralsintegrals: 5: 26A39 Denjoy and Perron integrals, other special integralsintegrals: 6: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XXintegrals: 7: 26D15 Inequalities for sums, series and integralsintegrals: 8: 28A35 Measures and integrals in product spacesintegrals: 9: 28Bxx Set functions, measures and integrals with values in abstract spacesintegrals: 10: 28B05 Vector-valued set functions, measures and integrals [See also]46G10integrals: 11: 28B10 Group- or semigroup-valued set functions, measures and integralsintegrals: 12: 28B15 Set functions, measures and integrals with values in ordered spacesintegrals: 13: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresintegrals: 14: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11integrals: 15: 30D10 Representations of entire functions by series and integralsintegrals: 16: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxintegrals: 17: 32A55 Singular integralsintegrals: 18: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel
integrals)integrals: 19: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)integrals: 20: 33C70 Other hypergeometric functions and integrals in several variablesintegrals: 21: 33C75 Elliptic integrals as hypergeometric functionsintegrals: 22: 33D05 q-gamma functions, q-beta functions and integralsintegrals: 23: 33D60 Basic hypergeometric integrals and functions defined by themintegrals: 24: 33D70 Other basic hypergeometric functions and integrals in several variablesintegrals: 25: 33E05 Elliptic functions and integralsintegrals: 26: 33E20 Other functions defined by series and integralsintegrals: 27: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)integrals: 28: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities for
integralsintegrals: 29: 40A10 Convergence and divergence of integralsintegrals: 30: 42A50 Conjugate functions, conjugate series, singular integralsintegrals: 31: 42B20 Singular and oscillatory integrals (Calderon-Zygmund, etc.)integrals: 32: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
integrals: 33: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
integrals: 34: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) onmanifolds [See also]28Cxx, 46G12, 60-XX
integrals: 35: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.integrals: 36: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)integrals: 37: 60H05 Stochastic integralsintegrals: 38: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40integrals: 39: 81S40 Path integrals [See also]58D30
integrated: 1: 47D62 Integrated semigroupsintegration: 1: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)integration: 2: 14E18 Arcs and motivic integrationintegration: 3: 26B15 Integration: length, area, volume [See also]28A75, 51M25
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integration: 4: 28-XX Measure and integration For analysis on manifolds, see 58-XXintegration: 5: 28A25 Integration with respect to measures and other set functionsintegration: 6: 28A50 Integration and disintegration of measuresintegration: 7: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurableselections [See also]26E25, 54C60, 54C65, 91B14integration: 8: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),representing set functions and measuresintegration: 9: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions[See also]45Exxintegration: 10: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27integration: 11: 37J35 Completely integrable systems, topological structure of phase space, integrationmethodsintegration: 12: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsintegration: 13: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)[See also]28-XX, 46Txxintegration: 14: 46G10 Vector-valued measures and integration [See also]28Bxx, 46B22integration: 15: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12integration: 16: 46L51 Noncommutative measure and integrationintegration: 17: 49Q15 Geometric measure and integration theory, integral and normal currents[See also]28A75, 32C30, 58A25, 58C35integration: 18: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,53Cxx For geometric integration theory, see 49Q15integration: 19: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxintegration: 20: 65D30 Numerical integrationintegration: 21: 70H06 Completely integrable systems and methods of integrationintegration: 22: 78M12 Finite volume methods, finite integration techniquesintegrators: 1: 37M15 Symplectic integratorsintegrators: 2: 65P10 Hamiltonian systems including symplectic integrators
integro-differential: 1: 47Gxx Integral, integro-differential, and pseudodifferential operators [See also]58Jxxintegro-differential: 2: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx
integro-ordinary: 1: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G20integro-ordinary: 2: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G20
integro-partial: 1: 35R09 Integro-partial differential equations [See also]45Kxxintegro-partial: 2: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20integro-partial: 3: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G20
intelligence: 1: 68Txx Artificial intelligenceintelligence: 2: 68T27 Logic in artificial intelligenceintelligence: 3: 97C40 Intelligence and aptitudesintelligence: 4: 97R40 Artificial intelligenceinteracting: 1: 60K35 Interacting random processes; statistical mechanics type models; percolation theory[See also]82B43, 82C43interacting: 2: 82C22 Interacting particle systems [See also]60K35interaction: 1: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction[See also]35Q30interaction: 2: 76D09 Viscous-inviscid interactioninteraction: 3: 76N17 Viscous-inviscid interactioninteraction: 4: 81V05 Strong interaction, including quantum chromodynamicsinteraction: 5: 81V10 Electromagnetic interaction; quantum electrodynamicsinteraction: 6: 81V15 Weak interactioninteraction: 7: 81V17 Gravitational interaction [See also]83Cxx and 83Exxinteraction: 8: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
interactions: 1: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)interactions: 2: 81V19 Other fundamental interactionsinteractive: 1: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)[See also]68Q85
interdisciplinarity: 1: 97M10 Modeling and interdisciplinarityinterest: 1: 00B10 Collections of articles of general interest
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interest: 2: 00B20 Proceedings of conferences of general interestinterest: 3: 00B25 Proceedings of conferences of miscellaneous specific interestinterest: 4: 91G30 Interest rates (stochastic models)
interface: 1: 82B24 Interface problems; diffusion-limited aggregationinterface: 2: 82C24 Interface problems; diffusion-limited aggregation
interfaces: 1: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)[See also]68M11interfaces: 2: 74A50 Structured surfaces and interfaces, coexistent phasesinterfacial: 1: 76E17 Interfacial stability and instability
interior-point: 1: 90C51 Interior-point methodsintermediate: 1: 03B55 Intermediate logics
internal: 1: 76B55 Internal wavesinternal-variable: 1: 74Cxx Plastic materials, materials of stress-rate and internal-variable type
internet: 1: 68M11 Internet topics [See also]68U35interpolation: 1: 03C40 Interpolation, preservation, definabilityinterpolation: 2: 30E05 Moment problems, interpolation problemsinterpolation: 3: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolationinterpolation: 4: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
interpolation: 5: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
interpolation: 6: 41A05 Interpolation [See also]42A15 and 65D05interpolation: 7: 42A15 Trigonometric interpolationinterpolation: 8: 46B70 Interpolation between normed linear spaces [See also]46M35interpolation: 9: 46M35 Abstract interpolation of topological vector spaces [See also]46B70interpolation: 10: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60interpolation: 11: 65D05 Interpolationinterpolation: 12: 65T40 Trigonometric approximation and interpolationinterpolation: 13: 97N50 Interpolation and approximation
interpretations: 1: 03F25 Relative consistency and interpretationsinterpreters: 1: 68N20 Compilers and interpretersintersection: 1: 05C62 Graph representations (geometric and intersection representations, etc.) For graphdrawing, see also 68R10
intersection: 2: 13D22 Homological conjectures (intersection theorems)intersection: 3: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15intersection: 4: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15intersection: 5: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne(co)homologies)
intersection: 6: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxxintersection: 7: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,32S60, 58J15
intersection: 8: 37G25 Bifurcations connected with nontransversal intersectionintersection: 9: 55N33 Intersection homology and cohomology
intersections: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,14M12
intersections: 2: 14M10 Complete intersections [See also]13C40intersections: 3: 55N45 Products and intersections
interval: 1: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)interval: 2: 65Gxx Error analysis and interval analysisinterval: 3: 65G30 Interval and finite arithmeticinterval: 4: 65G40 General methods in interval analysis
intervals: 1: 11L26 Sums over arbitrary intervalsintervals: 2: 34B40 Boundary value problems on infinite intervals
into: 1: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
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computer science [See also]05C12, 68Rxxinto: 2: 51A45 Incidence structures imbeddable into projective geometries
intuitionistic: 1: 03B20 Subsystems of classical logic (including intuitionistic logic)intuitionistic: 2: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionistic
and similar approaches see 03F55intuitionistic: 3: 03F55 Intuitionistic mathematics
invariance: 1: 58J70 Invariance and symmetry properties [See also]35A30invariance: 2: 60F17 Functional limit theorems; invariance principlesinvariant: 1: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24invariant: 2: 14L24 Geometric invariant theory [See also]13A50invariant: 3: 16R30 Trace rings and invariant theoryinvariant: 4: 16U70 Center, normalizer (invariant elements)invariant: 5: 16W22 Actions of groups and semigroups; invariant theoryinvariant: 6: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05invariant: 7: 32F45 Invariant metrics and pseudodistancesinvariant: 8: 34C45 Invariant manifoldsinvariant: 9: 34K19 Invariant manifoldsinvariant: 10: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setsinvariant: 11: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxxinvariant: 12: 37D10 Invariant manifold theoryinvariant: 13: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D20invariant: 14: 37L25 Inertial manifolds and other invariant attracting setsinvariant: 15: 37L40 Invariant measuresinvariant: 16: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)invariant: 17: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40invariant: 18: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)invariant: 19: 47A15 Invariant subspaces [See also]47A46invariant: 20: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.invariant: 21: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductioninvariant: 22: 70K43 Quasi-periodic motions and invariant tori
invariants: 1: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)invariants: 2: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D45invariants: 3: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D45invariants: 4: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D45invariants: 5: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L24invariants: 6: 28D20 Entropy and other invariantsinvariants: 7: 32S10 Invariants of analytic local ringsinvariants: 8: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantsinvariants: 9: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundariesinvariants: 10: 34C14 Symmetries, invariantsinvariants: 11: 35B06 Symmetries, invariants, etc.invariants: 12: 37A35 Entropy and other invariants, isomorphism, classificationinvariants: 13: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationinvariants: 14: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D20invariants: 15: 46A63 Topological invariants ((DN), (Ω), etc.)invariants: 16: 53A55 Differential invariants (local theory), geometric objectsinvariants: 17: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35invariants: 18: 55Q25 Hopf invariants
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invariants: 19: 57M27 Invariants of knots and 3-manifoldsinvariants: 20: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXinvariants: 21: 58J28 Eta-invariants, Chern-Simons invariantsinvariants: 22: 58K65 Topological invariantsinvariants: 23: 70H11 Adiabatic invariantsinventory: 1: 90B05 Inventory, storage, reservoirs
inverse: 1: 11P70 Inverse problems of additive number theory, including sumsetsinverse: 2: 12F12 Inverse Galois theoryinverse: 3: 15A29 Inverse problemsinverse: 4: 20M18 Inverse semigroupsinverse: 5: 31A25 Boundary value and inverse problemsinverse: 6: 31B20 Boundary value and inverse problemsinverse: 7: 34A55 Inverse problemsinverse: 8: 34K29 Inverse problemsinverse: 9: 34L25 Scattering theory, inverse scatteringinverse: 10: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)inverse: 11: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)inverse: 12: 35R30 Inverse problemsinverse: 13: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsinverse: 14: 41A27 Inverse theoremsinverse: 15: 43A50 Convergence of Fourier series and of inverse transformsinverse: 16: 45Qxx Inverse problemsinverse: 17: 45Q05 Inverse problemsinverse: 18: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15inverse: 19: 49N45 Inverse problemsinverse: 20: 65F18 Inverse eigenvalue problemsinverse: 21: 65J22 Inverse problemsinverse: 22: 65L09 Inverse problemsinverse: 23: 65M32 Inverse problemsinverse: 24: 65N21 Inverse problemsinverse: 25: 65R32 Inverse problemsinverse: 26: 70F17 Inverse problemsinverse: 27: 74G75 Inverse problemsinverse: 28: 74J25 Inverse problemsinverse: 29: 78A46 Inverse scattering problemsinverse: 30: 80A23 Inverse problemsinverse: 31: 81U40 Inverse scattering problemsinverse: 32: 86A22 Inverse problems [See also]35R30
inverses: 1: 15A09 Matrix inversion, generalized inversesinverses: 2: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)inverses: 3: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)inverses: 4: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
inversion: 1: 11A25 Arithmetic functions; related numbers; inversion formulasinversion: 2: 15A09 Matrix inversion, generalized inversesinversion: 3: 40Exx Inversion theoremsinversion: 4: 40E15 Lacunary inversion theoremsinversion: 5: 65F05 Direct methods for linear systems and matrix inversioninvertible: 1: 14C20 Divisors, linear systems, invertible sheaves
investigation: 1: 34C60 Qualitative investigation and simulation of modelsinvestigation: 2: 34K60 Qualitative investigation and simulation of modelsinvestigation: 3: 65L07 Numerical investigation of stability of solutions
inviscid: 1: 76Bxx Incompressible inviscid fluidsinviscid: 2: 76B70 Stratification effects in inviscid fluids
involution: 1: 16R50 Other kinds of identities (generalized polynomial, rational, involution)involution: 2: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
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17C50, 46Kxxinvolution: 3: 46Kxx Topological (rings and) algebras with an involution [See also]16W10involution: 4: 46K05 General theory of topological algebras with involutioninvolution: 5: 46K10 Representations of topological algebras with involutioninvolution: 6: 46K50 Nonselfadjoint (sub)algebras in algebras with involutioninvolution: 7: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L70involving: 1: 11J95 Results involving abelian varietiesinvolving: 2: 11P32 Goldbach-type theorems; other additive questions involving primesinvolving: 3: 15A42 Inequalities involving eigenvalues and eigenvectorsinvolving: 4: 15A45 Miscellaneous inequalities involving matricesinvolving: 5: 26D07 Inequalities involving other types of functionsinvolving: 6: 26D10 Inequalities involving derivatives and differential and integral operatorsinvolving: 7: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities for
integralsinvolving: 8: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txxinvolving: 9: 47A50 Equations and inequalities involving linear operators, with vector unknownsinvolving: 10: 47A62 Equations involving linear operators, with operator unknownsinvolving: 11: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXinvolving: 12: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J25involving: 13: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J40involving: 14: 49J15 Optimal control problems involving ordinary differential equationsinvolving: 15: 49J20 Optimal control problems involving partial differential equationsinvolving: 16: 49J21 Optimal control problems involving relations other than differential equationsinvolving: 17: 49J45 Methods involving semicontinuity and convergence; relaxationinvolving: 18: 49J55 Problems involving randomness [See also]93E20involving: 19: 49K15 Problems involving ordinary differential equationsinvolving: 20: 49K20 Problems involving partial differential equationsinvolving: 21: 49K21 Problems involving relations other than differential equationsinvolving: 22: 49K45 Problems involving randomness [See also]93E20involving: 23: 49M29 Methods involving dualityinvolving: 24: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areainvolving: 25: 74N25 Transformations involving diffusioninvolving: 26: 74N30 Problems involving hysteresisinvolving: 27: 90C35 Programming involving graphs or networks [See also]90C27involving: 28: 91A43 Games involving graphs [See also]05C57involving: 29: 91A44 Games involving topology or set theoryinvolving: 30: 93C83 Control problems involving computers (process control, etc.)
ion: 1: 78A37 Ion trapsionized: 1: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10ionized: 2: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10
irrationality: 1: 11J72 Irrationality; linear independence over a fieldirrationality: 2: 11J82 Measures of irrationality and of transcendence
irreducibility: 1: 08B26 Subdirect products and subdirect irreducibilityirreducibility: 2: 11R09 Polynomials (irreducibility, etc.)irreducibility: 3: 12E05 Polynomials (irreducibility, etc.)irreducibility: 4: 12E25 Hilbertian fields; Hilbert’s irreducibility theoremirregularities: 1: 11K38 Irregularities of distribution, discrepancy [See also]11Nxx
irreversible: 1: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E20irreversible: 2: 82C35 Irreversible thermodynamics, including Onsager-Machlup theory
ising: 1: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphsising: 2: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)ising: 3: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphsising: 4: 82C44 Dynamics of disordered systems (random Ising systems, etc.)
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islam: 1: 01A30 Islam (Medieval)isogeny: 1: 14K02 Isogenyisolated: 1: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets
isols: 1: 03D50 Recursive equivalence types of sets and structures, isolsisometric: 1: 46B04 Isometric theory of Banach spaces
isomomorphic: 1: 05C51 Graph designs and isomomorphic decomposition [See also]05B30isomonodromic: 1: 34M56 Isomonodromic deformations
isomorphic: 1: 46B03 Isomorphic theory (including renorming) of Banach spacesisomorphism: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)isomorphism: 2: 37A35 Entropy and other invariants, isomorphism, classification
isomorphisms: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
isomorphisms: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
isoperimetric: 1: 52B60 Isoperimetric problems for polytopesisospectrality: 1: 58J53 Isospectrality
isotopy: 1: 57N37 Isotopy and pseudo-isotopyisotopy: 2: 57Q37 Isotopyisotopy: 3: 57R52 Isotopy
isotropic: 1: 76F05 Isotropic turbulence; homogeneous turbulenceissues: 1: 03F40 Godel numberings and issues of incompletenessissues: 2: 53C29 Issues of holonomyissues: 3: 65D19 Computational issues in computer and robotic vision
iteration: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25iteration: 2: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XXiteration: 3: 32H50 Iteration problemsiteration: 4: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XXiterative: 1: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XXiterative: 2: 47J25 Iterative procedures [See also]65J15iterative: 3: 65F08 Preconditioners for iterative methodsiterative: 4: 65F10 Iterative methods for linear systems [See also]65N22
its: 1: 03E30 Axiomatics of classical set theory and its fragmentsits: 2: 34B20 Weyl theory and its generalizations
iwasawa: 1: 11R23 Iwasawa theoryjackknife: 1: 62F40 Bootstrap, jackknife and other resampling methods
jackson: 1: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)jacobi: 1: 11F50 Jacobi formsjacobi: 2: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsjacobi: 3: 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
jacobian: 1: 14R15 Jacobian problem [See also]13F20jacobians: 1: 14H40 Jacobians, Prym varieties [See also]32G20jacobians: 2: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G20jacobians: 3: 26B10 Implicit function theorems, Jacobians, transformations with several variablesjacobson: 1: 16N20 Jacobson radical, quasimultiplication
jacobsthal: 1: 11L10 Jacobsthal and Brewer sums; other complete character sumsjanet: 1: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)japan: 1: 01A27 Japan
japanese: 1: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings(Japanese, etc.)
jets: 1: 58A20 Jetsjets: 2: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingjets: 3: 76D25 Wakes and jets
joins: 1: 55Q20 Homotopy groups of wedges, joins, and simple spaces
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jordan: 1: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,17C50, 46Kxx
jordan: 2: 17A15 Noncommutative Jordan algebrasjordan: 3: 17A45 Quadratic algebras (but not quadratic Jordan algebras)jordan: 4: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50jordan: 5: 17Cxx Jordan algebras (algebras, triples and pairs)jordan: 6: 17C05 Identities and free Jordan structuresjordan: 7: 17C40 Exceptional Jordan structuresjordan: 8: 17C50 Jordan structures associated with other structures [See also]16W10jordan: 9: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70jordan: 10: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15julia: 1: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setsjulia: 2: 37P40 Non-Archimedean Fatou and Julia sets
jump: 1: 60J75 Jump processesjunctions: 1: 74K30 Junctions
kahler: 1: 32J27 Compact Kahler manifolds: generalizations, classificationkahler: 2: 32Q15 Kahler manifoldskahler: 3: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometry
kahler-einstein: 1: 32Q20 Kahler-Einstein manifolds [See also]53Cxxkahlerian: 1: 53B35 Hermitian and Kahlerian structures [See also]32Cxxkahlerian: 2: 53C55 Hermitian and Kahlerian manifolds [See also]32Cxx
kothe: 1: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45kothe: 2: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)kunneth: 1: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U25kunneth: 2: 55U25 Homology of a product, Kunneth formula
kac-moody: 1: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebraskac-moody: 2: 20G44 Kac-Moody groupskac-moody: 3: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
kaluza-klein: 1: 83E15 Kaluza-Klein and other higher-dimensional theorieskam: 1: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionkam: 2: 37K55 Perturbations, KAM for infinite-dimensional systemskam: 3: 70H08 Nearly integrable Hamiltonian systems, KAM theory
kampen: 1: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05kan: 1: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
karoubi-villamayor-gersten: 1: 19D25 Karoubi-Villamayor-Gersten K-theorykasparov: 1: 19K35 Kasparov theory (KK-theory) [See also]58J22
kdv: 1: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)
kdv-like: 1: 35Q53 KdV-like equations (Korteweg-de Vries) [See also]37K10kernel: 1: 30C40 Kernel functions and applicationskernel: 2: 35K08 Heat kernelkernel: 3: 47B34 Kernel operators
kernels: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
kernels: 2: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)kernels: 3: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)kernels: 4: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)kernels: 5: 32W30 Heat kernels in several complex variableskernels: 6: 45E05 Integral equations with kernels of Cauchy type [See also]35J15kernels: 7: 45Hxx Miscellaneous special kernels [See also]44A15kernels: 8: 45H05 Miscellaneous special kernels [See also]44A15kernels: 9: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
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de Branges-Rovnyak and other structured spaces) [See also]47B32kinds: 1: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30kinds: 2: 16R50 Other kinds of identities (generalized polynomial, rational, involution)kinds: 3: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variableskinds: 4: 74Mxx Special kinds of problems
kinematic: 1: 51J15 Kinematic spaceskinematics: 1: 53A17 Kinematicskinematics: 2: 70Bxx Kinematics [See also]53A17kinematics: 3: 70B05 Kinematics of a particlekinematics: 4: 70B10 Kinematics of a rigid bodykinematics: 5: 74A05 Kinematics of deformation
kinetic: 1: 74A25 Molecular, statistical, and kinetic theorieskinetic: 2: 82B40 Kinetic theory of gaseskinetic: 3: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphskinetic: 4: 82C40 Kinetic theory of gases
kinetics: 1: 80A30 Chemical kinetics [See also]76V05, 92C45, 92E20kinetics: 2: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A30kinetics: 3: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A30klein: 1: 30F50 Klein surfaces
klein-gordon: 1: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and otherequations of quantum mechanics
kleinian: 1: 30F40 Kleinian groups [See also]20H10kleinian: 2: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemskleisli: 1: 18C20 Algebras and Kleisli categories associated with monads
kloosterman: 1: 11L05 Gauss and Kloosterman sums; generalizationsknizhnik-zamolodchikov: 1: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxknot: 1: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45
knots: 1: 57M25 Knots and links in S3 For higher dimensions, see 57Q45knots: 2: 57M27 Invariants of knots and 3-manifoldsknots: 3: 57M30 Wild knots and surfaces, etc., wild embeddingsknots: 4: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25
knowledge: 1: 03B42 Logics of knowledge and belief (including belief change)knowledge: 2: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; fortemporal logic, see 03B44; for provability logic, see also 03F45knowledge: 3: 68T30 Knowledge representation
knowledge-based: 1: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)kobayashi: 1: 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
kolmogorov: 1: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,Kolmogorov numbers, entropy numbers, etc. of operators
kolmogorov: 2: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32korteweg-de: 1: 35Q53 KdV-like equations (Korteweg-de Vries) [See also]37K10
koszul: 1: 16S37 Quadratic and Koszul algebraskp: 1: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,
hierarchies (KdV, KP, Toda, etc.)krasner-tate: 1: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S10
kreın: 1: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)[See also]47B50
kreın-milman: 1: 46B22 Radon-Nikodym, Kreın-Milman and related properties [See also]46G10kronecker: 1: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
krull: 1: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizationskrull: 2: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions
[See also]16U20, Krull dimensionlevy: 1: 60G51 Processes with independent increments; Levy processes
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la: 1: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysison metric spaces
la: 2: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)la: 3: 53D18 Generalized geometries (a la Hitchin)la: 4: 58B34 Noncommutative geometry (a la Connes)
labelling: 1: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)labor: 1: 91B40 Labor market, contracts
lacunary: 1: 30B10 Power series (including lacunary series)lacunary: 2: 40E15 Lacunary inversion theoremslacunary: 3: 42A55 Lacunary series of trigonometric and other functions; Riesz productslagrange: 1: 11J06 Markov and Lagrange spectra and generalizationslagrange: 2: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
lagrange’s: 1: 70H03 Lagrange’s equationslagrangian: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems[See also]53Dxx, 70Fxx, 70Hxxlagrangian: 2: 53D12 Lagrangian submanifolds; Maslov indexlagrangian: 3: 70Hxx Hamiltonian and Lagrangian mechanics [See also]37Jxxlagrangian: 4: 70S05 Lagrangian formalism and Hamiltonian formalism
laguerre: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
laguerre: 2: 51B15 Laguerre geometrieslame: 1: 33E10 Lame, Mathieu, and spheroidal wave functions
lambda: 1: 68N18 Functional programming and lambda calculus [See also]03B40lambda-calculus: 1: 03B40 Combinatory logic and lambda-calculus [See also]68N18
lambek: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
lane: 1: 55P20 Eilenberg-Mac Lane spaceslangevin: 1: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H10
langlands: 1: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationslanglands: 2: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E57langlands: 3: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D24
langlands-weil: 1: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55langlands-weil: 2: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50
language: 1: 68T50 Natural language processing [See also]03B65language: 2: 97C50 Language and verbal communitieslanguage: 3: 97E40 Language of mathematicslanguage: 4: 97M80 Arts, music, language, architecture
languages: 1: 03B65 Logic of natural languages [See also]68T50, 91F20languages: 2: 03C07 Basic properties of first-order languages and structureslanguages: 3: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q65languages: 4: 68N15 Programming languageslanguages: 5: 68Q45 Formal languages and automata [See also]03D05, 68Q70, 94A45languages: 6: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M35languages: 7: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)languages: 8: 97P40 Programming languages
laplace: 1: 44A10 Laplace transformlaplacian: 1: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxlaplacian: 2: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianlaplacian: 3: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
large: 1: 03E55 Large cardinalslarge: 2: 60F10 Large deviationslarge: 3: 74B15 Equations linearized about a deformed state (small deformations superposed on large)large: 4: 76F65 Direct numerical and large eddy simulation of turbulencelarge: 5: 93A15 Large scale systems
large-scale: 1: 90C06 Large-scale problemslarge-strain: 1: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)
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large-strain: 2: 74C20 Large-strain, rate-dependent theorieslaser: 1: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)lasers: 1: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80latin: 1: 05B15 Orthogonal arrays, Latin squares, Room squares
lattice: 1: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C17lattice: 2: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,
etc. [See also]11A63lattice: 3: 11P21 Lattice points in specified regionslattice: 4: 34A33 Lattice differential equationslattice: 5: 34K31 Lattice functional-differential equationslattice: 6: 37K60 Lattice dynamics [See also]37L60lattice: 7: 37L60 Lattice dynamics [See also]37K60lattice: 8: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxlattice: 9: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphslattice: 10: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41lattice: 11: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphslattice: 12: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50lattice: 13: 83C27 Lattice gravity, Regge calculus and other discrete methods
lattice-gas: 1: 76M28 Particle methods and lattice-gas methodslattices: 1: 03G10 Lattices and related structures [See also]06Bxxlattices: 2: 05B35 Matroids, geometric lattices [See also]52B40, 90C27lattices: 3: 06-XX Order, lattices, ordered algebraic structures [See also]18B35lattices: 4: 06Bxx Lattices [See also]03G10lattices: 5: 06B20 Varieties of latticeslattices: 6: 06B23 Complete lattices, completionslattices: 7: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10lattices: 8: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10lattices: 9: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H12lattices: 10: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q55lattices: 11: 06B75 Generalizations of latticeslattices: 12: 06Cxx Modular lattices, complemented latticeslattices: 13: 06Cxx Modular lattices, complemented latticeslattices: 14: 06C05 Modular lattices, Desarguesian latticeslattices: 15: 06C05 Modular lattices, Desarguesian latticeslattices: 16: 06C10 Semimodular lattices, geometric latticeslattices: 17: 06C10 Semimodular lattices, geometric latticeslattices: 18: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P10lattices: 19: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P10lattices: 20: 06C20 Complemented modular lattices, continuous geometrieslattices: 21: 06Dxx Distributive latticeslattices: 22: 06D15 Pseudocomplemented latticeslattices: 23: 06D50 Lattices and dualitylattices: 24: 06D72 Fuzzy lattices (soft algebras) and related topicslattices: 25: 06D75 Other generalizations of distributive latticeslattices: 26: 06F10 Noether latticeslattices: 27: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H12lattices: 28: 08B15 Lattices of varietieslattices: 29: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C07lattices: 30: 11H56 Automorphism groups of latticeslattices: 31: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxxlattices: 32: 16H20 Lattices over orderslattices: 33: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XXlattices: 34: 20D30 Series and lattices of subgroupslattices: 35: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F22
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lattices: 36: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F30lattices: 37: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42lattices: 38: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxlattices: 39: 46B42 Banach lattices [See also]46A40, 46B40lattices: 40: 46E05 Lattices of continuous, differentiable or analytic functionslattices: 41: 51D25 Lattices of subspaces [See also]05B35lattices: 42: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P21lattices: 43: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P21lattices: 44: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)lattices: 45: 54H12 Topological lattices, etc. [See also]06B30, 06F30lattices: 46: 81T25 Quantum field theory on latticeslaurent: 1: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial rings
lauricella: 1: 33C65 Appell, Horn and Lauricella functionslaws: 1: 08A02 Relational systems, laws of compositionlaws: 2: 13F50 Rings with straightening laws, Hodge algebraslaws: 3: 35L65 Conservation lawslaws: 4: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawslaws: 5: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R90laws: 6: 60F20 Zero-one lawslaws: 7: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductionlaws: 8: 70S10 Symmetries and conservation lawslaws: 9: 83C40 Gravitational energy and conservation laws; groups of motions
lawson: 1: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne(co)homologies)
layers: 1: 76F40 Turbulent boundary layerslb: 1: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40
lca: 1: 22Bxx Locally compact abelian groups (LCA groups)lca: 2: 22B05 General properties and structure of LCA groupslca: 3: 22B10 Structure of group algebras of LCA groups
learning: 1: 60J20 Applications of Markov chains and discrete-time Markov processes on general statespaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40
learning: 2: 68Q32 Computational learning theory [See also]68T05learning: 3: 68T05 Learning and adaptive systems [See also]68Q32, 91E40learning: 4: 91A26 Rationality, learninglearning: 5: 91E40 Memory and learning [See also]68T05learning: 6: 93E35 Stochastic learning and adaptive controllearning: 7: 97C30 Cognitive processes, learning theorieslearning: 8: 97C60 Sociological aspects of learninglearning: 9: 97D70 Learning difficulties and student errors
least: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assignedat least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35
least: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)
least: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
least: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
least: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classificationnumber in this section)
least: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
least: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
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least: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)
least: 9: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
least: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)
least: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)
least: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)
least: 13: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)
least: 14: 51Pxx Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
least: 15: 51P05 Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
least: 16: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned atleast one other classification number in this section)
least: 17: 92Fxx Other natural sciences (should also be assigned at least one other classification numberin this section)
least: 18: 92F05 Other natural sciences (should also be assigned at least one other classification numberin section 92)
least: 19: 93E24 Least squares and related methodslebesgue: 1: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XXlectures: 1: 00B05 Collections of abstracts of lectures
lefschetz: 1: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantslegendre: 1: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)legendre: 2: 44A15 Special transforms (Legendre, Hilbert, etc.)
leibniz: 1: 17A32 Leibniz algebraslelong: 1: 32U25 Lelong numbers
lemma: 1: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)lemma: 2: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
subordinationlemma: 3: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericitylength: 1: 26B15 Integration: length, area, volume [See also]28A75, 51M25length: 2: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15length: 3: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85length: 4: 31B15 Potentials and capacities, extremal lengthlength: 5: 51M25 Length, area and volume [See also]26B15length: 6: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q20
length-variable: 1: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q45lerch: 1: 11M35 Hurwitz and Lerch zeta functions
lessons: 1: 97D80 Teaching units and draft lessonslevi: 1: 32C55 The Levi problem in complex spaces; generalizationslevi: 2: 32E40 The Levi problem
lf: 1: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40lidstone: 1: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
lie: 1: 11F22 Relationship to Lie algebras and finite simple groupslie: 2: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45lie: 3: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B35lie: 4: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxxlie: 5: 16W25 Derivations, actions of Lie algebraslie: 6: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxlie: 7: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxlie: 8: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exx
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lie: 9: 17B01 Identities, free Lie (super)algebraslie: 10: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxxlie: 11: 17B50 Modular Lie (super)algebraslie: 12: 17B55 Homological methods in Lie (super)algebraslie: 13: 17B56 Cohomology of Lie (super)algebraslie: 14: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50lie: 15: 17B62 Lie bialgebras; Lie coalgebraslie: 16: 17B62 Lie bialgebras; Lie coalgebraslie: 17: 17B65 Infinite-dimensional Lie (super)algebras [See also]22E65lie: 18: 17B66 Lie algebras of vector fields and related (super) algebraslie: 19: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebraslie: 20: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebraslie: 21: 17B70 Graded Lie (super)algebraslie: 22: 17B75 Color Lie (super)algebraslie: 23: 20C33 Representations of finite groups of Lie typelie: 24: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxlie: 25: 20F40 Associated Lie structureslie: 26: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXlie: 27: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05lie: 28: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90lie: 29: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90lie: 30: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H05lie: 31: 22E10 General properties and structure of complex Lie groups [See also]32M05lie: 32: 22E15 General properties and structure of real Lie groupslie: 33: 22E20 General properties and structure of other Lie groupslie: 34: 22E25 Nilpotent and solvable Lie groupslie: 35: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)lie: 36: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXlie: 37: 22E35 Analysis on p-adic Lie groupslie: 38: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxxlie: 39: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05lie: 40: 22E46 Semisimple Lie groups and their representationslie: 41: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10lie: 42: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05lie: 43: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05lie: 44: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxlie: 45: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxlie: 46: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxlie: 47: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05lie: 48: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05lie: 49: 22E66 Analysis on and representations of infinite-dimensional Lie groupslie: 50: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10lie: 51: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40lie: 52: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10lie: 53: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.lie: 54: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structures
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lie: 55: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exx
lie: 56: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exx
lie: 57: 43A80 Analysis on other specific Lie groups [See also]22Exxlie: 58: 51B25 Lie geometrieslie: 59: 57S15 Compact Lie groups of differentiable transformationslie: 60: 57S20 Noncompact Lie groups of transformationslie: 61: 57T10 Homology and cohomology of Lie groupslie: 62: 57T15 Homology and cohomology of homogeneous spaces of Lie groupslie: 63: 76M60 Symmetry analysis, Lie group and algebra methods
lie-admissible: 1: 17D25 Lie-admissible algebraslie-algebra: 1: 70G65 Symmetries, Lie-group and Lie-algebra methods
lie-backlund: 1: 37K35 Lie-Backlund and other transformationslie-backlund: 2: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22
lie-group: 1: 70G65 Symmetries, Lie-group and Lie-algebra methodslife: 1: 47N60 Applications in chemistry and life scienceslife: 2: 62N05 Reliability and life testing [See also]90B25life: 3: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxlife: 4: 97F90 Real life mathematics, practical arithmetic
lifting: 1: 28A51 Lifting theory [See also]46G15lifting: 2: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
[See also]46M10lifting: 3: 46G15 Functional analytic lifting theory [See also]28A51lifting: 4: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)limit: 1: 34C05 Location of integral curves, singular points, limit cycleslimit: 2: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)limit: 3: 37G15 Bifurcations of limit cycles and periodic orbitslimit: 4: 47L40 Limit algebras, subalgebras of C∗-algebraslimit: 5: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)limit: 6: 60Fxx Limit theorems [See also]28Dxx, 60B12limit: 7: 60F05 Central limit and other weak theoremslimit: 8: 60F17 Functional limit theorems; invariance principleslimit: 9: 65B05 Extrapolation to the limit, deferred correctionslimit: 10: 70K05 Phase plane analysis, limit cycles
limiting: 1: 40Axx Convergence and divergence of infinite limiting processeslimiting: 2: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15limits: 1: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30limits: 2: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)limits: 3: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)limits: 4: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionslimits: 5: 18A35 Categories admitting limits (complete categories), functors preserving limits, comple-
tionslimits: 6: 20E18 Limits, profinite groupslimits: 7: 26A03 Foundations: limits and generalizations, elementary topology of the linelimits: 8: 37F40 Geometric limitslimits: 9: 40D10 Tauberian constants and oscillation limitslimits: 10: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40limits: 11: 46M40 Inductive and projective limits [See also]46A13limits: 12: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)limits: 13: 81T27 Continuum limits
lindelof: 1: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
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subordinationlindelof: 2: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)
line: 1: 05C76 Graph operations (line graphs, products, etc.)line: 2: 26A03 Foundations: limits and generalizations, elementary topology of the lineline: 3: 51M30 Line geometries and their generalizations [See also]53A25line: 4: 53A25 Differential line geometry
linear: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
linear: 2: 03F52 Linear logic and other substructural logics [See also]03B47linear: 3: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)linear: 4: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40linear: 5: 11D04 Linear equationslinear: 6: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63linear: 7: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63linear: 8: 11E72 Galois cohomology of linear algebraic groups [See also]20G10linear: 9: 11H46 Products of linear formslinear: 10: 11J13 Simultaneous homogeneous approximation, linear formslinear: 11: 11J20 Inhomogeneous linear formslinear: 12: 11J72 Irrationality; linear independence over a fieldlinear: 13: 11J86 Linear forms in logarithms; Baker’s methodlinear: 14: 14C20 Divisors, linear systems, invertible sheaveslinear: 15: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45linear: 16: 14N20 Configurations and arrangements of linear subspaceslinear: 17: 15-XX Linear and multilinear algebra; matrix theorylinear: 18: 15Axx Basic linear algebralinear: 19: 15A03 Vector spaces, linear dependence, ranklinear: 20: 15A04 Linear transformations, semilinear transformationslinear: 21: 15A06 Linear equationslinear: 22: 15A39 Linear inequalitieslinear: 23: 15A86 Linear preserver problemslinear: 24: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxxlinear: 25: 19B14 Stability for linear groupslinear: 26: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
linear: 27: 20G15 Linear algebraic groups over arbitrary fieldslinear: 28: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionslinear: 29: 20G25 Linear algebraic groups over local fields and their integerslinear: 30: 20G30 Linear algebraic groups over global fields and their integerslinear: 31: 20G35 Linear algebraic groups over adeles and other rings and schemeslinear: 32: 20G40 Linear algebraic groups over finite fieldslinear: 33: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05linear: 34: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05linear: 35: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05linear: 36: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measureslinear: 37: 34A30 Linear equations and systems, generallinear: 38: 34B05 Linear boundary value problemslinear: 39: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterlinear: 40: 34G10 Linear equations [See also]47D06, 47D09linear: 41: 34K06 Linear functional-differential equationslinear: 42: 34M03 Linear equations and systemslinear: 43: 34M40 Stokes phenomena and connection problems (linear and nonlinear)
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linear: 44: 35F05 Linear first-order equationslinear: 45: 35F10 Initial value problems for linear first-order equationslinear: 46: 35F15 Boundary value problems for linear first-order equationslinear: 47: 35F16 Initial-boundary value problems for linear first-order equationslinear: 48: 35F35 Linear first-order systemslinear: 49: 35F40 Initial value problems for linear first-order systemslinear: 50: 35F45 Boundary value problems for linear first-order systemslinear: 51: 35F46 Initial-boundary value problems for linear first-order systemslinear: 52: 35G05 Linear higher-order equationslinear: 53: 35G10 Initial value problems for linear higher-order equationslinear: 54: 35G15 Boundary value problems for linear higher-order equationslinear: 55: 35G16 Initial-boundary value problems for linear higher-order equationslinear: 56: 35G35 Linear higher-order systemslinear: 57: 35G40 Initial value problems for linear higher-order systemslinear: 58: 35G45 Boundary value problems for linear higher-order systemslinear: 59: 35G46 Initial-boundary value problems for linear higher-order systemslinear: 60: 35J65 Nonlinear boundary value problems for linear elliptic equationslinear: 61: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J40linear: 62: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J40linear: 63: 35K60 Nonlinear initial value problems for linear parabolic equationslinear: 64: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40linear: 65: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40linear: 66: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J40linear: 67: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J40linear: 68: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J40linear: 69: 35P05 General topics in linear spectral theorylinear: 70: 39A06 Linear equationslinear: 71: 41A45 Approximation by arbitrary linear expressionslinear: 72: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)linear: 73: 45Axx Linear integral equationslinear: 74: 45A05 Linear integral equationslinear: 75: 45Fxx Systems of linear integral equationslinear: 76: 45F05 Systems of nonsingular linear integral equationslinear: 77: 45F15 Systems of singular linear integral equationslinear: 78: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxlinear: 79: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxlinear: 80: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)linear: 81: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)linear: 82: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20linear: 83: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42linear: 84: 46A50 Compactness in topological linear spaces; angelic spaces, etc.linear: 85: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07linear: 86: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxlinear: 87: 46B20 Geometry and structure of normed linear spaces
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linear: 88: 46B70 Interpolation between normed linear spaces [See also]46M35linear: 89: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J10linear: 90: 46E10 Topological linear spaces of continuous, differentiable or analytic functionslinear: 91: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E35linear: 92: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12linear: 93: 46S50 Functional analysis in probabilistic metric linear spaceslinear: 94: 47Axx General theory of linear operatorslinear: 95: 47A06 Linear relations (multivalued linear operators)linear: 96: 47A06 Linear relations (multivalued linear operators)linear: 97: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.linear: 98: 47A50 Equations and inequalities involving linear operators, with vector unknownslinear: 99: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)linear: 100: 47A62 Equations involving linear operators, with operator unknownslinear: 101: 47Bxx Special classes of linear operatorslinear: 102: 47Cxx Individual linear operators as elements of algebraic systemslinear: 103: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationslinear: 104: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20linear: 105: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K30linear: 106: 47Lxx Linear spaces and algebras of operators [See also]46Lxxlinear: 107: 47L05 Linear spaces of operators [See also]46A32 and 46B28linear: 108: 47L10 Algebras of operators on Banach spaces and other topological linear spaceslinear: 109: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70linear: 110: 49N05 Linear optimal control problems [See also]93C05linear: 111: 51Axx Linear incidence geometrylinear: 112: 51E22 Linear codes and caps in Galois spaces [See also]94B05linear: 113: 51E26 Other finite linear geometrieslinear: 114: 51H10 Topological linear incidence structureslinear: 115: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)linear: 116: 53B05 Linear and affine connectionslinear: 117: 60B11 Probability theory on linear topological spaces [See also]28C20linear: 118: 62Jxx Linear inference, regressionlinear: 119: 62J05 Linear regressionlinear: 120: 62J12 Generalized linear modelslinear: 121: 62J86 Fuzziness, and linear inference and regressionlinear: 122: 65Fxx Numerical linear algebralinear: 123: 65F05 Direct methods for linear systems and matrix inversionlinear: 124: 65F10 Iterative methods for linear systems [See also]65N22linear: 125: 65J10 Equations with linear operators (do not use 65Fxx)linear: 126: 70Jxx Linear vibration theorylinear: 127: 74B05 Classical linear elasticitylinear: 128: 74B10 Linear elasticity with initial stresseslinear: 129: 74D05 Linear constitutive equationslinear: 130: 74J05 Linear waveslinear: 131: 90C05 Linear programminglinear: 132: 90C08 Special problems of linear programming (transportation, multi-index, etc.)linear: 133: 93C05 Linear systemslinear: 134: 94B05 Linear codes, generallinear: 135: 97H60 Linear algebra
linear-quadratic: 1: 49N10 Linear-quadratic problemslinearization: 1: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets
linearizations: 1: 93B18 Linearizationslinearized: 1: 74B15 Equations linearized about a deformed state (small deformations superposed on large)
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linearly: 1: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially orderedspaces [See also]06B30, 06F30
lines: 1: 52C30 Planar arrangements of lines and pseudolineslines: 2: 65M20 Method of lineslines: 3: 65N40 Method of lines
linguistics: 1: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50linguistics: 2: 91F20 Linguistics [See also]03B65, 68T50
linkage: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,14M12
linkage: 2: 14M06 Linkage [See also]13C40links: 1: 57M25 Knots and links in S3 For higher dimensions, see 57Q45links: 2: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25
liouville: 1: 35B53 Liouville theorems, Phragmen-Lindelof theoremslipschitz: 1: 26A16 Lipschitz (Holder) classeslipschitz: 2: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)liquid: 1: 76A15 Liquid crystals [See also]82D30liquid: 2: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
liquid-gas: 1: 76T10 Liquid-gas two-phase flows, bubbly flowsliquids: 1: 82D15 Liquids
littlewood-paley: 1: 42B25 Maximal functions, Littlewood-Paley theoryljusternik-schnirelman: 1: 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirel′man) category of a spaceljusternik-schnirelman: 2: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)local: 1: 11E08 Quadratic forms over local rings and fieldslocal: 2: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldslocal: 3: 11F85 p-adic theory, local fields [See also]14G20, 22E50local: 4: 11G07 Elliptic curves over local fields [See also]14G20, 14H52local: 5: 11G20 Curves over finite and local fields [See also]14H25local: 6: 11G25 Varieties over finite and local fields [See also]14G15, 14G20local: 7: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72local: 8: 11Sxx Algebraic number theory: local and p-adic fieldslocal: 9: 11S70 K-theory of local fields [See also]19Fxxlocal: 10: 13D45 Local cohomology [See also]14B15local: 11: 13Hxx Local rings and semilocal ringslocal: 12: 13H05 Regular local ringslocal: 13: 14Bxx Local theorylocal: 14: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10local: 15: 14B15 Local cohomology [See also]13D45, 32C36local: 16: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B40local: 17: 14D10 Arithmetic ground fields (finite, local, global)local: 18: 14G20 Local ground fieldslocal: 19: 14H20 Singularities, local rings [See also]13Hxx, 14B05local: 20: 16Lxx Local rings and generalizationslocal: 21: 16L30 Noncommutative local and semilocal rings, perfect ringslocal: 22: 18F05 Local categories and functorslocal: 23: 20E25 Local propertieslocal: 24: 20G25 Linear algebraic groups over local fields and their integerslocal: 25: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H05local: 26: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05local: 27: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30local: 28: 32A27 Local theory of residues [See also]32C30local: 29: 32Bxx Local analytic geometry [See also]13-XX and 14-XXlocal: 30: 32B10 Germs of analytic sets, local parametrization
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local: 31: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27local: 32: 32C36 Local cohomology of analytic spaceslocal: 33: 32S05 Local singularities [See also]14J17local: 34: 32S10 Invariants of analytic local ringslocal: 35: 34M35 Singularities, monodromy, local behavior of solutions, normal formslocal: 36: 35A01 Existence problems: global existence, local existence, non-existencelocal: 37: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenesslocal: 38: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K18local: 39: 37P20 Non-Archimedean local ground fieldslocal: 40: 46B07 Local theory of Banach spaceslocal: 41: 47A11 Local spectral propertieslocal: 42: 53A55 Differential invariants (local theory), geometric objectslocal: 43: 53Bxx Local differential geometrylocal: 44: 53B20 Local Riemannian geometrylocal: 45: 53B25 Local submanifolds [See also]53C40local: 46: 54D45 Local compactness, σ-compactnesslocal: 47: 54F35 Higher-dimensional local connectedness [See also]55Mxx, 55Nxxlocal: 48: 55N25 Homology with local coefficients, equivariant cohomologylocal: 49: 57P05 Local properties of generalized manifoldslocal: 50: 60J55 Local time and additive functionalslocal: 51: 74G20 Local existence of solutions (near a given solution)
locales: 1: 06D22 Frames, locales For topological questions see 54-XXlocalization: 1: 13B30 Rings of fractions and localization [See also]16S85localization: 2: 16P50 Localization and Noetherian rings [See also]16U20localization: 3: 16U20 Ore rings, multiplicative sets, Ore localizationlocalization: 4: 18E35 Localization of categorieslocalization: 5: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localization
localization: 6: 42C25 Uniqueness and localization for orthogonal serieslocalization: 7: 55P60 Localization and completion
localizations: 1: 16S85 Rings of fractions and localizations [See also]13B30locally: 1: 18C35 Accessible and locally presentable categorieslocally: 2: 20F50 Periodic groups; locally finite groupslocally: 3: 22Bxx Locally compact abelian groups (LCA groups)locally: 4: 22Dxx Locally compact groups and their algebraslocally: 5: 22D05 General properties and structure of locally compact groupslocally: 6: 22D10 Unitary representations of locally compact groupslocally: 7: 22D12 Other representations of locally compact groupslocally: 8: 22D15 Group algebras of locally compact groupslocally: 9: 22D45 Automorphism groups of locally compact groupslocally: 10: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setslocally: 11: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupslocally: 12: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05locally: 13: 46A03 General theory of locally convex spaceslocally: 14: 46A04 Locally convex Frechet spaces and (DF)-spaceslocally: 15: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)locally: 16: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)locally: 17: 54D05 Connected and locally connected spaces (general aspects)locally: 18: 54E45 Compact (locally compact) metric spaces
location: 1: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,30C15
location: 2: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H05location: 3: 34C05 Location of integral curves, singular points, limit cycleslocation: 4: 90B80 Discrete location and assignment [See also]90C10location: 5: 90B85 Continuous location
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logarithm: 1: 33B30 Higher logarithm functionslogarithms: 1: 11J86 Linear forms in logarithms; Baker’s method
logic: 1: 03-XX Mathematical logic and foundationslogic: 2: 03Axx Philosophical aspects of logic and foundationslogic: 3: 03A10 Logic in the philosophy of sciencelogic: 4: 03Bxx General logiclogic: 5: 03B05 Classical propositional logiclogic: 6: 03B10 Classical first-order logiclogic: 7: 03B15 Higher-order logic and type theorylogic: 8: 03B20 Subsystems of classical logic (including intuitionistic logic)logic: 9: 03B20 Subsystems of classical logic (including intuitionistic logic)logic: 10: 03B40 Combinatory logic and lambda-calculus [See also]68N18logic: 11: 03B44 Temporal logiclogic: 12: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45logic: 13: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45logic: 14: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45logic: 15: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45logic: 16: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52logic: 17: 03B48 Probability and inductive logic [See also]60A05logic: 18: 03B50 Many-valued logiclogic: 19: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D05logic: 20: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D05logic: 21: 03B60 Other nonclassical logiclogic: 22: 03B65 Logic of natural languages [See also]68T50, 91F20logic: 23: 03B70 Logic in computer science [See also]68-XXlogic: 24: 03B80 Other applications of logiclogic: 25: 03C70 Logic on admissible setslogic: 26: 03C75 Other infinitary logiclogic: 27: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B48logic: 28: 03F52 Linear logic and other substructural logics [See also]03B47logic: 29: 03Gxx Algebraic logiclogic: 30: 03G12 Quantum logic [See also]06C15, 81P10logic: 31: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F35logic: 32: 03G27 Abstract algebraic logiclogic: 33: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C10logic: 34: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionslogic: 35: 11Uxx Connections with logiclogic: 36: 12Lxx Connections with logiclogic: 37: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxxlogic: 38: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxxlogic: 39: 16B70 Applications of logic [See also]03Cxxlogic: 40: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXlogic: 41: 20A15 Applications of logic to group theorylogic: 42: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70logic: 43: 28E15 Other connections with logic and set theorylogic: 44: 68N17 Logic programminglogic: 45: 68T27 Logic in artificial intelligencelogic: 46: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15logic: 47: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10logic: 48: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
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28E10logic: 49: 97E30 Logic
logical: 1: 03B35 Mechanization of proofs and logical operations [See also]68T15logical: 2: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R15logical: 3: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15logics: 1: 03B42 Logics of knowledge and belief (including belief change)logics: 2: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52logics: 3: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52logics: 4: 03B53 Paraconsistent logicslogics: 5: 03B55 Intermediate logicslogics: 6: 03B62 Combined logicslogics: 7: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E25logics: 8: 03F52 Linear logic and other substructural logics [See also]03B47logics: 9: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70
logistics: 1: 90B06 Transportation, logisticslong-time: 1: 74H40 Long-time behavior of solutions
loop: 1: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05loop: 2: 55P35 Loop spacesloop: 3: 55P47 Infinite loop spacesloop: 4: 55P48 Loop space machines, operads [See also]18D50loop: 5: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity
loops: 1: 20N05 Loops, quasigroups [See also]05Bxxlorentz: 1: 22E43 Structure and representation of the Lorentz grouplorentz: 2: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)lorentz: 3: 53B30 Lorentz metrics, indefinite metricslorentz: 4: 53C50 Lorentz manifolds, manifolds with indefinite metrics
low: 1: 14H45 Special curves and curves of low genuslow: 2: 14M07 Low codimension problemslow: 3: 14N25 Varieties of low degreelow: 4: 57M60 Group actions in low dimensions
low-dimensional: 1: 37Exx Low-dimensional dynamical systemslow-dimensional: 2: 57Mxx Low-dimensional topologylow-dimensional: 3: 57M50 Geometric structures on low-dimensional manifoldslow-dimensional: 4: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25
lower: 1: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundslower: 2: 35P15 Estimation of eigenvalues, upper and lower boundslower: 3: 54D10 Lower separation axioms (T0–T3, etc.)lower: 4: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15lower: 5: 83C80 Analogues in lower dimensions
lubrication: 1: 76D08 Lubrication theorylucas: 1: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations
lyapunov: 1: 34D08 Characteristic and Lyapunov exponentslyapunov: 2: 37B25 Lyapunov functions and stability; attractors, repellerslyapunov: 3: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)lyapunov: 4: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxxlyapunov: 5: 37L30 Attractors and their dimensions, Lyapunov exponentslyapunov: 6: 37L45 Hyperbolicity; Lyapunov functionslyapunov: 7: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)lyapunov: 8: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
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lyapunov: 9: 93D30 Scalar and vector Lyapunov functionslyness: 1: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness type
lyusternik-shnirel′: 1: 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirel′man) category of a spacelyusternik-shnirel′: 2: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)mobius: 1: 51B10 Mobius geometries
macdonald: 1: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonaldpolynomials, etc.)
machine: 1: 68-XX Computer science For papers involving machine computations and programs in aspecific mathematical area, see Section–04 in that area
machine: 2: 68T45 Machine vision and scene understandingmachines: 1: 03D10 Turing machines and related notions [See also]68Q05machines: 2: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxxmachines: 3: 55P48 Loop space machines, operads [See also]18D50machines: 4: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P68
mackey: 1: 46A17 Bornologies and related structures; Mackey convergence, etc.macro-economic: 1: 91B64 Macro-economic models (monetary models, models of taxation)
macroscopic: 1: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)maeda: 1: 51D05 Abstract (Maeda) geometries
magnetic: 1: 82D40 Magnetic materialsmagnetohydrodynamic: 1: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
magnetohydrodynamics: 1: 76Wxx Magnetohydrodynamics and electrohydrodynamicsmagnetohydrodynamics: 2: 76W05 Magnetohydrodynamics and electrohydrodynamics
magnetostatics: 1: 78A30 Electro- and magnetostaticsmahler: 1: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measuremainly: 1: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35mainly: 2: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30mainly: 3: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30
maintenance: 1: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N05majority: 1: 94B30 Majority codes
making: 1: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,91A35, 91B06
mal′: 1: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionsmal′: 2: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionsmal′: 3: 17D10 Mal′cev (Mal′tsev) rings and algebrasmal′: 4: 17D10 Mal′cev (Mal′tsev) rings and algebras
malliavin: 1: 60H07 Stochastic calculus of variations and the Malliavin calculusman: 1: 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirel′man) category of a spaceman: 2: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)management: 1: 90Bxx Operations research and management sciencemanagement: 2: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B06mandelbrot: 1: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
manifold: 1: 37D10 Invariant manifold theorymanifold: 2: 37L10 Normal forms, center manifold theory, bifurcation theorymanifold: 3: 51H30 Geometries with algebraic manifold structure [See also]14-XXmanifold: 4: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)
manifolds: 1: 14J32 Calabi-Yau manifoldsmanifolds: 2: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M35manifolds: 3: 14P20 Nash functions and manifolds [See also]32C07, 58A07manifolds: 4: 17C36 Associated manifoldsmanifolds: 5: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxxmanifolds: 6: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40
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manifolds: 7: 28-XX Measure and integration For analysis on manifolds, see 58-XXmanifolds: 8: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXmanifolds: 9: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14manifolds: 10: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A07manifolds: 11: 32C09 Embedding of real analytic manifoldsmanifolds: 12: 32E10 Stein spaces, Stein manifoldsmanifolds: 13: 32J27 Compact Kahler manifolds: generalizations, classificationmanifolds: 14: 32M10 Homogeneous complex manifolds [See also]14M17, 57T15manifolds: 15: 32M12 Almost homogeneous manifolds and spaces [See also]14M17manifolds: 16: 32M17 Automorphism groups of Cn and affine manifoldsmanifolds: 17: 32Qxx Complex manifoldsmanifolds: 18: 32Q05 Negative curvature manifoldsmanifolds: 19: 32Q10 Positive curvature manifoldsmanifolds: 20: 32Q15 Kahler manifoldsmanifolds: 21: 32Q20 Kahler-Einstein manifolds [See also]53Cxxmanifolds: 22: 32Q28 Stein manifoldsmanifolds: 23: 32Q35 Complex manifolds as subdomains of Euclidean spacemanifolds: 24: 32Q45 Hyperbolic and Kobayashi hyperbolic manifoldsmanifolds: 25: 32Q55 Topological aspects of complex manifoldsmanifolds: 26: 32Q60 Almost complex manifoldsmanifolds: 27: 32Vxx CR manifoldsmanifolds: 28: 32V15 CR manifolds as boundaries of domainsmanifolds: 29: 32V20 Analysis on CR manifoldsmanifolds: 30: 32V25 Extension of functions and other analytic objects from CR manifoldsmanifolds: 31: 32V30 Embeddings of CR manifoldsmanifolds: 32: 32V35 Finite type conditions on CR manifoldsmanifolds: 33: 32V40 Real submanifolds in complex manifoldsmanifolds: 34: 34C40 Equations and systems on manifoldsmanifolds: 35: 34C45 Invariant manifoldsmanifolds: 36: 34D35 Stability of manifolds of solutionsmanifolds: 37: 34K19 Invariant manifoldsmanifolds: 38: 34M45 Differential equations on complex manifoldsmanifolds: 39: 35B42 Inertial manifoldsmanifolds: 40: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15manifolds: 41: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15manifolds: 42: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxxmanifolds: 43: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D20manifolds: 44: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricsmanifolds: 45: 37L25 Inertial manifolds and other invariant attracting setsmanifolds: 46: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxmanifolds: 47: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxxmanifolds: 48: 46T10 Manifolds of mappingsmanifolds: 49: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXmanifolds: 50: 49Qxx Manifolds [See also]58Exxmanifolds: 51: 51H20 Topological geometries on manifolds [See also]57-XXmanifolds: 52: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15manifolds: 53: 52B70 Polyhedral manifoldsmanifolds: 54: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxmanifolds: 55: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
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etc.)manifolds: 56: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)manifolds: 57: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T15manifolds: 58: 53C50 Lorentz manifolds, manifolds with indefinite metricsmanifolds: 59: 53C50 Lorentz manifolds, manifolds with indefinite metricsmanifolds: 60: 53C55 Hermitian and Kahlerian manifolds [See also]32Cxxmanifolds: 61: 53D05 Symplectic manifolds, generalmanifolds: 62: 53D10 Contact manifolds, generalmanifolds: 63: 53D15 Almost contact and almost symplectic manifoldsmanifolds: 64: 53D17 Poisson manifolds; Poisson groupoids and algebroidsmanifolds: 65: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxxmanifolds: 66: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35manifolds: 67: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxmanifolds: 68: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxmanifolds: 69: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxmanifolds: 70: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxmanifolds: 71: 57M50 Geometric structures on low-dimensional manifoldsmanifolds: 72: 57Nxx Topological manifoldsmanifolds: 73: 57N16 Geometric structures on manifolds [See also]57M50manifolds: 74: 57N20 Topology of infinite-dimensional manifolds [See also]58Bxxmanifolds: 75: 57N65 Algebraic topology of manifoldsmanifolds: 76: 57Pxx Generalized manifolds [See also]18F15manifolds: 77: 57P05 Local properties of generalized manifoldsmanifolds: 78: 57Q15 Triangulating manifoldsmanifolds: 79: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxmanifolds: 80: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxmanifolds: 81: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)manifolds: 82: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)manifolds: 83: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)manifolds: 84: 57R19 Algebraic topology on manifoldsmanifolds: 85: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B05manifolds: 86: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXmanifolds: 87: 57R91 Equivariant algebraic topology of manifoldsmanifolds: 88: 57S25 Groups acting on specific manifoldsmanifolds: 89: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15manifolds: 90: 58Axx General theory of differentiable manifolds [See also]32Cxxmanifolds: 91: 58A03 Topos-theoretic approach to differentiable manifoldsmanifolds: 92: 58A05 Differentiable manifolds, foundationsmanifolds: 93: 58A07 Real-analytic and Nash manifolds [See also]14P20, 32C07manifolds: 94: 58A50 Supermanifolds and graded manifolds [See also]14A22, 32C11manifolds: 95: 58Bxx Infinite-dimensional manifoldsmanifolds: 96: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D05manifolds: 97: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxxmanifolds: 98: 58C30 Fixed point theorems on manifolds [See also]47H10manifolds: 99: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxmanifolds: 100: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxmanifolds: 101: 58C50 Analysis on supermanifolds or graded manifoldsmanifolds: 102: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxmanifolds: 103: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S05manifolds: 104: 58D15 Manifolds of mappings [See also]46T10, 54C35
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manifolds: 105: 58D17 Manifolds of metrics (esp. Riemannian)manifolds: 106: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12manifolds: 107: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldsmanifolds: 108: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxxmanifolds: 109: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXmanifolds: 110: 58J32 Boundary value problems on manifoldsmanifolds: 111: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxxmanifolds: 112: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60manifolds: 113: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductionmanifolds: 114: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
manipulative: 1: 97U60 Manipulative materialsmanpower: 1: 90B70 Theory of organizations, manpower planning [See also]91D35manpower: 2: 91D35 Manpower systems [See also]91B40, 90B70
manuals: 1: 97U30 Teachers’ manuals and planning aidsmany: 1: 11D72 Equations in many variables [See also]11P55many: 2: 11D79 Congruences in many variablesmany: 3: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25many: 4: 91A13 Games with infinitely many players
many-body: 1: 81V70 Many-body theory; quantum Hall effectmany-valued: 1: 03B50 Many-valued logic
map: 1: 58K40 Classification; finite determinacy of map germsmapping: 1: 30C25 Covering theorems in conformal mapping theorymapping: 2: 30C30 Numerical methods in conformal mapping theory [See also]65E05mapping: 3: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)mapping: 4: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15mapping: 5: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30mapping: 6: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30mapping: 7: 86A30 Geodesy, mapping problems
mappings: 1: 18B30 Categories of topological spaces and continuous mappings [See also]54-XXmappings: 2: 20M15 Mappings of semigroupsmappings: 3: 30C20 Conformal mappings of special domainsmappings: 4: 30C35 General theory of conformal mappingsmappings: 5: 30C62 Quasiconformal mappings in the planemappings: 6: 30C65 Quasiconformal mappings in Rn, other generalizationsmappings: 7: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsmappings: 8: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsmappings: 9: 30L10 Quasiconformal mappings in metric spacesmappings: 10: 32A19 Normal families of functions, mappingsmappings: 11: 32Hxx Holomorphic mappings and correspondencesmappings: 12: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsmappings: 13: 32H04 Meromorphic mappingsmappings: 14: 32H12 Boundary uniqueness of mappingsmappings: 15: 32H35 Proper mappings, finiteness theoremsmappings: 16: 32H40 Boundary regularity of mappingsmappings: 17: 37C05 Smooth mappings and diffeomorphismsmappings: 18: 37J10 Symplectic mappings, fixed pointsmappings: 19: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricsmappings: 20: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H60mappings: 21: 46T10 Manifolds of mappingsmappings: 22: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.
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mappings: 23: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.mappings: 24: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.mappings: 25: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.mappings: 26: 47L22 Ideals of polynomials and of multilinear mappingsmappings: 27: 55S36 Extension and compression of mappingsmappings: 28: 55S37 Classification of mappingsmappings: 29: 57R35 Differentiable mappingsmappings: 30: 57R45 Singularities of differentiable mappingsmappings: 31: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C60mappings: 32: 58C07 Continuity properties of mappingsmappings: 33: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxmappings: 34: 58D15 Manifolds of mappings [See also]46T10, 54C35mappings: 35: 58K05 Critical points of functions and mappingsmappings: 36: 58K15 Topological properties of mappingsmappings: 37: 58K20 Algebraic and analytic properties of mappingsmappings: 38: 97I20 Mappings and functions
maps: 1: 14E05 Rational and birational mapsmaps: 2: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)maps: 3: 37E10 Maps of the circlemaps: 4: 37E25 Maps of trees and graphsmaps: 5: 37E40 Twist mapsmaps: 6: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04maps: 7: 37F15 Expanding maps; hyperbolicity; structural stabilitymaps: 8: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D20maps: 9: 37P05 Polynomial and rational mapsmaps: 10: 37P10 Analytic and meromorphic mapsmaps: 11: 46L07 Operator spaces and completely bounded maps [See also]47L25maps: 12: 46T20 Continuous and differentiable maps [See also]46G05maps: 13: 46T25 Holomorphic maps [See also]46G20maps: 14: 53C43 Differential geometric aspects of harmonic maps [See also]58E20maps: 15: 53D20 Momentum maps; symplectic reductionmaps: 16: 54Cxx Maps and general types of spaces defined by mapsmaps: 17: 54Cxx Maps and general types of spaces defined by mapsmaps: 18: 54C05 Continuous mapsmaps: 19: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)maps: 20: 54C20 Extension of mapsmaps: 21: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C06maps: 22: 54E40 Special maps on metric spacesmaps: 23: 55R37 Maps between classifying spacesmaps: 24: 58C10 Holomorphic maps [See also]32-XXmaps: 25: 58C25 Differentiable mapsmaps: 26: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12maps: 27: 58E20 Harmonic maps [See also]53C43, etc.
market: 1: 91B24 Price theory and market structuremarket: 2: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)market: 3: 91B40 Labor market, contracts
marketing: 1: 90B60 Marketing, advertising [See also]91B60markov: 1: 11J06 Markov and Lagrange spectra and generalizationsmarkov: 2: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35markov: 3: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxmarkov: 4: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxx
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markov: 5: 60Jxx Markov processesmarkov: 6: 60J05 Discrete-time Markov processes on general state spacesmarkov: 7: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)markov: 8: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)markov: 9: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40markov: 10: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40markov: 11: 60J22 Computational methods in Markov chains [See also]65C40markov: 12: 60J25 Continuous-time Markov processes on general state spacesmarkov: 13: 60J27 Continuous-time Markov processes on discrete state spacesmarkov: 14: 60J28 Applications of continuous-time Markov processes on discrete state spacesmarkov: 15: 60K15 Markov renewal processes, semi-Markov processesmarkov: 16: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxmarkov: 17: 62M02 Markov processes: hypothesis testingmarkov: 18: 62M05 Markov processes: estimationmarkov: 19: 65C40 Computational Markov chainsmarkov: 20: 90C40 Markov and semi-Markov decision processesmartin: 1: 31C35 Martin boundary theory [See also]60J50
martin’s: 1: 03E50 Continuum hypothesis and Martin’s axiom [See also]03E57martingales: 1: 60G42 Martingales with discrete parametermartingales: 2: 60G44 Martingales with continuous parametermartingales: 3: 60G46 Martingales and classical analysismartingales: 4: 60G48 Generalizations of martingales
masers: 1: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80maslov: 1: 53D12 Lagrangian submanifolds; Maslov indexmaslov: 2: 81Q20 Semiclassical techniques, including WKB and Maslov methods
mass: 1: 70Pxx Variable mass, rocketsmass: 2: 70P05 Variable mass, rocketsmass: 3: 80A20 Heat and mass transfer, heat flow
massey: 1: 55S30 Massey productsmaster: 1: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31
matching: 1: 05C70 Factorization, matching, partitioning, covering and packingmatching: 2: 05D15 Transversal (matching) theorymatching: 3: 91B68 Matching modelsmaterial: 1: 74Exx Material properties given special treatmentmaterial: 2: 97Uxx Educational material and media, educational technology
materials: 1: 74A30 Nonsimple materialsmaterials: 2: 74A35 Polar materialsmaterials: 3: 74A40 Random materials and composite materialsmaterials: 4: 74A40 Random materials and composite materialsmaterials: 5: 74A65 Reactive materialsmaterials: 6: 74Bxx Elastic materialsmaterials: 7: 74Cxx Plastic materials, materials of stress-rate and internal-variable typematerials: 8: 74Cxx Plastic materials, materials of stress-rate and internal-variable typematerials: 9: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic
materials)materials: 10: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)materials: 11: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)materials: 12: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)materials: 13: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)materials: 14: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
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materials: 15: 82D40 Magnetic materialsmaterials: 16: 97U60 Manipulative materials
materials”: 1: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxxmathematical: 1: 00A71 Theory of mathematical modelingmathematical: 2: 03-XX Mathematical logic and foundationsmathematical: 3: 03C65 Models of other mathematical theoriesmathematical: 4: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxmathematical: 5: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L05mathematical: 6: 35Q90 PDEs in connection with mathematical programmingmathematical: 7: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsmathematical: 8: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsmathematical: 9: 65Kxx Mathematical programming, optimization and variational techniquesmathematical: 10: 65K05 Mathematical programming methods [See also]90Cxxmathematical: 11: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areamathematical: 12: 68M07 Mathematical problems of computer architecturemathematical: 13: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)mathematical: 14: 68U15 Text processing; mathematical typographymathematical: 15: 81Qxx General mathematical topics and methods in quantum theorymathematical: 16: 90-XX Operations research, mathematical programmingmathematical: 17: 90Cxx Mathematical programming [See also]49Mxx, 65Kxxmathematical: 18: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q25mathematical: 19: 90C90 Applications of mathematical programmingmathematical: 20: 91Bxx Mathematical economics For econometrics, see 62P20mathematical: 21: 91Dxx Mathematical sociology (including anthropology)mathematical: 22: 91D20 Mathematical geography and demographymathematical: 23: 91Exx Mathematical psychologymathematical: 24: 91Fxx Other social and behavioral sciences (mathematical treatment)mathematical: 25: 91Gxx Mathematical financemathematical: 26: 92Bxx Mathematical biology in generalmathematical: 27: 93A30 Mathematical modeling (models of systems, model-matching, etc.)mathematical: 28: 97Mxx Mathematical modeling, applications of mathematicsmathematical: 29: 97N60 Mathematical programmingmathematical: 30: 97N80 Mathematical software, computer programs
mathematically: 1: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned atleast one other classification number in this section)
mathematicians: 1: 01Axx History of mathematics and mathematiciansmathematics: 1: 00A05 General mathematicsmathematics: 2: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)mathematics: 3: 00A08 Recreational mathematics [See also]97A20mathematics: 4: 00A09 Popularization of mathematicsmathematics: 5: 00A30 Philosophy of mathematics [See also]03A05mathematics: 6: 00A35 Methodology of mathematics, didactics [See also]97Cxx, 97Dxxmathematics: 7: 00A65 Mathematics and musicmathematics: 8: 00A66 Mathematics and visual arts, visualizationmathematics: 9: 00A67 Mathematics and architecturemathematics: 10: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86mathematics: 11: 01Axx History of mathematics and mathematiciansmathematics: 12: 01A72 Schools of mathematicsmathematics: 13: 01A80 Sociology (and profession) of mathematicsmathematics: 14: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30mathematics: 15: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35mathematics: 16: 03Fxx Proof theory and constructive mathematics
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mathematics: 17: 03F55 Intuitionistic mathematicsmathematics: 18: 03F65 Other constructive mathematics [See also]03D45mathematics: 19: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J05mathematics: 20: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J22mathematics: 21: 62P05 Applications to actuarial sciences and financial mathematicsmathematics: 22: 68Rxx Discrete mathematics in relation to computer sciencemathematics: 23: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)mathematics: 24: 97-XX Mathematics educationmathematics: 25: 97Axx General, mathematics and educationmathematics: 26: 97A20 Recreational mathematics, games [See also]00A08mathematics: 27: 97A30 History of mathematics and mathematics education [See also]01-XXmathematics: 28: 97A30 History of mathematics and mathematics education [See also]01-XXmathematics: 29: 97A40 Mathematics and societymathematics: 30: 97A80 Popularization of mathematicsmathematics: 31: 97Cxx Psychology of mathematics education, research in mathematics educationmathematics: 32: 97Cxx Psychology of mathematics education, research in mathematics educationmathematics: 33: 97Dxx Education and instruction in mathematicsmathematics: 34: 97Exx Foundations of mathematicsmathematics: 35: 97E20 Philosophy and mathematicsmathematics: 36: 97E40 Language of mathematicsmathematics: 37: 97E50 Reasoning and proving in the mathematics classroommathematics: 38: 97F90 Real life mathematics, practical arithmeticmathematics: 39: 97Mxx Mathematical modeling, applications of mathematicsmathematics: 40: 97M20 Mathematics in vocational training and career educationmathematics: 41: 97M30 Financial and insurance mathematicsmathematics: 42: 97Nxx Numerical mathematicsmathematics: 43: 97N70 Discrete mathematicsmathematics: 44: 97R20 Applications in mathematics
mathieu: 1: 33E10 Lame, Mathieu, and spheroidal wave functionsmathieu: 2: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)
maths: 1: 97D20 Philosophical and theoretical contributions (maths didactics)matrices: 1: 05A05 Permutations, words, matricesmatrices: 2: 05B20 Matrices (incidence, Hadamard, etc.)matrices: 3: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)matrices: 4: 11Cxx Polynomials and matricesmatrices: 5: 11C20 Matrices, determinants [See also]15B36matrices: 6: 11M50 Relations with random matricesmatrices: 7: 15A12 Conditioning of matrices [See also]65F35matrices: 8: 15A16 Matrix exponential and similar functions of matricesmatrices: 9: 15A23 Factorization of matricesmatrices: 10: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxxmatrices: 11: 15A45 Miscellaneous inequalities involving matricesmatrices: 12: 15A54 Matrices over function rings in one or more variablesmatrices: 13: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05matrices: 14: 15Bxx Special matricesmatrices: 15: 15B05 Toeplitz, Cauchy, and related matricesmatrices: 16: 15B10 Orthogonal matricesmatrices: 17: 15B15 Fuzzy matricesmatrices: 18: 15B33 Matrices over special rings (quaternions, finite fields, etc.)matrices: 19: 15B34 Boolean and Hadamard matricesmatrices: 20: 15B35 Sign pattern matricesmatrices: 21: 15B36 Matrices of integers [See also]11C20matrices: 22: 15B48 Positive matrices and their generalizations; cones of matrices
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matrices: 23: 15B48 Positive matrices and their generalizations; cones of matricesmatrices: 24: 15B51 Stochastic matricesmatrices: 25: 15B52 Random matricesmatrices: 26: 15B57 Hermitian, skew-Hermitian, and related matricesmatrices: 27: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsmatrices: 28: 16R40 Identities other than those of matrices over commutative ringsmatrices: 29: 20Hxx Other groups of matrices [See also]15A30matrices: 30: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K30matrices: 31: 47B36 Jacobi (tridiagonal) operators (matrices) and generalizationsmatrices: 32: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)matrices: 33: 65F50 Sparse matrices
matricially: 1: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07matrix: 1: 15-XX Linear and multilinear algebra; matrix theorymatrix: 2: 15A09 Matrix inversion, generalized inversesmatrix: 3: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14matrix: 4: 15A16 Matrix exponential and similar functions of matricesmatrix: 5: 15A22 Matrix pencils [See also]47A56matrix: 6: 15A24 Matrix equations and identitiesmatrix: 7: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05matrix: 8: 15A83 Matrix completion problemsmatrix: 9: 16S50 Endomorphism rings; matrix rings [See also]15-XXmatrix: 10: 20H20 Other matrix groups over fieldsmatrix: 11: 20H25 Other matrix groups over ringsmatrix: 12: 20H30 Other matrix groups over finite fieldsmatrix: 13: 39B42 Matrix and operator equations [See also]47Jxxmatrix: 14: 40C05 Matrix methodsmatrix: 15: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)matrix: 16: 65F05 Direct methods for linear systems and matrix inversionmatrix: 17: 65F30 Other matrix algorithmsmatrix: 18: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A60matrix: 19: 65F60 Matrix exponential and similar matrix functionsmatrix: 20: 65F60 Matrix exponential and similar matrix functions
matroids: 1: 05B35 Matroids, geometric lattices [See also]52B40, 90C27matroids: 2: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxmatroids: 3: 52C40 Oriented matroids
matter: 1: 82-XX Statistical mechanics, structure of mattermatter: 2: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
max-plus: 1: 15A80 Max-plus and related algebrasmaximal: 1: 20E28 Maximal subgroupsmaximal: 2: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E15maximal: 3: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setsmaximal: 4: 42B25 Maximal functions, Littlewood-Paley theorymaximal: 5: 46J20 Ideals, maximal ideals, boundaries
maximum: 1: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;subordinationmaximum: 2: 35B50 Maximum principles
maxwell: 1: 35Q61 Maxwell equationsmckay: 1: 14E16 McKay correspondencemean: 1: 11H60 Mean value and transfer theoremsmean: 2: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxmean: 3: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
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vanishing mean oscillation (VMOA)) [See also]46Exxmean: 4: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.mean: 5: 35J93 Quasilinear elliptic equations with mean curvature operatormean: 6: 35K93 Quasilinear parabolic equations with mean curvature operatormean: 7: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60mean: 8: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42mean: 9: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
mean-value: 1: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also]28A15
means: 1: 26E60 Means [See also]47A64means: 2: 43A07 Means on groups, semigroups, etc.; amenable groupsmeans: 3: 47A64 Operator means, shorted operators, etc.
measurable: 1: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axxmeasurable: 2: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
measurable: 3: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes ofconvergence
measurable: 4: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes ofconvergence
measurable: 5: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurableselections [See also]26E25, 54C60, 54C65, 91B14
measurable: 6: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
measure: 1: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension[See also]11N99, 28Dxx
measure: 2: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measuremeasure: 3: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05measure: 4: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05measure: 5: 28-XX Measure and integration For analysis on manifolds, see 58-XXmeasure: 6: 28Axx Classical measure theorymeasure: 7: 28A60 Measures on Boolean rings, measure algebras [See also]54H10measure: 8: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15measure: 9: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11measure: 10: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11measure: 11: 28Exx Miscellaneous topics in measure theorymeasure: 12: 28E05 Nonstandard measure theory [See also]03H05, 26E35measure: 13: 28E10 Fuzzy measure theory [See also]03E72, 26E50, 94D05measure: 14: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15measure: 15: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85measure: 16: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70measure: 17: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70measure: 18: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70measure: 19: 35R06 Partial differential equations with measuremeasure: 20: 43A10 Measure algebras on groups, semigroups, etc.measure: 21: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20measure: 22: 46L51 Noncommutative measure and integrationmeasure: 23: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XX
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measure: 24: 49Q15 Geometric measure and integration theory, integral and normal currents[See also]28A75, 32C30, 58A25, 58C35
measure: 25: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxmeasure-preserving: 1: 28D05 Measure-preserving transformationsmeasure-preserving: 2: 28D10 One-parameter continuous families of measure-preserving transformationsmeasure-preserving: 3: 28D15 General groups of measure-preserving transformationsmeasure-preserving: 4: 37A05 Measure-preserving transformationsmeasure-preserving: 5: 37A10 One-parameter continuous families of measure-preserving transformationsmeasure-preserving: 6: 37A15 General groups of measure-preserving transformations [See mainly]22Fxx
measure-theoretic: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35,54H20, 60Fxx, 60G10
measure-theoretic: 2: 49Q20 Variational problems in a geometric measure-theoretic settingmeasurement: 1: 81P15 Quantum measurement theorymeasurement: 2: 91C05 Measurement theorymeasurement: 3: 91E45 Measurement and performance
measures: 1: 11J82 Measures of irrationality and of transcendencemeasures: 2: 28A12 Contents, measures, outer measures, capacitiesmeasures: 3: 28A12 Contents, measures, outer measures, capacitiesmeasures: 4: 28A25 Integration with respect to measures and other set functionsmeasures: 5: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxxmeasures: 6: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxxmeasures: 7: 28A35 Measures and integrals in product spacesmeasures: 8: 28A50 Integration and disintegration of measuresmeasures: 9: 28A60 Measures on Boolean rings, measure algebras [See also]54H10measures: 10: 28A78 Hausdorff and packing measuresmeasures: 11: 28Bxx Set functions, measures and integrals with values in abstract spacesmeasures: 12: 28B05 Vector-valued set functions, measures and integrals [See also]46G10measures: 13: 28B10 Group- or semigroup-valued set functions, measures and integralsmeasures: 14: 28B15 Set functions, measures and integrals with values in ordered spacesmeasures: 15: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B14measures: 16: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20measures: 17: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresmeasures: 18: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresmeasures: 19: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05measures: 20: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05measures: 21: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05measures: 22: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)measures: 23: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)measures: 24: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11measures: 25: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxxmeasures: 26: 37J50 Action-minimizing orbits and measuresmeasures: 27: 37L40 Invariant measuresmeasures: 28: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)measures: 29: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G40measures: 30: 43A05 Measures on groups and semigroups, etc.measures: 31: 46E27 Spaces of measures [See also]28A33, 46Gxxmeasures: 32: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txx
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measures: 33: 46G10 Vector-valued measures and integration [See also]28Bxx, 46B22measures: 34: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12measures: 35: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)measures: 36: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.measures: 37: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxmeasures: 38: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12measures: 39: 60B05 Probability measures on topological spacesmeasures: 40: 60B10 Convergence of probability measuresmeasures: 41: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationmeasures: 42: 60G30 Continuity and singularity of induced measuresmeasures: 43: 60G57 Random measuresmeasures: 44: 62H20 Measures of association (correlation, canonical correlation, etc.)measures: 45: 91B82 Statistical methods; economic indices and measuresmeasures: 46: 94A17 Measures of information, entropymeasures: 47: 97F70 Measures and units
mechanical: 1: 70Qxx Control of mechanical systems [See also]60Gxx, 60Jxxmechanical: 2: 70Q05 Control of mechanical systemsmechanics: 1: 35Q35 PDEs in connection with fluid mechanicsmechanics: 2: 35Q40 PDEs in connection with quantum mechanicsmechanics: 3: 35Q70 PDEs in connection with mechanics of particles and systemsmechanics: 4: 35Q74 PDEs in connection with mechanics of deformable solidsmechanics: 5: 35Q82 PDEs in connection with statistical mechanicsmechanics: 6: 37A60 Dynamical systems in statistical mechanics [See also]82Cxxmechanics: 7: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,70Kxxmechanics: 8: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-XX, especially 76D05, 76F20, 86A05, 86A10mechanics: 9: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxxmechanics: 10: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,laser physics)mechanics: 11: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluiddynamics, etc.)mechanics: 12: 60K35 Interacting random processes; statistical mechanics type models; percolation theory[See also]82B43, 82C43mechanics: 13: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;for statistical mechanics, see 82-XXmechanics: 14: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;for statistical mechanics, see 82-XXmechanics: 15: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;for statistical mechanics, see 82-XXmechanics: 16: 70Fxx Dynamics of a system of particles, including celestial mechanicsmechanics: 17: 70F15 Celestial mechanicsmechanics: 18: 70F16 Collisions in celestial mechanics, regularizationmechanics: 19: 70Hxx Hamiltonian and Lagrangian mechanics [See also]37Jxxmechanics: 20: 70Mxx Orbital mechanicsmechanics: 21: 70M20 Orbital mechanicsmechanics: 22: 74-XX Mechanics of deformable solidsmechanics: 23: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solidsmechanics: 24: 74Fxx Coupling of solid mechanics with other effectsmechanics: 25: 74Lxx Special subfields of solid mechanicsmechanics: 26: 74L05 Geophysical solid mechanics [See also]86-XXmechanics: 27: 74L10 Soil and rock mechanicsmechanics: 28: 74L15 Biomechanical solid mechanics [See also]92C10mechanics: 29: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXmechanics: 30: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXmechanics: 31: 76A02 Foundations of fluid mechanicsmechanics: 32: 76Mxx Basic methods in fluid mechanics [See also]65-XX
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mechanics: 33: 76Zxx Biological fluid mechanics [See also]74F10, 74L15, 92Cxxmechanics: 34: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15mechanics: 35: 81P20 Stochastic mechanics (including stochastic electrodynamics)mechanics: 36: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and otherequations of quantum mechanicsmechanics: 37: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.mechanics: 38: 81Q60 Supersymmetry and quantum mechanicsmechanics: 39: 81Q65 Alternative quantum mechanicsmechanics: 40: 81Sxx General quantum mechanics and problems of quantizationmechanics: 41: 82-XX Statistical mechanics, structure of mattermechanics: 42: 82Bxx Equilibrium statistical mechanicsmechanics: 43: 82B05 Classical equilibrium statistical mechanics (general)mechanics: 44: 82B10 Quantum equilibrium statistical mechanics (general)mechanics: 45: 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)mechanics: 46: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)mechanics: 47: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)mechanics: 48: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15mechanics: 49: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15mechanics: 50: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)
mechanisms: 1: 70B15 Mechanisms, robots [See also]68T40, 70Q05, 93C85mechanization: 1: 03B35 Mechanization of proofs and logical operations [See also]68T15
media: 1: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50media: 2: 76Sxx Flows in porous media; filtration; seepagemedia: 3: 76S05 Flows in porous media; filtration; seepagemedia: 4: 78A48 Composite media; random mediamedia: 5: 78A48 Composite media; random mediamedia: 6: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)media: 7: 97Uxx Educational material and media, educational technologymedia: 8: 97U80 Audiovisual media
medical: 1: 62P10 Applications to biology and medical sciencesmedical: 2: 92Cxx Physiological, cellular and medical topicsmedical: 3: 92C50 Medical applications (general)medical: 4: 92C60 Medical epidemiology
medicine: 1: 97M60 Biology, chemistry, medicinemedieval: 1: 01A30 Islam (Medieval)medieval: 2: 01A35 Medieval
membranes: 1: 74K15 Membranesmemory: 1: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)memory: 2: 91E40 Memory and learning [See also]68T05
meromorphic: 1: 30Dxx Entire and meromorphic functions, and related topicsmeromorphic: 2: 30D30 Meromorphic functions, general theorymeromorphic: 3: 32A20 Meromorphic functionsmeromorphic: 4: 32H04 Meromorphic mappingsmeromorphic: 5: 34M05 Entire and meromorphic solutionsmeromorphic: 6: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04meromorphic: 7: 37P10 Analytic and meromorphic mapsmeromorphic: 8: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)mesh: 1: 65L50 Mesh generation and refinementmesh: 2: 65M50 Mesh generation and refinementmesh: 3: 65N50 Mesh generation and refinement
metabelian: 1: 11R20 Other abelian and metabelian extensionsmetals: 1: 82D35 Metals
metamathematical: 1: 20A10 Metamathematical considerations For word problems, see 20F10metamathematics: 1: 03F50 Metamathematics of constructive systems
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meteorology: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-XX, especially 76D05, 76F20, 86A05, 86A10
meteorology: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,76U05
method: 1: 11J85 Algebraic independence; Gel′fond’s methodmethod: 2: 11J86 Linear forms in logarithms; Baker’s methodmethod: 3: 11P55 Applications of the Hardy-Littlewood method [See also]11D85method: 4: 34C29 Averaging methodmethod: 5: 49L20 Dynamic programming methodmethod: 6: 65M20 Method of linesmethod: 7: 65M25 Method of characteristicsmethod: 8: 65N40 Method of linesmethod: 9: 65N45 Method of contraction of the boundarymethod: 10: 78M05 Method of moments
methodologies: 1: 68Uxx Computing methodologies and applicationsmethodology: 1: 00A35 Methodology of mathematics, didactics [See also]97Cxx, 97Dxxmethodology: 2: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)methodology: 3: 97K70 Foundations and methodology of statistics
methods: 1: 00A72 General methods of simulationmethods: 2: 05D40 Probabilistic methodsmethods: 3: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsmethods: 4: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)methods: 5: 11K45 Pseudo-random numbers; Monte Carlo methodsmethods: 6: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72methods: 7: 11N36 Applications of sieve methodsmethods: 8: 12Gxx Homological methods (field theory)methods: 9: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxmethods: 10: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxxmethods: 11: 14B10 Infinitesimal methods [See also]13D10methods: 12: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecturemethods: 13: 14C35 Applications of methods of algebraic K-theory [See also]19Exxmethods: 14: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxxmethods: 15: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXmethods: 16: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxmethods: 17: 17B55 Homological methods in Lie (super)algebrasmethods: 18: 20B40 Computational methodsmethods: 19: 20C40 Computational methodsmethods: 20: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
methods: 21: 20J05 Homological methods in group theorymethods: 22: 20K40 Homological and categorical methodsmethods: 23: 20K45 Topological methods [See also]22A05, 22B05methods: 24: 20Pxx Probabilistic methods in group theory [See also]60Bxxmethods: 25: 20P05 Probabilistic methods in group theory [See also]60Bxxmethods: 26: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05methods: 27: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10methods: 28: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10
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methods: 29: 30C30 Numerical methods in conformal mapping theory [See also]65E05methods: 30: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsmethods: 31: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsmethods: 32: 31A10 Integral representations, integral operators, integral equations methodsmethods: 33: 31B10 Integral representations, integral operators, integral equations methodsmethods: 34: 31C20 Discrete potential theory and numerical methodsmethods: 35: 32J25 Transcendental methods of algebraic geometry [See also]14C30methods: 36: 34A26 Geometric methods in differential equationsmethods: 37: 34E13 Multiple scale methodsmethods: 38: 34E18 Methods of nonstandard analysismethods: 39: 34E20 Singular perturbations, turning point theory, WKB methodsmethods: 40: 34M30 Asymptotics, summation methodsmethods: 41: 35A15 Variational methodsmethods: 42: 35A16 Topological and monotonicity methodsmethods: 43: 35A20 Analytic methods, singularitiesmethods: 44: 35A22 Transform methods (e.g. integral transforms)methods: 45: 35A24 Methods of ordinary differential equationsmethods: 46: 35A25 Other special methodsmethods: 47: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15methods: 48: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15methods: 49: 35J20 Variational methods for second-order elliptic equationsmethods: 50: 35J35 Variational methods for higher-order elliptic equationsmethods: 51: 35J50 Variational methods for elliptic systemsmethods: 52: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemsmethods: 53: 37J35 Completely integrable systems, topological structure of phase space, integration
methodsmethods: 54: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic
methodsmethods: 55: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic
methodsmethods: 56: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsmethods: 57: 37L65 Special approximation methods (nonlinear Galerkin, etc.)methods: 58: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxmethods: 59: 37M20 Computational methods for bifurcation problemsmethods: 60: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)methods: 61: 40Cxx General summability methodsmethods: 62: 40C05 Matrix methodsmethods: 63: 40C10 Integral methodsmethods: 64: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)methods: 65: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)methods: 66: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)methods: 67: 40D20 Summability and bounded fields of methodsmethods: 68: 40Gxx Special methods of summabilitymethods: 69: 40G05 Cesaro, Euler, Norlund and Hausdorff methodsmethods: 70: 40G10 Abel, Borel and power series methodsmethods: 71: 40G15 Summability methods using statistical convergence [See also]40A35methods: 72: 40Hxx Functional analytic methods in summabilitymethods: 73: 40H05 Functional analytic methods in summabilitymethods: 74: 42A61 Probabilistic methodsmethods: 75: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05
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methods: 76: 43A95 Categorical methods [See also]46Mxxmethods: 77: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
methods: 78: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
methods: 79: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxmethods: 80: 46Mxx Methods of category theory in functional analysis [See also]18-XXmethods: 81: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)methods: 82: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxmethods: 83: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60methods: 84: 47J30 Variational methods [See also]58Exxmethods: 85: 49J40 Variational methods including variational inequalities [See also]47J20methods: 86: 49J45 Methods involving semicontinuity and convergence; relaxationmethods: 87: 49Mxx Numerical methods [See also]90Cxx, 65Kxxmethods: 88: 49M05 Methods based on necessary conditionsmethods: 89: 49M15 Newton-type methodsmethods: 90: 49M20 Methods of relaxation typemethods: 91: 49M27 Decomposition methodsmethods: 92: 49M29 Methods involving dualitymethods: 93: 49M30 Other methodsmethods: 94: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxxmethods: 95: 49Rxx Variational methods for eigenvalues of operators [See also]47A75methods: 96: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)methods: 97: 51L15 n-vertex theorems via direct methodsmethods: 98: 53B21 Methods of Riemannian geometrymethods: 99: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60methods: 100: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60methods: 101: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesmethods: 102: 53C28 Twistor methods [See also]32L25methods: 103: 53C70 Direct methods (G-spaces of Busemann, etc.)methods: 104: 54B30 Categorical methods [See also]18B30methods: 105: 57M07 Topological methods in group theorymethods: 106: 58C15 Implicit function theorems; global Newton methodsmethods: 107: 58J35 Heat and other parabolic equation methodsmethods: 108: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22methods: 109: 60H35 Computational methods for stochastic equations [See also]65C30methods: 110: 60J22 Computational methods in Markov chains [See also]65C40methods: 111: 62F40 Bootstrap, jackknife and other resampling methodsmethods: 112: 62G09 Resampling methodsmethods: 113: 62Lxx Sequential methodsmethods: 114: 62L86 Fuzziness and sequential methodsmethods: 115: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35methods: 116: 65C05 Monte Carlo methodsmethods: 117: 65C20 Models, numerical methods [See also]68U20methods: 118: 65C35 Stochastic particle methods [See also]82C80methods: 119: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30methods: 120: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
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methods in conformal mapping, see also 30C30methods: 121: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30methods: 122: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30methods: 123: 65F05 Direct methods for linear systems and matrix inversionmethods: 124: 65F08 Preconditioners for iterative methodsmethods: 125: 65F10 Iterative methods for linear systems [See also]65N22methods: 126: 65G40 General methods in interval analysismethods: 127: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C30methods: 128: 65K05 Mathematical programming methods [See also]90Cxxmethods: 129: 65K15 Numerical methods for variational inequalities and related problemsmethods: 130: 65L06 Multistep, Runge-Kutta and extrapolation methodsmethods: 131: 65L12 Finite difference methodsmethods: 132: 65L20 Stability and convergence of numerical methodsmethods: 133: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodsmethods: 134: 65L80 Methods for differential-algebraic equationsmethods: 135: 65M06 Finite difference methodsmethods: 136: 65M08 Finite volume methodsmethods: 137: 65M12 Stability and convergence of numerical methodsmethods: 138: 65M38 Boundary element methodsmethods: 139: 65M55 Multigrid methods; domain decompositionmethods: 140: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsmethods: 141: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsmethods: 142: 65M70 Spectral, collocation and related methodsmethods: 143: 65M75 Probabilistic methods, particle methods, etc.methods: 144: 65M75 Probabilistic methods, particle methods, etc.methods: 145: 65M80 Fundamental solutions, Green’s function methods, etc.methods: 146: 65M85 Fictitious domain methodsmethods: 147: 65N06 Finite difference methodsmethods: 148: 65N08 Finite volume methodsmethods: 149: 65N12 Stability and convergence of numerical methodsmethods: 150: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsmethods: 151: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsmethods: 152: 65N35 Spectral, collocation and related methodsmethods: 153: 65N38 Boundary element methodsmethods: 154: 65N55 Multigrid methods; domain decompositionmethods: 155: 65N75 Probabilistic methods, particle methods, etc.methods: 156: 65N75 Probabilistic methods, particle methods, etc.methods: 157: 65N80 Fundamental solutions, Green’s function methods, etc.methods: 158: 65N85 Fictitious domain methodsmethods: 159: 65Sxx Graphical methodsmethods: 160: 65S05 Graphical methodsmethods: 161: 65Txx Numerical methods in Fourier analysismethods: 162: 65Y15 Packaged methodsmethods: 163: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)methods: 164: 70E20 Perturbation methods for rigid body dynamicsmethods: 165: 70Gxx General models, approaches, and methods [See also]37-XXmethods: 166: 70G40 Topological and differential-topological methodsmethods: 167: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxmethods: 168: 70G55 Algebraic geometry methodsmethods: 169: 70G60 Dynamical systems methodsmethods: 170: 70G65 Symmetries, Lie-group and Lie-algebra methodsmethods: 171: 70G70 Functional-analytic methodsmethods: 172: 70G75 Variational methods
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methods: 173: 70H06 Completely integrable systems and methods of integrationmethods: 174: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)methods: 175: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)methods: 176: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)methods: 177: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)methods: 178: 74P15 Topological methodsmethods: 179: 74P20 Geometrical methodsmethods: 180: 74Sxx Numerical methods [See also]65-XX, 74G15, 74H15methods: 181: 74S05 Finite element methodsmethods: 182: 74S10 Finite volume methodsmethods: 183: 74S15 Boundary element methodsmethods: 184: 74S20 Finite difference methodsmethods: 185: 74S25 Spectral and related methodsmethods: 186: 74S30 Other numerical methodsmethods: 187: 74S60 Stochastic methodsmethods: 188: 74S70 Complex variable methodsmethods: 189: 76F30 Renormalization and other field-theoretical methods [See also]81T99methods: 190: 76Mxx Basic methods in fluid mechanics [See also]65-XXmethods: 191: 76M10 Finite element methodsmethods: 192: 76M12 Finite volume methodsmethods: 193: 76M15 Boundary element methodsmethods: 194: 76M20 Finite difference methodsmethods: 195: 76M22 Spectral methodsmethods: 196: 76M23 Vortex methodsmethods: 197: 76M25 Other numerical methodsmethods: 198: 76M28 Particle methods and lattice-gas methodsmethods: 199: 76M28 Particle methods and lattice-gas methodsmethods: 200: 76M30 Variational methodsmethods: 201: 76M40 Complex-variables methodsmethods: 202: 76M45 Asymptotic methods, singular perturbationsmethods: 203: 76M60 Symmetry analysis, Lie group and algebra methodsmethods: 204: 78Mxx Basic methodsmethods: 205: 78M10 Finite element methodsmethods: 206: 78M12 Finite volume methods, finite integration techniquesmethods: 207: 78M15 Boundary element methodsmethods: 208: 78M16 Multipole methodsmethods: 209: 78M20 Finite difference methodsmethods: 210: 78M22 Spectral methodsmethods: 211: 78M25 Other numerical methodsmethods: 212: 78M30 Variational methodsmethods: 213: 78M31 Monte Carlo methodsmethods: 214: 78M32 Neural and heuristic methodsmethods: 215: 80Mxx Basic methodsmethods: 216: 80M10 Finite element methodsmethods: 217: 80M12 Finite volume methodsmethods: 218: 80M15 Boundary element methodsmethods: 219: 80M20 Finite difference methodsmethods: 220: 80M22 Spectral methodsmethods: 221: 80M25 Other numerical methodsmethods: 222: 80M30 Variational methodsmethods: 223: 80M31 Monte Carlo methodsmethods: 224: 81Qxx General mathematical topics and methods in quantum theorymethods: 225: 81Q20 Semiclassical techniques, including WKB and Maslov methods
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methods: 226: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.methods: 227: 81R15 Operator algebra methods [See also]46Lxx, 81T05methods: 228: 81R25 Spinor and twistor methods [See also]32L25methods: 229: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B37methods: 230: 81S10 Geometry and quantization, symplectic methods [See also]53D50methods: 231: 81S30 Phase-space methods including Wigner distributions, etc.methods: 232: 81T15 Perturbative methods of renormalizationmethods: 233: 81T16 Nonperturbative methods of renormalizationmethods: 234: 81T17 Renormalization group methodsmethods: 235: 81T70 Quantization in field theory; cohomological methods [See also]58D29methods: 236: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B34methods: 237: 82B28 Renormalization group methods [See also]81T17methods: 238: 82B31 Stochastic methodsmethods: 239: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80methods: 240: 82C28 Dynamic renormalization group methods [See also]81T17methods: 241: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H10methods: 242: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)methods: 243: 83C27 Lattice gravity, Regge calculus and other discrete methodsmethods: 244: 83C47 Methods of quantum field theory [See also]81T20methods: 245: 83C60 Spinor and twistor methods; Newman-Penrose formalismmethods: 246: 83C65 Methods of noncommutative geometry [See also]58B34methods: 247: 90C49 Extreme-point and pivoting methodsmethods: 248: 90C51 Interior-point methodsmethods: 249: 90C52 Methods of reduced gradient typemethods: 250: 90C53 Methods of quasi-Newton typemethods: 251: 90C55 Methods of successive quadratic programming typemethods: 252: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52methods: 253: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52methods: 254: 90C59 Approximation methods and heuristicsmethods: 255: 91B82 Statistical methods; economic indices and measuresmethods: 256: 91G60 Numerical methods (including Monte Carlo methods)methods: 257: 91G60 Numerical methods (including Monte Carlo methods)methods: 258: 91G70 Statistical methods, econometricsmethods: 259: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)methods: 260: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)methods: 261: 93B25 Algebraic methodsmethods: 262: 93B27 Geometric methodsmethods: 263: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N70methods: 264: 93B40 Computational methodsmethods: 265: 93C80 Frequency-response methodsmethods: 266: 93E24 Least squares and related methodsmethods: 267: 93E25 Other computational methodsmethods: 268: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G50methods: 269: 97D40 Teaching methods and classroom techniquesmethods: 270: 97Q60 Teaching methods and classroom techniquesmethods: 1: 78A45 Diffraction, scattering [See also]34E20 for WKB methodsmethods: 2: 81U05 2-body potential scattering theory [See also]34E20 for WKB methods
metric: 1: 11A63 Radix representation; digital problems For metric results, see 11K16metric: 2: 11J83 Metric theorymetric: 3: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmsmetric: 4: 11K50 Metric theory of continued fractions [See also]11A55, 11J70metric: 5: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
[See also]11N99, 28Dxxmetric: 6: 30Lxx Analysis on metric spacesmetric: 7: 30L05 Geometric embeddings of metric spacesmetric: 8: 30L10 Quasiconformal mappings in metric spaces
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metric: 9: 31Exx Potential theory on metric spacesmetric: 10: 31E05 Potential theory on metric spacesmetric: 11: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)metric: 12: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxmetric: 13: 46S50 Functional analysis in probabilistic metric linear spacesmetric: 14: 47B50 Operators on spaces with an indefinite metric [See also]46C50metric: 15: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70metric: 16: 51Fxx Metric geometrymetric: 17: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesmetric: 18: 54E35 Metric spaces, metrizabilitymetric: 19: 54E40 Special maps on metric spacesmetric: 20: 54E45 Compact (locally compact) metric spacesmetric: 21: 54E50 Complete metric spacesmetric: 22: 54E70 Probabilistic metric spaces
metrics: 1: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)metrics: 2: 32F45 Invariant metrics and pseudodistancesmetrics: 3: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricsmetrics: 4: 53B30 Lorentz metrics, indefinite metricsmetrics: 5: 53B30 Lorentz metrics, indefinite metricsmetrics: 6: 53B40 Finsler spaces and generalizations (areal metrics)metrics: 7: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
[See also]32Q20metrics: 8: 53C50 Lorentz manifolds, manifolds with indefinite metricsmetrics: 9: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B20metrics: 10: 58D17 Manifolds of metrics (esp. Riemannian)metrics: 11: 58E11 Critical metricsmetrics: 12: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)metrics: 13: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
metrizability: 1: 54E35 Metric spaces, metrizabilitymetrizable: 1: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,quasi-Banach spaces, etc.)
microbundles: 1: 55R60 Microbundles and block bundles [See also]57N55, 57Q50microbundles: 2: 57N55 Microbundles and block bundles [See also]55R60, 57Q50microbundles: 3: 57Q50 Microbundles and block bundles [See also]55R60, 57N55
microlocal: 1: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE[See also]32C38, 58J15
micromechanical: 1: 74A60 Micromechanical theoriesmicromechanics: 1: 74M25 Micromechanicsmicrostructure: 1: 74N15 Analysis of microstructure
mikusinski: 1: 44A40 Calculus of Mikusinski and other operational calculimilnor: 1: 19D45 Higher symbols, Milnor K-theorymilnor: 2: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45
minima: 1: 11H50 Minima of formsminimal: 1: 14E30 Minimal model program (Mori theory, extremal rays)minimal: 2: 49Q05 Minimal surfaces [See also]53A10, 58E12minimal: 3: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90minimal: 4: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42minimal: 5: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R42minimal: 6: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05
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minimal: 7: 93B20 Minimal systems representationsminimality: 1: 37B05 Transformations and group actions with special properties (minimality, distality,proximality, etc.)
minimax: 1: 49J35 Minimax problemsminimax: 2: 49K35 Minimax problemsminimax: 3: 62C20 Minimax proceduresminimax: 4: 90C47 Minimax problems [See also]49K35
minimization: 1: 74G65 Energy minimizationminkowski: 1: 51B20 Minkowski geometries
minors: 1: 05C83 Graph minorsmirror: 1: 11G42 Arithmetic mirror symmetry [See also]14J33mirror: 2: 14J33 Mirror symmetry [See also]11G42, 53D37mirror: 3: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J33mirror: 4: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J33miscellaneous: 1: 00Axx General and miscellaneous specific topicsmiscellaneous: 2: 00B15 Collections of articles of miscellaneous specific contentmiscellaneous: 3: 00B25 Proceedings of conferences of miscellaneous specific interestmiscellaneous: 4: 00B55 Miscellaneous volumes of translationsmiscellaneous: 5: 11Zxx Miscellaneous applications of number theorymiscellaneous: 6: 11Z05 Miscellaneous applications of number theorymiscellaneous: 7: 15A45 Miscellaneous inequalities involving matricesmiscellaneous: 8: 16Bxx General and miscellaneousmiscellaneous: 9: 19Mxx Miscellaneous applications of K-theorymiscellaneous: 10: 19M05 Miscellaneous applications of K-theorymiscellaneous: 11: 26Exx Miscellaneous topics [See also]58Cxxmiscellaneous: 12: 28Exx Miscellaneous topics in measure theorymiscellaneous: 13: 30Exx Miscellaneous topics of analysis in the complex domainmiscellaneous: 14: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15miscellaneous: 15: 45Hxx Miscellaneous special kernels [See also]44A15miscellaneous: 16: 45H05 Miscellaneous special kernels [See also]44A15miscellaneous: 17: 46Nxx Miscellaneous applications of functional analysis [See also]47Nxxmiscellaneous: 18: 47Nxx Miscellaneous applications of operator theory [See also]46Nxxmiscellaneous: 19: 49Nxx Miscellaneous topicsmittag-leffler: 1: 33E12 Mittag-Leffler functions and generalizations
mixed: 1: 20K21 Mixed groupsmixed: 2: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D07mixed: 3: 35Mxx Equations and systems of special type (mixed, composite, etc.)mixed: 4: 35M10 Equations of mixed typemixed: 5: 35M11 Initial value problems for equations of mixed typemixed: 6: 35M12 Boundary value problems for equations of mixed typemixed: 7: 35M13 Initial-boundary value problems for equations of mixed typemixed: 8: 35M30 Systems of mixed typemixed: 9: 35M31 Initial value problems for systems of mixed typemixed: 10: 35M32 Boundary value problems for systems of mixed typemixed: 11: 35M33 Initial-boundary value problems for systems of mixed typemixed: 12: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J40mixed: 13: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40mixed: 14: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J40mixed: 15: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)mixed: 16: 52A39 Mixed volumes and related topicsmixed: 17: 90C11 Mixed integer programming
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mixing: 1: 37A25 Ergodicity, mixing, rates of mixingmixing: 2: 37A25 Ergodicity, mixing, rates of mixingmixing: 3: 76F25 Turbulent transport, mixing
mixture: 1: 74E30 Composite and mixture propertiesmixture: 2: 74F20 Mixture effectsmobility: 1: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40mod: 1: 11B50 Sequences (mod m)
modal: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; fortemporal logic, see 03B44; for provability logic, see also 03F45
modal: 2: 70J10 Modal analysismodel: 1: 03Cxx Model theorymodel: 2: 03C10 Quantifier elimination, model completeness and related topicsmodel: 3: 03C30 Other model constructionsmodel: 4: 03C55 Set-theoretic model theorymodel: 5: 03C57 Effective and recursion-theoretic model theory [See also]03D45model: 6: 03C64 Model theory of ordered structures; o-minimalitymodel: 7: 03C68 Other classical first-order model theorymodel: 8: 03C85 Second- and higher-order model theorymodel: 9: 03C95 Abstract model theorymodel: 10: 03C98 Applications of model theory [See also]03C60model: 11: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C60model: 12: 11U09 Model theory [See also]03Cxxmodel: 13: 12L12 Model theory [See also]03C60model: 14: 14E30 Minimal model program (Mori theory, extremal rays)model: 15: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70model: 16: 78M34 Model reductionmodel: 17: 81T10 Model quantum field theories
model-matching: 1: 93A30 Mathematical modeling (models of systems, model-matching, etc.)model-theoretic: 1: 03C25 Model-theoretic forcingmodel-theoretic: 2: 03C60 Model-theoretic algebra [See also]08C10, 12Lxx, 13L05
modeled: 1: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,58Bxx
modeling: 1: 00A71 Theory of mathematical modelingmodeling: 2: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07modeling: 3: 76F55 Statistical turbulence modeling [See also]76M35modeling: 4: 76F60 k-ε modelingmodeling: 5: 81T80 Simulation and numerical modelingmodeling: 6: 93A30 Mathematical modeling (models of systems, model-matching, etc.)modeling: 7: 97Mxx Mathematical modeling, applications of mathematicsmodeling: 8: 97M10 Modeling and interdisciplinarity
models: 1: 03C50 Models with special properties (saturated, rigid, etc.)models: 2: 03C52 Properties of classes of modelsmodels: 3: 03C62 Models of arithmetic and set theory [See also]03Hxxmodels: 4: 03C65 Models of other mathematical theoriesmodels: 5: 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)models: 6: 03E40 Other aspects of forcing and Boolean-valued modelsmodels: 7: 03E45 Inner models, including constructibility, ordinal definability, and core modelsmodels: 8: 03E45 Inner models, including constructibility, ordinal definability, and core modelsmodels: 9: 03Hxx Nonstandard models [See also]03C62models: 10: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J05models: 11: 03H10 Other applications of nonstandard models (economics, physics, etc.)models: 12: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L05models: 13: 34C60 Qualitative investigation and simulation of modelsmodels: 14: 34K60 Qualitative investigation and simulation of modelsmodels: 15: 47A45 Canonical models for contractions and nonselfadjoint operators
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models: 16: 60K35 Interacting random processes; statistical mechanics type models; percolation theory[See also]82B43, 82C43
models: 17: 62J12 Generalized linear modelsmodels: 18: 62N01 Censored data modelsmodels: 19: 65C20 Models, numerical methods [See also]68U20models: 20: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxmodels: 21: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P68models: 22: 68Q19 Descriptive complexity and finite models [See also]03C13models: 23: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)models: 24: 70Gxx General models, approaches, and methods [See also]37-XXmodels: 25: 82B21 Continuum models (systems of particles, etc.)models: 26: 82B23 Exactly solvable models; Bethe ansatzmodels: 27: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)models: 28: 82C21 Dynamic continuum models (systems of particles, etc.)models: 29: 82C23 Exactly solvable dynamic models [See also]37K60models: 30: 90B10 Network models, deterministicmodels: 31: 90B15 Network models, stochasticmodels: 32: 90B30 Production modelsmodels: 33: 91A40 Game-theoretic modelsmodels: 34: 91B25 Asset pricing modelsmodels: 35: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)models: 36: 91B60 Trade modelsmodels: 37: 91B62 Growth modelsmodels: 38: 91B64 Macro-economic models (monetary models, models of taxation)models: 39: 91B64 Macro-economic models (monetary models, models of taxation)models: 40: 91B64 Macro-economic models (monetary models, models of taxation)models: 41: 91B66 Multisectoral modelsmodels: 42: 91B68 Matching modelsmodels: 43: 91B69 Heterogeneous agent modelsmodels: 44: 91B70 Stochastic modelsmodels: 45: 91B72 Spatial modelsmodels: 46: 91B74 Models of real-world systemsmodels: 47: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)models: 48: 91D10 Models of societies, social and urban evolutionmodels: 49: 91D25 Spatial models [See also]91B72models: 50: 91G30 Interest rates (stochastic models)models: 51: 93A30 Mathematical modeling (models of systems, model-matching, etc.)models: 52: 94A40 Channel models (including quantum)modes: 1: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of
convergencemodes: 2: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85modes: 3: 70K75 Nonlinear modes
modifications: 1: 32S45 Modifications; resolution of singularities [See also]14E15modular: 1: 06Cxx Modular lattices, complemented latticesmodular: 2: 06C05 Modular lattices, Desarguesian latticesmodular: 3: 06C20 Complemented modular lattices, continuous geometriesmodular: 4: 11F03 Modular and automorphic functionsmodular: 5: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E40modular: 6: 11F11 Holomorphic modular forms of integral weightmodular: 7: 11F32 Modular correspondences, etc.modular: 8: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50modular: 9: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E50modular: 10: 11F37 Forms of half-integer weight; nonholomorphic modular forms
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modular: 11: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
modular: 12: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
modular: 13: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
modular: 14: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formsmodular: 15: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formsmodular: 16: 11F52 Modular forms associated to Drinfel′d modulesmodular: 17: 11F55 Other groups and their modular and automorphic forms (several variables)modular: 18: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsmodular: 19: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsmodular: 20: 11G16 Elliptic and modular units [See also]11R27modular: 21: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G35modular: 22: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G18modular: 23: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13modular: 24: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35modular: 25: 17B50 Modular Lie (super)algebrasmodular: 26: 20C20 Modular representations and charactersmodular: 27: 46A80 Modular spaces
modularity: 1: 08B10 Congruence modularity, congruence distributivitymodulation: 1: 94A14 Modulation and demodulationmodulation: 2: 94B12 Combined modulation schemes (including trellis codes)
module: 1: 11R33 Integral representations related to algebraic numbers; Galois module structure of ringsof integers [See also]20C10
module: 2: 13C60 Module categoriesmodule: 3: 16D10 General module theorymodule: 4: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitymodule: 5: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitymodule: 6: 16N80 General radicals and rings For radicals in module categories, see 16S90module: 7: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxmodules: 1: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80modules: 2: 11F52 Modular forms associated to Drinfel′d modulesmodules: 3: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05modules: 4: 13Cxx Theory of modules and idealsmodules: 5: 13C10 Projective and free modules and ideals [See also]19A13modules: 6: 13C11 Injective and flat modules and idealsmodules: 7: 13C12 Torsion modules and idealsmodules: 8: 13C14 Cohen-Macaulay modules [See also]13H10modules: 9: 13D07 Homological functors on modules (Tor, Ext, etc.)modules: 10: 13E05 Noetherian rings and modulesmodules: 11: 13E10 Artinian rings and modules, finite-dimensional algebrasmodules: 12: 13E15 Rings and modules of finite generation or presentation; number of generatorsmodules: 13: 13Jxx Topological rings and modules [See also]16W60, 16W80modules: 14: 13N05 Modules of differentialsmodules: 15: 13N10 Rings of differential operators and their modules [See also]16S32, 32C38modules: 16: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)modules: 17: 15A78 Other algebras built from modulesmodules: 18: 16Dxx Modules, bimodules and idealsmodules: 19: 16D40 Free, projective, and flat modules and ideals [See also]19A13modules: 20: 16D50 Injective modules, self-injective rings [See also]16L60modules: 21: 16D60 Simple and semisimple modules, primitive rings and ideals
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modules: 22: 16D80 Other classes of modules and ideals [See also]16G50modules: 23: 16E30 Homological functors on modules (Tor, Ext, etc.)modules: 24: 16G50 Cohen-Macaulay modulesmodules: 25: 16P20 Artinian rings and modulesmodules: 26: 16P40 Noetherian rings and modulesmodules: 27: 16W50 Graded rings and modulesmodules: 28: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxxmodules: 29: 19A13 Stability for projective modules [See also]13C10modules: 30: 19G05 Stability for quadratic modulesmodules: 31: 20C05 Group rings of finite groups and their modules [See also]16S34modules: 32: 20C07 Group rings of infinite groups and their modules [See also]16S34modules: 33: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10modules: 34: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J15modules: 35: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)modules: 36: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)modules: 37: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)moduli: 1: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K22moduli: 2: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13moduli: 3: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13moduli: 4: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13moduli: 5: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxmoduli: 6: 14D22 Fine and coarse moduli spacesmoduli: 7: 14D23 Stacks and moduli problemsmoduli: 8: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)moduli: 9: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)moduli: 10: 14H10 Families, moduli (algebraic)moduli: 11: 14H15 Families, moduli (analytic) [See also]30F10, 32G15moduli: 12: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05moduli: 13: 14J10 Families, moduli, classification: algebraic theorymoduli: 14: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13moduli: 15: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxmoduli: 16: 14K10 Algebraic moduli, classification [See also]11G15moduli: 17: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15moduli: 18: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15moduli: 19: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxxmoduli: 20: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxmoduli: 21: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationmoduli: 22: 37P45 Families and moduli spacesmoduli: 23: 53D30 Symplectic structures of moduli spacesmoduli: 24: 58D27 Moduli problems for differential geometric structuresmoduli: 25: 58D29 Moduli problems for topological structuresmodulo: 1: 11J71 Distribution modulo one [See also]11K06
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modulo: 2: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmsmodulo: 3: 11K06 General theory of distribution modulo 1 [See also]11J71
modulus: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27molecular: 1: 74A25 Molecular, statistical, and kinetic theoriesmolecular: 2: 81V55 Molecular physics [See also]92E10molecular: 3: 92C40 Biochemistry, molecular biologymolecular: 4: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
moment: 1: 30E05 Moment problems, interpolation problemsmoment: 2: 42A70 Trigonometric moment problemsmoment: 3: 44A60 Moment problemsmoment: 4: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60moments: 1: 78M05 Method of moments
momentum: 1: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction[See also]53D20
momentum: 2: 53D20 Momentum maps; symplectic reductionmonad: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxmonads: 1: 18C20 Algebras and Kleisli categories associated with monads
monetary: 1: 91B64 Macro-economic models (monetary models, models of taxation)monge-ampere: 1: 32W20 Complex Monge-Ampere operatorsmonge-ampere: 2: 35J96 Elliptic Monge-Ampere equationsmonge-ampere: 3: 35K96 Parabolic Monge-Ampere equations
monodromy: 1: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)monodromy: 2: 32S40 Monodromy; relations with differential equations and D-modulesmonodromy: 3: 34M35 Singularities, monodromy, local behavior of solutions, normal formsmonodromy: 4: 58K10 Monodromy
monogenic: 1: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenicfunctions)monogenic: 2: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenicfunctions)
monoidal: 1: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,braided categories [See also]19D23
monoidal: 2: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,braided categories [See also]19D23
monoidal: 3: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)monoidal: 4: 18D20 Enriched categories (over closed or monoidal categories)monoidal: 5: 19D23 Symmetric monoidal categories [See also]18D10monoids: 1: 06F05 Ordered semigroups and monoids [See also]20Mxxmonoids: 2: 20M13 Arithmetic theory of monoidsmonoids: 3: 20M32 Algebraic monoids
monomorphisms: 1: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsmonotone: 1: 34C12 Monotone systemsmonotone: 2: 37C65 Monotone flowsmonotone: 3: 47H05 Monotone operators and generalizationsmonotone: 4: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesmonotonic: 1: 26A48 Monotonic functions, generalizationsmonotonic: 2: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
monotonicity: 1: 35A16 Topological and monotonicity methodsmonte: 1: 11K45 Pseudo-random numbers; Monte Carlo methodsmonte: 2: 65C05 Monte Carlo methodsmonte: 3: 78M31 Monte Carlo methodsmonte: 4: 80M31 Monte Carlo methodsmonte: 5: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80
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monte: 6: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)monte: 7: 91G60 Numerical methods (including Monte Carlo methods)montel: 1: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)moore: 1: 54E30 Moore spacesmore: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)more: 2: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesmore: 3: 15A54 Matrices over function rings in one or more variablesmore: 4: 39B52 Equations for functions with more general domains and/or rangesmore: 5: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)more: 6: 47A30 Norms (inequalities, more than one norm, etc.)more: 7: 49J10 Free problems in two or more independent variablesmore: 8: 49K10 Free problems in two or more independent variablesmore: 9: 70S20 More general nonquantum field theoriesmore: 10: 76T30 Three or more component flows
morgan: 1: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G20mori: 1: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizationsmori: 2: 14E30 Minimal model program (Mori theory, extremal rays)
morita: 1: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoreticcontext; Morita equivalence and duality
morley: 1: 20F11 Groups of finite Morley rank [See also]03C45, 03C60morphisms: 1: 13B10 Morphismsmorphisms: 2: 14A10 Varieties and morphismsmorphisms: 3: 14A15 Schemes and morphismsmorphisms: 4: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B40morphisms: 5: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsmorphisms: 6: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsmorphisms: 7: 18A23 Natural morphisms, dinatural morphismsmorphisms: 8: 18A23 Natural morphisms, dinatural morphismsmorphisms: 9: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamsmorphisms: 10: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05morphisms: 11: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05
morse: 1: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel′man) theory, etc.)
morse-conley: 1: 37B30 Index theory, Morse-Conley indicesmorse-smale: 1: 37D15 Morse-Smale systems
motion: 1: 60G22 Fractional processes, including fractional Brownian motionmotion: 2: 60J65 Brownian motion [See also]58J65motion: 3: 70E05 Motion of the gyroscopemotion: 4: 70E15 Free motion of a rigid body [See also]70M20motion: 5: 70E17 Motion of a rigid body with a fixed pointmotion: 6: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25motion: 7: 70E40 Integrable cases of motionmotion: 8: 78A35 Motion of charged particlesmotion: 9: 83C10 Equations of motion
motions: 1: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorptionproblems, etc.) [See also]92Dxx
motions: 2: 70J30 Free motionsmotions: 3: 70J35 Forced motionsmotions: 4: 70K25 Free motionsmotions: 5: 70K40 Forced motionsmotions: 6: 70K43 Quasi-periodic motions and invariant torimotions: 7: 70K70 Systems with slow and fast motionsmotions: 8: 83C40 Gravitational energy and conservation laws; groups of motions
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motivated: 1: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations[See also]20C35, 22E70motivated: 2: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
motives: 1: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05motives: 2: 14C15 (Equivariant) Chow groups and rings; motivesmotivic: 1: 14E18 Arcs and motivic integrationmotivic: 2: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E15motivic: 3: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E15motivic: 4: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F42
movement: 1: 92C17 Cell movement (chemotaxis, etc.)moving: 1: 35R37 Moving boundary problems
multi-dimensional: 1: 37B50 Multi-dimensional shifts of finite type, tiling dynamicsmulti-index: 1: 90C08 Special problems of linear programming (transportation, multi-index, etc.)
multi-objective: 1: 90C29 Multi-objective and goal programmingmultibody: 1: 70Exx Dynamics of a rigid body and of multibody systemsmultibody: 2: 70E55 Dynamics of multibody systems
multichannel: 1: 81U35 Inelastic and multichannel scatteringmulticoherence: 1: 54F55 Unicoherence, multicoherence
multidimensional: 1: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
multidimensional: 2: 91C15 One- and multidimensional scalingmultifrequency: 1: 34C46 Multifrequency systemsmultifunctions: 1: 32A12 Multifunctions
multigrid: 1: 65M55 Multigrid methods; domain decompositionmultigrid: 2: 65N55 Multigrid methods; domain decomposition
multilinear: 1: 15-XX Linear and multilinear algebra; matrix theorymultilinear: 2: 15A69 Multilinear algebra, tensor productsmultilinear: 3: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H60multilinear: 4: 47A07 Forms (bilinear, sesquilinear, multilinear)multilinear: 5: 47H60 Multilinear and polynomial operators [See also]46G25multilinear: 6: 47L22 Ideals of polynomials and of multilinear mappingsmultiphase: 1: 76Txx Two-phase and multiphase flows
multiple: 1: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weylgroup multiple Dirichlet series
multiple: 2: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesmultiple: 3: 33D65 Bibasic functions and multiple basesmultiple: 4: 34E13 Multiple scale methodsmultiple: 5: 40Bxx Multiple sequences and seriesmultiple: 6: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)multiple: 7: 44A30 Multiple transformsmultiple: 8: 62J15 Paired and multiple comparisonsmultiple: 9: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B06multiplication: 1: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K22multiplication: 2: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15multiplication: 3: 14K22 Complex multiplication [See also]11G15multiplicative: 1: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsmultiplicative: 2: 11D57 Multiplicative and norm form equationsmultiplicative: 3: 11Nxx Multiplicative number theorymultiplicative: 4: 11N25 Distribution of integers with specified multiplicative constraintsmultiplicative: 5: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuesmultiplicative: 6: 11N60 Distribution functions associated with additive and positive multiplicative functionsmultiplicative: 7: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxx
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multiplicative: 8: 13A15 Ideals; multiplicative ideal theorymultiplicative: 9: 16U20 Ore rings, multiplicative sets, Ore localizationmultiplicative: 10: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D23multiplicative: 11: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y60multiplicative: 12: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxxmultiplicative: 13: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typemultiplicative: 14: 60J57 Multiplicative functionalsmultiplicities: 1: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15
multiplicity: 1: 13H15 Multiplicity theory and related topics [See also]14C17multiplicity: 2: 74G35 Multiplicity of solutions
multiplier: 1: 14F18 Multiplier idealsmultipliers: 1: 19C09 Central extensions and Schur multipliersmultipliers: 2: 20C25 Projective representations and multipliersmultipliers: 3: 42A45 Multipliersmultipliers: 4: 42B15 Multipliersmultipliers: 5: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
multiply: 1: 20B20 Multiply transitive finite groupsmultiply: 2: 20B22 Multiply transitive infinite groups
multipoint: 1: 34B10 Nonlocal and multipoint boundary value problemsmultipole: 1: 78M16 Multipole methods
multisectoral: 1: 91B66 Multisectoral modelsmultistage: 1: 91A20 Multistage and repeated gamesmultistep: 1: 65L06 Multistep, Runge-Kutta and extrapolation methods
multivalent: 1: 30C45 Special classes of univalent and multivalent functions (starlike, convex, boundedrotation, etc.)
multivalent: 2: 30C50 Coefficient problems for univalent and multivalent functionsmultivalent: 3: 30C55 General theory of univalent and multivalent functionsmultivalued: 1: 35R70 Partial differential equations with multivalued right-hand sidesmultivalued: 2: 47A06 Linear relations (multivalued linear operators)
multivariable: 1: 93C35 Multivariable systemsmultivariate: 1: 62Hxx Multivariate analysis [See also]60Exxmultivariate: 2: 62H86 Multivariate analysis and fuzziness
multizeta: 1: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesmusic: 1: 00A65 Mathematics and musicmusic: 2: 97M80 Arts, music, language, architecturemust: 1: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)mv-algebras: 1: 06D35 MV-algebras
norlund: 1: 40G05 Cesaro, Euler, Norlund and Hausdorff methodsnanoparticles: 1: 82D80 Nanostructures and nanoparticles
nanostructures: 1: 82D80 Nanostructures and nanoparticlesnash: 1: 14P20 Nash functions and manifolds [See also]32C07, 58A07nash: 2: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P20nash: 3: 58A07 Real-analytic and Nash manifolds [See also]14P20, 32C07
natural: 1: 03B65 Logic of natural languages [See also]68T50, 91F20natural: 2: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A30natural: 3: 18A23 Natural morphisms, dinatural morphismsnatural: 4: 35Q92 PDEs in connection with biology and other natural sciencesnatural: 5: 58A32 Natural bundlesnatural: 6: 68T50 Natural language processing [See also]03B65natural: 7: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)natural: 8: 92-XX Biology and other natural sciencesnatural: 9: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)natural: 10: 92F05 Other natural sciences (should also be assigned at least one other classification number
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in section 92)natural: 11: 97F30 Natural numbers
navier-stokes: 1: 35Q30 Navier-Stokes equations [See also]76D05, 76D07, 76N10navier-stokes: 2: 76D05 Navier-Stokes equations [See also]35Q30navier-stokes: 3: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M35
navigation: 1: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)[See also]68M11
near: 1: 74G20 Local existence of solutions (near a given solution)near-algebras: 1: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y30
near-fields: 1: 12K05 Near-fields [See also]16Y30near-fields: 2: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y30near-rings: 1: 16Y30 Near-rings [See also]12K05
nearly: 1: 70H08 Nearly integrable Hamiltonian systems, KAM theorynearness: 1: 54E17 Nearness spaces
necessary: 1: 49M05 Methods based on necessary conditionsnegative: 1: 19D35 Negative K-theory, NK and Nilnegative: 2: 32Q05 Negative curvature manifolds
neighborhood: 1: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract(ANR), absolute retract spaces (general properties) [See also]55M15
neighborhood: 2: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract(ANR), absolute retract spaces (general properties) [See also]55M15
neighborhood: 3: 55M15 Absolute neighborhood retracts [See also]54C55neighborhoods: 1: 14B20 Formal neighborhoodsneighborhoods: 2: 57N40 Neighborhoods of submanifoldsneighborhoods: 3: 57Q40 Regular neighborhoods
nemytskiı: 1: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)[See also]45Gxx, 45P05
neolithic: 1: 01A10 Paleolithic, Neolithicnest: 1: 47L35 Nest algebras, CSL algebras
nests: 1: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.nets: 1: 14C21 Pencils, nets, webs [See also]53A60nets: 2: 51E14 Finite partial geometries (general), nets, partial spreadsnets: 3: 62M45 Neural nets and related approachesnets: 4: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)nets: 5: 82C32 Neural nets [See also]68T05, 91E40, 92B20
network: 1: 68M10 Network design and communication [See also]68R10, 90B18network: 2: 68M12 Network protocolsnetwork: 3: 90B10 Network models, deterministicnetwork: 4: 90B15 Network models, stochastic
networks: 1: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D30networks: 2: 34B45 Boundary value problems on graphs and networksnetworks: 3: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)networks: 4: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxnetworks: 5: 81P45 Quantum information, communication, networks [See also]94A15, 94A17networks: 6: 90B18 Communication networks [See also]68M10, 94A05networks: 7: 90C35 Programming involving graphs or networks [See also]90C27networks: 8: 91D30 Social networksnetworks: 9: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxnetworks: 10: 92C42 Systems biology, networksnetworks: 11: 94Cxx Circuits, networksneumann: 1: 16E50 von Neumann regular rings and generalizationsneumann: 2: 46L10 General theory of von Neumann algebrasneumann: 3: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20neumann: 4: 47C15 Operators in C∗- or von Neumann algebras
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neural: 1: 62M45 Neural nets and related approachesneural: 2: 78M32 Neural and heuristic methodsneural: 3: 82C32 Neural nets [See also]68T05, 91E40, 92B20neural: 4: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxneural: 5: 92C20 Neural biology
neutral: 1: 34K40 Neutral equationsneutron: 1: 82D75 Nuclear reactor theory; neutron transport
nevanlinna: 1: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)nevanlinna: 2: 30D35 Distribution of values, Nevanlinna theorynevanlinna: 3: 30H15 Nevanlinna class and Smirnov classnevanlinna: 4: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,see 32H25, 32H30nevanlinna: 5: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J15
newman-penrose: 1: 83C60 Spinor and twistor methods; Newman-Penrose formalismnews: 1: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
newton: 1: 14M25 Toric varieties, Newton polyhedra [See also]52B20newton: 2: 58C15 Implicit function theorems; global Newton methods
newton-type: 1: 49M15 Newton-type methodsnikol′: 1: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)
nil: 1: 16N40 Nil and nilpotent radicals, sets, ideals, ringsnil: 2: 19D35 Negative K-theory, NK and Nil
nilpotent: 1: 16N40 Nil and nilpotent radicals, sets, ideals, ringsnilpotent: 2: 17B08 Coadjoint orbits; nilpotent varietiesnilpotent: 3: 17B30 Solvable, nilpotent (super)algebrasnilpotent: 4: 20D15 Nilpotent groups, p-groupsnilpotent: 5: 20F18 Nilpotent groups [See also]20D15nilpotent: 6: 20F19 Generalizations of solvable and nilpotent groupsnilpotent: 7: 22E25 Nilpotent and solvable Lie groupsnilpotent: 8: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)nk: 1: 19D35 Negative K-theory, NK and Nil
nls-like: 1: 35Q55 NLS-like equations (nonlinear Schrodinger) [See also]37K10nodes: 1: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.noether: 1: 06F10 Noether lattices
noetherian: 1: 13E05 Noetherian rings and modulesnoetherian: 2: 16P40 Noetherian rings and modulesnoetherian: 3: 16P50 Localization and Noetherian rings [See also]16U20
noise: 1: 60H40 White noise theorynon-archimedean: 1: 11J61 Approximation in non-Archimedean valuationsnon-archimedean: 2: 11S82 Non-Archimedean dynamical systems [See mainly]37Pxxnon-archimedean: 3: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S10non-archimedean: 4: 26E30 Non-Archimedean analysis [See also]12J25non-archimedean: 5: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05non-archimedean: 6: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)non-archimedean: 7: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)non-archimedean: 8: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A45non-archimedean: 9: 37P20 Non-Archimedean local ground fieldsnon-archimedean: 10: 37P40 Non-Archimedean Fatou and Julia setsnon-archimedean: 11: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05non-archimedean: 12: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theorynon-commutative: 1: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22
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non-desarguesian: 1: 51A35 Non-Desarguesian affine and projective planesnon-euclidean: 1: 53A35 Non-Euclidean differential geometrynon-european: 1: 01A13 Other indigenous cultures (non-European)non-existence: 1: 35A01 Existence problems: global existence, local existence, non-existence
non-markovian: 1: 62M07 Non-Markovian processes: hypothesis testingnon-markovian: 2: 62M09 Non-Markovian processes: estimationnon-newtonian: 1: 76A05 Non-Newtonian fluidsnon-selfadjoint: 1: 81Q12 Non-selfadjoint operator theory in quantum theory
non-type: 1: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-typeI representations, etc.)
non-uniqueness: 1: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenessnonabelian: 1: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55nonabelian: 2: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50nonabelian: 3: 18G50 Nonabelian homological algebranonabelian: 4: 20E05 Free nonabelian groupsnonabelian: 5: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
nonalgebraically: 1: 14G27 Other nonalgebraically closed ground fieldsnonanalytic: 1: 11S85 Other nonanalytic theory
nonassociative: 1: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,17C50, 46Kxx
nonassociative: 2: 16Yxx Generalizations For nonassociative rings, see 17-XXnonassociative: 3: 17-XX Nonassociative rings and algebrasnonassociative: 4: 17Axx General nonassociative ringsnonassociative: 5: 17Dxx Other nonassociative rings and algebrasnonassociative: 6: 46H70 Nonassociative topological algebras [See also]46K70, 46L70nonassociative: 7: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L70nonassociative: 8: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K70nonassociative: 9: 47L70 Nonassociative nonselfadjoint operator algebrasnonasymptotic: 1: 62E17 Approximations to distributions (nonasymptotic)
nonautonomous: 1: 37B55 Nonautonomous dynamical systemsnonautonomous: 2: 37C60 Nonautonomous smooth dynamical systems [See also]37B55
nonclassical: 1: 03B60 Other nonclassical logicnonclassical: 2: 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)nonclassical: 3: 03E70 Nonclassical and second-order set theoriesnonclassical: 4: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxxnonclassical: 5: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxx
noncommutative: 1: 11M55 Relations with noncommutative geometrynoncommutative: 2: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxnoncommutative: 3: 14A22 Noncommutative algebraic geometry [See also]16S38noncommutative: 4: 16L30 Noncommutative local and semilocal rings, perfect ringsnoncommutative: 5: 16U30 Divisibility, noncommutative UFDsnoncommutative: 6: 17A15 Noncommutative Jordan algebrasnoncommutative: 7: 46L51 Noncommutative measure and integrationnoncommutative: 8: 46L52 Noncommutative function spacesnoncommutative: 9: 46L53 Noncommutative probability and statisticsnoncommutative: 10: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H20noncommutative: 11: 46L85 Noncommutative topology [See also]58B32, 58B34, 58J22noncommutative: 12: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J22noncommutative: 13: 58B34 Noncommutative geometry (a la Connes)noncommutative: 14: 58J42 Noncommutative global analysis, noncommutative residuesnoncommutative: 15: 58J42 Noncommutative global analysis, noncommutative residuesnoncommutative: 16: 81R60 Noncommutative geometrynoncommutative: 17: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B34noncommutative: 18: 83C65 Methods of noncommutative geometry [See also]58B34
noncompact: 1: 22Fxx Noncompact transformation groupsnoncompact: 2: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
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noncompact: 3: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)noncompact: 4: 57S20 Noncompact Lie groups of transformations
noncompactness: 1: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.nonconvex: 1: 11H16 Nonconvex bodiesnonconvex: 2: 90C26 Nonconvex programming, global optimization
noncooperative: 1: 91A10 Noncooperative gamesnondeterministic: 1: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85nondifferentiability: 1: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativesnondifferentiability: 2: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativesnondifferentiable: 1: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativesnondifferentiable: 2: 51L05 Geometry of orders of nondifferentiable curves
nonequilibrium: 1: 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)nonequilibrium: 2: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)nonequilibrium: 3: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)nonequilibrium: 4: 82C26 Dynamic and nonequilibrium phase transitions (general)nonequivariant: 1: 55P92 Relations between equivariant and nonequivariant homotopy theory
nonexpansive: 1: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.nonholomorphic: 1: 11F37 Forms of half-integer weight; nonholomorphic modular forms
nonholonomic: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems[See also]53Dxx, 70Fxx, 70Hxx
nonholonomic: 2: 37J60 Nonholonomic dynamical systems [See also]70F25nonholonomic: 3: 70F25 Nonholonomic systemsnonholonomic: 4: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxnonintegrability: 1: 37J30 Obstructions to integrability (nonintegrability criteria)
nonintegrable: 1: 70H07 Nonintegrable systemsnonlinear: 1: 31C45 Other generalizations (nonlinear potential theory, etc.)nonlinear: 2: 34A34 Nonlinear equations and systems, generalnonlinear: 3: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameternonlinear: 4: 34B15 Nonlinear boundary value problemsnonlinear: 5: 34B16 Singular nonlinear boundary value problemsnonlinear: 6: 34B18 Positive solutions of nonlinear boundary value problemsnonlinear: 7: 34C15 Nonlinear oscillations, coupled oscillatorsnonlinear: 8: 34G20 Nonlinear equations [See also]47Hxx, 47Jxxnonlinear: 9: 34L30 Nonlinear ordinary differential operatorsnonlinear: 10: 34M40 Stokes phenomena and connection problems (linear and nonlinear)nonlinear: 11: 35F20 Nonlinear first-order equationsnonlinear: 12: 35F25 Initial value problems for nonlinear first-order equationsnonlinear: 13: 35F30 Boundary value problems for nonlinear first-order equationsnonlinear: 14: 35F31 Initial-boundary value problems for nonlinear first-order equationsnonlinear: 15: 35F50 Nonlinear first-order systemsnonlinear: 16: 35F55 Initial value problems for nonlinear first-order systemsnonlinear: 17: 35F60 Boundary value problems for nonlinear first-order systemsnonlinear: 18: 35F61 Initial-boundary value problems for nonlinear first-order systemsnonlinear: 19: 35G20 Nonlinear higher-order equationsnonlinear: 20: 35G25 Initial value problems for nonlinear higher-order equationsnonlinear: 21: 35G30 Boundary value problems for nonlinear higher-order equationsnonlinear: 22: 35G31 Initial-boundary value problems for nonlinear higher-order equationsnonlinear: 23: 35G50 Nonlinear higher-order systemsnonlinear: 24: 35G55 Initial value problems for nonlinear higher-order systemsnonlinear: 25: 35G60 Boundary value problems for nonlinear higher-order systemsnonlinear: 26: 35G61 Initial-boundary value problems for nonlinear higher-order systemsnonlinear: 27: 35J60 Nonlinear elliptic equations
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nonlinear: 28: 35J65 Nonlinear boundary value problems for linear elliptic equationsnonlinear: 29: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsnonlinear: 30: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsnonlinear: 31: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J40nonlinear: 32: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J40nonlinear: 33: 35K55 Nonlinear parabolic equationsnonlinear: 34: 35K60 Nonlinear initial value problems for linear parabolic equationsnonlinear: 35: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsnonlinear: 36: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsnonlinear: 37: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40nonlinear: 38: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40nonlinear: 39: 35L60 Nonlinear first-order hyperbolic equationsnonlinear: 40: 35L70 Nonlinear second-order hyperbolic equationsnonlinear: 41: 35L75 Nonlinear higher-order hyperbolic equationsnonlinear: 42: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J40nonlinear: 43: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J40nonlinear: 44: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40nonlinear: 45: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40nonlinear: 46: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theorynonlinear: 47: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theorynonlinear: 48: 35Q55 NLS-like equations (nonlinear Schrodinger) [See also]37K10nonlinear: 49: 37L05 General theory, nonlinear semigroups, evolution equationsnonlinear: 50: 37L65 Special approximation methods (nonlinear Galerkin, etc.)nonlinear: 51: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropynonlinear: 52: 45Gxx Nonlinear integral equations [See also]47H30, 47Jxxnonlinear: 53: 45G05 Singular nonlinear integral equationsnonlinear: 54: 45G10 Other nonlinear integral equationsnonlinear: 55: 45G15 Systems of nonlinear integral equationsnonlinear: 56: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsnonlinear: 57: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsnonlinear: 58: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)nonlinear: 59: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxxnonlinear: 60: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxnonlinear: 61: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20nonlinear: 62: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxnonlinear: 63: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q15nonlinear: 64: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D07nonlinear: 65: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A35nonlinear: 66: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P05nonlinear: 67: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXnonlinear: 68: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J25nonlinear: 69: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R30nonlinear: 70: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05nonlinear: 71: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05
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nonlinear: 72: 47J20 Variational and other types of inequalities involving nonlinear operators (general)[See also]49J40nonlinear: 73: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D25nonlinear: 74: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxxnonlinear: 75: 51Bxx Nonlinear incidence geometrynonlinear: 76: 51E25 Other finite nonlinear geometriesnonlinear: 77: 51H15 Topological nonlinear incidence structuresnonlinear: 78: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxxnonlinear: 79: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxnonlinear: 80: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H20nonlinear: 81: 62J02 General nonlinear regressionnonlinear: 82: 65Hxx Nonlinear algebraic or transcendental equationsnonlinear: 83: 65J15 Equations with nonlinear operators (do not use 65Hxx)nonlinear: 84: 65P40 Nonlinear stabilitiesnonlinear: 85: 70Kxx Nonlinear dynamics [See also]34Cxx, 37-XXnonlinear: 86: 70K30 Nonlinear resonancesnonlinear: 87: 70K75 Nonlinear modesnonlinear: 88: 74B20 Nonlinear elasticitynonlinear: 89: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)nonlinear: 90: 74D10 Nonlinear constitutive equationsnonlinear: 91: 74J30 Nonlinear wavesnonlinear: 92: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30nonlinear: 93: 76E30 Nonlinear effectsnonlinear: 94: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80nonlinear: 95: 90C30 Nonlinear programmingnonlinear: 96: 93C10 Nonlinear systemsnonlocal: 1: 34B10 Nonlocal and multipoint boundary value problemsnonlocal: 2: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K18
nonmathematicians: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)nonmeasurable: 1: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of
convergencenonnumerical: 1: 68W05 Nonnumerical algorithms
nonparallel: 1: 76E09 Stability and instability of nonparallel flowsnonparametric: 1: 62Gxx Nonparametric inferencenonparametric: 2: 62G08 Nonparametric regressionnonparametric: 3: 62G86 Nonparametric inference and fuzziness
nonperturbative: 1: 81T16 Nonperturbative methods of renormalizationnonpositively: 1: 20F67 Hyperbolic groups and nonpositively curved groupsnonquantum: 1: 70S20 More general nonquantum field theories
nonquasidiagonal: 1: 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operatorsnonquasitriangular: 1: 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
nonreal: 1: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypothesesnonselfadjoint: 1: 46K50 Nonselfadjoint (sub)algebras in algebras with involutionnonselfadjoint: 2: 47A45 Canonical models for contractions and nonselfadjoint operatorsnonselfadjoint: 3: 47L55 Representations of (nonselfadjoint) operator algebrasnonselfadjoint: 4: 47L70 Nonassociative nonselfadjoint operator algebrasnonselfadjoint: 5: 47L75 Other nonselfadjoint operator algebrasnonseparable: 1: 46B26 Nonseparable Banach spaces
nonsimple: 1: 74A30 Nonsimple materialsnonsingular: 1: 37A40 Nonsingular (and infinite-measure preserving) transformationsnonsingular: 2: 45F05 Systems of nonsingular linear integral equationsnonsmooth: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see49J52, 58Cxx, 90Cxxnonsmooth: 2: 49J52 Nonsmooth analysis [See also]46G05, 58C50, 90C56
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nonstandard: 1: 03Hxx Nonstandard models [See also]03C62nonstandard: 2: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J05nonstandard: 3: 03H10 Other applications of nonstandard models (economics, physics, etc.)nonstandard: 4: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L05nonstandard: 5: 11U10 Nonstandard arithmetic [See also]03H15nonstandard: 6: 12L15 Nonstandard arithmetic [See also]03H15nonstandard: 7: 26E35 Nonstandard analysis [See also]03H05, 28E05, 54J05nonstandard: 8: 28E05 Nonstandard measure theory [See also]03H05, 26E35nonstandard: 9: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05nonstandard: 10: 34E18 Methods of nonstandard analysisnonstandard: 11: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)nonstandard: 12: 46S20 Nonstandard functional analysis [See also]03H05nonstandard: 13: 47S20 Nonstandard operator theory [See also]03H05nonstandard: 14: 54Jxx Nonstandard topology [See also]03H05nonstandard: 15: 54J05 Nonstandard topology [See also]03H05
nontransversal: 1: 37G25 Bifurcations connected with nontransversal intersectionnontrigonometric: 1: 42Cxx Nontrigonometric harmonic analysis
nonuniformly: 1: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)nonwandering: 1: 37G30 Infinite nonwandering sets arising in bifurcations
norm: 1: 11D57 Multiplicative and norm form equationsnorm: 2: 47A30 Norms (inequalities, more than one norm, etc.)
normal: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
normal: 2: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)normal: 3: 30D45 Bloch functions, normal functions, normal familiesnormal: 4: 30D45 Bloch functions, normal functions, normal familiesnormal: 5: 32A18 Bloch functions, normal functionsnormal: 6: 32A19 Normal families of functions, mappingsnormal: 7: 32C20 Normal analytic spacesnormal: 8: 34C20 Transformation and reduction of equations and systems, normal formsnormal: 9: 34K17 Transformation and reduction of equations and systems, normal formsnormal: 10: 34M35 Singularities, monodromy, local behavior of solutions, normal formsnormal: 11: 37G05 Normal formsnormal: 12: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionnormal: 13: 37L10 Normal forms, center manifold theory, bifurcation theorynormal: 14: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)normal: 15: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C35normal: 16: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)normal: 17: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)normal: 18: 58K50 Normal formsnormal: 19: 70K45 Normal forms
normal-form: 1: 03F05 Cut-elimination and normal-form theoremsnormalizer: 1: 16U70 Center, normalizer (invariant elements)
normalizing: 1: 16S20 Centralizing and normalizing extensionsnormed: 1: 12J05 Normed fieldsnormed: 2: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)normed: 3: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxnormed: 4: 46B20 Geometry and structure of normed linear spacesnormed: 5: 46B40 Ordered normed spaces [See also]46A40, 46B42normed: 6: 46B50 Compactness in Banach (or normed) spaces
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normed: 7: 46B70 Interpolation between normed linear spaces [See also]46M35normed: 8: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20normed: 9: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)normed: 10: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07
norms: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; fortemporal logic, see 03B44; for provability logic, see also 03F45
norms: 2: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory[See also]65F35, 65J05
norms: 3: 47A30 Norms (inequalities, more than one norm, etc.)norms: 4: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxnorms: 5: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A60
not: 1: 17A45 Quadratic algebras (but not quadratic Jordan algebras)not: 2: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)not: 3: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)not: 4: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)not: 5: 65J10 Equations with linear operators (do not use 65Fxx)not: 6: 65J15 Equations with nonlinear operators (do not use 65Hxx)
notations: 1: 03F15 Recursive ordinals and ordinal notationsnotions: 1: 03D10 Turing machines and related notions [See also]68Q05notions: 2: 03E47 Other notions of set-theoretic definabilitynotions: 3: 32F17 Other notions of convexitynotions: 4: 32Q26 Notions of stabilitynotions: 5: 37B20 Notions of recurrencenuclear: 1: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)nuclear: 2: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20nuclear: 3: 81V35 Nuclear physicsnuclear: 4: 82D75 Nuclear reactor theory; neutron transport
null: 1: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsnumber: 1: 11-XX Number theorynumber: 2: 11Axx Elementary number theory For analogues in number fields, see 11R04number: 3: 11Axx Elementary number theory For analogues in number fields, see 11R04number: 4: 11B75 Other combinatorial number theorynumber: 5: 11Jxx Diophantine approximation, transcendental number theory [See also]11K60number: 6: 11J04 Homogeneous approximation to one numbernumber: 7: 11Nxx Multiplicative number theorynumber: 8: 11Pxx Additive number theory; partitionsnumber: 9: 11P70 Inverse problems of additive number theory, including sumsetsnumber: 10: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15number: 11: 11R21 Other number fieldsnumber: 12: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F27number: 13: 11Sxx Algebraic number theory: local and p-adic fieldsnumber: 14: 11Yxx Computational number theory [See also]11-04number: 15: 11Y40 Algebraic number theory computationsnumber: 16: 11Zxx Miscellaneous applications of number theorynumber: 17: 11Z05 Miscellaneous applications of number theorynumber: 18: 13E15 Rings and modules of finite generation or presentation; number of generatorsnumber: 19: 19Fxx K-theory in number theory [See also]11R70, 11S70number: 20: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35number: 21: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
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tion number from Section 32 describing the type of problem)number: 22: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)number: 23: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)number: 24: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxnumber: 25: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)number: 26: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)number: 27: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)number: 28: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)number: 29: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)number: 30: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)number: 31: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)number: 32: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)number: 33: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)number: 34: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)number: 35: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)number: 36: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxxnumber: 37: 55M25 Degree, winding numbernumber: 38: 65C10 Random number generationnumber: 39: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)number: 40: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)number: 41: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)number: 42: 97Fxx Arithmetic, number theorynumber: 43: 97F60 Number theory
number–03: 1: 01-XX History and biography [See also]the classification number–03 in the other sectionsnumber-theoretic: 1: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B13number-theoretic: 2: 11Txx Finite fields and commutative rings (number-theoretic aspects)number-theoretic: 3: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxnumber-theoretic: 4: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
numberings: 1: 03F40 Godel numberings and issues of incompletenessnumbers: 1: 03E10 Ordinal and cardinal numbersnumbers: 2: 11A25 Arithmetic functions; related numbers; inversion formulasnumbers: 3: 11B39 Fibonacci and Lucas numbers and polynomials and generalizationsnumbers: 4: 11B68 Bernoulli and Euler numbers and polynomialsnumbers: 5: 11B73 Bell and Stirling numbersnumbers: 6: 11D68 Rational numbers as sums of fractionsnumbers: 7: 11E41 Class numbers of quadratic and Hermitian formsnumbers: 8: 11Hxx Geometry of numbers For applications in coding theory, see 94B75numbers: 9: 11J17 Approximation by numbers from a fixed fieldnumbers: 10: 11J68 Approximation to algebraic numbers
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numbers: 11: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
numbers: 12: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
numbers: 13: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
numbers: 14: 11K45 Pseudo-random numbers; Monte Carlo methodsnumbers: 15: 11R04 Algebraic numbers; rings of algebraic integersnumbers: 16: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measurenumbers: 17: 11R29 Class numbers, class groups, discriminantsnumbers: 18: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10numbers: 19: 32U25 Lelong numbersnumbers: 20: 37E45 Rotation numbers and vectorsnumbers: 21: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsnumbers: 22: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsnumbers: 23: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsnumbers: 24: 57R20 Characteristic classes and numbersnumbers: 25: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71numbers: 26: 97F20 Pre-numerical stage, concept of numbersnumbers: 27: 97F30 Natural numbersnumbers: 28: 97F40 Integers, rational numbersnumbers: 29: 97F50 Real numbers, complex numbersnumbers: 30: 97F50 Real numbers, complex numbers
numerations: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-tic and similar approaches see 03F55numerical: 1: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05numerical: 2: 30C30 Numerical methods in conformal mapping theory [See also]65E05numerical: 3: 31C20 Discrete potential theory and numerical methodsnumerical: 4: 33F05 Numerical approximation and evaluation [See also]65D20numerical: 5: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxnumerical: 6: 34K28 Numerical approximation of solutionsnumerical: 7: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumnumerical: 8: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxnumerical: 9: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxnumerical: 10: 37N30 Dynamical systems in numerical analysisnumerical: 11: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxxnumerical: 12: 41Axx Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxxnumerical: 13: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10numerical: 14: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10numerical: 15: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxnumerical: 16: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxnumerical: 17: 46N40 Applications in numerical analysis [See also]65Jxxnumerical: 18: 47A12 Numerical range, numerical radius
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numerical: 19: 47A12 Numerical range, numerical radiusnumerical: 20: 47N40 Applications in numerical analysis [See also]65Jxxnumerical: 21: 49Mxx Numerical methods [See also]90Cxx, 65Kxxnumerical: 22: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxnumerical: 23: 65-XX Numerical analysisnumerical: 24: 65C20 Models, numerical methods [See also]68U20numerical: 25: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxnumerical: 26: 65D25 Numerical differentiationnumerical: 27: 65D30 Numerical integrationnumerical: 28: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30numerical: 29: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30numerical: 30: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30numerical: 31: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30numerical: 32: 65Fxx Numerical linear algebranumerical: 33: 65Jxx Numerical analysis in abstract spacesnumerical: 34: 65K15 Numerical methods for variational inequalities and related problemsnumerical: 35: 65L07 Numerical investigation of stability of solutionsnumerical: 36: 65L20 Stability and convergence of numerical methodsnumerical: 37: 65M12 Stability and convergence of numerical methodsnumerical: 38: 65N12 Stability and convergence of numerical methodsnumerical: 39: 65Pxx Numerical problems in dynamical systems [See also]37Mxxnumerical: 40: 65P20 Numerical chaosnumerical: 41: 65Txx Numerical methods in Fourier analysisnumerical: 42: 65Yxx Computer aspects of numerical algorithmsnumerical: 43: 65Y20 Complexity and performance of numerical algorithms [See also]68Q25numerical: 44: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxnumerical: 45: 74G15 Numerical approximation of solutionsnumerical: 46: 74H15 Numerical approximation of solutionsnumerical: 47: 74Sxx Numerical methods [See also]65-XX, 74G15, 74H15numerical: 48: 74S30 Other numerical methodsnumerical: 49: 76F65 Direct numerical and large eddy simulation of turbulencenumerical: 50: 76M25 Other numerical methodsnumerical: 51: 78M25 Other numerical methodsnumerical: 52: 80M25 Other numerical methodsnumerical: 53: 81T80 Simulation and numerical modelingnumerical: 54: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80numerical: 55: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)numerical: 56: 91G60 Numerical methods (including Monte Carlo methods)numerical: 57: 97Nxx Numerical mathematicsnumerical: 58: 97N30 Numerical algebranumerical: 59: 97N40 Numerical analysis
o-minimality: 1: 03C64 Model theory of ordered structures; o-minimalityobituaries: 1: 01A70 Biographies, obituaries, personalia, bibliographies
object-oriented: 1: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,etc.)objectives: 1: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B06objectives: 2: 97D30 Objectives and goalsobjectives: 3: 97Q50 Objectives
objects: 1: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
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objects: 2: 18D35 Structured objects in a category (group objects, etc.)objects: 3: 18D35 Structured objects in a category (group objects, etc.)objects: 4: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10objects: 5: 32D15 Continuation of analytic objectsobjects: 6: 32V25 Extension of functions and other analytic objects from CR manifoldsobjects: 7: 43A40 Character groups and dual objectsobjects: 8: 46M10 Projective and injective objects [See also]46A22objects: 9: 53A55 Differential invariants (local theory), geometric objectsobjects: 10: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30
observability: 1: 93Bxx Controllability, observability, and system structureobservability: 2: 93B07 Observabilityobservational: 1: 83Bxx Observational and experimental questionsobservational: 2: 83B05 Observational and experimental questions
obstruction: 1: 55S35 Obstruction theoryobstruction: 2: 57Q12 Wall finiteness obstruction for CW-complexes
obstructions: 1: 19Jxx Obstructions from topologyobstructions: 2: 19J05 Finiteness and other obstructions in K0
obstructions: 3: 19J25 Surgery obstructions [See also]57R67obstructions: 4: 19J35 Obstructions to group actionsobstructions: 5: 37J30 Obstructions to integrability (nonintegrability criteria)obstructions: 6: 55Sxx Operations and obstructionsobstructions: 7: 55S91 Equivariant operations and obstructions [See also]19L47obstructions: 8: 57R67 Surgery obstructions, Wall groups [See also]19J25
oceanography: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-XX, especially 76D05, 76F20, 86A05, 86A10
oceanography: 2: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U05of: 1: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesof: 2: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H60on: 1: 03C70 Logic on admissible setson: 2: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.on: 3: 05C57 Games on graphs [See also]91A43, 91A46on: 4: 05C81 Random walks on graphson: 5: 05E18 Group actions on combinatorial structureson: 6: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20on: 7: 11L07 Estimates on exponential sumson: 8: 11L40 Estimates on character sumson: 9: 11N37 Asymptotic results on arithmetic functionson: 10: 11N45 Asymptotic results on counting functions for algebraic and topological structureson: 11: 11N64 Other results on the distribution of values or the characterization of arithmetic functionson: 12: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24on: 13: 13D07 Homological functors on modules (Tor, Ext, etc.)on: 14: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05on: 15: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxon: 16: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17on: 17: 14R20 Group actions on affine varieties [See also]13A50, 14L30on: 18: 16E30 Homological functors on modules (Tor, Ext, etc.)on: 19: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)on: 20: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions
[See also]16U20, Krull dimensionon: 21: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceon: 22: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxon: 23: 16Uxx Conditions on elementson: 24: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70
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on: 25: 20E08 Groups acting on trees [See also]20F65on: 26: 20M30 Representation of semigroups; actions of semigroups on setson: 27: 22A10 Analysis on general topological groupson: 28: 22A20 Analysis on topological semigroupson: 29: 22D40 Ergodic theory on groups [See also]28Dxxon: 30: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXon: 31: 22E35 Analysis on p-adic Lie groupson: 32: 22E66 Analysis on and representations of infinite-dimensional Lie groupson: 33: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40on: 34: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxxon: 35: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05on: 36: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05on: 37: 28-XX Measure and integration For analysis on manifolds, see 58-XXon: 38: 28A60 Measures on Boolean rings, measure algebras [See also]54H10on: 39: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20on: 40: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05on: 41: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)on: 42: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXon: 43: 30F15 Harmonic functions on Riemann surfaceson: 44: 30F30 Differentials on Riemann surfaceson: 45: 30Jxx Function theory on the discon: 46: 30Lxx Analysis on metric spaceson: 47: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14on: 48: 31Exx Potential theory on metric spaceson: 49: 31E05 Potential theory on metric spaceson: 50: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27on: 51: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25on: 52: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10on: 53: 32S70 Other operations on singularitieson: 54: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundarieson: 55: 32V20 Analysis on CR manifoldson: 56: 32V35 Finite type conditions on CR manifoldson: 57: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameteron: 58: 34B40 Boundary value problems on infinite intervalson: 59: 34B45 Boundary value problems on graphs and networkson: 60: 34C40 Equations and systems on manifoldson: 61: 34M45 Differential equations on complex manifoldson: 62: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70on: 63: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70on: 64: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70on: 65: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70on: 66: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxon: 67: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15on: 68: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxxon: 69: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)on: 70: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.on: 71: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
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infinitely many variables) [See also]46Gxx, 58D25on: 72: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxon: 73: 37E35 Flows on surfaceson: 74: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricson: 75: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricson: 76: 37P50 Dynamical systems on Berkovich spaceson: 77: 37P55 Arithmetic dynamics on general algebraic varietieson: 78: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05on: 79: 40Dxx Direct theorems on summabilityon: 80: 42-XX Harmonic analysis on Euclidean spaceson: 81: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxon: 82: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxon: 83: 43A05 Measures on groups and semigroups, etc.on: 84: 43A07 Means on groups, semigroups, etc.; amenable groupson: 85: 43A10 Measure algebras on groups, semigroups, etc.on: 86: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.on: 87: 43A17 Analysis on ordered groups, Hp-theoryon: 88: 43A20 L1-algebras on groups, semigroups, etc.on: 89: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.on: 90: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupson: 91: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.on: 92: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.on: 93: 43A35 Positive definite functions on groups, semigroups, etc.on: 94: 43A45 Spectral synthesis on groups, semigroups, etc.on: 95: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05on: 96: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionson: 97: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05on: 98: 43A75 Analysis on specific compact groupson: 99: 43A77 Analysis on general compact groupson: 100: 43A80 Analysis on other specific Lie groups [See also]22Exxon: 101: 43A85 Analysis on homogeneous spaceson: 102: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxon: 103: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60on: 104: 46F25 Distributions on infinite-dimensional spaces [See also]58C35on: 105: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12on: 106: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J22on: 107: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50on: 108: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXon: 109: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxon: 110: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)on: 111: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)on: 112: 47B38 Operators on function spaces (general)on: 113: 47B48 Operators on Banach algebrason: 114: 47B49 Transformers, preservers (operators on spaces of operators)on: 115: 47B50 Operators on spaces with an indefinite metric [See also]46C50
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on: 116: 47B60 Operators on ordered spaceson: 117: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spaceson: 118: 47L10 Algebras of operators on Banach spaces and other topological linear spaceson: 119: 47L30 Abstract operator algebras on Hilbert spaceson: 120: 49M05 Methods based on necessary conditionson: 121: 51H20 Topological geometries on manifolds [See also]57-XXon: 122: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
[See also]32Q20on: 123: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)on: 124: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spaceson: 125: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)on: 126: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)on: 127: 54E40 Special maps on metric spaceson: 128: 57M50 Geometric structures on low-dimensional manifoldson: 129: 57N16 Geometric structures on manifolds [See also]57M50on: 130: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)on: 131: 57R19 Algebraic topology on manifoldson: 132: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B05on: 133: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXon: 134: 57S25 Groups acting on specific manifoldson: 135: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15on: 136: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D05on: 137: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxxon: 138: 58C30 Fixed point theorems on manifolds [See also]47H10on: 139: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxon: 140: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxxon: 141: 58C50 Analysis on supermanifolds or graded manifoldson: 142: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12on: 143: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldson: 144: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxxon: 145: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXon: 146: 58J32 Boundary value problems on manifoldson: 147: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxxon: 148: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60on: 149: 60Bxx Probability theory on algebraic and topological structureson: 150: 60B05 Probability measures on topological spaceson: 151: 60B11 Probability theory on linear topological spaces [See also]28C20on: 152: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationon: 153: 60J05 Discrete-time Markov processes on general state spaceson: 154: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)on: 155: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40on: 156: 60J25 Continuous-time Markov processes on general state spaceson: 157: 60J27 Continuous-time Markov processes on discrete state spaceson: 158: 60J28 Applications of continuous-time Markov processes on discrete state spaceson: 159: 62E86 Fuzziness in connection with the topics on distributions in this sectionon: 160: 68R15 Combinatorics on wordson: 161: 68W32 Algorithms on strings
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on: 162: 74B15 Equations linearized about a deformed state (small deformations superposed on large)on: 163: 74Q20 Bounds on effective propertieson: 164: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.on: 165: 81T20 Quantum field theory on curved space backgroundson: 166: 81T25 Quantum field theory on latticeson: 167: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphson: 168: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphson: 169: 94B65 Bounds on codes
one: 1: 11F12 Automorphic forms, one variableone: 2: 11F25 Hecke-Petersson operators, differential operators (one variable)one: 3: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsone: 4: 11J04 Homogeneous approximation to one numberone: 5: 11J71 Distribution modulo one [See also]11K06one: 6: 15A54 Matrices over function rings in one or more variablesone: 7: 26Axx Functions of one variableone: 8: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15one: 9: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35one: 10: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35one: 11: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)one: 12: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)one: 13: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)one: 14: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variableone: 15: 33D15 Basic hypergeometric functions in one variable, rϕs
one: 16: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
one: 17: 40B05 Multiple sequences and series (should also be assigned at least one other classificationnumber in this section)
one: 18: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
one: 19: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
one: 20: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)
one: 21: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
one: 22: 42Axx Harmonic analysis in one variableone: 23: 47A30 Norms (inequalities, more than one norm, etc.)one: 24: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)one: 25: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)one: 26: 49J05 Free problems in one independent variableone: 27: 49K05 Free problems in one independent variableone: 28: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)one: 29: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)one: 30: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)one: 31: 51P05 Geometry and physics (should also be assigned at least one other classification number
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from Sections 70–86)one: 32: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)one: 33: 58E10 Applications to the theory of geodesics (problems in one independent variable)one: 34: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)one: 35: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)one: 36: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)one-: 1: 91C15 One- and multidimensional scaling
one-dimensional: 1: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)one-parameter: 1: 28D10 One-parameter continuous families of measure-preserving transformationsone-parameter: 2: 37A10 One-parameter continuous families of measure-preserving transformationsone-parameter: 3: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K30
one-variable: 1: 26A06 One-variable calculusones: 1: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)online: 1: 68W27 Online algorithms
onsager-machlup: 1: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E20onsager-machlup: 2: 82C35 Irreversible thermodynamics, including Onsager-Machlup theory
open: 1: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-completeness)
open: 2: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)open: 3: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31
operads: 1: 18D50 Operads [See also]55P48operads: 2: 55P48 Loop space machines, operads [See also]18D50
operating: 1: 68N25 Operating systemsoperation: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05operation: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05operation: 3: 20N02 Sets with a single binary operation (groupoids)
operational: 1: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.[See also]44-XX
operational: 2: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
operational: 3: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
operational: 4: 44A40 Calculus of Mikusinski and other operational calculioperational: 5: 44A45 Classical operational calculusoperational: 6: 44A55 Discrete operational calculusoperational: 7: 81P16 Quantum state spaces, operational and probabilistic conceptsoperations: 1: 03B35 Mechanization of proofs and logical operations [See also]68T15operations: 2: 05C76 Graph operations (line graphs, products, etc.)operations: 3: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)[See also]03G25, 03F45operations: 4: 08A40 Operations, polynomials, primal algebrasoperations: 5: 19L20 J-homomorphism, Adams operations [See also]55Q50operations: 6: 32S70 Other operations on singularitiesoperations: 7: 46F10 Operations with distributionsoperations: 8: 55Q35 Operations in homotopy groupsoperations: 9: 55Sxx Operations and obstructionsoperations: 10: 55S05 Primary cohomology operationsoperations: 11: 55S12 Dyer-Lashof operations
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operations: 12: 55S20 Secondary and higher cohomology operationsoperations: 13: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxxoperations: 14: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxxoperations: 15: 55S91 Equivariant operations and obstructions [See also]19L47operations: 16: 90-XX Operations research, mathematical programmingoperations: 17: 90Bxx Operations research and management scienceoperations: 18: 97M40 Operations research, economicsoperative: 1: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxxoperator: 1: 17B69 Vertex operators; vertex operator algebras and related structuresoperator: 2: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M20operator: 3: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxoperator: 4: 35J10 Schrodinger operator [See also]35Pxxoperator: 5: 35J93 Quasilinear elliptic equations with mean curvature operatoroperator: 6: 35K93 Quasilinear parabolic equations with mean curvature operatoroperator: 7: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35operator: 8: 39B42 Matrix and operator equations [See also]47Jxxoperator: 9: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35operator: 10: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)
[See also]22D25, 47Lxxoperator: 11: 46L07 Operator spaces and completely bounded maps [See also]47L25operator: 12: 46L54 Free probability and free operator algebrasoperator: 13: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C10operator: 14: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K70operator: 15: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22operator: 16: 47-XX Operator theoryoperator: 17: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)operator: 18: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.operator: 19: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)operator: 20: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60operator: 21: 47A58 Operator approximation theoryoperator: 22: 47A62 Equations involving linear operators, with operator unknownsoperator: 23: 47A63 Operator inequalitiesoperator: 24: 47A64 Operator means, shorted operators, etc.operator: 25: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20operator: 26: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10operator: 27: 47L15 Operator algebras with symbol structureoperator: 28: 47L20 Operator ideals [See also]47B10operator: 29: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07operator: 30: 47L30 Abstract operator algebras on Hilbert spacesoperator: 31: 47L45 Dual algebras; weakly closed singly generated operator algebrasoperator: 32: 47L50 Dual spaces of operator algebrasoperator: 33: 47L55 Representations of (nonselfadjoint) operator algebrasoperator: 34: 47L70 Nonassociative nonselfadjoint operator algebrasoperator: 35: 47L75 Other nonselfadjoint operator algebrasoperator: 36: 47L90 Applications of operator algebras to physicsoperator: 37: 47Nxx Miscellaneous applications of operator theory [See also]46Nxxoperator: 38: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxxoperator: 39: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
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operator theoryoperator: 40: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theoryoperator: 41: 47S20 Nonstandard operator theory [See also]03H05operator: 42: 47S30 Constructive operator theory [See also]03F60operator: 43: 47S40 Fuzzy operator theory [See also]03E72operator: 44: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70operator: 45: 55U20 Universal coefficient theorems, Bockstein operatoroperator: 46: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysisoperator: 47: 81Q12 Non-selfadjoint operator theory in quantum theoryoperator: 48: 81R15 Operator algebra methods [See also]46Lxx, 81T05operator: 49: 81T05 Axiomatic quantum field theory; operator algebras
operator-differential: 1: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces forabstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx
operator-theoretic: 1: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N70operator-valued: 1: 46E40 Spaces of vector- and operator-valued functions
operators: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B48operators: 2: 06A15 Galois correspondences, closure operatorsoperators: 3: 11F25 Hecke-Petersson operators, differential operators (one variable)operators: 4: 11F25 Hecke-Petersson operators, differential operators (one variable)operators: 5: 11F60 Hecke-Petersson operators, differential operators (several variables)operators: 6: 11F60 Hecke-Petersson operators, differential operators (several variables)operators: 7: 13N10 Rings of differential operators and their modules [See also]16S32, 32C38operators: 8: 16S32 Rings of differential operators [See also]13N10, 32C38operators: 9: 17A36 Automorphisms, derivations, other operatorsoperators: 10: 17B40 Automorphisms, derivations, other operatorsoperators: 11: 17B69 Vertex operators; vertex operator algebras and related structuresoperators: 12: 26D10 Inequalities involving derivatives and differential and integral operatorsoperators: 13: 31A10 Integral representations, integral operators, integral equations methodsoperators: 14: 31B10 Integral representations, integral operators, integral equations methodsoperators: 15: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J15operators: 16: 32V05 CR structures, CR operators, and generalizationsoperators: 17: 32Wxx Differential operators in several variablesoperators: 18: 32W05 ∂ and ∂-Neumann operatorsoperators: 19: 32W10 ∂b and ∂b-Neumann operatorsoperators: 20: 32W20 Complex Monge-Ampere operatorsoperators: 21: 32W25 Pseudodifferential operators in several complex variablesoperators: 22: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxoperators: 23: 34K08 Spectral theory of functional-differential operatorsoperators: 24: 34Lxx Ordinary differential operators [See also]47E05operators: 25: 34L30 Nonlinear ordinary differential operatorsoperators: 26: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)operators: 27: 35A23 Inequalities involving derivatives and differential and integral operators, inequalities for
integralsoperators: 28: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40operators: 29: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40operators: 30: 35S05 Pseudodifferential operatorsoperators: 31: 35S10 Initial value problems for pseudodifferential operatorsoperators: 32: 35S11 Initial-boundary value problems for pseudodifferential operatorsoperators: 33: 35S15 Boundary value problems for pseudodifferential operatorsoperators: 34: 35S30 Fourier integral operatorsoperators: 35: 35S50 Paradifferential operatorsoperators: 36: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35
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operators: 37: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytictechniques in dynamical systemsoperators: 38: 39A70 Difference operators [See also]47B39operators: 39: 41A35 Approximation by operators (in particular, by integral operators)operators: 40: 41A35 Approximation by operators (in particular, by integral operators)operators: 41: 41A36 Approximation by positive operatorsoperators: 42: 43A32 Other transforms and operators of Fourier typeoperators: 43: 45Pxx Integral operators [See also]47B38, 47G10operators: 44: 45P05 Integral operators [See also]47B38, 47G10operators: 45: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
[See also]46M10operators: 46: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20operators: 47: 46A61 Graded Frechet spaces and tame operatorsoperators: 48: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L20operators: 49: 46H35 Topological algebras of operators [See mainly]47Lxxoperators: 50: 47Axx General theory of linear operatorsoperators: 51: 47A06 Linear relations (multivalued linear operators)operators: 52: 47A16 Cyclic vectors, hypercyclic and chaotic operatorsoperators: 53: 47A45 Canonical models for contractions and nonselfadjoint operatorsoperators: 54: 47A50 Equations and inequalities involving linear operators, with vector unknownsoperators: 55: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J20operators: 56: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)operators: 57: 47A62 Equations involving linear operators, with operator unknownsoperators: 58: 47A64 Operator means, shorted operators, etc.operators: 59: 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operatorsoperators: 60: 47A80 Tensor products of operators [See also]46M05operators: 61: 47Bxx Special classes of linear operatorsoperators: 62: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsoperators: 63: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsoperators: 64: 47B07 Operators defined by compactness propertiesoperators: 65: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20operators: 66: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)operators: 67: 47B20 Subnormal operators, hyponormal operators, etc.operators: 68: 47B20 Subnormal operators, hyponormal operators, etc.operators: 69: 47B25 Symmetric and selfadjoint operators (unbounded)operators: 70: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22operators: 71: 47B33 Composition operatorsoperators: 72: 47B34 Kernel operatorsoperators: 73: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15operators: 74: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15operators: 75: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15operators: 76: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15operators: 77: 47B36 Jacobi (tridiagonal) operators (matrices) and generalizationsoperators: 78: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)operators: 79: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)operators: 80: 47B38 Operators on function spaces (general)
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operators: 81: 47B39 Difference operators [See also]39A70operators: 82: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.operators: 83: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.operators: 84: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.operators: 85: 47B44 Accretive operators, dissipative operators, etc.operators: 86: 47B44 Accretive operators, dissipative operators, etc.operators: 87: 47B47 Commutators, derivations, elementary operators, etc.operators: 88: 47B48 Operators on Banach algebrasoperators: 89: 47B49 Transformers, preservers (operators on spaces of operators)operators: 90: 47B49 Transformers, preservers (operators on spaces of operators)operators: 91: 47B50 Operators on spaces with an indefinite metric [See also]46C50operators: 92: 47B60 Operators on ordered spacesoperators: 93: 47B65 Positive operators and order-bounded operatorsoperators: 94: 47B65 Positive operators and order-bounded operatorsoperators: 95: 47B80 Random operators [See also]47H40, 60H25operators: 96: 47Cxx Individual linear operators as elements of algebraic systemsoperators: 97: 47C05 Operators in algebrasoperators: 98: 47C10 Operators in ∗-algebrasoperators: 99: 47C15 Operators in C∗- or von Neumann algebrasoperators: 100: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationsoperators: 101: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20operators: 102: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20operators: 103: 47Exx Ordinary differential operators [See also]34Bxx, 34Lxxoperators: 104: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)operators: 105: 47Fxx Partial differential operators [See also]35Pxx, 58Jxxoperators: 106: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)operators: 107: 47Gxx Integral, integro-differential, and pseudodifferential operators [See also]58Jxxoperators: 108: 47G10 Integral operators [See also]45P05operators: 109: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxxoperators: 110: 47G30 Pseudodifferential operators [See also]35Sxx, 58Jxxoperators: 111: 47G40 Potential operators [See also]31-XXoperators: 112: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxoperators: 113: 47H04 Set-valued operators [See also]28B20, 54C60, 58C06operators: 114: 47H05 Monotone operators and generalizationsoperators: 115: 47H06 Accretive operators, dissipative operators, etc.operators: 116: 47H06 Accretive operators, dissipative operators, etc.operators: 117: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesoperators: 118: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q15operators: 119: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D07operators: 120: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P05operators: 121: 47H40 Random operators [See also]47B80, 60H25operators: 122: 47H60 Multilinear and polynomial operators [See also]46G25operators: 123: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXoperators: 124: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J25operators: 125: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J40operators: 126: 47J40 Equations with hysteresis operators [See also]34C55, 74N30operators: 127: 47Lxx Linear spaces and algebras of operators [See also]46Lxxoperators: 128: 47L05 Linear spaces of operators [See also]46A32 and 46B28
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operators: 129: 47L07 Convex sets and cones of operators [See also]46A55operators: 130: 47L10 Algebras of operators on Banach spaces and other topological linear spacesoperators: 131: 47L60 Algebras of unbounded operators; partial algebras of operatorsoperators: 132: 47L60 Algebras of unbounded operators; partial algebras of operatorsoperators: 133: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)operators: 134: 49Rxx Variational methods for eigenvalues of operators [See also]47A75operators: 135: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)operators: 136: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxxoperators: 137: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H20operators: 138: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxxoperators: 139: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxxoperators: 140: 60H25 Random operators and equations [See also]47B80operators: 141: 65J10 Equations with linear operators (do not use 65Fxx)operators: 142: 65J15 Equations with nonlinear operators (do not use 65Hxx)operators: 143: 81Q15 Perturbation theories for operators and differential equationsoperators: 144: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)
optical: 1: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80optics: 1: 35Q60 PDEs in connection with optics and electromagnetic theoryoptics: 2: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80optics: 3: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80optics: 4: 78A05 Geometric opticsoptics: 5: 78A10 Physical opticsoptics: 6: 78A15 Electron opticsoptics: 7: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V80optics: 8: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)optics: 9: 81V80 Quantum optics
optimal: 1: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,90Cxx, 93-XX
optimal: 2: 49J15 Optimal control problems involving ordinary differential equationsoptimal: 3: 49J20 Optimal control problems involving partial differential equationsoptimal: 4: 49J21 Optimal control problems involving relations other than differential equationsoptimal: 5: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)optimal: 6: 49K30 Optimal solutions belonging to restricted classesoptimal: 7: 49N05 Linear optimal control problems [See also]93C05optimal: 8: 49N25 Impulsive optimal control problemsoptimal: 9: 49N35 Optimal feedback synthesis [See also]93B52optimal: 10: 49N90 Applications of optimal control and differential games [See also]90C90, 93C95optimal: 11: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60optimal: 12: 62K05 Optimal designsoptimal: 13: 62L15 Optimal stopping [See also]60G40, 91A60optimal: 14: 93-XX Systems theory; control For optimal control, see 49-XXoptimal: 15: 93E20 Optimal stochastic control
optimality: 1: 49Kxx Optimality conditionsoptimality: 2: 58E17 Pareto optimality, etc., applications to economics [See also]90C29optimality: 3: 90C46 Optimality conditions, duality [See also]49N15
optimization: 1: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,etc.)
optimization: 2: 35Q93 PDEs in connection with control and optimizationoptimization: 3: 37N40 Dynamical systems in optimization and economicsoptimization: 4: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsoptimization: 5: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsoptimization: 6: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XX
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optimization: 7: 49N20 Periodic optimizationoptimization: 8: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90optimization: 9: 65Kxx Mathematical programming, optimization and variational techniquesoptimization: 10: 65K10 Optimization and variational techniques [See also]49Mxx, 93B40optimization: 11: 74Pxx Optimization [See also]49Qxxoptimization: 12: 74P05 Compliance or weight optimizationoptimization: 13: 74P10 Optimization of other propertiesoptimization: 14: 76B75 Flow control and optimization [See also]49Q10, 93C20, 93C95optimization: 15: 76D55 Flow control and optimization [See also]49Q10, 93C20, 93C95optimization: 16: 76N25 Flow control and optimizationoptimization: 17: 78M50 Optimizationoptimization: 18: 80M50 Optimizationoptimization: 19: 90C26 Nonconvex programming, global optimizationoptimization: 20: 90C27 Combinatorial optimizationoptimization: 21: 90C31 Sensitivity, stability, parametric optimization
or: 1: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60or: 2: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60or: 3: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25or: 4: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsor: 5: 13E15 Rings and modules of finite generation or presentation; number of generatorsor: 6: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17or: 7: 15A54 Matrices over function rings in one or more variablesor: 8: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66or: 9: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxor: 10: 18D20 Enriched categories (over closed or monoidal categories)or: 11: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXor: 12: 20Exx Structure and classification of infinite or finite groupsor: 13: 20Fxx Special aspects of infinite or finite groupsor: 14: 20F38 Other groups related to topology or analysisor: 15: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40or: 16: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05or: 17: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05or: 18: 28A10 Real- or complex-valued set functionsor: 19: 28B10 Group- or semigroup-valued set functions, measures and integralsor: 20: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05or: 21: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)or: 22: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27or: 23: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70or: 24: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70or: 25: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70or: 26: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianor: 27: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacianor: 28: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)or: 29: 35R05 Partial differential equations with discontinuous coefficients or dataor: 30: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)or: 31: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40
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or: 32: 46B50 Compactness in Banach (or normed) spacesor: 33: 46E05 Lattices of continuous, differentiable or analytic functionsor: 34: 46E10 Topological linear spaces of continuous, differentiable or analytic functionsor: 35: 46E15 Banach spaces of continuous, differentiable or analytic functionsor: 36: 46E20 Hilbert spaces of continuous, differentiable or analytic functionsor: 37: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15or: 38: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60or: 39: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)or: 40: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B30or: 41: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05or: 42: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50or: 43: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.or: 44: 47C15 Operators in C∗- or von Neumann algebrasor: 45: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesor: 46: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theoryor: 47: 49J10 Free problems in two or more independent variablesor: 48: 49K10 Free problems in two or more independent variablesor: 49: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)or: 50: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismsor: 51: 58C50 Analysis on supermanifolds or graded manifoldsor: 52: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationor: 53: 65Hxx Nonlinear algebraic or transcendental equationsor: 54: 70F35 Collision of rigid or pseudo-rigid bodiesor: 55: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spaceor: 56: 74P05 Compliance or weight optimizationor: 57: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXor: 58: 76T30 Three or more component flowsor: 59: 90C35 Programming involving graphs or networks [See also]90C27or: 60: 91A44 Games involving topology or set theoryor: 61: 93D21 Adaptive or robust stabilization
orbifold: 1: 55N32 Orbifold cohomologyorbifolds: 1: 57R18 Topology and geometry of orbifolds
orbit: 1: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationsorbit: 2: 37C35 Orbit growth
orbital: 1: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-typeI representations, etc.)
orbital: 2: 70Mxx Orbital mechanicsorbital: 3: 70M20 Orbital mechanicsorbits: 1: 17B08 Coadjoint orbits; nilpotent varietiesorbits: 2: 37C27 Periodic orbits of vector fields and flowsorbits: 3: 37C29 Homoclinic and heteroclinic orbitsorbits: 4: 37D05 Hyperbolic orbits and setsorbits: 5: 37E15 Combinatorial dynamics (types of periodic orbits)orbits: 6: 37G15 Bifurcations of limit cycles and periodic orbitsorbits: 7: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic
methodsorbits: 8: 37J50 Action-minimizing orbits and measuresorder: 1: 06-XX Order, lattices, ordered algebraic structures [See also]18B35
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order: 2: 06A05 Total orderorder: 3: 06A06 Partial order, generalorder: 4: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H12order: 5: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H12order: 6: 34A35 Differential equations of infinite orderorder: 7: 35R50 Partial differential equations of infinite orderorder: 8: 51Lxx Geometric order structures [See also]53C75order: 9: 53C75 Geometric orders, order geometry [See also]51Lxxorder: 10: 62G30 Order statistics; empirical distribution functions
order-bounded: 1: 47B65 Positive operators and order-bounded operatorsordered: 1: 03C64 Model theory of ordered structures; o-minimalityordered: 2: 03E04 Ordered sets and their cofinalities; pcf theoryordered: 3: 06-XX Order, lattices, ordered algebraic structures [See also]18B35ordered: 4: 06Axx Ordered setsordered: 5: 06A07 Combinatorics of partially ordered setsordered: 6: 06A75 Generalizations of ordered setsordered: 7: 06Fxx Ordered structuresordered: 8: 06F05 Ordered semigroups and monoids [See also]20Mxxordered: 9: 06F15 Ordered groups [See also]20F60ordered: 10: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40ordered: 11: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40ordered: 12: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80ordered: 13: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80ordered: 14: 12J15 Ordered fieldsordered: 15: 13J25 Ordered rings [See also]06F25ordered: 16: 16G20 Representations of quivers and partially ordered setsordered: 17: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxxordered: 18: 19K14 K0 as an ordered group, tracesordered: 19: 20F60 Ordered groups [See mainly]06F15ordered: 20: 28B15 Set functions, measures and integrals with values in ordered spacesordered: 21: 43A17 Analysis on ordered groups, Hp-theoryordered: 22: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)ordered: 23: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42ordered: 24: 46B40 Ordered normed spaces [See also]46A40, 46B42ordered: 25: 47B60 Operators on ordered spacesordered: 26: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesordered: 27: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesordered: 28: 51Gxx Ordered geometries (ordered incidence structures, etc.)ordered: 29: 51Gxx Ordered geometries (ordered incidence structures, etc.)ordered: 30: 51G05 Ordered geometries (ordered incidence structures, etc.)ordered: 31: 51G05 Ordered geometries (ordered incidence structures, etc.)ordered: 32: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30ordered: 33: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30ordered: 34: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30ordered: 35: 97H50 Ordered algebraic structures
orderings: 1: 60E15 Inequalities; stochastic orderingsorders: 1: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxxorders: 2: 11R65 Class groups and Picard groups of ordersorders: 3: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxxorders: 4: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxx
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orders: 5: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-tion theory, see 16G30
orders: 6: 16H10 Orders in separable algebrasorders: 7: 16H15 Commutative ordersorders: 8: 16H20 Lattices over ordersorders: 9: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XXorders: 10: 19A31 K0 of group rings and ordersorders: 11: 19B28 K1 of group rings and orders [See also]57Q10orders: 12: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48orders: 13: 51L05 Geometry of orders of nondifferentiable curvesorders: 14: 51L20 Geometry of orders of surfacesorders: 15: 53C75 Geometric orders, order geometry [See also]51Lxx
ordinal: 1: 03E10 Ordinal and cardinal numbersordinal: 2: 03E45 Inner models, including constructibility, ordinal definability, and core modelsordinal: 3: 03F15 Recursive ordinals and ordinal notations
ordinals: 1: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.ordinals: 2: 03F15 Recursive ordinals and ordinal notations
ordinary: 1: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25ordinary: 2: 20C15 Ordinary representations and charactersordinary: 3: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxordinary: 4: 34-XX Ordinary differential equationsordinary: 5: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxordinary: 6: 34Lxx Ordinary differential operators [See also]47E05ordinary: 7: 34L30 Nonlinear ordinary differential operatorsordinary: 8: 35A24 Methods of ordinary differential equationsordinary: 9: 37C10 Vector fields, flows, ordinary differential equationsordinary: 10: 47Exx Ordinary differential operators [See also]34Bxx, 34Lxxordinary: 11: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)ordinary: 12: 49J15 Optimal control problems involving ordinary differential equationsordinary: 13: 49K15 Problems involving ordinary differential equationsordinary: 14: 60H10 Stochastic ordinary differential equations [See also]34F05ordinary: 15: 65Lxx Ordinary differential equationsordinary: 16: 93C15 Systems governed by ordinary differential equations [See also]34H05
ore: 1: 16U20 Ore rings, multiplicative sets, Ore localizationore: 2: 16U20 Ore rings, multiplicative sets, Ore localization
organization: 1: 68Mxx Computer system organizationorganizations: 1: 90B70 Theory of organizations, manpower planning [See also]91D35
oriented: 1: 52C40 Oriented matroidsorigin: 1: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
etc.)orlicz: 1: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)orthocomplemented: 1: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P10
orthodox: 1: 20M19 Orthodox semigroupsorthogonal: 1: 05B15 Orthogonal arrays, Latin squares, Room squaresorthogonal: 2: 15B10 Orthogonal matricesorthogonal: 3: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exxorthogonal: 4: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsorthogonal: 5: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsorthogonal: 6: 33C47 Other special orthogonal polynomials and functionsorthogonal: 7: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
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functions in one variableorthogonal: 8: 33C52 Orthogonal polynomials and functions associated with root systemsorthogonal: 9: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)orthogonal: 10: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variableorthogonal: 11: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonaldpolynomials, etc.)orthogonal: 12: 39B55 Orthogonal additivity and other conditional equationsorthogonal: 13: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45orthogonal: 14: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,etc.)orthogonal: 15: 42C25 Uniqueness and localization for orthogonal seriesorthogonal: 16: 51A50 Polar geometry, symplectic spaces, orthogonal spacesorthogonal: 17: 51F25 Orthogonal and unitary groups [See also]20H05orthogonal: 18: 94A11 Application of orthogonal and other special functions
orthogonality: 1: 51F20 Congruence and orthogonality [See also]20H05orthogonalization: 1: 65F25 Orthogonalization
oscillation: 1: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),vanishing mean oscillation (VMOA)) [See also]46Exxoscillation: 2: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),vanishing mean oscillation (VMOA)) [See also]46Exxoscillation: 3: 34C10 Oscillation theory, zeros, disconjugacy and comparison theoryoscillation: 4: 34K11 Oscillation theoryoscillation: 5: 34M10 Oscillation, growth of solutionsoscillation: 6: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.oscillation: 7: 39A21 Oscillation theoryoscillation: 8: 40D10 Tauberian constants and oscillation limits
oscillations: 1: 34C15 Nonlinear oscillations, coupled oscillatorsoscillations: 2: 34C26 Relaxation oscillationsoscillations: 3: 74Q10 Homogenization and oscillations in dynamical problemsoscillators: 1: 34C15 Nonlinear oscillations, coupled oscillatorsoscillatory: 1: 42B20 Singular and oscillatory integrals (Calderon-Zygmund, etc.)
oseen: 1: 76D07 Stokes and related (Oseen, etc.) flowsother: 1: 00A20 Dictionaries and other general reference worksother: 2: 01-XX History and biography [See also]the classification number–03 in the other sectionsother: 3: 01A13 Other indigenous cultures (non-European)other: 4: 01A74 Other institutions and academiesother: 5: 03B60 Other nonclassical logicother: 6: 03B80 Other applications of logicother: 7: 03C30 Other model constructionsother: 8: 03C65 Models of other mathematical theoriesother: 9: 03C68 Other classical first-order model theoryother: 10: 03C75 Other infinitary logicother: 11: 03D28 Other Turing degree structuresother: 12: 03D30 Other degrees and reducibilitiesother: 13: 03E05 Other combinatorial set theoryother: 14: 03E20 Other classical set theory (including functions, relations, and set algebra)other: 15: 03E40 Other aspects of forcing and Boolean-valued modelsother: 16: 03E47 Other notions of set-theoretic definabilityother: 17: 03E65 Other hypotheses and axiomsother: 18: 03F52 Linear logic and other substructural logics [See also]03B47other: 19: 03F65 Other constructive mathematics [See also]03D45other: 20: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F35other: 21: 03H10 Other applications of nonstandard models (economics, physics, etc.)other: 22: 05B30 Other designs, configurations [See also]51E30other: 23: 06D75 Other generalizations of distributive latticesother: 24: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30
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other: 25: 08Cxx Other classes of algebrasother: 26: 11A67 Other representationsother: 27: 11B75 Other combinatorial number theoryother: 28: 11E25 Sums of squares and representations by other particular quadratic formsother: 29: 11F55 Other groups and their modular and automorphic forms (several variables)other: 30: 11J91 Transcendence theory of other special functionsother: 31: 11K36 Well-distributed sequences and other variationsother: 32: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
[See also]11N99, 28Dxxother: 33: 11L10 Jacobsthal and Brewer sums; other complete character sumsother: 34: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypothesesother: 35: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72other: 36: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuesother: 37: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsother: 38: 11P32 Goldbach-type theorems; other additive questions involving primesother: 39: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measureother: 40: 11R20 Other abelian and metabelian extensionsother: 41: 11R21 Other number fieldsother: 42: 11R47 Other analytic theory [See also]11Nxxother: 43: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsother: 44: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxxother: 45: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)other: 46: 11S85 Other nonanalytic theoryother: 47: 11T24 Other character sums and Gauss sumsother: 48: 13C13 Other special typesother: 49: 13Fxx Arithmetic rings and other special ringsother: 50: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)other: 51: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and
polynomials [See also]13Nxx, 32C38other: 52: 14F20 Etale and other Grothendieck topologies and (co)homologiesother: 53: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne
(co)homologies)other: 54: 14G27 Other nonalgebraically closed ground fieldsother: 55: 14L40 Other algebraic groups (geometric aspects)other: 56: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14other: 57: 15A78 Other algebras built from modulesother: 58: 16D80 Other classes of modules and ideals [See also]16G50other: 59: 16Pxx Chain conditions, growth conditions, and other forms of finitenessother: 60: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceother: 61: 16R40 Identities other than those of matrices over commutative ringsother: 62: 16R50 Other kinds of identities (generalized polynomial, rational, involution)other: 63: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxxother: 64: 17A30 Algebras satisfying other identitiesother: 65: 17A36 Automorphisms, derivations, other operatorsother: 66: 17A42 Other n-ary compositions (n≥ 3)other: 67: 17B40 Automorphisms, derivations, other operatorsother: 68: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50other: 69: 17C50 Jordan structures associated with other structures [See also]16W10other: 70: 17Dxx Other nonassociative rings and algebrasother: 71: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J22other: 72: 19A49 K0 of other ringsother: 73: 19J05 Finiteness and other obstructions in K0
other: 74: 20E22 Extensions, wreath products, and other compositions [See also]20J05
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other: 75: 20F10 Word problems, other decision problems, connections with logic and automata[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70
other: 76: 20F22 Other classes of groups defined by subgroup chainsother: 77: 20F38 Other groups related to topology or analysisother: 78: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
other: 79: 20G35 Linear algebraic groups over adeles and other rings and schemesother: 80: 20Hxx Other groups of matrices [See also]15A30other: 81: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D25other: 82: 20H20 Other matrix groups over fieldsother: 83: 20H25 Other matrix groups over ringsother: 84: 20H30 Other matrix groups over finite fieldsother: 85: 20Nxx Other generalizations of groupsother: 86: 22A30 Other topological algebraic systems and their representationsother: 87: 22D12 Other representations of locally compact groupsother: 88: 22E20 General properties and structure of other Lie groupsother: 89: 22F50 Groups as automorphisms of other structuresother: 90: 26A30 Singular functions, Cantor functions, functions with other special propertiesother: 91: 26A39 Denjoy and Perron integrals, other special integralsother: 92: 26D07 Inequalities involving other types of functionsother: 93: 26D20 Other analytical inequalitiesother: 94: 28A25 Integration with respect to measures and other set functionsother: 95: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15other: 96: 28D20 Entropy and other invariantsother: 97: 28E15 Other connections with logic and set theoryother: 98: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXother: 99: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10other: 100: 30C65 Quasiconformal mappings in Rn, other generalizationsother: 101: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsother: 102: 30D60 Quasi-analytic and other classes of functionsother: 103: 30G30 Other generalizations of analytic functions (including abstract-valued functions)other: 104: 31Cxx Other generalizationsother: 105: 31C45 Other generalizations (nonlinear potential theory, etc.)other: 106: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30other: 107: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35other: 108: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxother: 109: 32F17 Other notions of convexityother: 110: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)other: 111: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)other: 112: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)other: 113: 32S70 Other operations on singularitiesother: 114: 32V25 Extension of functions and other analytic objects from CR manifoldsother: 115: 32W50 Other partial differential equations of complex analysisother: 116: 33C47 Other special orthogonal polynomials and functionsother: 117: 33C70 Other hypergeometric functions and integrals in several variablesother: 118: 33D70 Other basic hypergeometric functions and integrals in several variablesother: 119: 33Exx Other special functionsother: 120: 33E15 Other wave functions
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other: 121: 33E20 Other functions defined by series and integralsother: 122: 33E30 Other functions coming from differential, difference and integral equationsother: 123: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumother: 124: 34M55 Painleve and other special equations; classification, hierarchies;other: 125: 35A25 Other special methodsother: 126: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L05other: 127: 35Q92 PDEs in connection with biology and other natural sciencesother: 128: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40other: 129: 37A35 Entropy and other invariants, isomorphism, classificationother: 130: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemsother: 131: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxother: 132: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresother: 133: 37K35 Lie-Backlund and other transformationsother: 134: 37L25 Inertial manifolds and other invariant attracting setsother: 135: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)other: 136: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typeother: 137: 39B55 Orthogonal additivity and other conditional equationsother: 138: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)other: 139: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)other: 140: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)other: 141: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)other: 142: 41A30 Approximation by other special function classesother: 143: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)other: 144: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)other: 145: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typeother: 146: 42A55 Lacunary series of trigonometric and other functions; Riesz productsother: 147: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typeother: 148: 42C20 Other transformations of harmonic typeother: 149: 42C40 Wavelets and other special systemsother: 150: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxother: 151: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxother: 152: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.other: 153: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupsother: 154: 43A32 Other transforms and operators of Fourier typeother: 155: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05other: 156: 43A80 Analysis on other specific Lie groups [See also]22Exxother: 157: 44A40 Calculus of Mikusinski and other operational calculiother: 158: 45G10 Other nonlinear integral equationsother: 159: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)other: 160: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32other: 161: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theorems
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other: 162: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,58B34, 58J22
other: 163: 46N60 Applications in biology and other sciencesother: 164: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxxother: 165: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05other: 166: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22other: 167: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15other: 168: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)other: 169: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)other: 170: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesother: 171: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J40other: 172: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K21other: 173: 47L10 Algebras of operators on Banach spaces and other topological linear spacesother: 174: 47L75 Other nonselfadjoint operator algebrasother: 175: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxxother: 176: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theoryother: 177: 49J21 Optimal control problems involving relations other than differential equationsother: 178: 49K21 Problems involving relations other than differential equationsother: 179: 49M30 Other methodsother: 180: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90other: 181: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)other: 182: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)other: 183: 51E25 Other finite nonlinear geometriesother: 184: 51E26 Other finite linear geometriesother: 185: 51E30 Other finite incidence structures [See also]05B30other: 186: 51N25 Analytic geometry with other transformation groupsother: 187: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)other: 188: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)other: 189: 52A37 Other problems of combinatorial convexityother: 190: 52B35 Gale and other diagramsother: 191: 53A40 Other special differential geometriesother: 192: 53B15 Other connectionsother: 193: 53C56 Other complex differential geometry [See also]32Cxxother: 194: 54Hxx Connections with other structures, applicationsother: 195: 55N35 Other homology theoriesother: 196: 57R90 Other types of cobordism [See also]55N22other: 197: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C60other: 198: 58J35 Heat and other parabolic equation methodsother: 199: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22other: 200: 60A05 Axioms; other general questionsother: 201: 60E10 Characteristic functions; other transformsother: 202: 60F05 Central limit and other weak theoremsother: 203: 60K40 Other physical applications of random processesother: 204: 62F40 Bootstrap, jackknife and other resampling methodsother: 205: 65C50 Other computational problems in probability
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other: 206: 65F30 Other matrix algorithmsother: 207: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,
etc.)other: 208: 70H30 Other variational principlesother: 209: 70S15 Yang-Mills and other gauge theoriesother: 210: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)other: 211: 74Fxx Coupling of solid mechanics with other effectsother: 212: 74P10 Optimization of other propertiesother: 213: 74S30 Other numerical methodsother: 214: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXother: 215: 76D27 Other free-boundary flows; Hele-Shaw flowsother: 216: 76F30 Renormalization and other field-theoretical methods [See also]81T99other: 217: 76M25 Other numerical methodsother: 218: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)other: 219: 78M25 Other numerical methodsother: 220: 80M25 Other numerical methodsother: 221: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsother: 222: 81Q40 Bethe-Salpeter and other integral equationsother: 223: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
other: 224: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E15other: 225: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30other: 226: 81V19 Other fundamental interactionsother: 227: 81V25 Other elementary particle theoryother: 228: 83C27 Lattice gravity, Regge calculus and other discrete methodsother: 229: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesother: 230: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesother: 231: 83E15 Kaluza-Klein and other higher-dimensional theoriesother: 232: 91Fxx Other social and behavioral sciences (mathematical treatment)other: 233: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)other: 234: 92-XX Biology and other natural sciencesother: 235: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)other: 236: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)other: 237: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)other: 238: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)other: 239: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)other: 240: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)other: 241: 93E25 Other computational methodsother: 242: 94A11 Application of orthogonal and other special functionsother: 243: 94B60 Other types of codesouter: 1: 28A12 Contents, measures, outer measures, capacitiesovals: 1: 51E21 Blocking sets, ovals, k-arcsover: 1: 03D78 Computation over the reals For constructive aspects, see 03F60over: 2: 11E04 Quadratic forms over general fieldsover: 3: 11E08 Quadratic forms over local rings and fields
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over: 4: 11E10 Forms over real fieldsover: 5: 11E12 Quadratic forms over global rings and fieldsover: 6: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsover: 7: 11G05 Elliptic curves over global fields [See also]14H52over: 8: 11G07 Elliptic curves over local fields [See also]14G20, 14H52over: 9: 11G20 Curves over finite and local fields [See also]14H25over: 10: 11G25 Varieties over finite and local fields [See also]14G15, 14G20over: 11: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H25over: 12: 11G35 Varieties over global fields [See also]14G25over: 13: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10over: 14: 11J72 Irrationality; linear independence over a fieldover: 15: 11L20 Sums over primesover: 16: 11L26 Sums over arbitrary intervalsover: 17: 11T55 Arithmetic theory of polynomial rings over finite fieldsover: 18: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M10over: 19: 15A54 Matrices over function rings in one or more variablesover: 20: 15B33 Matrices over special rings (quaternions, finite fields, etc.)over: 21: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxxover: 22: 16H20 Lattices over ordersover: 23: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsover: 24: 16R40 Identities other than those of matrices over commutative ringsover: 25: 18D20 Enriched categories (over closed or monoidal categories)over: 26: 20F70 Algebraic geometry over groups; equations over groupsover: 27: 20F70 Algebraic geometry over groups; equations over groupsover: 28: 20G15 Linear algebraic groups over arbitrary fieldsover: 29: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionsover: 30: 20G25 Linear algebraic groups over local fields and their integersover: 31: 20G30 Linear algebraic groups over global fields and their integersover: 32: 20G35 Linear algebraic groups over adeles and other rings and schemesover: 33: 20G40 Linear algebraic groups over finite fieldsover: 34: 20H20 Other matrix groups over fieldsover: 35: 20H25 Other matrix groups over ringsover: 36: 20H30 Other matrix groups over finite fieldsover: 37: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05over: 38: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05over: 39: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05over: 40: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05over: 41: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theoryover: 42: 94A55 Shift register sequences and sequences over finite alphabets
over-convergence: 1: 30B30 Boundary behavior of power series, over-convergenceoverdetermined: 1: 35Nxx Overdetermined systems [See also]58Hxx, 58J10, 58J15overdetermined: 2: 35N05 Overdetermined systems with constant coefficientsoverdetermined: 3: 35N10 Overdetermined systems with variable coefficientsoverdetermined: 4: 35N20 Overdetermined initial value problemsoverdetermined: 5: 35N25 Overdetermined boundary value problemsoverdetermined: 6: 35N30 Overdetermined initial-boundary value problemsoverdetermined: 7: 65F20 Overdetermined systems, pseudoinverses
packaged: 1: 65Y15 Packaged methodspacking: 1: 05B40 Packing and covering [See also]11H31, 52C15, 52C17packing: 2: 05C70 Factorization, matching, partitioning, covering and packingpacking: 3: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C17
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packing: 4: 28A78 Hausdorff and packing measurespacking: 5: 51E23 Spreads and packing problemspacking: 6: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H31packing: 7: 52C17 Packing and covering in n dimensions [See also]05B40, 11H31
packings: 1: 52C26 Circle packings and discrete conformal geometrypade: 1: 41A21 Pade approximation
painleve: 1: 34M55 Painleve and other special equations; classification, hierarchies;painleve-type: 1: 33E17 Painleve-type functions
paired: 1: 62J15 Paired and multiple comparisonspairs: 1: 17Cxx Jordan algebras (algebras, triples and pairs)pairs: 2: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation
paleolithic: 1: 01A10 Paleolithic, Neolithicpapers: 1: 00Bxx Conference proceedings and collections of paperspapers: 2: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areapappian: 1: 51A30 Desarguesian and Pappian geometries
parabolic: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J35parabolic: 2: 35K10 Second-order parabolic equationsparabolic: 3: 35K15 Initial value problems for second-order parabolic equationsparabolic: 4: 35K20 Initial-boundary value problems for second-order parabolic equationsparabolic: 5: 35K25 Higher-order parabolic equationsparabolic: 6: 35K30 Initial value problems for higher-order parabolic equationsparabolic: 7: 35K35 Initial-boundary value problems for higher-order parabolic equationsparabolic: 8: 35K40 Second-order parabolic systemsparabolic: 9: 35K41 Higher-order parabolic systemsparabolic: 10: 35K45 Initial value problems for second-order parabolic systemsparabolic: 11: 35K46 Initial value problems for higher-order parabolic systemsparabolic: 12: 35K51 Initial-boundary value problems for second-order parabolic systemsparabolic: 13: 35K52 Initial-boundary value problems for higher-order parabolic systemsparabolic: 14: 35K55 Nonlinear parabolic equationsparabolic: 15: 35K58 Semilinear parabolic equationsparabolic: 16: 35K59 Quasilinear parabolic equationsparabolic: 17: 35K60 Nonlinear initial value problems for linear parabolic equationsparabolic: 18: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsparabolic: 19: 35K65 Degenerate parabolic equationsparabolic: 20: 35K67 Singular parabolic equationsparabolic: 21: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40parabolic: 22: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40parabolic: 23: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40parabolic: 24: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40parabolic: 25: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J40parabolic: 26: 35K90 Abstract parabolic equationsparabolic: 27: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacianparabolic: 28: 35K92 Quasilinear parabolic equations with p-Laplacianparabolic: 29: 35K93 Quasilinear parabolic equations with mean curvature operatorparabolic: 30: 35K96 Parabolic Monge-Ampere equationsparabolic: 31: 58J35 Heat and other parabolic equation methods
paracompact: 1: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)paraconsistent: 1: 03B53 Paraconsistent logics
paradifferential: 1: 35S50 Paradifferential operatorsparallel: 1: 65Y05 Parallel computationparallel: 2: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85
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parallel: 3: 68W10 Parallel algorithmsparallel: 4: 76E05 Parallel shear flows
parallelism: 1: 51A15 Structures with parallelismparallelism: 2: 51D15 Abstract geometries with parallelismparameter: 1: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterparameter: 2: 34B08 Parameter dependent boundary value problemsparameter: 3: 60G42 Martingales with discrete parameterparameter: 4: 60G44 Martingales with continuous parameterparameter: 5: 62K25 Robust parameter designs
parameters: 1: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxparametric: 1: 62Fxx Parametric inferenceparametric: 2: 62F86 Parametric inference and fuzzinessparametric: 3: 70J40 Parametric resonancesparametric: 4: 70K28 Parametric resonancesparametric: 5: 90C31 Sensitivity, stability, parametric optimization
parametrices: 1: 35A17 Parametricesparametrization: 1: 14C05 Parametrization (Chow and Hilbert schemes)parametrization: 2: 32B10 Germs of analytic sets, local parametrization
pareto: 1: 58E17 Pareto optimality, etc., applications to economics [See also]90C29partial: 1: 06A06 Partial order, generalpartial: 2: 08A55 Partial algebraspartial: 3: 32W50 Other partial differential equations of complex analysispartial: 4: 35-XX Partial differential equationspartial: 5: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxxpartial: 6: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)partial: 7: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.partial: 8: 35R05 Partial differential equations with discontinuous coefficients or datapartial: 9: 35R06 Partial differential equations with measurepartial: 10: 35R10 Partial functional-differential equationspartial: 11: 35R11 Fractional partial differential equationspartial: 12: 35R12 Impulsive partial differential equationspartial: 13: 35R13 Fuzzy partial differential equationspartial: 14: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25partial: 15: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxpartial: 16: 35R45 Partial differential inequalitiespartial: 17: 35R50 Partial differential equations of infinite orderpartial: 18: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15partial: 19: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15partial: 20: 35R70 Partial differential equations with multivalued right-hand sidespartial: 21: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40partial: 22: 39A14 Partial difference equationspartial: 23: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)partial: 24: 47Fxx Partial differential operators [See also]35Pxx, 58Jxxpartial: 25: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)partial: 26: 47L60 Algebras of unbounded operators; partial algebras of operatorspartial: 27: 49J20 Optimal control problems involving partial differential equationspartial: 28: 49K20 Problems involving partial differential equationspartial: 29: 51E14 Finite partial geometries (general), nets, partial spreadspartial: 30: 51E14 Finite partial geometries (general), nets, partial spreadspartial: 31: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxx
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partial: 32: 60H15 Stochastic partial differential equations [See also]35R60partial: 33: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemspartial: 34: 65Nxx Partial differential equations, boundary value problemspartial: 35: 93C20 Systems governed by partial differential equations
partially: 1: 06A07 Combinatorics of partially ordered setspartially: 2: 16G20 Representations of quivers and partially ordered setspartially: 3: 37D30 Partially hyperbolic systems and dominated splittingspartially: 4: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30particle: 1: 65C35 Stochastic particle methods [See also]82C80particle: 2: 65M75 Probabilistic methods, particle methods, etc.particle: 3: 65N75 Probabilistic methods, particle methods, etc.particle: 4: 70B05 Kinematics of a particleparticle: 5: 70F45 Infinite particle systemsparticle: 6: 76M28 Particle methods and lattice-gas methodsparticle: 7: 81V25 Other elementary particle theoryparticle: 8: 82C22 Interacting particle systems [See also]60K35
particles: 1: 35Q70 PDEs in connection with mechanics of particles and systemsparticles: 2: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXparticles: 3: 70Fxx Dynamics of a system of particles, including celestial mechanicsparticles: 4: 78A35 Motion of charged particlesparticles: 5: 82B21 Continuum models (systems of particles, etc.)particles: 6: 82C21 Dynamic continuum models (systems of particles, etc.)
particular: 1: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C60particular: 2: 11E25 Sums of squares and representations by other particular quadratic formsparticular: 3: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)particular: 4: 41A35 Approximation by operators (in particular, by integral operators)particular: 5: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P05particular: 6: 54F65 Topological characterizations of particular spacespartition: 1: 03E02 Partition relationspartition: 2: 11P84 Partition identities; identities of Rogers-Ramanujan type
partitioning: 1: 05C70 Factorization, matching, partitioning, covering and packingpartitions: 1: 05A17 Partitions of integers [See also]11P81, 11P82, 11P83partitions: 2: 05A18 Partitions of setspartitions: 3: 11Pxx Additive number theory; partitionspartitions: 4: 11P81 Elementary theory of partitions [See also]05A17partitions: 5: 11P82 Analytic theory of partitionspartitions: 6: 11P83 Partitions; congruences and congruential restrictions
parts: 1: 11J54 Small fractional parts of polynomials and generalizationsparts: 2: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumparts: 3: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXpath: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXpath: 2: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)path: 3: 60G17 Sample path propertiespath: 4: 81S40 Path integrals [See also]58D30
pathological: 1: 54G15 Pathological spacespaths: 1: 05C38 Paths and cycles [See also]90B10paths: 2: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxx
pattern: 1: 15B35 Sign pattern matricespattern: 2: 35B36 Pattern formationpattern: 3: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30pattern: 4: 92C15 Developmental biology, pattern formation
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pcf: 1: 03E04 Ordered sets and their cofinalities; pcf theorypde: 1: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15pde: 2: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15pde: 3: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25pde: 4: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxpde: 5: 42B37 Harmonic analysis and PDE [See also]35-XXpde: 6: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J60pde: 7: 60H30 Applications of stochastic analysis (to PDE, etc.)pde: 8: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)pdes: 1: 35Q35 PDEs in connection with fluid mechanicspdes: 2: 35Q40 PDEs in connection with quantum mechanicspdes: 3: 35Q60 PDEs in connection with optics and electromagnetic theorypdes: 4: 35Q62 PDEs in connection with statisticspdes: 5: 35Q68 PDEs in connection with computer sciencepdes: 6: 35Q70 PDEs in connection with mechanics of particles and systemspdes: 7: 35Q74 PDEs in connection with mechanics of deformable solidspdes: 8: 35Q75 PDEs in connection with relativity and gravitational theorypdes: 9: 35Q79 PDEs in connection with classical thermodynamics and heat transferpdes: 10: 35Q82 PDEs in connection with statistical mechanicspdes: 11: 35Q85 PDEs in connection with astronomy and astrophysicspdes: 12: 35Q86 PDEs in connection with geophysicspdes: 13: 35Q90 PDEs in connection with mathematical programmingpdes: 14: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencespdes: 15: 35Q92 PDEs in connection with biology and other natural sciencespdes: 16: 35Q93 PDEs in connection with control and optimizationpdes: 17: 35Q94 PDEs in connection with information and communicationpeak: 1: 32T40 Peak functions
peculiar: 1: 54Gxx Peculiar spacespeirce: 1: 17C27 Idempotents, Peirce decompositions
pencils: 1: 14C21 Pencils, nets, webs [See also]53A60pencils: 2: 15A22 Matrix pencils [See also]47A56
percentages: 1: 97F80 Ratio and proportion, percentagesperception: 1: 91E30 Psychophysics and psychophysiology; perceptionpercolation: 1: 60K35 Interacting random processes; statistical mechanics type models; percolation theory[See also]82B43, 82C43percolation: 2: 82B43 Percolation [See also]60K35percolation: 3: 82C43 Time-dependent percolation [See also]60K35
perfect: 1: 05C17 Perfect graphsperfect: 2: 16L30 Noncommutative local and semilocal rings, perfect ringsperfect: 3: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)
perfectly: 1: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwisenormal, etc.)
performance: 1: 65Y20 Complexity and performance of numerical algorithms [See also]68Q25performance: 2: 68M20 Performance evaluation; queueing; scheduling [See also]60K25, 90Bxxperformance: 3: 91E45 Measurement and performance
period: 1: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,14K30
periodic: 1: 20F50 Periodic groups; locally finite groupsperiodic: 2: 34C25 Periodic solutionsperiodic: 3: 34C27 Almost and pseudo-almost periodic solutionsperiodic: 4: 34K13 Periodic solutions
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periodic: 5: 35B10 Periodic solutionsperiodic: 6: 35B15 Almost and pseudo-almost periodic solutionsperiodic: 7: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50periodic: 8: 37C25 Fixed points, periodic points, fixed-point index theoryperiodic: 9: 37C27 Periodic orbits of vector fields and flowsperiodic: 10: 37C55 Periodic and quasiperiodic flows and diffeomorphismsperiodic: 11: 37E15 Combinatorial dynamics (types of periodic orbits)periodic: 12: 37G15 Bifurcations of limit cycles and periodic orbitsperiodic: 13: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic
methodsperiodic: 14: 37P35 Arithmetic properties of periodic pointsperiodic: 15: 39A23 Periodic solutionsperiodic: 16: 39A24 Almost periodic solutionsperiodic: 17: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60periodic: 18: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A60periodic: 19: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsperiodic: 20: 45M15 Periodic solutionsperiodic: 21: 49N20 Periodic optimizationperiodic: 22: 70H12 Periodic and almost periodic solutionsperiodic: 23: 70H12 Periodic and almost periodic solutionsperiodic: 24: 70K42 Equilibria and periodic trajectories
periodicity: 1: 11K70 Harmonic analysis and almost periodicityperiodicity: 2: 55R45 Homology and homotopy of BO and BU; Bott periodicity
periods: 1: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modularsymbols
permanents: 1: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14permutation: 1: 20Bxx Permutation groups
permutations: 1: 05A05 Permutations, words, matricesperron: 1: 26A39 Denjoy and Perron integrals, other special integrals
personalia: 1: 01A70 Biographies, obituaries, personalia, bibliographiesperturbation: 1: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20perturbation: 2: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q15perturbation: 3: 70E20 Perturbation methods for rigid body dynamicsperturbation: 4: 70H09 Perturbation theoriesperturbation: 5: 70K60 General perturbation schemesperturbation: 6: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods,
series, etc.)perturbation: 7: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods,
series, etc.)perturbation: 8: 81Q15 Perturbation theories for operators and differential equations
perturbations: 1: 34D10 Perturbationsperturbations: 2: 34D15 Singular perturbationsperturbations: 3: 34E10 Perturbations, asymptoticsperturbations: 4: 34E15 Singular perturbations, general theoryperturbations: 5: 34E20 Singular perturbations, turning point theory, WKB methodsperturbations: 6: 34K26 Singular perturbationsperturbations: 7: 34K27 Perturbationsperturbations: 8: 35B20 Perturbationsperturbations: 9: 35B25 Singular perturbationsperturbations: 10: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionperturbations: 11: 37K55 Perturbations, KAM for infinite-dimensional systemsperturbations: 12: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemsperturbations: 13: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q15perturbations: 14: 58J37 Perturbations; asymptoticsperturbations: 15: 70K65 Averaging of perturbations
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perturbations: 16: 76M45 Asymptotic methods, singular perturbationsperturbations: 17: 93C70 Time-scale analysis and singular perturbationsperturbations: 18: 93C73 Perturbationsperturbative: 1: 81T15 Perturbative methods of renormalization
perturbed: 1: 65L11 Singularly perturbed problemspesin: 1: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
pfaffian: 1: 58A17 Pfaffian systemspharmacokinetics: 1: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A30phase: 1: 37J35 Completely integrable systems, topological structure of phase space, integration
methodsphase: 2: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40phase: 3: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spacephase: 4: 70K05 Phase plane analysis, limit cyclesphase: 5: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C26phase: 6: 74N20 Dynamics of phase boundariesphase: 7: 80A22 Stefan problems, phase changes, etc. [See also]74Nxxphase: 8: 82B26 Phase transitions (general)phase: 9: 82C26 Dynamic and nonequilibrium phase transitions (general)
phase-space: 1: 81S30 Phase-space methods including Wigner distributions, etc.phases: 1: 74A50 Structured surfaces and interfaces, coexistent phasesphases: 2: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
phenomena: 1: 34F15 Resonance phenomenaphenomena: 2: 34M40 Stokes phenomena and connection problems (linear and nonlinear)phenomena: 3: 82B27 Critical phenomenaphenomena: 4: 82C27 Dynamic critical phenomena
philosophical: 1: 03Axx Philosophical aspects of logic and foundationsphilosophical: 2: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30philosophical: 3: 62Axx Foundational and philosophical topicsphilosophical: 4: 62A01 Foundations and philosophical topicsphilosophical: 5: 81P05 General and philosophicalphilosophical: 6: 97D20 Philosophical and theoretical contributions (maths didactics)
philosophy: 1: 00A30 Philosophy of mathematics [See also]03A05philosophy: 2: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30philosophy: 3: 03A10 Logic in the philosophy of sciencephilosophy: 4: 81Pxx Axiomatics, foundations, philosophyphilosophy: 5: 97E20 Philosophy and mathematics
phragmen-lindelof: 1: 35B53 Liouville theorems, Phragmen-Lindelof theoremsphysical: 1: 47N50 Applications in the physical sciencesphysical: 2: 60K40 Other physical applications of random processesphysical: 3: 78A10 Physical opticsphysical: 4: 81Vxx Applications to specific physical systemsphysical: 5: 82Dxx Applications to specific types of physical systemsphysics: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86physics: 2: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)physics: 3: 03H10 Other applications of nonstandard models (economics, physics, etc.)physics: 4: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxphysics: 5: 14H81 Relationships with physicsphysics: 6: 14J81 Relationships with physicsphysics: 7: 17B81 Applications to physicsphysics: 8: 17C90 Applications to physicsphysics: 9: 20C35 Applications of group representations to physicsphysics: 10: 20G45 Applications to physicsphysics: 11: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10physics: 12: 32C81 Applications to physics
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physics: 13: 32G81 Applications to physicsphysics: 14: 32J81 Applications to physicsphysics: 15: 32L81 Applications to physicsphysics: 16: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L05physics: 17: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)physics: 18: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)physics: 19: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C10physics: 20: 46N50 Applications in quantum physicsphysics: 21: 46N55 Applications in statistical physicsphysics: 22: 47L90 Applications of operator algebras to physicsphysics: 23: 49Sxx Variational principles of physicsphysics: 24: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)physics: 25: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)physics: 26: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)physics: 27: 53B50 Applications to physicsphysics: 28: 53C80 Applications to physicsphysics: 29: 53Zxx Applications to physicsphysics: 30: 53Z05 Applications to physicsphysics: 31: 58Zxx Applications to physicsphysics: 32: 58Z05 Applications to physicsphysics: 33: 62P35 Applications to physicsphysics: 34: 65Zxx Applications to physicsphysics: 35: 65Z05 Applications to physicsphysics: 36: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70physics: 37: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
physics: 38: 81V35 Nuclear physicsphysics: 39: 81V45 Atomic physicsphysics: 40: 81V55 Molecular physics [See also]92E10physics: 41: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U05physics: 42: 97M50 Physics, astronomy, technology, engineering
physiological: 1: 76Z05 Physiological flows [See also]92C35physiological: 2: 92Cxx Physiological, cellular and medical topicsphysiological: 3: 92C35 Physiological flow [See also]76Z05
physiology: 1: 92C30 Physiology (general)picard: 1: 11R65 Class groups and Picard groups of orderspicard: 2: 14C22 Picard groupspicard: 3: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G20picard: 4: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35picard-lefschetz: 1: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
picard-type: 1: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see 32A22piecewise: 1: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)pinching: 1: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B20
pisot: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
pivoting: 1: 90C49 Extreme-point and pivoting methods
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pl-structures: 1: 57Q25 Comparison of PL-structures: classification, Hauptvermutungpl-topology: 1: 57Qxx PL-topologypl-topology: 2: 57Q91 Equivariant PL-topology
placed: 1: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or16-XX)placement: 1: 93B55 Pole and zero placement problems
planar: 1: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,57M25
planar: 2: 52C30 Planar arrangements of lines and pseudolinesplane: 1: 14H50 Plane and space curvesplane: 2: 30C62 Quasiconformal mappings in the planeplane: 3: 30C85 Capacity and harmonic measure in the complex plane [See also]31A15plane: 4: 70K05 Phase plane analysis, limit cyclesplane: 5: 97G40 Plane and solid geometryplane: 6: 97G60 Plane and spherical trigonometry
planes: 1: 37E30 Homeomorphisms and diffeomorphisms of planes and surfacesplanes: 2: 51A35 Non-Desarguesian affine and projective planesplanes: 3: 51A40 Translation planes and spreadsplanes: 4: 51E15 Affine and projective planesplanes: 5: 51F05 Absolute planes
planetary: 1: 85A20 Planetary atmospheresplanning: 1: 90B70 Theory of organizations, manpower planning [See also]91D35planning: 2: 97B10 Educational research and planningplanning: 3: 97U30 Teachers’ manuals and planning aids
plant: 1: 92C80 Plant biologyplasmas: 1: 82D10 Plasmasplasmic: 1: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10plasmic: 2: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D10plastic: 1: 74Cxx Plastic materials, materials of stress-rate and internal-variable type
plasticity: 1: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)plates: 1: 74K20 Plates
players: 1: 91A13 Games with infinitely many playerspluricomplex: 1: 32U35 Pluricomplex Green functions
pluriharmonic: 1: 31C10 Pluriharmonic and plurisubharmonic functions [See also]32U05pluripotential: 1: 32Uxx Pluripotential theorypluripotential: 2: 32U15 General pluripotential theory
plurisubharmonic: 1: 31C10 Pluriharmonic and plurisubharmonic functions [See also]32U05plurisubharmonic: 2: 32U05 Plurisubharmonic functions and generalizations [See also]31C10plurisubharmonic: 3: 32U10 Plurisubharmonic exhaustion functionsplus-constructions: 1: 19D06 Q- and plus-constructions
poincare: 1: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincare seriespoincare: 2: 30F45 Conformal metrics (hyperbolic, Poincare, distance functions)poincare: 3: 57M40 Characterizations of E3 and S3 (Poincare conjecture) [See also]57N12poincare: 4: 57P10 Poincare duality spacespoincare: 5: 57R60 Homotopy spheres, Poincare conjecture
point: 1: 34E20 Singular perturbations, turning point theory, WKB methodspoint: 2: 58C30 Fixed point theorems on manifolds [See also]47H10point: 3: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)point: 4: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80point: 5: 60G55 Point processespoint: 6: 62F10 Point estimationpoint: 7: 70E17 Motion of a rigid body with a fixed point
points: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
points: 2: 11P21 Lattice points in specified regionspoints: 3: 14G05 Rational points
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points: 4: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxxpoints: 5: 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability),
discontinuous derivativespoints: 6: 34C05 Location of integral curves, singular points, limit cyclespoints: 7: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20points: 8: 35B38 Critical pointspoints: 9: 37C25 Fixed points, periodic points, fixed-point index theorypoints: 10: 37C25 Fixed points, periodic points, fixed-point index theorypoints: 11: 37G10 Bifurcations of singular pointspoints: 12: 37G20 Hyperbolic singular points with homoclinic trajectoriespoints: 13: 37J10 Symplectic mappings, fixed pointspoints: 14: 37P35 Arithmetic properties of periodic pointspoints: 15: 52C35 Arrangements of points, flats, hyperplanes [See also]32S22points: 16: 55M20 Fixed points and coincidences [See also]54H25points: 17: 57R70 Critical points and critical submanifoldspoints: 18: 58K05 Critical points of functions and mappings
poisson: 1: 17B63 Poisson algebraspoisson: 2: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxpoisson: 3: 53D17 Poisson manifolds; Poisson groupoids and algebroidspoisson: 4: 53D17 Poisson manifolds; Poisson groupoids and algebroidspoisson: 5: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxpoisson: 6: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
poisson’s: 1: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationpolar: 1: 51A50 Polar geometry, symplectic spaces, orthogonal spacespolar: 2: 74A35 Polar materialspole: 1: 93B55 Pole and zero placement problems
policy: 1: 97Bxx Educational policy and systemspolitical: 1: 91F10 History, political science
pollution: 1: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)poly-laplacian: 1: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianpoly-laplacian: 2: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
polyadic: 1: 03G15 Cylindric and polyadic algebras; relation algebraspolygamma: 1: 33B15 Gamma, beta and polygamma functions
polygenic: 1: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenicfunctions)polygonal: 1: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)polygons: 1: 51E12 Generalized quadrangles, generalized polygons
polyharmonic: 1: 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equationpolyharmonic: 2: 31B30 Biharmonic and polyharmonic equations and functions
polyhedra: 1: 14M25 Toric varieties, Newton polyhedra [See also]52B20polyhedra: 2: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15polyhedra: 3: 52Bxx Polytopes and polyhedrapolyhedral: 1: 52B70 Polyhedral manifoldspolyhedral: 2: 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
polylogarithms: 1: 11G55 Polylogarithms and relations with K-theorypolymers: 1: 82D60 Polymers
polynomial: 1: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuespolynomial: 2: 11T55 Arithmetic theory of polynomial rings over finite fieldspolynomial: 3: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25polynomial: 4: 13P15 Solving polynomial systems; resultantspolynomial: 5: 16Rxx Rings with polynomial identitypolynomial: 6: 16R50 Other kinds of identities (generalized polynomial, rational, involution)polynomial: 7: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial ringspolynomial: 8: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25
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polynomial: 9: 32E20 Polynomial convexitypolynomial: 10: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolationpolynomial: 11: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)polynomial: 12: 35C11 Polynomial solutionspolynomial: 13: 37P05 Polynomial and rational mapspolynomial: 14: 47H60 Multilinear and polynomial operators [See also]46G25polynomial: 15: 65H04 Roots of polynomial equations
polynomials: 1: 05C31 Graph polynomialspolynomials: 2: 08A40 Operations, polynomials, primal algebraspolynomials: 3: 11B39 Fibonacci and Lucas numbers and polynomials and generalizationspolynomials: 4: 11B68 Bernoulli and Euler numbers and polynomialspolynomials: 5: 11B83 Special sequences and polynomialspolynomials: 6: 11Cxx Polynomials and matricespolynomials: 7: 11C08 Polynomials [See also]13F20polynomials: 8: 11J54 Small fractional parts of polynomials and generalizationspolynomials: 9: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuespolynomials: 10: 11R09 Polynomials (irreducibility, etc.)polynomials: 11: 11S05 Polynomialspolynomials: 12: 11T06 Polynomialspolynomials: 13: 12-XX Field theory and polynomialspolynomials: 14: 12D05 Polynomials: factorizationpolynomials: 15: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15polynomials: 16: 12E05 Polynomials (irreducibility, etc.)polynomials: 17: 12E10 Special polynomialspolynomials: 18: 12Yxx Computational aspects of field theory and polynomialspolynomials: 19: 12Y05 Computational aspects of field theory and polynomialspolynomials: 20: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M10polynomials: 21: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25polynomials: 22: 13M10 Polynomialspolynomials: 23: 13P05 Polynomials, factorization [See also]12Y05polynomials: 24: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C38polynomials: 25: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)polynomials: 26: 26Cxx Polynomials, rational functionspolynomials: 27: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exxpolynomials: 28: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H05polynomials: 29: 26D05 Inequalities for trigonometric functions and polynomialspolynomials: 30: 30C10 Polynomialspolynomials: 31: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10polynomials: 32: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionspolynomials: 33: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionspolynomials: 34: 33C47 Other special orthogonal polynomials and functionspolynomials: 35: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablepolynomials: 36: 33C52 Orthogonal polynomials and functions associated with root systemspolynomials: 37: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)polynomials: 38: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)polynomials: 39: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variablepolynomials: 40: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)polynomials: 41: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
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polynomials, etc.)polynomials: 42: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04polynomials: 43: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see
42A10polynomials: 44: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see
42A10polynomials: 45: 42A05 Trigonometric polynomials, inequalities, extremal problemspolynomials: 46: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45polynomials: 47: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)polynomials: 48: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H60polynomials: 49: 47L22 Ideals of polynomials and of multilinear mappingspolyominoes: 1: 05B50 Polyominoes
polytopes: 1: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15polytopes: 2: 52Bxx Polytopes and polyhedrapolytopes: 3: 52B10 Three-dimensional polytopespolytopes: 4: 52B11 n-dimensional polytopespolytopes: 5: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)polytopes: 6: 52B15 Symmetry properties of polytopespolytopes: 7: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxpolytopes: 8: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxpolytopes: 9: 52B60 Isoperimetric problems for polytopes
pontryagin: 1: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)[See also]47B50
popov-type: 1: 93D10 Popov-type stability of feedback systemspopularization: 1: 00A09 Popularization of mathematicspopularization: 2: 97A80 Popularization of mathematics
population: 1: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorptionproblems, etc.) [See also]92Dxxpopulation: 2: 92Dxx Genetics and population dynamicspopulation: 3: 92D25 Population dynamics (general)
porosity: 1: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)porous: 1: 76Sxx Flows in porous media; filtration; seepageporous: 2: 76S05 Flows in porous media; filtration; seepage
portfolio: 1: 91G10 Portfolio theoryposed: 1: 35R25 Improperly posed problemsposed: 2: 65J20 Improperly posed problems; regularizationposed: 3: 65L08 Improperly posed problemsposed: 4: 65M30 Improperly posed problemsposed: 5: 65R30 Improperly posed problemsposets: 1: 06A11 Algebraic aspects of posetsposets: 2: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q55posets: 3: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P10
position: 1: 57N75 General position and transversalityposition: 2: 57Q65 General position and transversality
positional: 1: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N75positive: 1: 11N60 Distribution functions associated with additive and positive multiplicative functionspositive: 2: 14G17 Positive characteristic ground fieldspositive: 3: 15B48 Positive matrices and their generalizations; cones of matricespositive: 4: 32Q10 Positive curvature manifoldspositive: 5: 34B18 Positive solutions of nonlinear boundary value problemspositive: 6: 35B09 Positive solutionspositive: 7: 41A36 Approximation by positive operators
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positive: 8: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)positive: 9: 42A82 Positive definite functionspositive: 10: 43A35 Positive definite functions on groups, semigroups, etc.positive: 11: 45M20 Positive solutionspositive: 12: 46L57 Derivations, dissipations and positive semigroups in C∗-algebraspositive: 13: 47B65 Positive operators and order-bounded operatorspositive: 14: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacespossible: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
post: 1: 03D03 Thue and Post systems, etc.post: 2: 03G20 Lukasiewicz and Post algebras [See also]06D25, 06D30post: 3: 06D25 Post algebras [See also]03G20
postdoctoral: 1: 97A70 Theses and postdoctoral thesespostnikov: 1: 55S45 Postnikov systems, k-invariantspotential: 1: 31-XX Potential theory For probabilistic potential theory, see 60J45potential: 2: 31-XX Potential theory For probabilistic potential theory, see 60J45potential: 3: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14potential: 4: 31C20 Discrete potential theory and numerical methodspotential: 5: 31C40 Fine potential theorypotential: 6: 31C45 Other generalizations (nonlinear potential theory, etc.)potential: 7: 31Dxx Axiomatic potential theorypotential: 8: 31D05 Axiomatic potential theorypotential: 9: 31Exx Potential theory on metric spacespotential: 10: 31E05 Potential theory on metric spacespotential: 11: 47G40 Potential operators [See also]31-XXpotential: 12: 60J45 Probabilistic potential theory [See also]31Cxx, 31D05potential: 13: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30potential: 14: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30potential: 15: 76B07 Free-surface potential flowspotential: 16: 81U05 2-body potential scattering theory [See also]34E20 for WKB methodspotential: 17: 81U10 n-body potential scattering theory
potentials: 1: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C85potentials: 2: 31B15 Potentials and capacities, extremal lengthpotentials: 3: 31C15 Potentials and capacitiespotentials: 4: 86A20 Potentials, prospecting
potts: 1: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphspower: 1: 11A15 Power residues, reciprocitypower: 2: 11D88 p-adic and power series fieldspower: 3: 13F25 Formal power series rings [See also]13J05power: 4: 13J05 Power series rings [See also]13F25power: 5: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxpower: 6: 30B10 Power series (including lacunary series)power: 7: 30B20 Random power seriespower: 8: 30B30 Boundary behavior of power series, over-convergencepower: 9: 32A05 Power series, series of functionspower: 10: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)power: 11: 40G10 Abel, Borel and power series methods
power-associative: 1: 17A05 Power-associative ringsprufer: 1: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizations
practical: 1: 97F90 Real life mathematics, practical arithmeticpre-greek: 1: 01A15 Indigenous European cultures (pre-Greek, etc.)
pre-hilbert: 1: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces withsemidefinite inner product)
pre-numerical: 1: 97F20 Pre-numerical stage, concept of numbers
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preadditive: 1: 18E05 Preadditive, additive categoriesprecategories: 1: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]
preconditioners: 1: 65F08 Preconditioners for iterative methodsprediction: 1: 60G25 Prediction theory [See also]62M20prediction: 2: 62M20 Prediction [See also]60G25; filtering [See also]60G35, 93E10, 93E11
preferences: 1: 91B08 Individual preferencespreferences: 2: 91B10 Group preferences
prefix: 1: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q45prehomogeneous: 1: 11S90 Prehomogeneous vector spaces
preorders: 1: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XXpreparation: 1: 32B05 Analytic algebras and generalizations, preparation theoremsprescribed: 1: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,53C42prescribed: 2: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,57R40, 57R42
presentability: 1: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)presentable: 1: 18C35 Accessible and locally presentable categories
presentation: 1: 13E15 Rings and modules of finite generation or presentation; number of generatorspresentations: 1: 19C20 Symbols, presentations and stability of K2
presentations: 2: 20F05 Generators, relations, and presentationspresentations: 3: 57M05 Fundamental group, presentations, free differential calculus
presented: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-tic and similar approaches see 03F55
preservation: 1: 03C40 Interpolation, preservation, definabilitypreserver: 1: 15A86 Linear preserver problems
preservers: 1: 47B49 Transformers, preservers (operators on spaces of operators)preserving: 1: 18A35 Categories admitting limits (complete categories), functors preserving limits,completionspreserving: 2: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometricalstructures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40preserving: 3: 37A40 Nonsingular (and infinite-measure preserving) transformationspresheaves: 1: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N30presheaves: 2: 54B40 Presheaves and sheaves [See also]18F20
price: 1: 91B24 Price theory and market structurepricing: 1: 91B25 Asset pricing modelsprimal: 1: 08A40 Operations, polynomials, primal algebras
primality: 1: 11A51 Factorization; primalityprimality: 2: 11Y11 Primalityprimarily: 1: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxprimary: 1: 20K10 Torsion groups, primary groups and generalized primary groupsprimary: 2: 20K10 Torsion groups, primary groups and generalized primary groupsprimary: 3: 55S05 Primary cohomology operations
prime: 1: 11R44 Distribution of prime ideals [See also]11N05prime: 2: 16N60 Prime and semiprime rings [See also]16D60, 16U10prime: 3: 30D40 Cluster sets, prime ends, boundary behavior
primes: 1: 11A41 Primesprimes: 2: 11L20 Sums over primesprimes: 3: 11N05 Distribution of primesprimes: 4: 11N13 Primes in progressions [See also]11B25primes: 5: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuesprimes: 6: 11N80 Generalized primes and integersprimes: 7: 11P32 Goldbach-type theorems; other additive questions involving primes
primitive: 1: 11A07 Congruences; primitive roots; residue systemsprimitive: 2: 16D60 Simple and semisimple modules, primitive rings and idealsprimitive: 3: 20B15 Primitive groupsprincipal: 1: 13F10 Principal ideal rings
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principal: 2: 62H25 Factor analysis and principal components; correspondence analysisprinciple: 1: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
subordinationprinciple: 2: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;
subordinationprinciple: 3: 70H25 Hamilton’s principleprinciple: 4: 74G50 Saint-Venant’s principle
principles: 1: 03E60 Determinacy principlesprinciples: 2: 35B50 Maximum principlesprinciples: 3: 35B51 Comparison principlesprinciples: 4: 37D35 Thermodynamic formalism, variational principles, equilibrium statesprinciples: 5: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawsprinciples: 6: 49Sxx Variational principles of physicsprinciples: 7: 49S05 Variational principles of physics (should also be assigned at least one other classification
number in section 49)principles: 8: 58E30 Variational principlesprinciples: 9: 60F17 Functional limit theorems; invariance principlesprinciples: 10: 70H30 Other variational principles
priori: 1: 35B45 A priori estimatesprobabilistic: 1: 05D40 Probabilistic methodsprobabilistic: 2: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmsprobabilistic: 3: 20Pxx Probabilistic methods in group theory [See also]60Bxxprobabilistic: 4: 20P05 Probabilistic methods in group theory [See also]60Bxxprobabilistic: 5: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E15probabilistic: 6: 31-XX Potential theory For probabilistic potential theory, see 60J45probabilistic: 7: 42A61 Probabilistic methodsprobabilistic: 8: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxprobabilistic: 9: 46S50 Functional analysis in probabilistic metric linear spacesprobabilistic: 10: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70probabilistic: 11: 54E70 Probabilistic metric spacesprobabilistic: 12: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxprobabilistic: 13: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)probabilistic: 14: 60J45 Probabilistic potential theory [See also]31Cxx, 31D05probabilistic: 15: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35probabilistic: 16: 65M75 Probabilistic methods, particle methods, etc.probabilistic: 17: 65N75 Probabilistic methods, particle methods, etc.probabilistic: 18: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85probabilistic: 19: 81P16 Quantum state spaces, operational and probabilistic conceptsprobabilistic: 20: 91A60 Probabilistic games; gambling [See also]60G40
probability: 1: 03B48 Probability and inductive logic [See also]60A05probability: 2: 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnelintegrals)probability: 3: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10probability: 4: 46L53 Noncommutative probability and statisticsprobability: 5: 46L54 Free probability and free operator algebrasprobability: 6: 46N30 Applications in probability theory and statisticsprobability: 7: 47N30 Applications in probability theory and statisticsprobability: 8: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXprobability: 9: 60Axx Foundations of probability theoryprobability: 10: 60A86 Fuzzy probabilityprobability: 11: 60Bxx Probability theory on algebraic and topological structuresprobability: 12: 60B05 Probability measures on topological spacesprobability: 13: 60B10 Convergence of probability measures
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probability: 14: 60B11 Probability theory on linear topological spaces [See also]28C20probability: 15: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationprobability: 16: 60Cxx Combinatorial probabilityprobability: 17: 60C05 Combinatorial probabilityprobability: 18: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C65probability: 19: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C65probability: 20: 65C50 Other computational problems in probabilityprobability: 21: 68Q87 Probability in computer science (algorithm analysis, random structures, phasetransitions, etc.) [See also]68W20, 68W40probability: 22: 94B70 Error probabilityprobability: 23: 97Kxx Combinatorics, graph theory, probability theory, statisticsprobability: 24: 97K50 Probability theory
problem: 1: 00A07 Problem booksproblem: 2: 11D07 The Frobenius problemproblem: 3: 11P05 Waring’s problem and variantsproblem: 4: 14C34 Torelli problem [See also]32G20problem: 5: 14H42 Theta functions; Schottky problem [See also]14K25, 32G20problem: 6: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)problem: 7: 14R15 Jacobian problem [See also]13F20problem: 8: 32C55 The Levi problem in complex spaces; generalizationsproblem: 9: 32E40 The Levi problemproblem: 10: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)problem: 11: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)problem: 12: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)problem: 13: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)problem: 14: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J10problem: 15: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)problem: 16: 57N50 Sn − 1⊂ En, Schoenflies problemproblem: 17: 68Q25 Analysis of algorithms and problem complexity [See also]68W40problem: 18: 68T20 Problem solving (heuristics, search strategies, etc.)problem: 19: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxxproblem: 20: 97U40 Problem books. Competitions. Examinations
problems: 1: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R15problems: 2: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxxproblems: 3: 05B45 Tessellation and tiling problems [See also]52C20, 52C22problems: 4: 05C35 Extremal problems [See also]90C35problems: 5: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)problems: 6: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10problems: 7: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R15problems: 8: 11A63 Radix representation; digital problems For metric results, see 11K16problems: 9: 11D85 Representation problems [See also]11P55problems: 10: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxproblems: 11: 11P70 Inverse problems of additive number theory, including sumsetsproblems: 12: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13problems: 13: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13problems: 14: 14D23 Stacks and moduli problemsproblems: 15: 14E22 Ramification problems [See also]11S15problems: 16: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxx
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Mathematics Subject Classification 2010
problems: 17: 14M07 Low codimension problemsproblems: 18: 14N10 Enumerative problems (combinatorial problems)problems: 19: 14N10 Enumerative problems (combinatorial problems)problems: 20: 14N15 Classical problems, Schubert calculusproblems: 21: 14N30 Adjunction problemsproblems: 22: 15A29 Inverse problemsproblems: 23: 15A83 Matrix completion problemsproblems: 24: 15A86 Linear preserver problemsproblems: 25: 19B37 Congruence subgroup problems [See also]20H05problems: 26: 20A10 Metamathematical considerations For word problems, see 20F10problems: 27: 20D60 Arithmetic and combinatorial problemsproblems: 28: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70problems: 29: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70problems: 30: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F10problems: 31: 30B60 Completeness problems, closure of a system of functionsproblems: 32: 30C50 Coefficient problems for univalent and multivalent functionsproblems: 33: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsproblems: 34: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsproblems: 35: 30E05 Moment problems, interpolation problemsproblems: 36: 30E05 Moment problems, interpolation problemsproblems: 37: 30E25 Boundary value problems [See also]45Exxproblems: 38: 31A25 Boundary value and inverse problemsproblems: 39: 31B20 Boundary value and inverse problemsproblems: 40: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15problems: 41: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15problems: 42: 32H50 Iteration problemsproblems: 43: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation
of solutionsproblems: 44: 34A55 Inverse problemsproblems: 45: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxproblems: 46: 34B05 Linear boundary value problemsproblems: 47: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterproblems: 48: 34B08 Parameter dependent boundary value problemsproblems: 49: 34B09 Boundary eigenvalue problemsproblems: 50: 34B10 Nonlocal and multipoint boundary value problemsproblems: 51: 34B15 Nonlinear boundary value problemsproblems: 52: 34B16 Singular nonlinear boundary value problemsproblems: 53: 34B18 Positive solutions of nonlinear boundary value problemsproblems: 54: 34B37 Boundary value problems with impulsesproblems: 55: 34B40 Boundary value problems on infinite intervalsproblems: 56: 34B45 Boundary value problems on graphs and networksproblems: 57: 34Hxx Control problems [See also]49J15, 49K15, 93C15problems: 58: 34H05 Control problems [See also]49J15, 49K15, 93C15problems: 59: 34K10 Boundary value problemsproblems: 60: 34K29 Inverse problemsproblems: 61: 34K35 Control problems [See also]49J21, 49K21, 93C23problems: 62: 34M40 Stokes phenomena and connection problems (linear and nonlinear)problems: 63: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)problems: 64: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20problems: 65: 35A01 Existence problems: global existence, local existence, non-existenceproblems: 66: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
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Mathematics Subject Classification 2010
problems: 67: 35E15 Initial value problemsproblems: 68: 35F10 Initial value problems for linear first-order equationsproblems: 69: 35F15 Boundary value problems for linear first-order equationsproblems: 70: 35F16 Initial-boundary value problems for linear first-order equationsproblems: 71: 35F25 Initial value problems for nonlinear first-order equationsproblems: 72: 35F30 Boundary value problems for nonlinear first-order equationsproblems: 73: 35F31 Initial-boundary value problems for nonlinear first-order equationsproblems: 74: 35F40 Initial value problems for linear first-order systemsproblems: 75: 35F45 Boundary value problems for linear first-order systemsproblems: 76: 35F46 Initial-boundary value problems for linear first-order systemsproblems: 77: 35F55 Initial value problems for nonlinear first-order systemsproblems: 78: 35F60 Boundary value problems for nonlinear first-order systemsproblems: 79: 35F61 Initial-boundary value problems for nonlinear first-order systemsproblems: 80: 35G10 Initial value problems for linear higher-order equationsproblems: 81: 35G15 Boundary value problems for linear higher-order equationsproblems: 82: 35G16 Initial-boundary value problems for linear higher-order equationsproblems: 83: 35G25 Initial value problems for nonlinear higher-order equationsproblems: 84: 35G30 Boundary value problems for nonlinear higher-order equationsproblems: 85: 35G31 Initial-boundary value problems for nonlinear higher-order equationsproblems: 86: 35G40 Initial value problems for linear higher-order systemsproblems: 87: 35G45 Boundary value problems for linear higher-order systemsproblems: 88: 35G46 Initial-boundary value problems for linear higher-order systemsproblems: 89: 35G55 Initial value problems for nonlinear higher-order systemsproblems: 90: 35G60 Boundary value problems for nonlinear higher-order systemsproblems: 91: 35G61 Initial-boundary value problems for nonlinear higher-order systemsproblems: 92: 35J25 Boundary value problems for second-order elliptic equationsproblems: 93: 35J40 Boundary value problems for higher-order elliptic equationsproblems: 94: 35J56 Boundary value problems for first-order elliptic systemsproblems: 95: 35J57 Boundary value problems for second-order elliptic systemsproblems: 96: 35J58 Boundary value problems for higher-order elliptic systemsproblems: 97: 35J65 Nonlinear boundary value problems for linear elliptic equationsproblems: 98: 35J66 Nonlinear boundary value problems for nonlinear elliptic equationsproblems: 99: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J40problems: 100: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J40problems: 101: 35K15 Initial value problems for second-order parabolic equationsproblems: 102: 35K20 Initial-boundary value problems for second-order parabolic equationsproblems: 103: 35K30 Initial value problems for higher-order parabolic equationsproblems: 104: 35K35 Initial-boundary value problems for higher-order parabolic equationsproblems: 105: 35K45 Initial value problems for second-order parabolic systemsproblems: 106: 35K46 Initial value problems for higher-order parabolic systemsproblems: 107: 35K51 Initial-boundary value problems for second-order parabolic systemsproblems: 108: 35K52 Initial-boundary value problems for higher-order parabolic systemsproblems: 109: 35K60 Nonlinear initial value problems for linear parabolic equationsproblems: 110: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsproblems: 111: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40problems: 112: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40problems: 113: 35L03 Initial value problems for first-order hyperbolic equationsproblems: 114: 35L04 Initial-boundary value problems for first-order hyperbolic equationsproblems: 115: 35L15 Initial value problems for second-order hyperbolic equationsproblems: 116: 35L20 Initial-boundary value problems for second-order hyperbolic equationsproblems: 117: 35L30 Initial value problems for higher-order hyperbolic equationsproblems: 118: 35L35 Initial-boundary value problems for higher-order hyperbolic equationsproblems: 119: 35L45 Initial value problems for first-order hyperbolic systems
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problems: 120: 35L50 Initial-boundary value problems for first-order hyperbolic systemsproblems: 121: 35L52 Initial value problems for second-order hyperbolic systemsproblems: 122: 35L53 Initial-boundary value problems for second-order hyperbolic systemsproblems: 123: 35L56 Initial value problems for higher-order hyperbolic systemsproblems: 124: 35L57 Initial-boundary value problems for higher-order hyperbolic systemsproblems: 125: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J40problems: 126: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J40problems: 127: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J40problems: 128: 35M11 Initial value problems for equations of mixed typeproblems: 129: 35M12 Boundary value problems for equations of mixed typeproblems: 130: 35M13 Initial-boundary value problems for equations of mixed typeproblems: 131: 35M31 Initial value problems for systems of mixed typeproblems: 132: 35M32 Boundary value problems for systems of mixed typeproblems: 133: 35M33 Initial-boundary value problems for systems of mixed typeproblems: 134: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J40problems: 135: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40problems: 136: 35N20 Overdetermined initial value problemsproblems: 137: 35N25 Overdetermined boundary value problemsproblems: 138: 35N30 Overdetermined initial-boundary value problemsproblems: 139: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F05problems: 140: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theoryproblems: 141: 35Q15 Riemann-Hilbert problems [See also]30E25, 31A25, 31B20problems: 142: 35R25 Improperly posed problemsproblems: 143: 35R30 Inverse problemsproblems: 144: 35R35 Free boundary problemsproblems: 145: 35R37 Moving boundary problemsproblems: 146: 35S10 Initial value problems for pseudodifferential operatorsproblems: 147: 35S11 Initial-boundary value problems for pseudodifferential operatorsproblems: 148: 35S15 Boundary value problems for pseudodifferential operatorsproblems: 149: 37J20 Bifurcation problemsproblems: 150: 37J25 Stability problemsproblems: 151: 37K45 Stability problemsproblems: 152: 37K50 Bifurcation problemsproblems: 153: 37L15 Stability problemsproblems: 154: 37M20 Computational methods for bifurcation problemsproblems: 155: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)problems: 156: 42A05 Trigonometric polynomials, inequalities, extremal problemsproblems: 157: 42A70 Trigonometric moment problemsproblems: 158: 44A60 Moment problemsproblems: 159: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A75problems: 160: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A75problems: 161: 45Qxx Inverse problemsproblems: 162: 45Q05 Inverse problemsproblems: 163: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R30problems: 164: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A60problems: 165: 47A75 Eigenvalue problems [See also]47J10, 49R05problems: 166: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10problems: 167: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R30
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problems: 168: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05problems: 169: 49J05 Free problems in one independent variableproblems: 170: 49J10 Free problems in two or more independent variablesproblems: 171: 49J15 Optimal control problems involving ordinary differential equationsproblems: 172: 49J20 Optimal control problems involving partial differential equationsproblems: 173: 49J21 Optimal control problems involving relations other than differential equationsproblems: 174: 49J27 Problems in abstract spaces [See also]90C48, 93C25problems: 175: 49J35 Minimax problemsproblems: 176: 49J55 Problems involving randomness [See also]93E20problems: 177: 49K05 Free problems in one independent variableproblems: 178: 49K10 Free problems in two or more independent variablesproblems: 179: 49K15 Problems involving ordinary differential equationsproblems: 180: 49K20 Problems involving partial differential equationsproblems: 181: 49K21 Problems involving relations other than differential equationsproblems: 182: 49K27 Problems in abstract spaces [See also]90C48, 93C25problems: 183: 49K35 Minimax problemsproblems: 184: 49K45 Problems involving randomness [See also]93E20problems: 185: 49N05 Linear optimal control problems [See also]93C05problems: 186: 49N10 Linear-quadratic problemsproblems: 187: 49N25 Impulsive optimal control problemsproblems: 188: 49N30 Problems with incomplete information [See also]93C41problems: 189: 49N45 Inverse problemsproblems: 190: 49Q20 Variational problems in a geometric measure-theoretic settingproblems: 191: 51E23 Spreads and packing problemsproblems: 192: 51M04 Elementary problems in Euclidean geometriesproblems: 193: 51M09 Elementary problems in hyperbolic and elliptic geometriesproblems: 194: 51M16 Inequalities and extremum problems For convex problems, see 52A40problems: 195: 51M16 Inequalities and extremum problems For convex problems, see 52A40problems: 196: 52A37 Other problems of combinatorial convexityproblems: 197: 52A40 Inequalities and extremum problemsproblems: 198: 52B60 Isoperimetric problems for polytopesproblems: 199: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxproblems: 200: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E07problems: 201: 58D27 Moduli problems for differential geometric structuresproblems: 202: 58D29 Moduli problems for topological structuresproblems: 203: 58Exx Variational problems in infinite-dimensional spacesproblems: 204: 58E10 Applications to the theory of geodesics (problems in one independent variable)problems: 205: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05problems: 206: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.problems: 207: 58E35 Variational inequalities (global problems)problems: 208: 58J32 Boundary value problems on manifoldsproblems: 209: 58J47 Propagation of singularities; initial value problemsproblems: 210: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxxproblems: 211: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60problems: 212: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxproblems: 213: 62C10 Bayesian problems; characterization of Bayes proceduresproblems: 214: 62C25 Compound decision problemsproblems: 215: 65C50 Other computational problems in probabilityproblems: 216: 65C60 Computational problems in statisticsproblems: 217: 65F18 Inverse eigenvalue problemsproblems: 218: 65J20 Improperly posed problems; regularizationproblems: 219: 65J22 Inverse problemsproblems: 220: 65K15 Numerical methods for variational inequalities and related problemsproblems: 221: 65L05 Initial value problems
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problems: 222: 65L08 Improperly posed problemsproblems: 223: 65L09 Inverse problemsproblems: 224: 65L10 Boundary value problemsproblems: 225: 65L11 Singularly perturbed problemsproblems: 226: 65L15 Eigenvalue problemsproblems: 227: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsproblems: 228: 65M30 Improperly posed problemsproblems: 229: 65M32 Inverse problemsproblems: 230: 65Nxx Partial differential equations, boundary value problemsproblems: 231: 65N20 Ill-posed problemsproblems: 232: 65N21 Inverse problemsproblems: 233: 65N25 Eigenvalue problemsproblems: 234: 65Pxx Numerical problems in dynamical systems [See also]37Mxxproblems: 235: 65P30 Bifurcation problemsproblems: 236: 65R30 Improperly posed problemsproblems: 237: 65R32 Inverse problemsproblems: 238: 68M07 Mathematical problems of computer architectureproblems: 239: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15problems: 240: 70E50 Stability problemsproblems: 241: 70F05 Two-body problemsproblems: 242: 70F07 Three-body problemsproblems: 243: 70F10 n-body problemsproblems: 244: 70F17 Inverse problemsproblems: 245: 70F40 Problems with frictionproblems: 246: 70H14 Stability problemsproblems: 247: 70J50 Systems arising from the discretization of structural vibration problemsproblems: 248: 74Gxx Equilibrium (steady-state) problemsproblems: 249: 74G75 Inverse problemsproblems: 250: 74Hxx Dynamical problemsproblems: 251: 74J25 Inverse problemsproblems: 252: 74Mxx Special kinds of problemsproblems: 253: 74N30 Problems involving hysteresisproblems: 254: 74Q05 Homogenization in equilibrium problemsproblems: 255: 74Q10 Homogenization and oscillations in dynamical problemsproblems: 256: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingproblems: 257: 78A46 Inverse scattering problemsproblems: 258: 80A22 Stefan problems, phase changes, etc. [See also]74Nxxproblems: 259: 80A23 Inverse problemsproblems: 260: 81Sxx General quantum mechanics and problems of quantizationproblems: 261: 81U40 Inverse scattering problemsproblems: 262: 82B24 Interface problems; diffusion-limited aggregationproblems: 263: 82C24 Interface problems; diffusion-limited aggregationproblems: 264: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)problems: 265: 85A30 Hydrodynamic and hydromagnetic problems [See also]76Y05problems: 266: 86A17 Global dynamics, earthquake problemsproblems: 267: 86A22 Inverse problems [See also]35R30problems: 268: 86A30 Geodesy, mapping problemsproblems: 269: 86A60 Geological problemsproblems: 270: 90B20 Traffic problemsproblems: 271: 90C06 Large-scale problemsproblems: 272: 90C08 Special problems of linear programming (transportation, multi-index, etc.)problems: 273: 90C33 Complementarity and equilibrium problems and variational inequalities (finite
dimensions)problems: 274: 90C47 Minimax problems [See also]49K35
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problems: 275: 90C60 Abstract computational complexity for mathematical programming problems[See also]68Q25
problems: 276: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)[See also]80A30
problems: 277: 92D15 Problems related to evolutionproblems: 278: 93B50 Synthesis problemsproblems: 279: 93B55 Pole and zero placement problemsproblems: 280: 93B60 Eigenvalue problemsproblems: 281: 93C41 Problems with incomplete informationproblems: 282: 93C83 Control problems involving computers (process control, etc.)
procedures: 1: 47J25 Iterative procedures [See also]65J15procedures: 2: 62C10 Bayesian problems; characterization of Bayes proceduresprocedures: 3: 62C12 Empirical decision procedures; empirical Bayes proceduresprocedures: 4: 62C12 Empirical decision procedures; empirical Bayes proceduresprocedures: 5: 62C20 Minimax proceduresprocedures: 6: 62F35 Robustness and adaptive proceduresprocedures: 7: 83C25 Approximation procedures, weak fieldsprocedures: 8: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)
proceedings: 1: 00Bxx Conference proceedings and collections of papersproceedings: 2: 00B20 Proceedings of conferences of general interestproceedings: 3: 00B25 Proceedings of conferences of miscellaneous specific interest
process: 1: 68Q85 Models and methods for concurrent and distributed computing (process algebras,bisimulation, transition nets, etc.)
process: 2: 93C83 Control problems involving computers (process control, etc.)processes: 1: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10processes: 2: 40Axx Convergence and divergence of infinite limiting processesprocesses: 3: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxprocesses: 4: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxprocesses: 5: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60processes: 6: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXprocesses: 7: 60Gxx Stochastic processesprocesses: 8: 60G05 Foundations of stochastic processesprocesses: 9: 60G07 General theory of processesprocesses: 10: 60G10 Stationary processesprocesses: 11: 60G12 General second-order processesprocesses: 12: 60G15 Gaussian processesprocesses: 13: 60G18 Self-similar processesprocesses: 14: 60G20 Generalized stochastic processesprocesses: 15: 60G22 Fractional processes, including fractional Brownian motionprocesses: 16: 60G51 Processes with independent increments; Levy processesprocesses: 17: 60G51 Processes with independent increments; Levy processesprocesses: 18: 60G52 Stable processesprocesses: 19: 60G55 Point processesprocesses: 20: 60G70 Extreme value theory; extremal processesprocesses: 21: 60Jxx Markov processesprocesses: 22: 60J05 Discrete-time Markov processes on general state spacesprocesses: 23: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)processes: 24: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40processes: 25: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40processes: 26: 60J25 Continuous-time Markov processes on general state spacesprocesses: 27: 60J27 Continuous-time Markov processes on discrete state spacesprocesses: 28: 60J28 Applications of continuous-time Markov processes on discrete state spaces
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processes: 29: 60J40 Right processesprocesses: 30: 60J60 Diffusion processes [See also]58J65processes: 31: 60J75 Jump processesprocesses: 32: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)processes: 33: 60J85 Applications of branching processes [See also]92Dxxprocesses: 34: 60Kxx Special processesprocesses: 35: 60K15 Markov renewal processes, semi-Markov processesprocesses: 36: 60K15 Markov renewal processes, semi-Markov processesprocesses: 37: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxprocesses: 38: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C43processes: 39: 60K37 Processes in random environmentsprocesses: 40: 60K40 Other physical applications of random processesprocesses: 41: 62Mxx Inference from stochastic processesprocesses: 42: 62M02 Markov processes: hypothesis testingprocesses: 43: 62M05 Markov processes: estimationprocesses: 44: 62M07 Non-Markovian processes: hypothesis testingprocesses: 45: 62M09 Non-Markovian processes: estimationprocesses: 46: 62M30 Spatial processesprocesses: 47: 62M86 Inference from stochastic processes and fuzzinessprocesses: 48: 82C70 Transport processesprocesses: 49: 90C40 Markov and semi-Markov decision processesprocesses: 50: 97C30 Cognitive processes, learning theoriesprocesses: 51: 97C70 Teaching-learning processesprocesses: 52: 97K60 Distributions and stochastic processesprocesses: 53: 97Q30 Cognitive processes
processing: 1: 68T50 Natural language processing [See also]03B65processing: 2: 68U10 Image processingprocessing: 3: 68U15 Text processing; mathematical typographyprocessing: 4: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A12processing: 5: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U10
product: 1: 28A35 Measures and integrals in product spacesproduct: 2: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxproduct: 3: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)product: 4: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50product: 5: 47L65 Crossed product algebras (analytic crossed products)product: 6: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)product: 7: 54B10 Product spacesproduct: 8: 55U25 Homology of a product, Kunneth formula
production: 1: 90B30 Production modelsproduction: 2: 91B38 Production theory, theory of the firm
products: 1: 05C76 Graph operations (line graphs, products, etc.)products: 2: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30products: 3: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A30products: 4: 08B26 Subdirect products and subdirect irreducibilityproducts: 5: 11H46 Products of linear formsproducts: 6: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exxproducts: 7: 15A69 Multilinear algebra, tensor productsproducts: 8: 16K20 Finite-dimensional For crossed products, see 16S35products: 9: 16S35 Twisted and skew group rings, crossed productsproducts: 10: 16S40 Smash products of general Hopf actions [See also]16T05products: 11: 16S60 Rings of functions, subdirect products, sheaves of rings
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Mathematics Subject Classification 2010
products: 12: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
products: 13: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
products: 14: 20D40 Products of subgroupsproducts: 15: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsproducts: 16: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationsproducts: 17: 20E22 Extensions, wreath products, and other compositions [See also]20J05products: 18: 20K25 Direct sums, direct products, etc.products: 19: 30J10 Blaschke productsproducts: 20: 40A20 Convergence and divergence of infinite productsproducts: 21: 42A55 Lacunary series of trigonometric and other functions; Riesz productsproducts: 22: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20products: 23: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L20products: 24: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)products: 25: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)products: 26: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)products: 27: 46L06 Tensor products of C∗-algebrasproducts: 28: 46L09 Free products of C∗-algebrasproducts: 29: 46M05 Tensor products [See also]46A32, 46B28, 47A80products: 30: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)products: 31: 47A80 Tensor products of operators [See also]46M05products: 32: 47L65 Crossed product algebras (analytic crossed products)products: 33: 53D55 Deformation quantization, star productsproducts: 34: 55N45 Products and intersectionsproducts: 35: 55Q15 Whitehead products and generalizationsproducts: 36: 55S15 Symmetric products, cyclic productsproducts: 37: 55S15 Symmetric products, cyclic productsproducts: 38: 55S30 Massey products
profession: 1: 01A80 Sociology (and profession) of mathematicsprofinite: 1: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)profinite: 2: 20E18 Limits, profinite groupsprogram: 1: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E57program: 2: 14E30 Minimal model program (Mori theory, extremal rays)program: 3: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D24program: 4: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70
programming: 1: 35Q90 PDEs in connection with mathematical programmingprogramming: 2: 46N10 Applications in optimization, convex analysis, mathematical programming, economicsprogramming: 3: 47N10 Applications in optimization, convex analysis, mathematical programming, economicsprogramming: 4: 49Lxx Hamilton-Jacobi theories, including dynamic programmingprogramming: 5: 49L20 Dynamic programming methodprogramming: 6: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxxprogramming: 7: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)programming: 8: 65Kxx Mathematical programming, optimization and variational techniquesprogramming: 9: 65K05 Mathematical programming methods [See also]90Cxxprogramming: 10: 68N15 Programming languagesprogramming: 11: 68N17 Logic programmingprogramming: 12: 68N18 Functional programming and lambda calculus [See also]03B40programming: 13: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,
etc.)programming: 14: 90-XX Operations research, mathematical programmingprogramming: 15: 90Cxx Mathematical programming [See also]49Mxx, 65Kxx
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Mathematics Subject Classification 2010
programming: 16: 90C05 Linear programmingprogramming: 17: 90C08 Special problems of linear programming (transportation, multi-index, etc.)programming: 18: 90C09 Boolean programmingprogramming: 19: 90C10 Integer programmingprogramming: 20: 90C11 Mixed integer programmingprogramming: 21: 90C15 Stochastic programmingprogramming: 22: 90C20 Quadratic programmingprogramming: 23: 90C22 Semidefinite programmingprogramming: 24: 90C25 Convex programmingprogramming: 25: 90C26 Nonconvex programming, global optimizationprogramming: 26: 90C29 Multi-objective and goal programmingprogramming: 27: 90C30 Nonlinear programmingprogramming: 28: 90C32 Fractional programmingprogramming: 29: 90C34 Semi-infinite programmingprogramming: 30: 90C35 Programming involving graphs or networks [See also]90C27programming: 31: 90C39 Dynamic programming [See also]49L20programming: 32: 90C48 Programming in abstract spacesprogramming: 33: 90C55 Methods of successive quadratic programming typeprogramming: 34: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q25programming: 35: 90C70 Fuzzy programmingprogramming: 36: 90C90 Applications of mathematical programmingprogramming: 37: 97N60 Mathematical programmingprogramming: 38: 97P40 Programming languagesprogramming: 39: 97P50 Programming techniques
programs: 1: 52A41 Convex functions and convex programs [See also]26B25, 90C25programs: 2: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areaprograms: 3: 97N80 Mathematical software, computer programsprograms: 4: 97R10 Comprehensive works, collections of programsprograms: 5: 97R70 User programs, administrative applications
progressions: 1: 11B25 Arithmetic progressions [See also]11N13progressions: 2: 11N13 Primes in progressions [See also]11B25projections: 1: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.projective: 1: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10projective: 2: 13C10 Projective and free modules and ideals [See also]19A13projective: 3: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,Galois theory)projective: 4: 14Nxx Projective and enumerative geometry [See also]51-XXprojective: 5: 14N05 Projective techniques [See also]51N35projective: 6: 16D40 Free, projective, and flat modules and ideals [See also]19A13projective: 7: 18G25 Relative homological algebra, projective classesprojective: 8: 19A13 Stability for projective modules [See also]13C10projective: 9: 20C25 Projective representations and multipliersprojective: 10: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40projective: 11: 46M10 Projective and injective objects [See also]46A22projective: 12: 46M40 Inductive and projective limits [See also]46A13projective: 13: 51A05 General theory and projective geometriesprojective: 14: 51A35 Non-Desarguesian affine and projective planesprojective: 15: 51A45 Incidence structures imbeddable into projective geometriesprojective: 16: 51E15 Affine and projective planesprojective: 17: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxprojective: 18: 51J10 Projective incidence groupsprojective: 19: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,Veronesians and their generalizations) [See also]14M15projective: 20: 51N15 Projective analytic geometryprojective: 21: 53A20 Projective differential geometry
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Mathematics Subject Classification 2010
projective: 22: 53B10 Projective connectionsprojective: 23: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)[See also]03E15, 26A21, 28A05projectives: 1: 08B30 Injectives, projectivesprojectives: 2: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D50
prolongation: 1: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxxproof: 1: 03Fxx Proof theory and constructive mathematicsproof: 2: 03F03 Proof theory, generalproof: 3: 03F10 Functionals in proof theory
proof-theoretic: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
proofs: 1: 03B35 Mechanization of proofs and logical operations [See also]68T15proofs: 2: 03F07 Structure of proofsproofs: 3: 03F20 Complexity of proofs
propagation: 1: 35A21 Propagation of singularitiespropagation: 2: 58J47 Propagation of singularities; initial value problems
proper: 1: 32H35 Proper mappings, finiteness theoremsproper: 2: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32proper: 3: 55P57 Proper homotopy theory
properties: 1: 03C07 Basic properties of first-order languages and structuresproperties: 2: 03C50 Models with special properties (saturated, rigid, etc.)properties: 3: 03C52 Properties of classes of modelsproperties: 4: 06E20 Ring-theoretic properties [See also]16E50, 16G30properties: 5: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)[See also]13A05, 14M05properties: 6: 14F45 Topological propertiesproperties: 7: 16Nxx Radicals and radical properties of ringsproperties: 8: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction ofinverses, etc.)properties: 9: 18A22 Special properties of functors (faithful, full, etc.)properties: 10: 20A05 Axiomatics and elementary propertiesproperties: 11: 20D20 Sylow subgroups, Sylow properties, π-groups, π-structureproperties: 12: 20E25 Local propertiesproperties: 13: 20E26 Residual properties and generalizations; residually finite groupsproperties: 14: 20F69 Asymptotic properties of groupsproperties: 15: 22B05 General properties and structure of LCA groupsproperties: 16: 22D05 General properties and structure of locally compact groupsproperties: 17: 22E10 General properties and structure of complex Lie groups [See also]32M05properties: 18: 22E15 General properties and structure of real Lie groupsproperties: 19: 22E20 General properties and structure of other Lie groupsproperties: 20: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties[See also]17B65, 58B25, 58H05properties: 21: 22F05 General theory of group and pseudogroup actions For topological properties of spaceswith an action, see 57S20properties: 22: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27properties: 23: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27properties: 24: 26A30 Singular functions, Cantor functions, functions with other special propertiesproperties: 25: 26B35 Special properties of functions of several variables, Holder conditions, etc.properties: 26: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exxproperties: 27: 30Axx General propertiesproperties: 28: 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenicfunctions)
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properties: 29: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see32A22properties: 30: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see32A22properties: 31: 32S20 Global theory of singularities; cohomological properties [See also]14E15properties: 32: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exxproperties: 33: 34D05 Asymptotic propertiesproperties: 34: 35Bxx Qualitative properties of solutionsproperties: 35: 35E10 Convexity propertiesproperties: 36: 37B05 Transformations and group actions with special properties (minimality, distality,proximality, etc.)properties: 37: 37C20 Generic properties, structural stabilityproperties: 38: 37P35 Arithmetic properties of periodic pointsproperties: 39: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30properties: 40: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartzspaces, Montel spaces, etc.)properties: 41: 46A32 Spaces of linear operators; topological tensor products; approximation properties[See also]46B28, 46M05, 47L05, 47L20properties: 42: 46B22 Radon-Nikodym, Kreın-Milman and related properties [See also]46G10properties: 43: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,47L05, 47L20properties: 44: 47A11 Local spectral propertiesproperties: 45: 47B07 Operators defined by compactness propertiesproperties: 46: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,58-XX, especially 58Cxxproperties: 47: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxxproperties: 48: 52B15 Symmetry properties of polytopesproperties: 49: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)[See also]03Exx For ultrafilters, see 54D80properties: 50: 54C40 Algebraic properties of function spaces [See also]46J10properties: 51: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract(ANR), absolute retract spaces (general properties) [See also]55M15properties: 52: 54Dxx Fairly general propertiesproperties: 53: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)properties: 54: 54D70 Base propertiesproperties: 55: 54Fxx Special propertiesproperties: 56: 55P05 Homotopy extension properties, cofibrationsproperties: 57: 57P05 Local properties of generalized manifoldsproperties: 58: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismsproperties: 59: 58C07 Continuity properties of mappingsproperties: 60: 58D19 Group actions and symmetry propertiesproperties: 61: 58J70 Invariance and symmetry properties [See also]35A30properties: 62: 58K15 Topological properties of mappingsproperties: 63: 58K20 Algebraic and analytic properties of mappingsproperties: 64: 60G17 Sample path propertiesproperties: 65: 62F05 Asymptotic properties of testsproperties: 66: 62F12 Asymptotic properties of estimatorsproperties: 67: 62G20 Asymptotic propertiesproperties: 68: 74Exx Material properties given special treatmentproperties: 69: 74E30 Composite and mixture propertiesproperties: 70: 74P10 Optimization of other propertiesproperties: 71: 74Qxx Homogenization, determination of effective propertiesproperties: 72: 74Q20 Bounds on effective propertiesproportion: 1: 97F80 Ratio and proportion, percentages
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Mathematics Subject Classification 2010
propositional: 1: 03B05 Classical propositional logicpropositions: 1: 03E25 Axiom of choice and related propositionsprospecting: 1: 86A20 Potentials, prospecting
prospectives: 1: 01A67 Future prospectivesprotein: 1: 92D20 Protein sequences, DNA sequences
protocols: 1: 68M12 Network protocolsprovability: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; fortemporal logic, see 03B44; for provability logic, see also 03F45provability: 2: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,03G25, 06E25
proving: 1: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B35proving: 2: 97E50 Reasoning and proving in the mathematics classroom
proximality: 1: 37B05 Transformations and group actions with special properties (minimality, distality,proximality, etc.)proximity: 1: 54E05 Proximity structures and generalizations
prym: 1: 14H40 Jacobians, Prym varieties [See also]32G20pseudo-almost: 1: 34C27 Almost and pseudo-almost periodic solutionspseudo-almost: 2: 35B15 Almost and pseudo-almost periodic solutionspseudo-isotopy: 1: 57N37 Isotopy and pseudo-isotopy
pseudo-periodic: 1: 34K14 Almost and pseudo-periodic solutionspseudo-random: 1: 11K45 Pseudo-random numbers; Monte Carlo methods
pseudo-rigid: 1: 70F35 Collision of rigid or pseudo-rigid bodiespseudoanalytic: 1: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)
pseudocomplemented: 1: 06D15 Pseudocomplemented latticespseudoconvex: 1: 32Txx Pseudoconvex domainspseudoconvex: 2: 32T15 Strongly pseudoconvex domainspseudoconvex: 3: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries
pseudodifferential: 1: 32W25 Pseudodifferential operators in several complex variablespseudodifferential: 2: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J40pseudodifferential: 3: 35S05 Pseudodifferential operatorspseudodifferential: 4: 35S10 Initial value problems for pseudodifferential operatorspseudodifferential: 5: 35S11 Initial-boundary value problems for pseudodifferential operatorspseudodifferential: 6: 35S15 Boundary value problems for pseudodifferential operatorspseudodifferential: 7: 47Gxx Integral, integro-differential, and pseudodifferential operators [See also]58Jxxpseudodifferential: 8: 47G30 Pseudodifferential operators [See also]35Sxx, 58Jxxpseudodifferential: 9: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)pseudodifferential: 10: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxx
pseudodistances: 1: 32F45 Invariant metrics and pseudodistancespseudogroup: 1: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20pseudogroup: 2: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32pseudogroups: 1: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldspseudogroups: 2: 58H05 Pseudogroups and differentiable groupoids [See also]22A22, 22E65
pseudoholomorphic: 1: 32Q65 Pseudoholomorphic curvespseudohyperbolic: 1: 35L82 Pseudohyperbolic equations
pseudoinverses: 1: 65F20 Overdetermined systems, pseudoinversespseudolines: 1: 52C30 Planar arrangements of lines and pseudolines
pseudoparabolic: 1: 35K70 Ultraparabolic equations, pseudoparabolic equations, etc.pseudotrajectories: 1: 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)
pseudovarieties: 1: 20M07 Varieties and pseudovarieties of semigroupspsychology: 1: 62P15 Applications to psychologypsychology: 2: 91Exx Mathematical psychologypsychology: 3: 91E10 Cognitive psychologypsychology: 4: 97Cxx Psychology of mathematics education, research in mathematics education
psychophysics: 1: 91E30 Psychophysics and psychophysiology; perception
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psychophysiology: 1: 91E30 Psychophysics and psychophysiology; perceptionpublic: 1: 91B18 Public goodspurely: 1: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05pursuit: 1: 49N75 Pursuit and evasion gamespursuit: 2: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N75
pushouts: 1: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,equalizers, kernels, ends and coends, etc.)
pv-numbers: 1: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measurepythagorean: 1: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxquadrangles: 1: 51E12 Generalized quadrangles, generalized polygons
quadratic: 1: 11D09 Quadratic and bilinear equationsquadratic: 2: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63quadratic: 3: 11E04 Quadratic forms over general fieldsquadratic: 4: 11E08 Quadratic forms over local rings and fieldsquadratic: 5: 11E12 Quadratic forms over global rings and fieldsquadratic: 6: 11E16 General binary quadratic formsquadratic: 7: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesquadratic: 8: 11E25 Sums of squares and representations by other particular quadratic formsquadratic: 9: 11E41 Class numbers of quadratic and Hermitian formsquadratic: 10: 11E70 K-theory of quadratic and Hermitian formsquadratic: 11: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24quadratic: 12: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A66quadratic: 13: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45quadratic: 14: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)quadratic: 15: 11R11 Quadratic extensionsquadratic: 16: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exxquadratic: 17: 16S37 Quadratic and Koszul algebrasquadratic: 18: 17A45 Quadratic algebras (but not quadratic Jordan algebras)quadratic: 19: 17A45 Quadratic algebras (but not quadratic Jordan algebras)quadratic: 20: 19G05 Stability for quadratic modulesquadratic: 21: 90C20 Quadratic programmingquadratic: 22: 90C55 Methods of successive quadratic programming type
quadrature: 1: 65D32 Quadrature and cubature formulasquadratures: 1: 41A55 Approximate quadratures
qualitative: 1: 34Cxx Qualitative theory [See also]37-XXqualitative: 2: 34C60 Qualitative investigation and simulation of modelsqualitative: 3: 34K60 Qualitative investigation and simulation of modelsqualitative: 4: 35Bxx Qualitative properties of solutionsqualitative: 5: 45Mxx Qualitative behaviorqualitative: 6: 74G55 Qualitative behavior of solutionsquantales: 1: 06F07 Quantalesquantifier: 1: 03C10 Quantifier elimination, model completeness and related topics
quantifiers: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B48quantization: 1: 53D50 Geometric quantizationquantization: 2: 53D55 Deformation quantization, star productsquantization: 3: 81Sxx General quantum mechanics and problems of quantizationquantization: 4: 81S05 Canonical quantization, commutation relations and statisticsquantization: 5: 81S10 Geometry and quantization, symplectic methods [See also]53D50quantization: 6: 81S20 Stochastic quantizationquantization: 7: 81T70 Quantization in field theory; cohomological methods [See also]58D29quantization: 8: 83C45 Quantization of the gravitational field
quantizations: 1: 46L65 Quantizations, deformationsquantized: 1: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
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Mathematics Subject Classification 2010
[See also]16T20, 20G42, 81R50, 82B23quantized: 2: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50quantum: 1: 03G12 Quantum logic [See also]06C15, 81P10quantum: 2: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxquantum: 3: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D45quantum: 4: 16Txx Hopf algebras, quantum groups and related topicsquantum: 5: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R50quantum: 6: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B23quantum: 7: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50quantum: 8: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and
related topicsquantum: 9: 35Q40 PDEs in connection with quantum mechanicsquantum: 10: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)quantum: 11: 46N50 Applications in quantum physicsquantum: 12: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N35quantum: 13: 57R56 Topological quantum field theoriesquantum: 14: 58B32 Geometry of quantum groupsquantum: 15: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)quantum: 16: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicityquantum: 17: 68Q12 Quantum algorithms and complexity [See also]68Q05, 81P68quantum: 18: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A30quantum: 19: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A30quantum: 20: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80quantum: 21: 81-XX Quantum theoryquantum: 22: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15quantum: 23: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C15quantum: 24: 81P15 Quantum measurement theoryquantum: 25: 81P16 Quantum state spaces, operational and probabilistic conceptsquantum: 26: 81P40 Quantum coherence, entanglement, quantum correlationsquantum: 27: 81P40 Quantum coherence, entanglement, quantum correlationsquantum: 28: 81P45 Quantum information, communication, networks [See also]94A15, 94A17quantum: 29: 81P50 Quantum state estimation, approximate cloningquantum: 30: 81P68 Quantum computation [See also]68Q05, 68Q12quantum: 31: 81P70 Quantum coding (general)quantum: 32: 81P94 Quantum cryptography [See also]94A60quantum: 33: 81Qxx General mathematical topics and methods in quantum theoryquantum: 34: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsquantum: 35: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysisquantum: 36: 81Q12 Non-selfadjoint operator theory in quantum theoryquantum: 37: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.quantum: 38: 81Q37 Quantum dots, waveguides, ratchets, etc.quantum: 39: 81Q50 Quantum chaos [See also]37Dxxquantum: 40: 81Q60 Supersymmetry and quantum mechanicsquantum: 41: 81Q65 Alternative quantum mechanicsquantum: 42: 81Q80 Special quantum systems, such as solvable systemsquantum: 43: 81Q93 Quantum controlquantum: 44: 81Rxx Groups and algebras in quantum theoryquantum: 45: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B37quantum: 46: 81Sxx General quantum mechanics and problems of quantization
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Mathematics Subject Classification 2010
quantum: 47: 81S25 Quantum stochastic calculusquantum: 48: 81Txx Quantum field theory; related classical field theories [See also]70Sxxquantum: 49: 81T05 Axiomatic quantum field theory; operator algebrasquantum: 50: 81T08 Constructive quantum field theoryquantum: 51: 81T10 Model quantum field theoriesquantum: 52: 81T20 Quantum field theory on curved space backgroundsquantum: 53: 81T25 Quantum field theory on latticesquantum: 54: 81T28 Thermal quantum field theory [See also]82B30quantum: 55: 81V05 Strong interaction, including quantum chromodynamicsquantum: 56: 81V10 Electromagnetic interaction; quantum electrodynamicsquantum: 57: 81V65 Quantum dots [See also]82D20quantum: 58: 81V70 Many-body theory; quantum Hall effectquantum: 59: 81V80 Quantum opticsquantum: 60: 82B10 Quantum equilibrium statistical mechanics (general)quantum: 61: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)quantum: 62: 82D77 Quantum wave guides, quantum wires [See also]78A50quantum: 63: 82D77 Quantum wave guides, quantum wires [See also]78A50quantum: 64: 83C47 Methods of quantum field theory [See also]81T20quantum: 65: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)quantum: 66: 94A40 Channel models (including quantum)
quartic: 1: 11D25 Cubic and quartic equationsquartic: 2: 11R16 Cubic and quartic extensions
quasi-analytic: 1: 26E10 C∞-functions, quasi-analytic functions [See also]58C25quasi-analytic: 2: 30D60 Quasi-analytic and other classes of functionsquasi-banach: 1: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)quasi-elliptic: 1: 35H30 Quasi-elliptic equations
quasi-frobenius: 1: 16L60 Quasi-Frobenius rings [See also]16D50quasi-newton: 1: 90C53 Methods of quasi-Newton type
quasi-periodic: 1: 70K43 Quasi-periodic motions and invariant toriquasi-solvable: 1: 81U15 Exactly and quasi-solvable systems
quasiconformal: 1: 30C62 Quasiconformal mappings in the planequasiconformal: 2: 30C65 Quasiconformal mappings in Rn, other generalizationsquasiconformal: 3: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsquasiconformal: 4: 30C75 Extremal problems for conformal and quasiconformal mappings, other methodsquasiconformal: 5: 30L10 Quasiconformal mappings in metric spacesquasiconformal: 6: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemsquasicrystals: 1: 52C23 Quasicrystals, aperiodic tilings
quasidiagonal: 1: 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operatorsquasigroups: 1: 20N05 Loops, quasigroups [See also]05Bxxquasilinear: 1: 35J62 Quasilinear elliptic equationsquasilinear: 2: 35J92 Quasilinear elliptic equations with p-Laplacianquasilinear: 3: 35J93 Quasilinear elliptic equations with mean curvature operatorquasilinear: 4: 35K59 Quasilinear parabolic equationsquasilinear: 5: 35K92 Quasilinear parabolic equations with p-Laplacianquasilinear: 6: 35K93 Quasilinear parabolic equations with mean curvature operatorquasilinear: 7: 35L72 Quasilinear second-order hyperbolic equationsquasilinear: 8: 35L77 Quasilinear higher-order hyperbolic equations
quasimultiplication: 1: 16N20 Jacobson radical, quasimultiplicationquasiperiodic: 1: 37C55 Periodic and quasiperiodic flows and diffeomorphisms
quasitriangular: 1: 47A66 Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operatorsquasivarieties: 1: 08C15 Quasivarietiesquasivarieties: 2: 20E10 Quasivarieties and varieties of groups
quaternary: 1: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesquaternion: 1: 11R52 Quaternion and other division algebras: arithmetic, zeta functionsquaternion: 2: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
314 Run: December 14, 2009
Mathematics Subject Classification 2010
quaternionic: 1: 53C26 Hyper-Kahler and quaternionic Kahler geometry, “special” geometryquaternions: 1: 15B33 Matrices over special rings (quaternions, finite fields, etc.)quaternions: 2: 20G20 Linear algebraic groups over the reals, the complexes, the quaternionsquaternions: 3: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedeanfunctional analysis [See also]12J25, 32P05
quaternions: 4: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedeanoperator theory
questionnaires: 1: 94A50 Theory of questionnairesquestions: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R15questions: 2: 06D22 Frames, locales For topological questions see 54-XXquestions: 3: 11P32 Goldbach-type theorems; other additive questions involving primesquestions: 4: 14A25 Elementary questionsquestions: 5: 14E08 Rationality questions [See also]14M20questions: 6: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyer
conjecture)questions: 7: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
questions: 8: 26B05 Continuity and differentiation questionsquestions: 9: 32B25 Triangulation and related questionsquestions: 10: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsquestions: 11: 51N35 Questions of classical algebraic geometry [See also]14Nxxquestions: 12: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxquestions: 13: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxquestions: 14: 58B05 Homotopy and topological questionsquestions: 15: 58B10 Differentiability questionsquestions: 16: 58B12 Questions of holomorphy [See also]32-XX, 46G20questions: 17: 60A05 Axioms; other general questionsquestions: 18: 83Bxx Observational and experimental questionsquestions: 19: 83B05 Observational and experimental questionsquestions: 20: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10questions: 21: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10queueing: 1: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxqueueing: 2: 60K25 Queueing theory [See also]68M20, 90B22queueing: 3: 68M20 Performance evaluation; queueing; scheduling [See also]60K25, 90Bxx
queues: 1: 90B22 Queues and service [See also]60K25, 68M20quivers: 1: 16G20 Representations of quivers and partially ordered setsquivers: 2: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
quotient: 1: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamsquotient: 2: 54B15 Quotient spaces, decompositions
quotients: 1: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17quotients: 2: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsradiation: 1: 78A40 Waves and radiationradiation: 2: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)radiative: 1: 85A25 Radiative transfer
radical: 1: 16Nxx Radicals and radical properties of ringsradical: 2: 16N20 Jacobson radical, quasimultiplicationradical: 3: 17A65 Radical theoryradical: 4: 20M11 Radical theoryradical: 5: 46J45 Radical Banach algebras
radicals: 1: 16Nxx Radicals and radical properties of rings
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Mathematics Subject Classification 2010
radicals: 2: 16N40 Nil and nilpotent radicals, sets, ideals, ringsradicals: 3: 16N80 General radicals and rings For radicals in module categories, see 16S90radicals: 4: 16N80 General radicals and rings For radicals in module categories, see 16S90radicals: 5: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxradicals: 6: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxradicals: 7: 17C17 Radicalsradicals: 8: 18E40 Torsion theories, radicals [See also]13D30, 16S90
radius: 1: 47A12 Numerical range, numerical radiusradius: 2: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71radix: 1: 11A63 Radix representation; digital problems For metric results, see 11K16radix: 2: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,
etc. [See also]11A63radon: 1: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresradon: 2: 44A12 Radon transform [See also]92C55
radon-nikodym: 1: 46B22 Radon-Nikodym, Kreın-Milman and related properties [See also]46G10ramification: 1: 11S15 Ramification and extension theoryramification: 2: 14E22 Ramification problems [See also]11S15
ramifications: 1: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)
ramified: 1: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)ramsey: 1: 05C55 Generalized Ramsey theory [See also]05D10ramsey: 2: 05D10 Ramsey theory [See also]05C55random: 1: 05C80 Random graphs [See also]60B20random: 2: 05C81 Random walks on graphsrandom: 3: 11M50 Relations with random matricesrandom: 4: 15B52 Random matricesrandom: 5: 30B20 Random power seriesrandom: 6: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exxrandom: 7: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H15random: 8: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H15random: 9: 45Rxx Random integral equations [See also]60H20random: 10: 45R05 Random integral equations [See also]60H20random: 11: 47B80 Random operators [See also]47H40, 60H25random: 12: 47H40 Random operators [See also]47B80, 60H25random: 13: 52A22 Random convex sets and integral geometry [See also]53C65, 60D05random: 14: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)random: 15: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)random: 16: 60G50 Sums of independent random variables; random walksrandom: 17: 60G50 Sums of independent random variables; random walksrandom: 18: 60G57 Random measuresrandom: 19: 60G60 Random fieldsrandom: 20: 60H25 Random operators and equations [See also]47B80random: 21: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C43random: 22: 60K37 Processes in random environmentsrandom: 23: 60K40 Other physical applications of random processesrandom: 24: 62M40 Random fields; image analysisrandom: 25: 65C10 Random number generationrandom: 26: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40
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random: 27: 70Lxx Random vibrations [See also]74H50random: 28: 70L05 Random vibrations [See also]74H50random: 29: 74A40 Random materials and composite materialsrandom: 30: 74E35 Random structurerandom: 31: 74H50 Random vibrationsrandom: 32: 78A48 Composite media; random mediarandom: 33: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41random: 34: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41random: 35: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)random: 36: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)random: 37: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50random: 38: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50random: 39: 82C44 Dynamics of disordered systems (random Ising systems, etc.)random: 40: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
randomized: 1: 68W20 Randomized algorithmsrandomness: 1: 03D32 Algorithmic randomness and dimension [See also]68Q30randomness: 2: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E03randomness: 3: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E03randomness: 4: 35R60 Partial differential equations with randomness, stochastic partial differential equations[See also]60H15
randomness: 5: 49J55 Problems involving randomness [See also]93E20randomness: 6: 49K45 Problems involving randomness [See also]93E20
range: 1: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory[See also]65F35, 65J05
range: 2: 19B10 Stable range conditionsrange: 3: 47A12 Numerical range, numerical radius
ranges: 1: 39B52 Equations for functions with more general domains and/or rangesranges: 2: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35ranges: 3: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
rank: 1: 15A03 Vector spaces, linear dependence, rankrank: 2: 20F11 Groups of finite Morley rank [See also]03C45, 03C60rank: 3: 20K15 Torsion-free groups, finite rankrank: 4: 20K20 Torsion-free groups, infinite rank
ranked: 1: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with ametric taking values in an ordered structure more general than R, etc.)
ranking: 1: 62F07 Ranking and selectionranks: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17rarefied: 1: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05rarefied: 2: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D05ratchets: 1: 81Q37 Quantum dots, waveguides, ratchets, etc.
rate: 1: 11N56 Rate of growth of arithmetic functionsrate: 2: 16P90 Growth rate, Gelfand-Kirillov dimensionrate: 3: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48rate: 4: 41A25 Rate of convergence, degree of approximation
rate-dependent: 1: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)rate-dependent: 2: 74C20 Large-strain, rate-dependent theoriesrate-distortion: 1: 94A34 Rate-distortion theory
rate-independent: 1: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plasticmaterials)
rate-independent: 2: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)rates: 1: 37A25 Ergodicity, mixing, rates of mixingrates: 2: 91G30 Interest rates (stochastic models)
rating: 1: 97D60 Student assessment, achievement control and ratingratio: 1: 97F80 Ratio and proportion, percentages
rational: 1: 11D68 Rational numbers as sums of fractions
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rational: 2: 14E05 Rational and birational mapsrational: 3: 14G05 Rational pointsrational: 4: 14J26 Rational and ruled surfacesrational: 5: 14M20 Rational and unirational varieties [See also]14E08rational: 6: 16R50 Other kinds of identities (generalized polynomial, rational, involution)rational: 7: 26Cxx Polynomials, rational functionsrational: 8: 26C15 Rational functions [See also]14Pxxrational: 9: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10rational: 10: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H04rational: 11: 37P05 Polynomial and rational mapsrational: 12: 41A20 Approximation by rational functionsrational: 13: 55P62 Rational homotopy theoryrational: 14: 97F40 Integers, rational numbers
rationality: 1: 14E08 Rationality questions [See also]14M20rationality: 2: 91A26 Rationality, learningrationally: 1: 14M22 Rationally connected varieties
rayleigh-ritz: 1: 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methodsrayleigh-ritz: 2: 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methodsrayleigh-ritz: 3: 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
rays: 1: 14E30 Minimal model program (Mori theory, extremal rays)reacting: 1: 80A32 Chemically reacting flows [See also]92C45, 92E20reaction: 1: 76Vxx Reaction effects in flows [See also]80A32reaction: 2: 76V05 Reaction effects in flows [See also]80A32
reaction-diffusion: 1: 35K57 Reaction-diffusion equationsreactions: 1: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A32reactive: 1: 74A65 Reactive materialsreactive: 2: 74F25 Chemical and reactive effectsreactor: 1: 82D75 Nuclear reactor theory; neutron transport
real: 1: 11E10 Forms over real fieldsreal: 2: 11M20 Real zeros of L(s, χ); results on L(1, χ)real: 3: 11R80 Totally real fields [See also]12J15real: 4: 12Dxx Real and complex fieldsreal: 5: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxreal: 6: 13J30 Real algebra [See also]12D15, 14Pxxreal: 7: 14F25 Classical real and complex (co)homologyreal: 8: 14Pxx Real algebraic and real analytic geometryreal: 9: 14Pxx Real algebraic and real analytic geometryreal: 10: 14P05 Real algebraic sets [See also]12D15, 13J30real: 11: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C05real: 12: 14P25 Topology of real algebraic varietiesreal: 13: 22E15 General properties and structure of real Lie groupsreal: 14: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XXreal: 15: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05real: 16: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10real: 17: 26-XX Real functions [See also]54C30real: 18: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05real: 19: 26E40 Constructive real analysis [See also]03F60real: 20: 26E50 Fuzzy real analysis [See also]03E72, 28E10real: 21: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N05real: 22: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
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functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10real: 23: 32C09 Embedding of real analytic manifoldsreal: 24: 32V40 Real submanifolds in complex manifoldsreal: 25: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)real: 26: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70real: 27: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70real: 28: 39B22 Equations for real functions [See also]26A51, 26B25real: 29: 51Mxx Real and complex geometryreal: 30: 97F50 Real numbers, complex numbersreal: 31: 97F90 Real life mathematics, practical arithmetic
real-: 1: 28A10 Real- or complex-valued set functionsreal-analytic: 1: 26E05 Real-analytic functions [See also]32B05, 32C05real-analytic: 2: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A07real-analytic: 3: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A07real-analytic: 4: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P20real-analytic: 5: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B05real-analytic: 6: 58A07 Real-analytic and Nash manifolds [See also]14P20, 32C07
real-valued: 1: 54C30 Real-valued functions [See also]26-XXreal-valued: 2: 58C05 Real-valued functionsreal-world: 1: 91B74 Models of real-world systems
realcompactification: 1: 54D60 Realcompactness and realcompactificationrealcompactness: 1: 54D60 Realcompactness and realcompactification
realizations: 1: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,realizations, etc.
realizations: 2: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorialstructures, etc.) [See also]05B35, 52Cxx
realizations: 3: 93B15 Realizations from input-output datarealizing: 1: 57R95 Realizing cycles by submanifolds
reals: 1: 03D78 Computation over the reals For constructive aspects, see 03F60reals: 2: 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
rearrangement: 1: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)reasoning: 1: 68T37 Reasoning under uncertaintyreasoning: 2: 97E50 Reasoning and proving in the mathematics classroom
reattachment: 1: 76D10 Boundary-layer theory, separation and reattachment, higher-order effectsreciprocity: 1: 11A15 Power residues, reciprocityrecognition: 1: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30recognition: 2: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30
reconstruction: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraphembedding, etc.)
reconstruction: 2: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U10reconstruction: 3: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
recreational: 1: 00A08 Recreational mathematics [See also]97A20recreational: 2: 97A20 Recreational mathematics, games [See also]00A08recreational: 3: 97R80 Recreational computingrecurrence: 1: 37B20 Notions of recurrencerecurrence: 2: 65Qxx Difference and functional equations, recurrence relationsrecurrence: 3: 65Q30 Recurrence relations
recurrences: 1: 11B37 Recurrences For applications to special functions, see 33-XXrecurrent: 1: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setsrecurrent: 2: 43A60 Almost periodic functions on groups and semigroups and their generalizations
(recurrent functions, distal functions, etc.); almost automorphic functionsrecursion: 1: 03Dxx Computability and recursion theory
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recursion: 2: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.recursion: 3: 03D65 Higher-type and set recursion theoryrecursion: 4: 03D75 Abstract and axiomatic computability and recursion theoryrecursion: 5: 03D80 Applications of computability and recursion theory
recursion-theoretic: 1: 03C57 Effective and recursion-theoretic model theory [See also]03D45recursive: 1: 03D20 Recursive functions and relations, subrecursive hierarchiesrecursive: 2: 03D50 Recursive equivalence types of sets and structures, isolsrecursive: 3: 03F15 Recursive ordinals and ordinal notationsrecursive: 4: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30,
47S30recursively: 1: 03D25 Recursively (computably) enumerable sets and degrees
reduced: 1: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation[See also]31Axx, 31Bxx
reduced: 2: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31reduced: 3: 90C52 Methods of reduced gradient type
reducibilities: 1: 03D30 Other degrees and reducibilitiesreduction: 1: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)reduction: 2: 32E05 Holomorphically convex complex spaces, reduction theoryreduction: 3: 34C20 Transformation and reduction of equations and systems, normal formsreduction: 4: 34K17 Transformation and reduction of equations and systems, normal formsreduction: 5: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D20reduction: 6: 53D20 Momentum maps; symplectic reductionreduction: 7: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductionreduction: 8: 78M34 Model reduction
reductions: 1: 15A21 Canonical forms, reductions, classificationreductions: 2: 34A05 Explicit solutions and reductionsreductive: 1: 17B20 Simple, semisimple, reductive (super)algebras
rees: 1: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and relatedtopics
reference: 1: 00A20 Dictionaries and other general reference worksreference: 2: 97A10 Comprehensive works, reference books
refinement: 1: 65L50 Mesh generation and refinementrefinement: 2: 65M50 Mesh generation and refinementrefinement: 3: 65N50 Mesh generation and refinement
reflection: 1: 20F55 Reflection and Coxeter groups [See also]22E40, 51F15reflection: 2: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55reflection: 3: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55reflective: 1: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
reflexivity: 1: 46A25 Reflexivity and semi-reflexivity [See also]46B10reflexivity: 2: 46B10 Duality and reflexivity [See also]46A25
regge: 1: 83C27 Lattice gravity, Regge calculus and other discrete methodsregions: 1: 11P21 Lattice points in specified regionsregions: 2: 62F25 Tolerance and confidence regionsregions: 3: 62G15 Tolerance and confidence regionsregister: 1: 94A55 Shift register sequences and sequences over finite alphabets
regression: 1: 62G08 Nonparametric regressionregression: 2: 62Jxx Linear inference, regressionregression: 3: 62J02 General nonlinear regressionregression: 4: 62J05 Linear regressionregression: 5: 62J07 Ridge regression; shrinkage estimatorsregression: 6: 62J86 Fuzziness, and linear inference and regressionregression: 7: 62M10 Time series, auto-correlation, regression, etc. [See also]91B84
regular: 1: 05E30 Association schemes, strongly regular graphs
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regular: 2: 13H05 Regular local ringsregular: 3: 16E50 von Neumann regular rings and generalizationsregular: 4: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)regular: 5: 20M17 Regular semigroupsregular: 6: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15regular: 7: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)regular: 8: 57Q40 Regular neighborhoods
regularity: 1: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)regularity: 2: 32H40 Boundary regularity of mappingsregularity: 3: 35B65 Smoothness and regularity of solutionsregularity: 4: 49N60 Regularity of solutionsregularity: 5: 74G40 Regularity of solutionsregularity: 6: 74H30 Regularity of solutionsregularity: 7: 76B03 Existence, uniqueness, and regularity theory [See also]35Q35regularity: 8: 76D03 Existence, uniqueness, and regularity theory [See also]35Q30regularity: 9: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q30
regularization: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,65R30
regularization: 2: 65F22 Ill-posedness, regularizationregularization: 3: 65J20 Improperly posed problems; regularizationregularization: 4: 70F16 Collisions in celestial mechanics, regularization
regularized: 1: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,Dirichlet series, Eisenstein series, etc. Explicit formulasregularized: 2: 47D60 C-semigroups, regularized semigroupsregulators: 1: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,11S40, 14F20, 14G10
reidemeister-franz: 1: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.[See also]19B28reinhardt: 1: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)
related: 1: 03C10 Quantifier elimination, model completeness and related topicsrelated: 2: 03C20 Ultraproducts and related constructionsrelated: 3: 03C45 Classification theory, stability and related concepts [See also]03C48related: 4: 03C48 Abstract elementary classes and related topics [See also]03C45related: 5: 03D10 Turing machines and related notions [See also]68Q05related: 6: 03E25 Axiom of choice and related propositionsrelated: 7: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E25related: 8: 03G10 Lattices and related structures [See also]06Bxxrelated: 9: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F35related: 10: 05A30 q-calculus and related topics [See also]33Dxxrelated: 11: 06D72 Fuzzy lattices (soft algebras) and related topicsrelated: 12: 06E15 Stone spaces (Boolean spaces) and related structuresrelated: 13: 11A25 Arithmetic functions; related numbers; inversion formulasrelated: 14: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10related: 15: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxrelated: 16: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsrelated: 17: 13Bxx Ring extensions and related topicsrelated: 18: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)related: 19: 13C15 Dimension theory, depth, related rings (catenary, etc.)related: 20: 13F35 Witt vectors and related ringsrelated: 21: 13H15 Multiplicity theory and related topics [See also]14C17
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related: 22: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,18F20, 32Lxx, 46M20
related: 23: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyerconjecture)
related: 24: 14P10 Semialgebraic sets and related spacesrelated: 25: 15A80 Max-plus and related algebrasrelated: 26: 15B05 Toeplitz, Cauchy, and related matricesrelated: 27: 15B57 Hermitian, skew-Hermitian, and related matricesrelated: 28: 16Txx Hopf algebras, quantum groups and related topicsrelated: 29: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxrelated: 30: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B23related: 31: 17B66 Lie algebras of vector fields and related (super) algebrasrelated: 32: 17B68 Virasoro and related algebrasrelated: 33: 17B69 Vertex operators; vertex operator algebras and related structuresrelated: 34: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
related: 35: 19J10 Whitehead (and related) torsionrelated: 36: 20F38 Other groups related to topology or analysisrelated: 37: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
related: 38: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05related: 39: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
related: 40: 30Dxx Entire and meromorphic functions, and related topicsrelated: 41: 32B25 Triangulation and related questionsrelated: 42: 32H02 Holomorphic mappings, (holomorphic) embeddings and related questionsrelated: 43: 33C80 Connections with groups and algebras, and related topicsrelated: 44: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and
related topicsrelated: 45: 39B82 Stability, separation, extension, and related topics [See also]46A22related: 46: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxrelated: 47: 46A17 Bornologies and related structures; Mackey convergence, etc.related: 48: 46B22 Radon-Nikodym, Kreın-Milman and related properties [See also]46G10related: 49: 51D30 Continuous geometries and related topics [See also]06Cxxrelated: 50: 52A39 Mixed volumes and related topicsrelated: 51: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxrelated: 52: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxrelated: 53: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxrelated: 54: 57Txx Homology and homotopy of topological groups and related structuresrelated: 55: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80related: 56: 62M45 Neural nets and related approachesrelated: 57: 62P12 Applications to environmental and related topicsrelated: 58: 65K15 Numerical methods for variational inequalities and related problemsrelated: 59: 65M70 Spectral, collocation and related methodsrelated: 60: 65N35 Spectral, collocation and related methodsrelated: 61: 74J40 Shocks and related discontinuitiesrelated: 62: 74S25 Spectral and related methodsrelated: 63: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M35related: 64: 76D07 Stokes and related (Oseen, etc.) flowsrelated: 65: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B37related: 66: 81Txx Quantum field theory; related classical field theories [See also]70Sxx
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related: 67: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxrelated: 68: 92D15 Problems related to evolutionrelated: 69: 93E24 Least squares and related methods
relation: 1: 03G15 Cylindric and polyadic algebras; relation algebrasrelation: 2: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxxrelation: 3: 68Rxx Discrete mathematics in relation to computer science
relational: 1: 08A02 Relational systems, laws of compositionrelations: 1: 03D20 Recursive functions and relations, subrecursive hierarchiesrelations: 2: 03E02 Partition relationsrelations: 3: 03E20 Other classical set theory (including functions, relations, and set algebra)relations: 4: 06B10 Ideals, congruence relationsrelations: 5: 08A30 Subalgebras, congruence relationsrelations: 6: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)relations: 7: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45relations: 8: 11F23 Relations with algebraic geometry and topologyrelations: 9: 11G55 Polylogarithms and relations with K-theoryrelations: 10: 11H71 Relations with coding theoryrelations: 11: 11M50 Relations with random matricesrelations: 12: 11M55 Relations with noncommutative geometryrelations: 13: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13relations: 14: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXrelations: 15: 18B10 Category of relations, additive relationsrelations: 16: 18B10 Category of relations, additive relationsrelations: 17: 19E20 Relations with cohomology theories [See also]14Fxxrelations: 18: 20F05 Generators, relations, and presentationsrelations: 19: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F10relations: 20: 32S22 Relations with arrangements of hyperplanes [See also]52C35relations: 21: 32S40 Monodromy; relations with differential equations and D-modulesrelations: 22: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45relations: 23: 37A20 Orbit equivalence, cocycles, ergodic equivalence relationsrelations: 24: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxrelations: 25: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10relations: 26: 37A55 Relations with the theory of C∗-algebras [See mainly]46L55relations: 27: 37F05 Relations and correspondencesrelations: 28: 37J05 General theory, relations with symplectic geometry and topologyrelations: 29: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70relations: 30: 37K25 Relations with differential geometryrelations: 31: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresrelations: 32: 47A06 Linear relations (multivalued linear operators)relations: 33: 49J21 Optimal control problems involving relations other than differential equationsrelations: 34: 49K21 Problems involving relations other than differential equationsrelations: 35: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxrelations: 36: 55P92 Relations between equivariant and nonequivariant homotopy theoryrelations: 37: 57M15 Relations with graph theory [See also]05Cxxrelations: 38: 58J15 Relations with hyperfunctionsrelations: 39: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicityrelations: 40: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)relations: 41: 65Qxx Difference and functional equations, recurrence relationsrelations: 42: 65Q30 Recurrence relationsrelations: 43: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q19relations: 44: 81R12 Relations with integrable systems [See also]17Bxx, 37J35relations: 45: 81S05 Canonical quantization, commutation relations and statistics
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relations: 46: 81U30 Dispersion theory, dispersion relationsrelations: 47: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)relations: 48: 97E60 Sets, relations, set theory
relationship: 1: 11F22 Relationship to Lie algebras and finite simple groupsrelationship: 2: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,Galois theory)
relationships: 1: 14H70 Relationships with integrable systemsrelationships: 2: 14H81 Relationships with physicsrelationships: 3: 14J81 Relationships with physics
relative: 1: 03F25 Relative consistency and interpretationsrelative: 2: 18G25 Relative homological algebra, projective classes
relativistic: 1: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;for statistical mechanics, see 82-XXrelativistic: 2: 70H40 Relativistic dynamicsrelativistic: 3: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30relativistic: 4: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55,85A30relativistic: 5: 80A10 Classical thermodynamics, including relativisticrelativistic: 6: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric fieldtheoriesrelativistic: 7: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric fieldtheoriesrelativistic: 8: 85A40 Cosmology For relativistic cosmology, see 83F05
relativity: 1: 35Q75 PDEs in connection with relativity and gravitational theoryrelativity: 2: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)relativity: 3: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
dynamics, etc.)relativity: 4: 83-XX Relativity and gravitational theoryrelativity: 5: 83Axx Special relativityrelativity: 6: 83A05 Special relativityrelativity: 7: 83Cxx General relativity
relaxation: 1: 34C26 Relaxation oscillationsrelaxation: 2: 49J45 Methods involving semicontinuity and convergence; relaxationrelaxation: 3: 49M20 Methods of relaxation typerelevance: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52relevant: 1: 14A05 Relevant commutative algebra [See also]13-XX
reliability: 1: 60K10 Applications (reliability, demand theory, etc.)reliability: 2: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxreliability: 3: 62N05 Reliability and life testing [See also]90B25reliability: 4: 68M15 Reliability, testing and fault tolerance [See also]94C12reliability: 5: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N05
remainders: 1: 41A80 Remainders in approximation formulasremainders: 2: 54D40 Remaindersremovable: 1: 32D20 Removable singularitiesremovable: 2: 32U30 Removable sets
renaissance: 1: 01A40 15th and 16th centuries, Renaissancerenewal: 1: 60K05 Renewal theoryrenewal: 2: 60K15 Markov renewal processes, semi-Markov processesrenewal: 3: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxrenormalization: 1: 37E20 Universality, renormalization [See also]37F25renormalization: 2: 37F25 Renormalization
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renormalization: 3: 76F30 Renormalization and other field-theoretical methods [See also]81T99renormalization: 4: 81T15 Perturbative methods of renormalizationrenormalization: 5: 81T16 Nonperturbative methods of renormalizationrenormalization: 6: 81T17 Renormalization group methodsrenormalization: 7: 82B28 Renormalization group methods [See also]81T17renormalization: 8: 82C28 Dynamic renormalization group methods [See also]81T17
renorming: 1: 46B03 Isomorphic theory (including renorming) of Banach spacesrepeated: 1: 91A20 Multistage and repeated gamesrepellers: 1: 37B25 Lyapunov functions and stability; attractors, repellersrepellers: 2: 37C70 Attractors and repellers, topological structure
representation: 1: 05E10 Combinatorial aspects of representation theory [See also]20C30representation: 2: 06B15 Representation theoryrepresentation: 3: 06D05 Structure and representation theoryrepresentation: 4: 11A63 Radix representation; digital problems For metric results, see 11K16representation: 5: 11B34 Representation functionsrepresentation: 6: 11D85 Representation problems [See also]11P55representation: 7: 11F27 Theta series; Weil representation; theta correspondencesrepresentation: 8: 16Gxx Representation theory of rings and algebrasrepresentation: 9: 16G60 Representation type (finite, tame, wild, etc.)representation: 10: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30representation: 11: 19A22 Frobenius induction, Burnside and representation ringsrepresentation: 12: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)representation: 13: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)representation: 14: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
representation: 15: 20G05 Representation theoryrepresentation: 16: 20M30 Representation of semigroups; actions of semigroups on setsrepresentation: 17: 22E43 Structure and representation of the Lorentz grouprepresentation: 18: 26B40 Representation and superposition of functionsrepresentation: 19: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
representation: 20: 47A67 Representation theoryrepresentation: 21: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y30representation: 22: 68T30 Knowledge representation
representation-theoretic: 1: 11F70 Representation-theoretic methods; automorphic representations over local and globalfields
representation-theoretic: 2: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D24representations: 1: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10representations: 2: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10representations: 3: 11A67 Other representationsrepresentations: 4: 11E25 Sums of squares and representations by other particular quadratic formsrepresentations: 5: 11F70 Representation-theoretic methods; automorphic representations over local and global
fieldsrepresentations: 6: 11F80 Galois representationsrepresentations: 7: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10representations: 8: 11S23 Integral representationsrepresentations: 9: 16G10 Representations of Artinian ringsrepresentations: 10: 16G20 Representations of quivers and partially ordered setsrepresentations: 11: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxx
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representations: 12: 17B10 Representations, algebraic theory (weights)representations: 13: 17B15 Representations, analytic theoryrepresentations: 14: 20C08 Hecke algebras and their representationsrepresentations: 15: 20C10 Integral representations of finite groupsrepresentations: 16: 20C11 p-adic representations of finite groupsrepresentations: 17: 20C12 Integral representations of infinite groupsrepresentations: 18: 20C15 Ordinary representations and charactersrepresentations: 19: 20C20 Modular representations and charactersrepresentations: 20: 20C25 Projective representations and multipliersrepresentations: 21: 20C30 Representations of finite symmetric groupsrepresentations: 22: 20C32 Representations of infinite symmetric groupsrepresentations: 23: 20C33 Representations of finite groups of Lie typerepresentations: 24: 20C34 Representations of sporadic groupsrepresentations: 25: 20C35 Applications of group representations to physicsrepresentations: 26: 20F29 Representations of groups as automorphism groups of algebraic systemsrepresentations: 27: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50representations: 28: 22A25 Representations of general topological groups and semigroupsrepresentations: 29: 22A30 Other topological algebraic systems and their representationsrepresentations: 30: 22D10 Unitary representations of locally compact groupsrepresentations: 31: 22D12 Other representations of locally compact groupsrepresentations: 32: 22D20 Representations of group algebrasrepresentations: 33: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxxrepresentations: 34: 22D30 Induced representationsrepresentations: 35: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)representations: 36: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)representations: 37: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05representations: 38: 22E46 Semisimple Lie groups and their representationsrepresentations: 39: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10representations: 40: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G05representations: 41: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05representations: 42: 22E66 Analysis on and representations of infinite-dimensional Lie groupsrepresentations: 43: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10representations: 44: 30D10 Representations of entire functions by series and integralsrepresentations: 45: 30E15 Asymptotic representations in the complex domainrepresentations: 46: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxrepresentations: 47: 31A10 Integral representations, integral operators, integral equations methodsrepresentations: 48: 31B10 Integral representations, integral operators, integral equations methodsrepresentations: 49: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)representations: 50: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)representations: 51: 35Cxx Representations of solutionsrepresentations: 52: 35C15 Integral representations of solutionsrepresentations: 53: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E45representations: 54: 46H15 Representations of topological algebrasrepresentations: 55: 46J25 Representations of commutative topological algebrasrepresentations: 56: 46K10 Representations of topological algebras with involutionrepresentations: 57: 47L55 Representations of (nonselfadjoint) operator algebrasrepresentations: 58: 54H10 Topological representations of algebraic systems [See also]22-XXrepresentations: 59: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70representations: 60: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
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Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
representations: 61: 93B20 Minimal systems representationsrepresented: 1: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial values
representing: 1: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),representing set functions and measuresreprinted: 1: 00B60 Collections of reprinted articles [See also]01A75
reprintings: 1: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60reproducing: 1: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32reproducing-kernel: 1: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22requirements: 1: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)resampling: 1: 62F40 Bootstrap, jackknife and other resampling methodsresampling: 2: 62G09 Resampling methods
research: 1: 90-XX Operations research, mathematical programmingresearch: 2: 90Bxx Operations research and management scienceresearch: 3: 97B10 Educational research and planningresearch: 4: 97B50 Teacher education For research aspects, see 97C70research: 5: 97Cxx Psychology of mathematics education, research in mathematics educationresearch: 6: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxxresearch: 7: 97M40 Operations research, economicsresearch: 8: 97U20 Textbooks. Textbook research
reservoirs: 1: 90B05 Inventory, storage, reservoirsresidual: 1: 20E26 Residual properties and generalizations; residually finite groups
residually: 1: 20E26 Residual properties and generalizations; residually finite groupsresidue: 1: 11A07 Congruences; primitive roots; residue systemsresidue: 2: 11N69 Distribution of integers in special residue classes
residues: 1: 11A15 Power residues, reciprocityresidues: 2: 32A27 Local theory of residues [See also]32C30residues: 3: 58J42 Noncommutative global analysis, noncommutative residues
resolution: 1: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S45resolution: 2: 32S45 Modifications; resolution of singularities [See also]14E15resolution: 3: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B35
resolutions: 1: 13D02 Syzygies, resolutions, complexesresolutions: 2: 16E05 Syzygies, resolutions, complexesresolutions: 3: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E25
resolvent: 1: 47A10 Spectrum, resolventresolvents: 1: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D07resonance: 1: 34F15 Resonance phenomena
resonances: 1: 35B34 Resonancesresonances: 2: 70J40 Parametric resonancesresonances: 3: 70K28 Parametric resonancesresonances: 4: 70K30 Nonlinear resonances
resource: 1: 91B32 Resource and cost allocationresource: 2: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)respect: 1: 28A25 Integration with respect to measures and other set functions
response: 1: 62K20 Response surface designsrestricted: 1: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang
controls, etc.)restricted: 2: 49K30 Optimal solutions belonging to restricted classes
restrictions: 1: 11P83 Partitions; congruences and congruential restrictionsrestrictions: 2: 52A05 Convex sets without dimension restrictionsrestrictions: 3: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions[See also]58J60
result: 1: 65G20 Algorithms with automatic result verification
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resultants: 1: 13P15 Solving polynomial systems; resultantsresults: 1: 03E35 Consistency and independence resultsresults: 2: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A15results: 3: 11A63 Radix representation; digital problems For metric results, see 11K16results: 4: 11J95 Results involving abelian varietiesresults: 5: 11N37 Asymptotic results on arithmetic functionsresults: 6: 11N45 Asymptotic results on counting functions for algebraic and topological structuresresults: 7: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsresults: 8: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XXresults: 9: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30results: 10: 53C24 Rigidity resultsresults: 11: 54A35 Consistency and independence results [See also]03E35results: 12: 62C07 Complete class results
resummation: 1: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80resummation: 2: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)
retract: 1: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract(ANR), absolute retract spaces (general properties) [See also]55M15
retract: 2: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract(ANR), absolute retract spaces (general properties) [See also]55M15retraction: 1: 54C15 Retraction
retracts: 1: 55M15 Absolute neighborhood retracts [See also]54C55retrieval: 1: 68P20 Information storage and retrievalreverse: 1: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35reverse: 2: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductionreviews: 1: 00A17 External book reviews
rewriting: 1: 68Q42 Grammars and rewriting systemsrham: 1: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L10rham: 2: 58A12 de Rham theory [See also]14Fxx
rheology: 1: 76Axx Foundations, constitutive equations, rheologyrhythms: 1: 92B25 Biological rhythms and synchronization
ricci: 1: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)richer: 1: 54Exx Spaces with richer structuresridge: 1: 62J07 Ridge regression; shrinkage estimators
riemann: 1: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypothesesriemann: 2: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxxriemann: 3: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XXriemann: 4: 30Fxx Riemann surfacesriemann: 5: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G15riemann: 6: 30F15 Harmonic functions on Riemann surfacesriemann: 7: 30F20 Classification theory of Riemann surfacesriemann: 8: 30F30 Differentials on Riemann surfacesriemann: 9: 32D26 Riemann domainsriemann: 10: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxxriemann: 11: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxriemann: 12: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann
theory, localizationriemann-hilbert: 1: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)riemann-hilbert: 2: 35Q15 Riemann-Hilbert problems [See also]30E25, 31A25, 31B20
riemann-roch: 1: 14C40 Riemann-Roch theorems [See also]19E20, 19L10riemann-roch: 2: 19L10 Riemann-Roch theorems, Chern characters
riemannian: 1: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14riemannian: 2: 53B20 Local Riemannian geometryriemannian: 3: 53B21 Methods of Riemannian geometry
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riemannian: 4: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B20riemannian: 5: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions[See also]58J60riemannian: 6: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)riemannian: 7: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C60riemannian: 8: 58D17 Manifolds of metrics (esp. Riemannian)riemannian: 9: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)riemannian: 10: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx
riesz: 1: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40riesz: 2: 42A55 Lacunary series of trigonometric and other functions; Riesz productsriesz: 3: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsrigged: 1: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spaces
right: 1: 17D15 Right alternative ringsright: 2: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)right: 3: 60J40 Right processes
right-hand: 1: 35R70 Partial differential equations with multivalued right-hand sidesrigid: 1: 03C50 Models with special properties (saturated, rigid, etc.)rigid: 2: 14G22 Rigid analytic geometryrigid: 3: 70B10 Kinematics of a rigid bodyrigid: 4: 70Exx Dynamics of a rigid body and of multibody systemsrigid: 5: 70E15 Free motion of a rigid body [See also]70M20rigid: 6: 70E17 Motion of a rigid body with a fixed pointrigid: 7: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25rigid: 8: 70E20 Perturbation methods for rigid body dynamicsrigid: 9: 70F35 Collision of rigid or pseudo-rigid bodies
rigid-plastic: 1: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plasticmaterials)
rigidity: 1: 52C25 Rigidity and flexibility of structures [See also]70B15rigidity: 2: 53C24 Rigidity results
ring: 1: 13Axx General commutative ring theoryring: 2: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsring: 3: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsring: 4: 13Bxx Ring extensions and related topicsring: 5: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H10ring: 6: 51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)ring: 7: 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)ring: 8: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)
ring-theoretic: 1: 06E20 Ring-theoretic properties [See also]16E50, 16G30ring-theoretic: 2: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R50
rings: 1: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65rings: 2: 06Exx Boolean algebras (Boolean rings) [See also]03G05rings: 3: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80rings: 4: 11E08 Quadratic forms over local rings and fieldsrings: 5: 11E12 Quadratic forms over global rings and fieldsrings: 6: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24rings: 7: 11R04 Algebraic numbers; rings of algebraic integersrings: 8: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10rings: 9: 11R56 Adele rings and groupsrings: 10: 11Txx Finite fields and commutative rings (number-theoretic aspects)rings: 11: 11T55 Arithmetic theory of polynomial rings over finite fieldsrings: 12: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxx
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rings: 13: 13A02 Graded rings [See also]16W50rings: 14: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicsrings: 15: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24rings: 16: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)rings: 17: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)rings: 18: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)rings: 19: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M10rings: 20: 13B30 Rings of fractions and localization [See also]16S85rings: 21: 13C15 Dimension theory, depth, related rings (catenary, etc.)rings: 22: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxrings: 23: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)rings: 24: 13E05 Noetherian rings and modulesrings: 25: 13E10 Artinian rings and modules, finite-dimensional algebrasrings: 26: 13E15 Rings and modules of finite generation or presentation; number of generatorsrings: 27: 13Fxx Arithmetic rings and other special ringsrings: 28: 13Fxx Arithmetic rings and other special ringsrings: 29: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizationsrings: 30: 13F07 Euclidean rings and generalizationsrings: 31: 13F10 Principal ideal ringsrings: 32: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M05rings: 33: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25rings: 34: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25rings: 35: 13F25 Formal power series rings [See also]13J05rings: 36: 13F30 Valuation rings [See also]13A18rings: 37: 13F35 Witt vectors and related ringsrings: 38: 13F40 Excellent ringsrings: 39: 13F45 Seminormal ringsrings: 40: 13F50 Rings with straightening laws, Hodge algebrasrings: 41: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U10rings: 42: 13Hxx Local rings and semilocal ringsrings: 43: 13Hxx Local rings and semilocal ringsrings: 44: 13H05 Regular local ringsrings: 45: 13Jxx Topological rings and modules [See also]16W60, 16W80rings: 46: 13J05 Power series rings [See also]13F25rings: 47: 13J07 Analytical algebras and rings [See also]32B05rings: 48: 13J10 Complete rings, completion [See also]13B35rings: 49: 13J15 Henselian rings [See also]13B40rings: 50: 13J20 Global topological ringsrings: 51: 13J25 Ordered rings [See also]06F25rings: 52: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxrings: 53: 13N10 Rings of differential operators and their modules [See also]16S32, 32C38rings: 54: 14C15 (Equivariant) Chow groups and rings; motivesrings: 55: 14H20 Singularities, local rings [See also]13Hxx, 14B05rings: 56: 15A54 Matrices over function rings in one or more variablesrings: 57: 15B33 Matrices over special rings (quaternions, finite fields, etc.)rings: 58: 16-XX Associative rings and algebras For the commutative case, see 13-XXrings: 59: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)rings: 60: 16D50 Injective modules, self-injective rings [See also]16L60rings: 61: 16D60 Simple and semisimple modules, primitive rings and idealsrings: 62: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
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18Gxxrings: 63: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)rings: 64: 16E50 von Neumann regular rings and generalizationsrings: 65: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.rings: 66: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.rings: 67: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.rings: 68: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)rings: 69: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)rings: 70: 16Gxx Representation theory of rings and algebrasrings: 71: 16G10 Representations of Artinian ringsrings: 72: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxxrings: 73: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A30rings: 74: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A30rings: 75: 16Lxx Local rings and generalizationsrings: 76: 16L30 Noncommutative local and semilocal rings, perfect ringsrings: 77: 16L30 Noncommutative local and semilocal rings, perfect ringsrings: 78: 16L60 Quasi-Frobenius rings [See also]16D50rings: 79: 16Nxx Radicals and radical properties of ringsrings: 80: 16N40 Nil and nilpotent radicals, sets, ideals, ringsrings: 81: 16N60 Prime and semiprime rings [See also]16D60, 16U10rings: 82: 16N80 General radicals and rings For radicals in module categories, see 16S90rings: 83: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxrings: 84: 16P20 Artinian rings and modulesrings: 85: 16P40 Noetherian rings and modulesrings: 86: 16P50 Localization and Noetherian rings [See also]16U20rings: 87: 16Rxx Rings with polynomial identityrings: 88: 16R10 T -ideals, identities, varieties of rings and algebrasrings: 89: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsrings: 90: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsrings: 91: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringsrings: 92: 16R30 Trace rings and invariant theoryrings: 93: 16R40 Identities other than those of matrices over commutative ringsrings: 94: 16Sxx Rings and algebras arising under various constructionsrings: 95: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)rings: 96: 16S32 Rings of differential operators [See also]13N10, 32C38rings: 97: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial ringsrings: 98: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial ringsrings: 99: 16S35 Twisted and skew group rings, crossed productsrings: 100: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25rings: 101: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25rings: 102: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A22rings: 103: 16S50 Endomorphism rings; matrix rings [See also]15-XXrings: 104: 16S50 Endomorphism rings; matrix rings [See also]15-XXrings: 105: 16S60 Rings of functions, subdirect products, sheaves of ringsrings: 106: 16S60 Rings of functions, subdirect products, sheaves of ringsrings: 107: 16S70 Extensions of rings by idealsrings: 108: 16S80 Deformations of rings [See also]13D10, 14D15rings: 109: 16S85 Rings of fractions and localizations [See also]13B30rings: 110: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxrings: 111: 16U20 Ore rings, multiplicative sets, Ore localizationrings: 112: 16Wxx Rings and algebras with additional structurerings: 113: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
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17C50, 46Kxxrings: 114: 16W50 Graded rings and modulesrings: 115: 16W70 Filtered rings; filtrational and graded techniquesrings: 116: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxxrings: 117: 16Yxx Generalizations For nonassociative rings, see 17-XXrings: 118: 16Zxx Computational aspects of associative ringsrings: 119: 16Z05 Computational aspects of associative rings [See also]68W30rings: 120: 17-XX Nonassociative rings and algebrasrings: 121: 17Axx General nonassociative ringsrings: 122: 17A05 Power-associative ringsrings: 123: 17Dxx Other nonassociative rings and algebrasrings: 124: 17D05 Alternative ringsrings: 125: 17D10 Mal′cev (Mal′tsev) rings and algebrasrings: 126: 17D15 Right alternative ringsrings: 127: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
rings: 128: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
rings: 129: 19A22 Frobenius induction, Burnside and representation ringsrings: 130: 19A31 K0 of group rings and ordersrings: 131: 19A49 K0 of other ringsrings: 132: 19B28 K1 of group rings and orders [See also]57Q10rings: 133: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E20rings: 134: 19G12 Witt groups of rings [See also]11E81rings: 135: 19G24 L-theory of group rings [See also]11E81rings: 136: 19G38 Hermitian K-theory, relations with K-theory of ringsrings: 137: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)rings: 138: 20C05 Group rings of finite groups and their modules [See also]16S34rings: 139: 20C07 Group rings of infinite groups and their modules [See also]16S34rings: 140: 20G35 Linear algebraic groups over adeles and other rings and schemesrings: 141: 20H25 Other matrix groups over ringsrings: 142: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y60rings: 143: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y60rings: 144: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W80rings: 145: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G05rings: 146: 28A60 Measures on Boolean rings, measure algebras [See also]54H10rings: 147: 32S10 Invariants of analytic local ringsrings: 148: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J15rings: 149: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A20rings: 150: 46Kxx Topological (rings and) algebras with an involution [See also]16W10rings: 151: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80rings: 152: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)rings: 153: 97H40 Groups, rings, fieldsrings: 1: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)risk: 1: 91B30 Risk theory, insurancerisk: 2: 91G40 Credit risk
robot: 1: 70E60 Robot dynamics and control [See also]68T40, 70Q05, 93C85robotic: 1: 65D19 Computational issues in computer and robotic vision
robotics: 1: 68T40 Robotics [See also]93C85
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robots: 1: 70B15 Mechanisms, robots [See also]68T40, 70Q05, 93C85robots: 2: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q05robust: 1: 62K25 Robust parameter designsrobust: 2: 93B51 Design techniques (robust design, computer-aided design, etc.)robust: 3: 93D09 Robust stabilityrobust: 4: 93D21 Adaptive or robust stabilization
robustness: 1: 62F35 Robustness and adaptive proceduresrobustness: 2: 62G35 Robustnessrobustness: 3: 93B35 Sensitivity (robustness)
rock: 1: 74L10 Soil and rock mechanicsrockets: 1: 70Pxx Variable mass, rocketsrockets: 2: 70P05 Variable mass, rockets
rods: 1: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)rogers-ramanujan: 1: 11P84 Partition identities; identities of Rogers-Ramanujan type
roman: 1: 01A20 Greek, Romanroom: 1: 05B15 Orthogonal arrays, Latin squares, Room squaresroot: 1: 17B22 Root systemsroot: 2: 33C52 Orthogonal polynomials and functions associated with root systemsroot: 3: 33C67 Hypergeometric functions associated with root systemsroot: 4: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)root: 5: 33D67 Basic hypergeometric functions associated with root systems
roots: 1: 11A07 Congruences; primitive roots; residue systemsroots: 2: 65H04 Roots of polynomial equations
rosinger: 1: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)rossby: 1: 76B65 Rossby waves [See also]86A05, 86A10
rotating: 1: 76Uxx Rotating fluidsrotating: 2: 76U05 Rotating fluidsrotation: 1: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)rotation: 2: 37E45 Rotation numbers and vectorsrotation: 3: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setsrotation: 4: 76E07 Rotation
rounding: 1: 97N20 Rounding, estimation, theory of errorsroundoff: 1: 65G50 Roundoff error
ruelle-frobenius: 1: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytictechniques in dynamical systems
ruled: 1: 14J26 Rational and ruled surfacesrunge: 1: 32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation
runge-kutta: 1: 65L06 Multistep, Runge-Kutta and extrapolation methodssaint-venant’s: 1: 74G50 Saint-Venant’s principle
saks: 1: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
salem: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,etc. [See also]11A63
sample: 1: 60G17 Sample path propertiessample: 2: 62Dxx Sampling theory, sample surveyssample: 3: 62D05 Sampling theory, sample surveys
sampled-data: 1: 93C57 Sampled-data systemssampling: 1: 62Dxx Sampling theory, sample surveyssampling: 2: 62D05 Sampling theory, sample surveyssampling: 3: 94A20 Sampling theorysasakian: 1: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)satellites: 1: 18E25 Derived functors and satellites
satisfying: 1: 17A30 Algebras satisfying other identitiessaturated: 1: 03C50 Models with special properties (saturated, rigid, etc.)
saturation: 1: 41A40 Saturation
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scalar: 1: 93D30 Scalar and vector Lyapunov functionsscale: 1: 34E13 Multiple scale methodsscale: 2: 93A15 Large scale systems
scales: 1: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scalesor measure chains see 34N05
scales: 2: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scalesor measure chains see 34N05
scales: 3: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scalessee 26E70
scales: 4: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scalessee 26E70
scales: 5: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales ormeasure chains, see 26E70
scales: 6: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales ormeasure chains, see 26E70
scales: 7: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations ontime scales, see 34N05
scaling: 1: 39A13 Difference equations, scaling (q-differences) [See also]33Dxxscaling: 2: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A60scaling: 3: 91C15 One- and multidimensional scaling
scattered: 1: 54G12 Scattered spacesscattering: 1: 34L25 Scattering theory, inverse scatteringscattering: 2: 34L25 Scattering theory, inverse scatteringscattering: 3: 35P25 Scattering theory [See also]47A40scattering: 4: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsscattering: 5: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxxscattering: 6: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxxscattering: 7: 74J20 Wave scatteringscattering: 8: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30scattering: 9: 78A45 Diffraction, scattering [See also]34E20 for WKB methodsscattering: 10: 78A46 Inverse scattering problemsscattering: 11: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A40scattering: 12: 81U05 2-body potential scattering theory [See also]34E20 for WKB methodsscattering: 13: 81U10 n-body potential scattering theoryscattering: 14: 81U35 Inelastic and multichannel scatteringscattering: 15: 81U40 Inverse scattering problems
scene: 1: 68T45 Machine vision and scene understandingschatten-von: 1: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20scheduling: 1: 68M20 Performance evaluation; queueing; scheduling [See also]60K25, 90Bxxscheduling: 2: 90B35 Scheduling theory, deterministic [See also]68M20scheduling: 3: 90B36 Scheduling theory, stochastic [See also]68M20
scheme: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions
schemes: 1: 05E30 Association schemes, strongly regular graphsschemes: 2: 14A15 Schemes and morphismsschemes: 3: 14C05 Parametrization (Chow and Hilbert schemes)schemes: 4: 14F22 Brauer groups of schemes [See also]12G05, 16K50schemes: 5: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30schemes: 6: 14Kxx Abelian varieties and schemesschemes: 7: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G20schemes: 8: 14L15 Group schemesschemes: 9: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17schemes: 10: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]schemes: 11: 19E08 K-theory of schemes [See also]14C35schemes: 12: 20G35 Linear algebraic groups over adeles and other rings and schemes
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schemes: 13: 68P30 Coding and information theory (compaction, compression, models of communication,encoding schemes, etc.) [See also]94Axx
schemes: 14: 70K60 General perturbation schemesschemes: 15: 94B12 Combined modulation schemes (including trellis codes)schmidt: 1: 11J87 Schmidt Subspace Theorem and applications
schoenflies: 1: 57N50 Sn − 1⊂ En, Schoenflies problemschools: 1: 01A72 Schools of mathematics
schottky: 1: 14H42 Theta functions; Schottky problem [See also]14K25, 32G20schrodinger: 1: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)schrodinger: 2: 35J10 Schrodinger operator [See also]35Pxxschrodinger: 3: 35Q41 Time-dependent Schrodinger equations, Dirac equationsschrodinger: 4: 35Q55 NLS-like equations (nonlinear Schrodinger) [See also]37K10schrodinger: 5: 47D08 Schrodinger and Feynman-Kac semigroupsschrodinger: 6: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and otherequations of quantum mechanics
schrodinger: 7: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)schramm-loewner: 1: 60J67 Stochastic (Schramm-)Loewner evolution (SLE)
schubert: 1: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M35schubert: 2: 14N15 Classical problems, Schubert calculusschunck: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17schur: 1: 19C09 Central extensions and Schur multipliersschur: 2: 20G43 Schur and q-Schur algebras
schwartz: 1: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartzspaces, Montel spaces, etc.)
schwarz’s: 1: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;subordination
science: 1: 03A10 Logic in the philosophy of sciencescience: 2: 03B70 Logic in computer science [See also]68-XXscience: 3: 08A70 Applications of universal algebra in computer sciencescience: 4: 35Q68 PDEs in connection with computer sciencescience: 5: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxscience: 6: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areascience: 7: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40science: 8: 68Rxx Discrete mathematics in relation to computer sciencescience: 9: 90Bxx Operations research and management sciencescience: 10: 91F10 History, political sciencescience: 11: 97Pxx Computer sciencescience: 12: 97P20 Theory of computer sciencescience: 13: 97P70 Computer science and societyscience: 14: 97Qxx Computer science educationscience: 15: 97Q20 Affective aspects in teaching computer sciencescience: 16: 97Rxx Computer science applications
sciences: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)sciences: 2: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencessciences: 3: 35Q92 PDEs in connection with biology and other natural sciencessciences: 4: 46N60 Applications in biology and other sciencessciences: 5: 47N50 Applications in the physical sciencessciences: 6: 47N60 Applications in chemistry and life sciencessciences: 7: 62P05 Applications to actuarial sciences and financial mathematicssciences: 8: 62P10 Applications to biology and medical sciencessciences: 9: 62P25 Applications to social sciencessciences: 10: 91-XX Game theory, economics, social and behavioral sciencessciences: 11: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XX
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sciences: 12: 91Fxx Other social and behavioral sciences (mathematical treatment)sciences: 13: 92-XX Biology and other natural sciencessciences: 14: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)sciences: 15: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)sciences: 16: 97M70 Behavioral and social sciencessciences: 17: 97R30 Applications in sciences
search: 1: 68T20 Problem solving (heuristics, search strategies, etc.)search: 2: 90B40 Search theory
searching: 1: 68P10 Searching and sortingsecond-: 1: 03C85 Second- and higher-order model theorysecond-: 2: 03F35 Second- and higher-order arithmetic and fragments [See also]03B30
second-order: 1: 03E70 Nonclassical and second-order set theoriessecond-order: 2: 35J15 Second-order elliptic equationssecond-order: 3: 35J20 Variational methods for second-order elliptic equationssecond-order: 4: 35J25 Boundary value problems for second-order elliptic equationssecond-order: 5: 35J47 Second-order elliptic systemssecond-order: 6: 35J57 Boundary value problems for second-order elliptic systemssecond-order: 7: 35K10 Second-order parabolic equationssecond-order: 8: 35K15 Initial value problems for second-order parabolic equationssecond-order: 9: 35K20 Initial-boundary value problems for second-order parabolic equationssecond-order: 10: 35K40 Second-order parabolic systemssecond-order: 11: 35K45 Initial value problems for second-order parabolic systemssecond-order: 12: 35K51 Initial-boundary value problems for second-order parabolic systemssecond-order: 13: 35L10 Second-order hyperbolic equationssecond-order: 14: 35L15 Initial value problems for second-order hyperbolic equationssecond-order: 15: 35L20 Initial-boundary value problems for second-order hyperbolic equationssecond-order: 16: 35L51 Second-order hyperbolic systemssecond-order: 17: 35L52 Initial value problems for second-order hyperbolic systemssecond-order: 18: 35L53 Initial-boundary value problems for second-order hyperbolic systemssecond-order: 19: 35L70 Nonlinear second-order hyperbolic equationssecond-order: 20: 35L71 Semilinear second-order hyperbolic equationssecond-order: 21: 35L72 Quasilinear second-order hyperbolic equationssecond-order: 22: 60G12 General second-order processes
secondary: 1: 55S20 Secondary and higher cohomology operationssecret: 1: 94A62 Authentication and secret sharing [See also]81P94
section: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assignedat least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35
section: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)
section: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
section: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
section: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classificationnumber in this section)
section: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
section: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
section: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)
section: 9: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
section: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)
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section: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)
section: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)
section: 13: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)
section: 14: 62E86 Fuzziness in connection with the topics on distributions in this sectionsection: 15: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)section: 16: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)section: 17: 92F05 Other natural sciences (should also be assigned at least one other classification number
in section 92)section: 18: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10section: 19: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10section–04: 1: 68-XX Computer science For papers involving machine computations and programs in aspecific mathematical area, see Section–04 in that areasectioning: 1: 55S40 Sectioning fiber spaces and bundles
sections: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86sections: 2: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)sections: 3: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30sections: 4: 51Pxx Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)sections: 5: 51P05 Geometry and physics (should also be assigned at least one other classification number
from Sections 70–86)sections: 1: 01-XX History and biography [See also]the classification number–03 in the other sections
securities: 1: 91G20 Derivative securitiessee: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86see: 2: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30see: 3: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45see: 4: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45see: 5: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45see: 6: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F52see: 7: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionistic
and similar approaches see 03F55see: 8: 03D78 Computation over the reals For constructive aspects, see 03F60see: 9: 05-XX Combinatorics For finite fields, see 11Txxsee: 10: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30see: 11: 05Bxx Designs and configurations For applications of design theory, see 94C30see: 12: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C15see: 13: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10see: 14: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A26see: 15: 06D22 Frames, locales For topological questions see 54-XXsee: 16: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80see: 17: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W80see: 18: 11Axx Elementary number theory For analogues in number fields, see 11R04see: 19: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A15
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see: 20: 11A63 Radix representation; digital problems For metric results, see 11K16see: 21: 11B37 Recurrences For applications to special functions, see 33-XXsee: 22: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A63see: 23: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45see: 24: 11Hxx Geometry of numbers For applications in coding theory, see 94B75see: 25: 11Lxx Exponential sums and character sums For finite fields, see 11Txxsee: 26: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72see: 27: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72see: 28: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72see: 29: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15see: 30: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15see: 31: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S10see: 32: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxsee: 33: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxxsee: 34: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txxsee: 35: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13see: 36: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32see: 37: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxsee: 38: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35see: 39: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45see: 40: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45see: 41: 16-XX Associative rings and algebras For the commutative case, see 13-XXsee: 42: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxsee: 43: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxxsee: 44: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30see: 45: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30see: 46: 16K20 Finite-dimensional For crossed products, see 16S35see: 47: 16N80 General radicals and rings For radicals in module categories, see 16S90see: 48: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxsee: 49: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxxsee: 50: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxsee: 51: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66see: 52: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66see: 53: 16Yxx Generalizations For nonassociative rings, see 17-XXsee: 54: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxsee: 55: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
see: 56: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
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associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
see: 57: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]see: 58: 20A10 Metamathematical considerations For word problems, see 20F10see: 59: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]see: 60: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
see: 61: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
see: 62: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
see: 63: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]see: 64: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05see: 65: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05see: 66: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05see: 67: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05see: 68: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXsee: 69: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XXsee: 70: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W80see: 71: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90see: 72: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90see: 73: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05see: 74: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxsee: 75: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20see: 76: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40see: 77: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40see: 78: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
see: 79: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
see: 80: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
see: 81: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
see: 82: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
see: 83: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see49J52, 58Cxx, 90Cxx
see: 84: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
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or measure chains see 34N05see: 85: 28-XX Measure and integration For analysis on manifolds, see 58-XXsee: 86: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXsee: 87: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10see: 88: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10see: 89: 31-XX Potential theory For probabilistic potential theory, see 60J45see: 90: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14see: 91: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12see: 92: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30see: 93: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35see: 94: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27see: 95: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15see: 96: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see 32A22see: 97: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22see: 98: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxsee: 99: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxsee: 100: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
see: 101: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
see: 102: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
see: 103: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX;for representation theory see 22Exx
see: 104: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxsee: 105: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxsee: 106: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E70see: 107: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E70see: 108: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxsee: 109: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15see: 110: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15see: 111: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15see: 112: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35see: 113: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05see: 114: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05see: 115: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
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summation formula, see 65B15see: 116: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 117: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 118: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 119: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 120: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 121: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
see: 122: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
see: 123: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30
see: 124: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30see: 125: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxsee: 126: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see
22Exxsee: 127: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 128: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 129: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 130: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 131: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 132: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 133: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 134: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
see: 135: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxsee: 136: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxsee: 137: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxsee: 138: 46Axx Topological linear spaces and related structures For function spaces, see 46Exx
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see: 139: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see46Exx
see: 140: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see46Exx
see: 141: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For functionalgebras, see 46J10
see: 142: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banachfunction algebras, see 46J10, 46J15
see: 143: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,convolution algebras and measure algebras, see 43A10, 43A20
see: 144: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20see: 145: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M15see: 146: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20see: 147: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M20see: 148: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxsee: 149: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxsee: 150: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XXsee: 151: 51-XX Geometry For algebraic geometry, see 14-XXsee: 152: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F55see: 153: 51M16 Inequalities and extremum problems For convex problems, see 52A40see: 154: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxsee: 155: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxsee: 156: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxsee: 157: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxsee: 158: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxsee: 159: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxsee: 160: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80see: 161: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80see: 162: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxsee: 163: 55N15 K-theory [See also]19Lxx For algebraic K-theory, see 18F25, 19-XXsee: 164: 55Pxx Homotopy theory For simple homotopy type, see 57Q10see: 165: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XXsee: 166: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxxsee: 167: 57M25 Knots and links in S3 For higher dimensions, see 57Q45see: 168: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M25see: 169: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxsee: 170: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxsee: 171: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15see: 172: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX
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see: 173: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxsee: 174: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)see: 175: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35see: 176: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35see: 177: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxsee: 178: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30see: 179: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30see: 180: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areasee: 181: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30see: 182: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxsee: 183: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxsee: 184: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXsee: 185: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXsee: 186: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XXsee: 187: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80see: 188: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15see: 189: 82D25 Crystals For crystallographic group theory, see 20H15see: 190: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F15see: 191: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F15see: 192: 85A40 Cosmology For relativistic cosmology, see 83F05see: 193: 91Bxx Mathematical economics For econometrics, see 62P20see: 194: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXsee: 195: 92D10 Genetics For genetic algebras, see 17D92see: 196: 92Exx Chemistry For biochemistry, see 92C40see: 197: 93-XX Systems theory; control For optimal control, see 49-XXsee: 198: 97B50 Teacher education For research aspects, see 97C70see: 199: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxx
seepage: 1: 76Sxx Flows in porous media; filtration; seepageseepage: 2: 76S05 Flows in porous media; filtration; seepage
seiberg-witten: 1: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)seiberg-witten: 2: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXseismology: 1: 86A15 Seismology
selberg: 1: 11F72 Spectral theory; Selberg trace formulaselberg: 2: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasselected: 1: 00B50 Volumes of selected translationsselected: 2: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60
selection: 1: 62F07 Ranking and selectionselections: 1: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B14selections: 2: 54C65 Selections [See also]28B20
self-injective: 1: 16D50 Injective modules, self-injective rings [See also]16L60self-similar: 1: 35C06 Self-similar solutionsself-similar: 2: 60G18 Self-similar processesselfadjoint: 1: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)[See also]22D25, 47Lxxselfadjoint: 2: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
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81T05, 82B10, 82C10selfadjoint: 3: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K70selfadjoint: 4: 47B25 Symmetric and selfadjoint operators (unbounded)selfadjoint: 5: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
selling: 1: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)semantics: 1: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30semantics: 2: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q65semantics: 3: 68Q55 Semantics [See also]03B70, 06B35, 18C50
semi-: 1: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J20semi-analytic: 1: 32B20 Semi-analytic sets and subanalytic sets [See also]14P15semi-infinite: 1: 90C34 Semi-infinite programming
semi-inner: 1: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)semi-markov: 1: 60K15 Markov renewal processes, semi-Markov processessemi-markov: 2: 90C40 Markov and semi-Markov decision processes
semi-reflexivity: 1: 46A25 Reflexivity and semi-reflexivity [See also]46B10semialgebraic: 1: 14P10 Semialgebraic sets and related spacessemianalytic: 1: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C05semiclassical: 1: 81Q20 Semiclassical techniques, including WKB and Maslov methods
semiconductors: 1: 82D37 Semiconductorssemicontinuity: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
semicontinuity: 2: 49J45 Methods involving semicontinuity and convergence; relaxationsemicontinuous: 1: 40C15 Function-theoretic methods (including power series methods and semicontinuous
methods)semidefinite: 1: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)semidefinite: 2: 90C22 Semidefinite programming
semifields: 1: 12J17 Topological semifieldssemifields: 2: 12K10 Semifields [See also]16Y60
semigroup: 1: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25semigroup: 2: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y60
semigroup-valued: 1: 28B10 Group- or semigroup-valued set functions, measures and integralssemigroupoids: 1: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
20L05, 20Mxxsemigroups: 1: 06F05 Ordered semigroups and monoids [See also]20Mxxsemigroups: 2: 16W22 Actions of groups and semigroups; invariant theorysemigroups: 3: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,20L05, 20Mxxsemigroups: 4: 20Mxx Semigroupssemigroups: 5: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,20F10semigroups: 6: 20M07 Varieties and pseudovarieties of semigroupssemigroups: 7: 20M14 Commutative semigroupssemigroups: 8: 20M15 Mappings of semigroupssemigroups: 9: 20M17 Regular semigroupssemigroups: 10: 20M18 Inverse semigroupssemigroups: 11: 20M19 Orthodox semigroupssemigroups: 12: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H15semigroups: 13: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y60semigroups: 14: 20M30 Representation of semigroups; actions of semigroups on setssemigroups: 15: 20M30 Representation of semigroups; actions of semigroups on setssemigroups: 16: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50semigroups: 17: 20M50 Connections of semigroups with homological algebra and category theorysemigroups: 18: 22A15 Structure of topological semigroupssemigroups: 19: 22A20 Analysis on topological semigroupssemigroups: 20: 22A25 Representations of general topological groups and semigroups
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semigroups: 21: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,invariant measures [See also]22Axx, 43A05semigroups: 22: 37L05 General theory, nonlinear semigroups, evolution equationssemigroups: 23: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemssemigroups: 24: 43A05 Measures on groups and semigroups, etc.semigroups: 25: 43A07 Means on groups, semigroups, etc.; amenable groupssemigroups: 26: 43A10 Measure algebras on groups, semigroups, etc.semigroups: 27: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.semigroups: 28: 43A20 L1-algebras on groups, semigroups, etc.semigroups: 29: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.semigroups: 30: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.semigroups: 31: 43A35 Positive definite functions on groups, semigroups, etc.semigroups: 32: 43A45 Spectral synthesis on groups, semigroups, etc.semigroups: 33: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05semigroups: 34: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrentfunctions, distal functions, etc.); almost automorphic functionssemigroups: 35: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E45semigroups: 36: 46L57 Derivations, dissipations and positive semigroups in C∗-algebrassemigroups: 37: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationssemigroups: 38: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; seealso 20M20semigroups: 39: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K30semigroups: 40: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see60Jxxsemigroups: 41: 47D08 Schrodinger and Feynman-Kac semigroupssemigroups: 42: 47D60 C-semigroups, regularized semigroupssemigroups: 43: 47D62 Integrated semigroupssemigroups: 44: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D07semigroups: 45: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxxsemigroups: 46: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H20semigroups: 47: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorizationsemiheaps: 1: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
semihereditary: 1: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.semilattices: 1: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A26semilattices: 2: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A26semilattices: 3: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F30
semilinear: 1: 15A04 Linear transformations, semilinear transformationssemilinear: 2: 35J61 Semilinear elliptic equationssemilinear: 3: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplaciansemilinear: 4: 35K58 Semilinear parabolic equationssemilinear: 5: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplaciansemilinear: 6: 35L71 Semilinear second-order hyperbolic equationssemilinear: 7: 35L76 Semilinear higher-order hyperbolic equationssemilocal: 1: 13Hxx Local rings and semilocal ringssemilocal: 2: 16L30 Noncommutative local and semilocal rings, perfect rings
semimetric: 1: 54E25 Semimetric spacessemimodular: 1: 06C10 Semimodular lattices, geometric lattices
seminormal: 1: 13F45 Seminormal ringsseminormal: 2: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)[See also]13F15, 13F45, 13H10semiprime: 1: 16N60 Prime and semiprime rings [See also]16D60, 16U10semiprime: 2: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative ringssemirings: 1: 16Y60 Semirings [See also]12K10
semisimple: 1: 16D60 Simple and semisimple modules, primitive rings and idealssemisimple: 2: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A30semisimple: 3: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-tive, see 11Txx, 13Mxx
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semisimple: 4: 17B20 Simple, semisimple, reductive (super)algebrassemisimple: 5: 17C20 Simple, semisimple algebrassemisimple: 6: 22E46 Semisimple Lie groups and their representationssensitivity: 1: 49K40 Sensitivity, stability, well-posedness [See also]90C31sensitivity: 2: 49Q12 Sensitivity analysissensitivity: 3: 90C31 Sensitivity, stability, parametric optimizationsensitivity: 4: 93B35 Sensitivity (robustness)sentences: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F10sentences: 2: 03D35 Undecidability and degrees of sets of sentences
separability: 1: 54D65 Separabilityseparable: 1: 12F10 Separable extensions, Galois theoryseparable: 2: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)separable: 3: 16H10 Orders in separable algebras
separation: 1: 39B82 Stability, separation, extension, and related topics [See also]46A22separation: 2: 54D10 Lower separation axioms (T0–T3, etc.)separation: 3: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwisenormal, etc.)separation: 4: 76D10 Boundary-layer theory, separation and reattachment, higher-order effects
sequence: 1: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45sequence: 2: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45sequence: 3: 46B45 Banach sequence spaces [See also]46A45sequence: 4: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
sequences: 1: 11Bxx Sequences and setssequences: 2: 11B50 Sequences (mod m)sequences: 3: 11B57 Farey sequences; the sequences 1k, 2k, · · ·sequences: 4: 11B57 Farey sequences; the sequences 1k, 2k, · · ·sequences: 5: 11B83 Special sequences and polynomialssequences: 6: 11B85 Automata sequencessequences: 7: 11K31 Special sequencessequences: 8: 11K36 Well-distributed sequences and other variationssequences: 9: 11Y55 Calculation of integer sequencessequences: 10: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxxsequences: 11: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quiverssequences: 12: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quiverssequences: 13: 18G40 Spectral sequences, hypercohomology [See also]55Txxsequences: 14: 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of
convergencesequences: 15: 40-XX Sequences, series, summabilitysequences: 16: 40A05 Convergence and divergence of series and sequencessequences: 17: 40A30 Convergence and divergence of series and sequences of functionssequences: 18: 40Bxx Multiple sequences and seriessequences: 19: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)sequences: 20: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)sequences: 21: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)sequences: 22: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txxsequences: 23: 55Txx Spectral sequences [See also]18G40, 55R20sequences: 24: 55T10 Serre spectral sequencessequences: 25: 55T15 Adams spectral sequencessequences: 26: 55T20 Eilenberg-Moore spectral sequences [See also]57T35sequences: 27: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T20sequences: 28: 92D20 Protein sequences, DNA sequencessequences: 29: 92D20 Protein sequences, DNA sequencessequences: 30: 94A55 Shift register sequences and sequences over finite alphabetssequences: 31: 94A55 Shift register sequences and sequences over finite alphabetssequences: 32: 97I30 Sequences and seriessequential: 1: 54D55 Sequential spaces
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sequential: 2: 62Lxx Sequential methodssequential: 3: 62L05 Sequential designsequential: 4: 62L10 Sequential analysissequential: 5: 62L12 Sequential estimationsequential: 6: 62L86 Fuzziness and sequential methodssequential: 7: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,etc.)
series: 1: 11D88 p-adic and power series fieldsseries: 2: 11F27 Theta series; Weil representation; theta correspondencesseries: 3: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsseries: 4: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesseries: 5: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesseries: 6: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesseries: 7: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasseries: 8: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasseries: 9: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72series: 10: 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincare seriesseries: 11: 13F25 Formal power series rings [See also]13J05series: 12: 13J05 Power series rings [See also]13F25series: 13: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxseries: 14: 20D30 Series and lattices of subgroupsseries: 15: 20F14 Derived series, central series, and generalizationsseries: 16: 20F14 Derived series, central series, and generalizationsseries: 17: 26D15 Inequalities for sums, series and integralsseries: 18: 30Bxx Series expansionsseries: 19: 30B10 Power series (including lacunary series)series: 20: 30B10 Power series (including lacunary series)series: 21: 30B20 Random power seriesseries: 22: 30B30 Boundary behavior of power series, over-convergenceseries: 23: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXseries: 24: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXseries: 25: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XXseries: 26: 30D10 Representations of entire functions by series and integralsseries: 27: 30K05 Universal Taylor seriesseries: 28: 30K10 Universal Dirichlet seriesseries: 29: 32A05 Power series, series of functionsseries: 30: 32A05 Power series, series of functionsseries: 31: 33C20 Generalized hypergeometric series, pFq
series: 32: 33E20 Other functions defined by series and integralsseries: 33: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XXseries: 34: 35C10 Series solutionsseries: 35: 37M10 Time series analysisseries: 36: 40-XX Sequences, series, summabilityseries: 37: 40A05 Convergence and divergence of series and sequencesseries: 38: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15series: 39: 40A30 Convergence and divergence of series and sequences of functionsseries: 40: 40Bxx Multiple sequences and seriesseries: 41: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)series: 42: 40C15 Function-theoretic methods (including power series methods and semicontinuous
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methods)series: 43: 40G10 Abel, Borel and power series methodsseries: 44: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)series: 45: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)series: 46: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)series: 47: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30series: 48: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30series: 49: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriesseries: 50: 42A24 Summability and absolute summability of Fourier and trigonometric seriesseries: 51: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)series: 52: 42A50 Conjugate functions, conjugate series, singular integralsseries: 53: 42A55 Lacunary series of trigonometric and other functions; Riesz productsseries: 54: 42B05 Fourier series and coefficientsseries: 55: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)series: 56: 42C25 Uniqueness and localization for orthogonal seriesseries: 57: 43A50 Convergence of Fourier series and of inverse transformsseries: 58: 45F10 Dual, triple, etc., integral and series equationsseries: 59: 62M10 Time series, auto-correlation, regression, etc. [See also]91B84series: 60: 65B10 Summation of seriesseries: 61: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods,
series, etc.)series: 62: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods,
series, etc.)series: 63: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80series: 64: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)series: 65: 91B84 Economic time series analysis [See also]62M10series: 66: 97I30 Sequences and seriesserre: 1: 55T10 Serre spectral sequences
service: 1: 90B22 Queues and service [See also]60K25, 68M20sesquilinear: 1: 47A07 Forms (bilinear, sesquilinear, multilinear)
set: 1: 03C62 Models of arithmetic and set theory [See also]03Hxxset: 2: 03D65 Higher-type and set recursion theoryset: 3: 03Exx Set theoryset: 4: 03E05 Other combinatorial set theoryset: 5: 03E15 Descriptive set theory [See also]28A05, 54H05set: 6: 03E20 Other classical set theory (including functions, relations, and set algebra)set: 7: 03E20 Other classical set theory (including functions, relations, and set algebra)set: 8: 03E30 Axiomatics of classical set theory and its fragmentsset: 9: 03E70 Nonclassical and second-order set theoriesset: 10: 03E72 Fuzzy set theoryset: 11: 03E75 Applications of set theoryset: 12: 05D05 Extremal set theoryset: 13: 28A10 Real- or complex-valued set functionsset: 14: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24set: 15: 28A25 Integration with respect to measures and other set functionsset: 16: 28Bxx Set functions, measures and integrals with values in abstract spacesset: 17: 28B05 Vector-valued set functions, measures and integrals [See also]46G10set: 18: 28B10 Group- or semigroup-valued set functions, measures and integralsset: 19: 28B15 Set functions, measures and integrals with values in ordered spacesset: 20: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B14set: 21: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20set: 22: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
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representing set functions and measuresset: 23: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A05set: 24: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)set: 25: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11set: 26: 28E15 Other connections with logic and set theoryset: 27: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationsset: 28: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)set: 29: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05set: 30: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C60set: 31: 91A44 Games involving topology or set theoryset: 32: 97E60 Sets, relations, set theory
set-theoretic: 1: 03C55 Set-theoretic model theoryset-theoretic: 2: 03E47 Other notions of set-theoretic definability
set-valued: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see49J52, 58Cxx, 90Cxxset-valued: 2: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurableselections [See also]26E25, 54C60, 54C65, 91B14set-valued: 3: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurableselections [See also]26E25, 54C60, 54C65, 91B14set-valued: 4: 47H04 Set-valued operators [See also]28B20, 54C60, 58C06set-valued: 5: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C06set-valued: 6: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C06
sets: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F10sets: 2: 03C70 Logic on admissible setssets: 3: 03D25 Recursively (computably) enumerable sets and degreessets: 4: 03D35 Undecidability and degrees of sets of sentencessets: 5: 03D50 Recursive equivalence types of sets and structures, isolssets: 6: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.sets: 7: 03E04 Ordered sets and their cofinalities; pcf theorysets: 8: 05A18 Partitions of setssets: 9: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B13sets: 10: 05C69 Dominating sets, independent sets, cliquessets: 11: 05C69 Dominating sets, independent sets, cliquessets: 12: 06Axx Ordered setssets: 13: 06A07 Combinatorics of partially ordered setssets: 14: 06A75 Generalizations of ordered setssets: 15: 11Bxx Sequences and setssets: 16: 14P05 Real algebraic sets [See also]12D15, 13J30sets: 17: 14P10 Semialgebraic sets and related spacessets: 18: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C05sets: 19: 16G20 Representations of quivers and partially ordered setssets: 20: 16N40 Nil and nilpotent radicals, sets, ideals, ringssets: 21: 16U20 Ore rings, multiplicative sets, Ore localizationsets: 22: 18B05 Category of sets, characterizations [See also]03-XXsets: 23: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10sets: 24: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05sets: 25: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05sets: 26: 20M30 Representation of semigroups; actions of semigroups on setssets: 27: 20N02 Sets with a single binary operation (groupoids)sets: 28: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H05
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sets: 29: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
sets: 30: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
sets: 31: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
sets: 32: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
sets: 33: 30D40 Cluster sets, prime ends, boundary behaviorsets: 34: 32A60 Zero sets of holomorphic functionssets: 35: 32B10 Germs of analytic sets, local parametrizationsets: 36: 32B20 Semi-analytic sets and subanalytic sets [See also]14P15sets: 37: 32B20 Semi-analytic sets and subanalytic sets [See also]14P15sets: 38: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P20sets: 39: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27sets: 40: 32U30 Removable setssets: 41: 35A18 Wave front setssets: 42: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J15sets: 43: 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant setssets: 44: 37D05 Hyperbolic orbits and setssets: 45: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setssets: 46: 37G30 Infinite nonwandering sets arising in bifurcationssets: 47: 37L25 Inertial manifolds and other invariant attracting setssets: 48: 37P40 Non-Archimedean Fatou and Julia setssets: 49: 42A65 Completeness of sets of functionssets: 50: 42C30 Completeness of sets of functionssets: 51: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 52: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 53: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 54: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 55: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 56: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)sets: 57: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07sets: 58: 47A25 Spectral setssets: 59: 47L07 Convex sets and cones of operators [See also]46A55sets: 60: 51E21 Blocking sets, ovals, k-arcssets: 61: 52A05 Convex sets without dimension restrictionssets: 62: 52A07 Convex sets in topological vector spaces [See also]46A55sets: 63: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A04sets: 64: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45sets: 65: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C45sets: 66: 52A22 Random convex sets and integral geometry [See also]53C65, 60D05sets: 67: 52A27 Approximation by convex setssets: 68: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)sets: 69: 54C50 Special sets defined by functions [See also]26A21sets: 70: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05sets: 71: 55Q05 Homotopy groups, general; sets of homotopy classessets: 72: 55U10 Simplicial sets and complexessets: 73: 58A35 Stratified sets [See also]32S60sets: 74: 93B03 Attainable setssets: 75: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71sets: 76: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10sets: 77: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
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28E10sets: 78: 97E60 Sets, relations, set theory
setting: 1: 49Q20 Variational problems in a geometric measure-theoretic settingseveral: 1: 11F55 Other groups and their modular and automorphic forms (several variables)several: 2: 11F60 Hecke-Petersson operators, differential operators (several variables)several: 3: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesseveral: 4: 26Bxx Functions of several variablesseveral: 5: 26B10 Implicit function theorems, Jacobians, transformations with several variablesseveral: 6: 26B35 Special properties of functions of several variables, Holder conditions, etc.several: 7: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12several: 8: 32Axx Holomorphic functions of several complex variablesseveral: 9: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35several: 10: 32A50 Harmonic analysis of several complex variables [See mainly]43-XXseveral: 11: 32N05 General theory of automorphic functions of several complex variablesseveral: 12: 32Wxx Differential operators in several variablesseveral: 13: 32W25 Pseudodifferential operators in several complex variablesseveral: 14: 32W30 Heat kernels in several complex variablesseveral: 15: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variableseveral: 16: 33C70 Other hypergeometric functions and integrals in several variablesseveral: 17: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variableseveral: 18: 33D70 Other basic hypergeometric functions and integrals in several variablesseveral: 19: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30several: 20: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)several: 21: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.several: 22: 97I60 Functions of several variables
several-variable: 1: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)shadowing: 1: 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)
shafts: 1: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)shannon: 1: 94A24 Coding theorems (Shannon theory)
shape: 1: 54C56 Shape theory [See also]55P55, 57N25shape: 2: 55P55 Shape theory [See also]54C56, 55Q07shape: 3: 55Q07 Shape groups
shapes: 1: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90shapes: 2: 57N25 Shapes [See also]54C56, 55P55, 55Q07
sharing: 1: 94A62 Authentication and secret sharing [See also]81P94sheaf: 1: 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)sheaf: 2: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15sheaf: 3: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxsheaf: 4: 55N30 Sheaf cohomology [See also]18F20, 32C35, 32L10shear: 1: 76E05 Parallel shear flowsshear: 2: 76F10 Shear flows
sheaves: 1: 14C20 Divisors, linear systems, invertible sheavessheaves: 2: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M20sheaves: 3: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M20sheaves: 4: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C38
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sheaves: 5: 16S60 Rings of functions, subdirect products, sheaves of ringssheaves: 6: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N30sheaves: 7: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N30sheaves: 8: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J15sheaves: 9: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30sheaves: 10: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxxsheaves: 11: 54B40 Presheaves and sheaves [See also]18F20
shellability: 1: 52B22 Shellabilityshells: 1: 74K25 Shellsshift: 1: 94A55 Shift register sequences and sequences over finite alphabets
shifts: 1: 37B50 Multi-dimensional shifts of finite type, tiling dynamicsshifts: 2: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
shimura: 1: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G35shimura: 2: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G18
ship: 1: 76B20 Ship wavesshock: 1: 76Lxx Shock waves and blast waves [See also]35L67shock: 2: 76L05 Shock waves and blast waves [See also]35L67
shocks: 1: 35L67 Shocks and singularities [See also]58Kxx, 76L05shocks: 2: 74J40 Shocks and related discontinuities
shorted: 1: 47A64 Operator means, shorted operators, etc.shortest: 1: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxx
should: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assignedat least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35
should: 2: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-tion number from Section 32 describing the type of problem)
should: 3: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
should: 4: 32P05 Non-Archimedean analysis (should also be assigned at least one other classificationnumber from Section 32 describing the type of problem)
should: 5: 40B05 Multiple sequences and series (should also be assigned at least one other classificationnumber in this section)
should: 6: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
should: 7: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-tion number in Section 40)
should: 8: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)
should: 9: 41A63 Multidimensional problems (should also be assigned at least one other classificationnumber in this section)
should: 10: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at leastone other classification number in section 47)
should: 11: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least oneother classification number in section 47)
should: 12: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)
should: 13: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)
should: 14: 51Pxx Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
should: 15: 51P05 Geometry and physics (should also be assigned at least one other classification numberfrom Sections 70–86)
should: 16: 92Fxx Other natural sciences (should also be assigned at least one other classification numberin this section)
should: 17: 92F05 Other natural sciences (should also be assigned at least one other classification numberin section 92)
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shrinkage: 1: 62J07 Ridge regression; shrinkage estimatorssides: 1: 35R70 Partial differential equations with multivalued right-hand sidessidon: 1: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)siegel: 1: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formssiegel: 2: 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic formssieve: 1: 11N36 Applications of sieve methods
sieves: 1: 11N35 Sievessign: 1: 15B35 Sign pattern matrices
signal: 1: 60G35 Signal detection and filtering [See also]62M20, 93E10, 93E11, 94Axxsignal: 2: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A12signal: 3: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
signaling: 1: 91A28 Signaling, communicationsigned: 1: 05C22 Signed and weighted graphssimilar: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionistic
and similar approaches see 03F55similar: 2: 15A16 Matrix exponential and similar functions of matricessimilar: 3: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablessimilar: 4: 54B17 Adjunction spaces and similar constructionssimilar: 5: 65F60 Matrix exponential and similar matrix functions
similarity: 1: 76M55 Dimensional analysis and similaritysimple: 1: 11F22 Relationship to Lie algebras and finite simple groupssimple: 2: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)simple: 3: 16D60 Simple and semisimple modules, primitive rings and idealssimple: 4: 17B20 Simple, semisimple, reductive (super)algebrassimple: 5: 17C20 Simple, semisimple algebrassimple: 6: 20D05 Finite simple groups and their classificationsimple: 7: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxsimple: 8: 20D08 Simple groups: sporadic groupssimple: 9: 20E32 Simple groups [See also]20D05simple: 10: 55Pxx Homotopy theory For simple homotopy type, see 57Q10simple: 11: 55Q20 Homotopy groups of wedges, joins, and simple spacessimple: 12: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28simplicial: 1: 05E45 Combinatorial aspects of simplicial complexessimplicial: 2: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U10simplicial: 3: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10simplicial: 4: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U10simplicial: 5: 55U10 Simplicial sets and complexes
simplification: 1: 93B11 System structure simplificationsimulation: 1: 00A72 General methods of simulationsimulation: 2: 34C60 Qualitative investigation and simulation of modelssimulation: 3: 34K60 Qualitative investigation and simulation of modelssimulation: 4: 37M05 Simulationsimulation: 5: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoreticalaspects, see 68U20 and 60H35simulation: 6: 68U20 Simulation [See also]65Cxxsimulation: 7: 76F65 Direct numerical and large eddy simulation of turbulencesimulation: 8: 81T80 Simulation and numerical modeling
simultaneous: 1: 11J13 Simultaneous homogeneous approximation, linear formssimultaneous: 2: 41A28 Simultaneous approximation
sine: 1: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G10single: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05single: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05single: 3: 20N02 Sets with a single binary operation (groupoids)single: 4: 65H05 Single equations
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singly: 1: 47L45 Dual algebras; weakly closed singly generated operator algebrassingular: 1: 15A18 Eigenvalues, singular values, and eigenvectorssingular: 2: 26A30 Singular functions, Cantor functions, functions with other special propertiessingular: 3: 30J15 Singular inner functionssingular: 4: 32A55 Singular integralssingular: 5: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D07singular: 6: 34B16 Singular nonlinear boundary value problemssingular: 7: 34C05 Location of integral curves, singular points, limit cyclessingular: 8: 34D15 Singular perturbationssingular: 9: 34E15 Singular perturbations, general theorysingular: 10: 34E20 Singular perturbations, turning point theory, WKB methodssingular: 11: 34K26 Singular perturbationssingular: 12: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20singular: 13: 35B25 Singular perturbationssingular: 14: 35J75 Singular elliptic equationssingular: 15: 35K67 Singular parabolic equationssingular: 16: 35L81 Singular hyperbolic equationssingular: 17: 37G10 Bifurcations of singular pointssingular: 18: 37G20 Hyperbolic singular points with homoclinic trajectoriessingular: 19: 42A50 Conjugate functions, conjugate series, singular integralssingular: 20: 42B20 Singular and oscillatory integrals (Calderon-Zygmund, etc.)singular: 21: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A35singular: 22: 45F15 Systems of singular linear integral equationssingular: 23: 45G05 Singular nonlinear integral equationssingular: 24: 55N10 Singular theorysingular: 25: 76M45 Asymptotic methods, singular perturbationssingular: 26: 93C70 Time-scale analysis and singular perturbations
singularities: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxxsingularities: 2: 14B07 Deformations of singularities [See also]14D15, 32S30singularities: 3: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S45singularities: 4: 14H20 Singularities, local rings [See also]13Hxx, 14B05singularities: 5: 14J17 Singularities [See also]14B05, 14E15singularities: 6: 32D20 Removable singularitiessingularities: 7: 32Sxx Singularities [See also]58Kxxsingularities: 8: 32S05 Local singularities [See also]14J17singularities: 9: 32S20 Global theory of singularities; cohomological properties [See also]14E15singularities: 10: 32S25 Surface and hypersurface singularities [See also]14J17singularities: 11: 32S30 Deformations of singularities; vanishing cycles [See also]14B07singularities: 12: 32S45 Modifications; resolution of singularities [See also]14E15singularities: 13: 32S65 Singularities of holomorphic vector fields and foliationssingularities: 14: 32S70 Other operations on singularitiessingularities: 15: 34M35 Singularities, monodromy, local behavior of solutions, normal formssingularities: 16: 35A20 Analytic methods, singularitiessingularities: 17: 35A21 Propagation of singularitiessingularities: 18: 35L67 Shocks and singularities [See also]58Kxx, 76L05singularities: 19: 37D50 Hyperbolic systems with singularities (billiards, etc.)singularities: 20: 55R55 Fiberings with singularitiessingularities: 21: 57R45 Singularities of differentiable mappingssingularities: 22: 58J47 Propagation of singularities; initial value problemssingularities: 23: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XXsingularities: 24: 58K45 Singularities of vector fields, topological aspectssingularities: 25: 58K60 Deformation of singularitiessingularities: 26: 74G70 Stress concentrations, singularitiessingularities: 27: 74H35 Singularities, blowup, stress concentrationssingularities: 28: 83C75 Space-time singularities, cosmic censorship, etc.
singularity: 1: 60G30 Continuity and singularity of induced measures
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singularly: 1: 65L11 Singularly perturbed problemssketches: 1: 18C30 Sketches and generalizations
skew: 1: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxxskew: 2: 16S35 Twisted and skew group rings, crossed productsskew: 3: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M25
skew-hermitian: 1: 15B57 Hermitian, skew-Hermitian, and related matricesskiı-type: 1: 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol′skiı-type inequalities)
sle: 1: 60J67 Stochastic (Schramm-)Loewner evolution (SLE)sloshing: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingslow: 1: 70K70 Systems with slow and fast motions
slowly: 1: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48small: 1: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D30small: 2: 11J54 Small fractional parts of polynomials and generalizationssmall: 3: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05small: 4: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05small: 5: 37F50 Small divisors, rotation domains and linearization; Fatou and Julia setssmall: 6: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusionsmall: 7: 74B15 Equations linearized about a deformed state (small deformations superposed on large)
small-strain: 1: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plasticmaterials)
small-strain: 2: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)smash: 1: 16S40 Smash products of general Hopf actions [See also]16T05
smirnov: 1: 30H15 Nevanlinna class and Smirnov classsmith: 1: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17
smooth: 1: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxxsmooth: 2: 37C05 Smooth mappings and diffeomorphismssmooth: 3: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxxsmooth: 4: 37C60 Nonautonomous smooth dynamical systems [See also]37B55smooth: 5: 37E05 Maps of the interval (piecewise continuous, continuous, smooth)smooth: 6: 57R12 Smooth approximations
smoothing: 1: 57R10 Smoothingsmoothing: 2: 65D10 Smoothing, curve fittingsmoothing: 3: 93E14 Data smoothing
smoothness: 1: 35B65 Smoothness and regularity of solutionssobolev: 1: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremssobolev: 2: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
social: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)social: 2: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencessocial: 3: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40social: 4: 62P25 Applications to social sciencessocial: 5: 91-XX Game theory, economics, social and behavioral sciencessocial: 6: 91B14 Social choicesocial: 7: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXsocial: 8: 91D10 Models of societies, social and urban evolutionsocial: 9: 91D30 Social networkssocial: 10: 91Fxx Other social and behavioral sciences (mathematical treatment)social: 11: 97M70 Behavioral and social sciences
societies: 1: 91D10 Models of societies, social and urban evolutionsociety: 1: 97A40 Mathematics and societysociety: 2: 97P70 Computer science and society
sociological: 1: 97C60 Sociological aspects of learningsociological: 2: 97Q40 Sociological aspects
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sociology: 1: 01A80 Sociology (and profession) of mathematicssociology: 2: 91Dxx Mathematical sociology (including anthropology)
soft: 1: 06D72 Fuzzy lattices (soft algebras) and related topicssoftware: 1: 68Nxx Softwaresoftware: 2: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)software: 3: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)software: 4: 97N80 Mathematical software, computer programssoftware: 5: 97P30 System software
soil: 1: 74L10 Soil and rock mechanicssolid: 1: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxxsolid: 2: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25solid: 3: 74Fxx Coupling of solid mechanics with other effectssolid: 4: 74Lxx Special subfields of solid mechanicssolid: 5: 74L05 Geophysical solid mechanics [See also]86-XXsolid: 6: 74L15 Biomechanical solid mechanics [See also]92C10solid: 7: 97G40 Plane and solid geometry
solids: 1: 35Q74 PDEs in connection with mechanics of deformable solidssolids: 2: 74-XX Mechanics of deformable solidssolids: 3: 74Axx Generalities, axiomatics, foundations of continuum mechanics of solidssolids: 4: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C26solids: 5: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15solids: 6: 82D20 Solids
solitary: 1: 74J35 Solitary wavessolitary: 2: 76B25 Solitary waves [See also]35C11soliton: 1: 35C08 Soliton solutionssoliton: 2: 37K40 Soliton theory, asymptotic behavior of solutions
soliton-like: 1: 35Q51 Soliton-like equations [See also]37K40solution: 1: 11Y50 Computer solution of Diophantine equationssolution: 2: 65M22 Solution of discretized equations [See also]65Fxx, 65Hxxsolution: 3: 65N22 Solution of discretized equations [See also]65Fxx, 65Hxxsolution: 4: 74G20 Local existence of solutions (near a given solution)
solutions: 1: 11D45 Counting solutions of Diophantine equationssolutions: 2: 34A05 Explicit solutions and reductionssolutions: 3: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation
of solutionssolutions: 4: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxsolutions: 5: 34B18 Positive solutions of nonlinear boundary value problemssolutions: 6: 34C25 Periodic solutionssolutions: 7: 34C27 Almost and pseudo-almost periodic solutionssolutions: 8: 34C37 Homoclinic and heteroclinic solutionssolutions: 9: 34D35 Stability of manifolds of solutionssolutions: 10: 34E17 Canard solutionssolutions: 11: 34K07 Theoretical approximation of solutionssolutions: 12: 34K12 Growth, boundedness, comparison of solutionssolutions: 13: 34K13 Periodic solutionssolutions: 14: 34K14 Almost and pseudo-periodic solutionssolutions: 15: 34K21 Stationary solutionssolutions: 16: 34K23 Complex (chaotic) behavior of solutionssolutions: 17: 34K28 Numerical approximation of solutionssolutions: 18: 34M05 Entire and meromorphic solutionssolutions: 19: 34M10 Oscillation, growth of solutionssolutions: 20: 34M25 Formal solutions, transform techniquessolutions: 21: 34M35 Singularities, monodromy, local behavior of solutions, normal formssolutions: 22: 35A08 Fundamental solutionssolutions: 23: 35A09 Classical solutionssolutions: 24: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxx
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solutions: 25: 35Bxx Qualitative properties of solutionssolutions: 26: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.solutions: 27: 35B07 Axially symmetric solutionssolutions: 28: 35B08 Entire solutionssolutions: 29: 35B09 Positive solutionssolutions: 30: 35B10 Periodic solutionssolutions: 31: 35B15 Almost and pseudo-almost periodic solutionssolutions: 32: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxxsolutions: 33: 35B40 Asymptotic behavior of solutionssolutions: 34: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxxsolutions: 35: 35B65 Smoothness and regularity of solutionssolutions: 36: 35Cxx Representations of solutionssolutions: 37: 35C05 Solutions in closed formsolutions: 38: 35C06 Self-similar solutionssolutions: 39: 35C07 Traveling wave solutionssolutions: 40: 35C08 Soliton solutionssolutions: 41: 35C09 Trigonometric solutionssolutions: 42: 35C10 Series solutionssolutions: 43: 35C11 Polynomial solutionssolutions: 44: 35C15 Integral representations of solutionssolutions: 45: 35Dxx Generalized solutionssolutions: 46: 35D30 Weak solutionssolutions: 47: 35D35 Strong solutionssolutions: 48: 35D40 Viscosity solutionssolutions: 49: 35E05 Fundamental solutionssolutions: 50: 35J67 Boundary values of solutions to elliptic equationssolutions: 51: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15solutions: 52: 37K40 Soliton theory, asymptotic behavior of solutionssolutions: 53: 39A22 Growth, boundedness, comparison of solutionssolutions: 54: 39A23 Periodic solutionssolutions: 55: 39A24 Almost periodic solutionssolutions: 56: 39A33 Complex (chaotic) behavior of solutionssolutions: 57: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxsolutions: 58: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxsolutions: 59: 45M15 Periodic solutionssolutions: 60: 45M20 Positive solutionssolutions: 61: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)solutions: 62: 49K30 Optimal solutions belonging to restricted classessolutions: 63: 49L25 Viscosity solutionssolutions: 64: 49N60 Regularity of solutionssolutions: 65: 65L07 Numerical investigation of stability of solutionssolutions: 66: 65M80 Fundamental solutions, Green’s function methods, etc.solutions: 67: 65N80 Fundamental solutions, Green’s function methods, etc.solutions: 68: 70H12 Periodic and almost periodic solutionssolutions: 69: 74G05 Explicit solutionssolutions: 70: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)solutions: 71: 74G15 Numerical approximation of solutionssolutions: 72: 74G20 Local existence of solutions (near a given solution)solutions: 73: 74G25 Global existence of solutionssolutions: 74: 74G30 Uniqueness of solutionssolutions: 75: 74G35 Multiplicity of solutionssolutions: 76: 74G40 Regularity of solutionssolutions: 77: 74G45 Bounds for solutionssolutions: 78: 74G55 Qualitative behavior of solutions
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solutions: 79: 74H05 Explicit solutionssolutions: 80: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)solutions: 81: 74H15 Numerical approximation of solutionssolutions: 82: 74H20 Existence of solutionssolutions: 83: 74H25 Uniqueness of solutionssolutions: 84: 74H30 Regularity of solutionssolutions: 85: 74H40 Long-time behavior of solutionssolutions: 86: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M35solutions: 87: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicssolutions: 88: 83C15 Exact solutionssolutions: 89: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetriessolutions: 90: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetriessolvable: 1: 17B30 Solvable, nilpotent (super)algebrassolvable: 2: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17solvable: 3: 20F16 Solvable groups, supersolvable groups [See also]20D10solvable: 4: 20F19 Generalizations of solvable and nilpotent groupssolvable: 5: 22E25 Nilpotent and solvable Lie groupssolvable: 6: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)solvable: 7: 81Q80 Special quantum systems, such as solvable systemssolvable: 8: 82B23 Exactly solvable models; Bethe ansatzsolvable: 9: 82C23 Exactly solvable dynamic models [See also]37K60solving: 1: 13P15 Solving polynomial systems; resultantssolving: 2: 68T20 Problem solving (heuristics, search strategies, etc.)solving: 3: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxxsorting: 1: 68P10 Searching and sortingsource: 1: 01A05 General histories, source bookssource: 2: 94A29 Source coding [See also]68P30
southeast: 1: 01A29 Southeast Asiaspace: 1: 14H50 Plane and space curvesspace: 2: 32B15 Analytic subsets of affine spacespace: 3: 32Q35 Complex manifolds as subdomains of Euclidean spacespace: 4: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxspace: 5: 37J35 Completely integrable systems, topological structure of phase space, integration
methodsspace: 6: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07space: 7: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxspace: 8: 53A04 Curves in Euclidean spacespace: 9: 53A05 Surfaces in Euclidean spacespace: 10: 55M30 Ljusternik-Schnirelman (Lyusternik-Shnirel′man) category of a spacespace: 11: 55P48 Loop space machines, operads [See also]18D50space: 12: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XXspace: 13: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spacespace: 14: 78A20 Space charge wavesspace: 15: 81T20 Quantum field theory on curved space backgrounds
space-time: 1: 83C75 Space-time singularities, cosmic censorship, etc.spaces: 1: 06E15 Stone spaces (Boolean spaces) and related structuresspaces: 2: 06E15 Stone spaces (Boolean spaces) and related structuresspaces: 3: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A40spaces: 4: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A66spaces: 5: 11S90 Prehomogeneous vector spacesspaces: 6: 14A20 Generalizations (algebraic spaces, stacks)
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spaces: 7: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistortheory, instantons, quantum field theory) [See also]32L25, 81Txx
spaces: 8: 14D22 Fine and coarse moduli spacesspaces: 9: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)spaces: 10: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T15spaces: 11: 14P10 Semialgebraic sets and related spacesspaces: 12: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)spaces: 13: 15A03 Vector spaces, linear dependence, rankspaces: 14: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70spaces: 15: 18B30 Categories of topological spaces and continuous mappings [See also]54-XXspaces: 16: 19D10 Algebraic K-theory of spacesspaces: 17: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90spaces: 18: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20spaces: 19: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40spaces: 20: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxxspaces: 21: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxspaces: 22: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxxspaces: 23: 28A35 Measures and integrals in product spacesspaces: 24: 28Bxx Set functions, measures and integrals with values in abstract spacesspaces: 25: 28B15 Set functions, measures and integrals with values in ordered spacesspaces: 26: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20spaces: 27: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)spaces: 28: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11spaces: 29: 30Hxx Spaces and algebras of analytic functionsspaces: 30: 30H10 Hardy spacesspaces: 31: 30H20 Bergman spaces, Fock spacesspaces: 32: 30H20 Bergman spaces, Fock spacesspaces: 33: 30H25 Besov spaces and Qp-spacesspaces: 34: 30H30 Bloch spacesspaces: 35: 30Lxx Analysis on metric spacesspaces: 36: 30L05 Geometric embeddings of metric spacesspaces: 37: 30L10 Quasiconformal mappings in metric spacesspaces: 38: 31C25 Dirichlet spacesspaces: 39: 31Exx Potential theory on metric spacesspaces: 40: 31E05 Potential theory on metric spacesspaces: 41: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12spaces: 42: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J15spaces: 43: 32A36 Bergman spacesspaces: 44: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxspaces: 45: 32Cxx Analytic spacesspaces: 46: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A07spaces: 47: 32C15 Complex spacesspaces: 48: 32C18 Topology of analytic spacesspaces: 49: 32C20 Normal analytic spacesspaces: 50: 32C22 Embedding of analytic spacesspaces: 51: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27spaces: 52: 32C36 Local cohomology of analytic spacesspaces: 53: 32C55 The Levi problem in complex spaces; generalizations
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spaces: 54: 32E05 Holomorphically convex complex spaces, reduction theoryspaces: 55: 32E10 Stein spaces, Stein manifoldsspaces: 56: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxspaces: 57: 32J05 Compactification of analytic spacesspaces: 58: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)spaces: 59: 32K05 Banach analytic spaces [See also]58Bxxspaces: 60: 32K07 Formal and graded complex spaces [See also]58C50spaces: 61: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25spaces: 62: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C25spaces: 63: 32Lxx Holomorphic fiber spaces [See also]55Rxxspaces: 64: 32Mxx Complex spaces with a group of automorphismsspaces: 65: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E10spaces: 66: 32M12 Almost homogeneous manifolds and spaces [See also]14M17spaces: 67: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T15spaces: 68: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D25spaces: 69: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxxspaces: 70: 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)spaces: 71: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25spaces: 72: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxspaces: 73: 37P45 Families and moduli spacesspaces: 74: 37P50 Dynamical systems on Berkovich spacesspaces: 75: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)spaces: 76: 41A65 Abstract approximation theory (approximation in normed linear spaces and other
abstract spaces)spaces: 77: 42-XX Harmonic analysis on Euclidean spacesspaces: 78: 42B35 Function spaces arising in harmonic analysisspaces: 79: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.spaces: 80: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.spaces: 81: 43A85 Analysis on homogeneous spacesspaces: 82: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
spaces: 83: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
spaces: 84: 45Nxx Abstract integral equations, integral equations in abstract spacesspaces: 85: 45N05 Abstract integral equations, integral equations in abstract spacesspaces: 86: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxxspaces: 87: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxspaces: 88: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxspaces: 89: 46A03 General theory of locally convex spacesspaces: 90: 46A04 Locally convex Frechet spaces and (DF)-spacesspaces: 91: 46A08 Barrelled spaces, bornological spacesspaces: 92: 46A08 Barrelled spaces, bornological spacesspaces: 93: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)spaces: 94: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)spaces: 95: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
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spaces, Montel spaces, etc.)spaces: 96: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)spaces: 97: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40spaces: 98: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)spaces: 99: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)spaces: 100: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)spaces: 101: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)spaces: 102: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)spaces: 103: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)spaces: 104: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)spaces: 105: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)spaces: 106: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20spaces: 107: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42spaces: 108: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45spaces: 109: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B45spaces: 110: 46A50 Compactness in topological linear spaces; angelic spaces, etc.spaces: 111: 46A50 Compactness in topological linear spaces; angelic spaces, etc.spaces: 112: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07spaces: 113: 46A61 Graded Frechet spaces and tame operatorsspaces: 114: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)spaces: 115: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)spaces: 116: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)spaces: 117: 46A80 Modular spacesspaces: 118: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxspaces: 119: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxspaces: 120: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exxspaces: 121: 46B03 Isomorphic theory (including renorming) of Banach spacesspaces: 122: 46B04 Isometric theory of Banach spacesspaces: 123: 46B06 Asymptotic theory of Banach spaces [See also]52A23spaces: 124: 46B07 Local theory of Banach spacesspaces: 125: 46B20 Geometry and structure of normed linear spacesspaces: 126: 46B25 Classical Banach spaces in the general theoryspaces: 127: 46B26 Nonseparable Banach spacesspaces: 128: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L20spaces: 129: 46B40 Ordered normed spaces [See also]46A40, 46B42spaces: 130: 46B45 Banach sequence spaces [See also]46A45spaces: 131: 46B50 Compactness in Banach (or normed) spacesspaces: 132: 46B70 Interpolation between normed linear spaces [See also]46M35spaces: 133: 46B80 Nonlinear classification of Banach spaces; nonlinear quotientsspaces: 134: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
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computer science [See also]05C12, 68Rxxspaces: 135: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxspaces: 136: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxspaces: 137: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxspaces: 138: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxspaces: 139: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)spaces: 140: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)spaces: 141: 46C15 Characterizations of Hilbert spacesspaces: 142: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50spaces: 143: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50spaces: 144: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50spaces: 145: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J10spaces: 146: 46E10 Topological linear spaces of continuous, differentiable or analytic functionsspaces: 147: 46E15 Banach spaces of continuous, differentiable or analytic functionsspaces: 148: 46E20 Hilbert spaces of continuous, differentiable or analytic functionsspaces: 149: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32spaces: 150: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32spaces: 151: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32spaces: 152: 46E27 Spaces of measures [See also]28A33, 46Gxxspaces: 153: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 154: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 155: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 156: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 157: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 158: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)spaces: 159: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremsspaces: 160: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremsspaces: 161: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesspaces: 162: 46E40 Spaces of vector- and operator-valued functionsspaces: 163: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60spaces: 164: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H60spaces: 165: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T30spaces: 166: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E35
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spaces: 167: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XXspaces: 168: 46F25 Distributions on infinite-dimensional spaces [See also]58C35spaces: 169: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txxspaces: 170: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T12spaces: 171: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H60spaces: 172: 46L07 Operator spaces and completely bounded maps [See also]47L25spaces: 173: 46L52 Noncommutative function spacesspaces: 174: 46M35 Abstract interpolation of topological vector spaces [See also]46B70spaces: 175: 46S50 Functional analysis in probabilistic metric linear spacesspaces: 176: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50spaces: 177: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxxspaces: 178: 47A70 (Generalized) eigenfunction expansions; rigged Hilbert spacesspaces: 179: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22spaces: 180: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E22spaces: 181: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)spaces: 182: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)spaces: 183: 47B38 Operators on function spaces (general)spaces: 184: 47B49 Transformers, preservers (operators on spaces of operators)spaces: 185: 47B50 Operators on spaces with an indefinite metric [See also]46C50spaces: 186: 47B60 Operators on ordered spacesspaces: 187: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesspaces: 188: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesspaces: 189: 47Lxx Linear spaces and algebras of operators [See also]46Lxxspaces: 190: 47L05 Linear spaces of operators [See also]46A32 and 46B28spaces: 191: 47L10 Algebras of operators on Banach spaces and other topological linear spacesspaces: 192: 47L10 Algebras of operators on Banach spaces and other topological linear spacesspaces: 193: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07spaces: 194: 47L25 Operator spaces (= matricially normed spaces) [See also]46L07spaces: 195: 47L30 Abstract operator algebras on Hilbert spacesspaces: 196: 47L50 Dual spaces of operator algebrasspaces: 197: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70spaces: 198: 49J27 Problems in abstract spaces [See also]90C48, 93C25spaces: 199: 49K27 Problems in abstract spaces [See also]90C48, 93C25spaces: 200: 51A50 Polar geometry, symplectic spaces, orthogonal spacesspaces: 201: 51A50 Polar geometry, symplectic spaces, orthogonal spacesspaces: 202: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxspaces: 203: 51E22 Linear codes and caps in Galois spaces [See also]94B05spaces: 204: 51F10 Absolute spacesspaces: 205: 51J15 Kinematic spacesspaces: 206: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F15spaces: 207: 52A07 Convex sets in topological vector spaces [See also]46A55spaces: 208: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxspaces: 209: 53B40 Finsler spaces and generalizations (areal metrics)spaces: 210: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysis
on metric spacesspaces: 211: 53C35 Symmetric spaces [See also]32M15, 57T15spaces: 212: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B20spaces: 213: 53D30 Symplectic structures of moduli spacesspaces: 214: 54A05 Topological spaces and generalizations (closure spaces, etc.)spaces: 215: 54A05 Topological spaces and generalizations (closure spaces, etc.)
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spaces: 216: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)spaces: 217: 54B10 Product spacesspaces: 218: 54B15 Quotient spaces, decompositionsspaces: 219: 54B17 Adjunction spaces and similar constructionsspaces: 220: 54Cxx Maps and general types of spaces defined by mapsspaces: 221: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)spaces: 222: 54C35 Function spaces [See also]46Exx, 58D15spaces: 223: 54C40 Algebraic properties of function spaces [See also]46J10spaces: 224: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M15spaces: 225: 54D05 Connected and locally connected spaces (general aspects)spaces: 226: 54D25 “P -minimal” and “P -closed” spacesspaces: 227: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)spaces: 228: 54D55 Sequential spacesspaces: 229: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)spaces: 230: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)spaces: 231: 54Exx Spaces with richer structuresspaces: 232: 54E17 Nearness spacesspaces: 233: 54E20 Stratifiable spaces, cosmic spaces, etc.spaces: 234: 54E20 Stratifiable spaces, cosmic spaces, etc.spaces: 235: 54E25 Semimetric spacesspaces: 236: 54E30 Moore spacesspaces: 237: 54E35 Metric spaces, metrizabilityspaces: 238: 54E40 Special maps on metric spacesspaces: 239: 54E45 Compact (locally compact) metric spacesspaces: 240: 54E50 Complete metric spacesspaces: 241: 54E52 Baire category, Baire spacesspaces: 242: 54E70 Probabilistic metric spacesspaces: 243: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30spaces: 244: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30spaces: 245: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F30spaces: 246: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A03spaces: 247: 54F65 Topological characterizations of particular spacesspaces: 248: 54Gxx Peculiar spacesspaces: 249: 54G05 Extremally disconnected spaces, F -spaces, etc.spaces: 250: 54G12 Scattered spacesspaces: 251: 54G15 Pathological spacesspaces: 252: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxspaces: 253: 55P20 Eilenberg-Mac Lane spacesspaces: 254: 55P35 Loop spacesspaces: 255: 55P47 Infinite loop spacesspaces: 256: 55Q20 Homotopy groups of wedges, joins, and simple spacesspaces: 257: 55Q52 Homotopy groups of special spacesspaces: 258: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25spaces: 259: 55R05 Fiber spacesspaces: 260: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txxspaces: 261: 55R35 Classifying spaces of groups and H-spacesspaces: 262: 55R37 Maps between classifying spacesspaces: 263: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R20spaces: 264: 55R65 Generalizations of fiber spaces and bundlesspaces: 265: 55R80 Discriminantal varieties, configuration spacesspaces: 266: 55R91 Equivariant fiber spaces and bundles [See also]19L47spaces: 267: 55S40 Sectioning fiber spaces and bundlesspaces: 268: 57M10 Covering spaces
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spaces: 269: 57N17 Topology of topological vector spacesspaces: 270: 57P10 Poincare duality spacesspaces: 271: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H10spaces: 272: 57T15 Homology and cohomology of homogeneous spaces of Lie groupsspaces: 273: 57T20 Homotopy groups of topological groups and homogeneous spacesspaces: 274: 58A40 Differential spacesspaces: 275: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxspaces: 276: 58D10 Spaces of imbeddings and immersionsspaces: 277: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxxspaces: 278: 58Exx Variational problems in infinite-dimensional spacesspaces: 279: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32spaces: 280: 60B05 Probability measures on topological spacesspaces: 281: 60B11 Probability theory on linear topological spaces [See also]28C20spaces: 282: 60J05 Discrete-time Markov processes on general state spacesspaces: 283: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)spaces: 284: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40spaces: 285: 60J25 Continuous-time Markov processes on general state spacesspaces: 286: 60J27 Continuous-time Markov processes on discrete state spacesspaces: 287: 60J28 Applications of continuous-time Markov processes on discrete state spacesspaces: 288: 65Jxx Numerical analysis in abstract spacesspaces: 289: 81P16 Quantum state spaces, operational and probabilistic conceptsspaces: 290: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.spaces: 291: 90C48 Programming in abstract spacesspaces: 292: 91A70 Spaces of gamesspaces: 293: 93C25 Systems in abstract spaces
spanier-whitehead: 1: 55P25 Spanier-Whitehead dualitysparse: 1: 65F50 Sparse matricesspatial: 1: 62H11 Directional data; spatial statisticsspatial: 2: 62M30 Spatial processesspatial: 3: 91B72 Spatial modelsspatial: 4: 91D25 Spatial models [See also]91B72
spde: 1: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,SPDE, dynamical systems)
special: 1: 03C50 Models with special properties (saturated, rigid, etc.)special: 2: 11B37 Recurrences For applications to special functions, see 33-XXspecial: 3: 11B83 Special sequences and polynomialsspecial: 4: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsspecial: 5: 11J91 Transcendence theory of other special functionsspecial: 6: 11K31 Special sequencesspecial: 7: 11N69 Distribution of integers in special residue classesspecial: 8: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measurespecial: 9: 12E10 Special polynomialsspecial: 10: 13C13 Other special typesspecial: 11: 13Fxx Arithmetic rings and other special ringsspecial: 12: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05special: 13: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C38special: 14: 14H45 Special curves and curves of low genusspecial: 15: 14H51 Special divisors (gonality, Brill-Noether theory)special: 16: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35special: 17: 14Mxx Special varietiesspecial: 18: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B14
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special: 19: 15Bxx Special matricesspecial: 20: 15B33 Matrices over special rings (quaternions, finite fields, etc.)special: 21: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphismsspecial: 22: 18A22 Special properties of functors (faithful, full, etc.)special: 23: 18Bxx Special categoriesspecial: 24: 20D25 Special subgroups (Frattini, Fitting, etc.)special: 25: 20Fxx Special aspects of infinite or finite groupsspecial: 26: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)special: 27: 26A30 Singular functions, Cantor functions, functions with other special propertiesspecial: 28: 26A39 Denjoy and Perron integrals, other special integralsspecial: 29: 26B35 Special properties of functions of several variables, Holder conditions, etc.special: 30: 30C20 Conformal mappings of special domainsspecial: 31: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)special: 32: 30D15 Special classes of entire functions and growth estimatesspecial: 33: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)special: 34: 32A17 Special families of functionsspecial: 35: 32G07 Deformations of special (e.g. CR) structuresspecial: 36: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
special: 37: 33C47 Other special orthogonal polynomials and functionsspecial: 38: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablespecial: 39: 33Exx Other special functionsspecial: 40: 33E50 Special functions in characteristic p (gamma functions, etc.)special: 41: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)special: 42: 34M55 Painleve and other special equations; classification, hierarchies;special: 43: 35A25 Other special methodsspecial: 44: 35Mxx Equations and systems of special type (mixed, composite, etc.)special: 45: 37B05 Transformations and group actions with special properties (minimality, distality,
proximality, etc.)special: 46: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70special: 47: 37L65 Special approximation methods (nonlinear Galerkin, etc.)special: 48: 40Gxx Special methods of summabilityspecial: 49: 41A30 Approximation by other special function classesspecial: 50: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30special: 51: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30special: 52: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)special: 53: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)special: 54: 42C40 Wavelets and other special systemsspecial: 55: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)special: 56: 44A15 Special transforms (Legendre, Hilbert, etc.)special: 57: 44A20 Transforms of special functionsspecial: 58: 45Hxx Miscellaneous special kernels [See also]44A15special: 59: 45H05 Miscellaneous special kernels [See also]44A15special: 60: 47Bxx Special classes of linear operatorsspecial: 61: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)special: 62: 51Exx Finite geometry and special incidence structuresspecial: 63: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxspecial: 64: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)special: 65: 53A40 Other special differential geometries
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special: 66: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)[See also]32Q20
special: 67: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)special: 68: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)special: 69: 54C50 Special sets defined by functions [See also]26A21special: 70: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)special: 71: 54E40 Special maps on metric spacesspecial: 72: 54Fxx Special propertiesspecial: 73: 55Q52 Homotopy groups of special spacesspecial: 74: 55Q70 Homotopy groups of special types [See also]55N05, 55N07special: 75: 57M12 Special coverings, e.g. branchedspecial: 76: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)special: 77: 60Kxx Special processesspecial: 78: 65D20 Computation of special functions, construction of tables [See also]33F05special: 79: 74Exx Material properties given special treatmentspecial: 80: 74Lxx Special subfields of solid mechanicsspecial: 81: 74Mxx Special kinds of problemsspecial: 82: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.special: 83: 81Q80 Special quantum systems, such as solvable systemsspecial: 84: 83Axx Special relativityspecial: 85: 83A05 Special relativityspecial: 86: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetriesspecial: 87: 90C08 Special problems of linear programming (transportation, multi-index, etc.)special: 88: 91B52 Special types of equilibriaspecial: 89: 91B54 Special types of economiesspecial: 90: 94A11 Application of orthogonal and other special functions
specialized: 1: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)specific: 1: 00Axx General and miscellaneous specific topicsspecific: 2: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)specific: 3: 00B15 Collections of articles of miscellaneous specific contentspecific: 4: 00B25 Proceedings of conferences of miscellaneous specific interestspecific: 5: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B05specific: 6: 43A75 Analysis on specific compact groupsspecific: 7: 43A80 Analysis on other specific Lie groups [See also]22Exxspecific: 8: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)specific: 9: 57S25 Groups acting on specific manifoldsspecific: 10: 65Y10 Algorithms for specific classes of architecturesspecific: 11: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areaspecific: 12: 81Vxx Applications to specific physical systemsspecific: 13: 82Dxx Applications to specific types of physical systems
specification: 1: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,requirements, etc.)
specification: 2: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70specification: 3: 68Q65 Abstract data types; algebraic specification [See also]18C50
specified: 1: 11N25 Distribution of integers with specified multiplicative constraintsspecified: 2: 11P21 Lattice points in specified regionsspectra: 1: 11J06 Markov and Lagrange spectra and generalizationsspectra: 2: 54B35 Spectraspectra: 3: 55P42 Stable homotopy theory, spectraspectra: 4: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)spectra: 5: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)spectral: 1: 11F72 Spectral theory; Selberg trace formulaspectral: 2: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasspectral: 3: 18G40 Spectral sequences, hypercohomology [See also]55Txxspectral: 4: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameter
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spectral: 5: 34K08 Spectral theory of functional-differential operatorsspectral: 6: 34L05 General spectral theoryspectral: 7: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F05spectral: 8: 35P05 General topics in linear spectral theoryspectral: 9: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theoryspectral: 10: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35spectral: 11: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodsspectral: 12: 43A45 Spectral synthesis on groups, semigroups, etc.spectral: 13: 47A11 Local spectral propertiesspectral: 14: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)spectral: 15: 47A25 Spectral setsspectral: 16: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)spectral: 17: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)spectral: 18: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.spectral: 19: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05spectral: 20: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txxspectral: 21: 55Txx Spectral sequences [See also]18G40, 55R20spectral: 22: 55T10 Serre spectral sequencesspectral: 23: 55T15 Adams spectral sequencesspectral: 24: 55T20 Eilenberg-Moore spectral sequences [See also]57T35spectral: 25: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T20spectral: 26: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E07spectral: 27: 58J30 Spectral flowsspectral: 28: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxxspectral: 29: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxxspectral: 30: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicityspectral: 31: 62M15 Spectral analysisspectral: 32: 65M70 Spectral, collocation and related methodsspectral: 33: 65N35 Spectral, collocation and related methodsspectral: 34: 74S25 Spectral and related methodsspectral: 35: 76M22 Spectral methodsspectral: 36: 78M22 Spectral methodsspectral: 37: 80M22 Spectral methodsspectral: 38: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
spectrum: 1: 34L16 Numerical approximation of eigenvalues and of other parts of the spectrumspectrum: 2: 47A10 Spectrum, resolvent
speech: 1: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H30spencer: 1: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32sphere: 1: 55R25 Sphere bundles and vector bundlessphere: 2: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity
spheres: 1: 55Q40 Homotopy groups of spheresspheres: 2: 55Q45 Stable homotopy of spheresspheres: 3: 57R60 Homotopy spheres, Poincare conjecture
spherical: 1: 14M27 Compactifications; symmetric and spherical varietiesspherical: 2: 33C55 Spherical harmonicsspherical: 3: 43A90 Spherical functions [See also]22E45, 22E46, 33C55spherical: 4: 52A55 Spherical and hyperbolic convexityspherical: 5: 97G60 Plane and spherical trigonometry
spheroidal: 1: 33E10 Lame, Mathieu, and spheroidal wave functionsspin: 1: 53C27 Spin and Spinc geometryspin: 2: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)spin: 3: 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
spin$<>$: 1: 53C27 Spin and Spinc geometryspinor: 1: 81R25 Spinor and twistor methods [See also]32L25spinor: 2: 83C60 Spinor and twistor methods; Newman-Penrose formalism
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spinors: 1: 15A66 Clifford algebras, spinorsspline: 1: 41A15 Spline approximation
splines: 1: 65D07 Splinessplit: 1: 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
splittings: 1: 37D30 Partially hyperbolic systems and dominated splittingssporadic: 1: 20C34 Representations of sporadic groupssporadic: 2: 20D08 Simple groups: sporadic groups
spread: 1: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and relatedtopics
spreads: 1: 51A40 Translation planes and spreadsspreads: 2: 51E14 Finite partial geometries (general), nets, partial spreadsspreads: 3: 51E23 Spreads and packing problemssquares: 1: 05B15 Orthogonal arrays, Latin squares, Room squaressquares: 2: 05B15 Orthogonal arrays, Latin squares, Room squaressquares: 3: 11E25 Sums of squares and representations by other particular quadratic formssquares: 4: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxsquares: 5: 93E24 Least squares and related methods
squeezed: 1: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V80stabilities: 1: 65P40 Nonlinear stabilitiesstabilities: 2: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)
stability: 1: 03C45 Classification theory, stability and related concepts [See also]03C48stability: 2: 19A13 Stability for projective modules [See also]13C10stability: 3: 19B14 Stability for linear groupsstability: 4: 19C20 Symbols, presentations and stability of K2
stability: 5: 19G05 Stability for quadratic modulesstability: 6: 32Q26 Notions of stabilitystability: 7: 34Dxx Stability theory [See also]37C75, 93Dxxstability: 8: 34D20 Stabilitystability: 9: 34D23 Global stabilitystability: 10: 34D30 Structural stability and analogous concepts [See also]37C20stability: 11: 34D35 Stability of manifolds of solutionsstability: 12: 34K20 Stability theorystability: 13: 35B35 Stabilitystability: 14: 37B25 Lyapunov functions and stability; attractors, repellersstability: 15: 37C20 Generic properties, structural stabilitystability: 16: 37C75 Stability theorystability: 17: 37F15 Expanding maps; hyperbolicity; structural stabilitystability: 18: 37J25 Stability problemsstability: 19: 37K45 Stability problemsstability: 20: 37L15 Stability problemsstability: 21: 39A30 Stability theorystability: 22: 39B82 Stability, separation, extension, and related topics [See also]46A22stability: 23: 45M10 Stability theorystability: 24: 49K40 Sensitivity, stability, well-posedness [See also]90C31stability: 25: 58K25 Stabilitystability: 26: 65L07 Numerical investigation of stability of solutionsstability: 27: 65L20 Stability and convergence of numerical methodsstability: 28: 65M12 Stability and convergence of numerical methodsstability: 29: 65N12 Stability and convergence of numerical methodsstability: 30: 70E50 Stability problemsstability: 31: 70H14 Stability problemsstability: 32: 70J25 Stabilitystability: 33: 70K20 Stabilitystability: 34: 74H55 Stabilitystability: 35: 76Exx Hydrodynamic stabilitystability: 36: 76E09 Stability and instability of nonparallel flows
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stability: 37: 76E15 Absolute and convective instability and stabilitystability: 38: 76E17 Interfacial stability and instabilitystability: 39: 76E20 Stability and instability of geophysical and astrophysical flowsstability: 40: 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flowsstability: 41: 90C31 Sensitivity, stability, parametric optimizationstability: 42: 93Dxx Stabilitystability: 43: 93D09 Robust stabilitystability: 44: 93D10 Popov-type stability of feedback systemsstability: 45: 93D20 Asymptotic stabilitystability: 46: 93E15 Stochastic stability
stabilization: 1: 34H15 Stabilizationstabilization: 2: 93D15 Stabilization of systems by feedbackstabilization: 3: 93D21 Adaptive or robust stabilization
stable: 1: 19B10 Stable range conditionsstable: 2: 55P42 Stable homotopy theory, spectrastable: 3: 55Q10 Stable homotopy groupsstable: 4: 55Q45 Stable homotopy of spheresstable: 5: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XXstable: 6: 60E07 Infinitely divisible distributions; stable distributionsstable: 7: 60G52 Stable processesstacks: 1: 14A20 Generalizations (algebraic spaces, stacks)stacks: 2: 14D23 Stacks and moduli problemsstage: 1: 97F20 Pre-numerical stage, concept of numbers
standard: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology andderived functors for triples [See also]18Gxxstandards: 1: 97B70 Syllabuses, educational standards
stanley-reisner: 1: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U10star: 1: 53D55 Deformation quantization, star products
star-shaped: 1: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)starlike: 1: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)state: 1: 60J05 Discrete-time Markov processes on general state spacesstate: 2: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)state: 3: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40state: 4: 60J25 Continuous-time Markov processes on general state spacesstate: 5: 60J27 Continuous-time Markov processes on discrete state spacesstate: 6: 60J28 Applications of continuous-time Markov processes on discrete state spacesstate: 7: 70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase spacestate: 8: 74B15 Equations linearized about a deformed state (small deformations superposed on large)state: 9: 81P16 Quantum state spaces, operational and probabilistic conceptsstate: 10: 81P50 Quantum state estimation, approximate cloning
states: 1: 37D35 Thermodynamic formalism, variational principles, equilibrium statesstates: 2: 46L30 Statesstates: 3: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V80states: 4: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V80statics: 1: 70Cxx Staticsstatics: 2: 70C20 Statics
stationary: 1: 34K21 Stationary solutionsstationary: 2: 60G10 Stationary processesstatistical: 1: 35Q82 PDEs in connection with statistical mechanicsstatistical: 2: 37A60 Dynamical systems in statistical mechanics [See also]82Cxxstatistical: 3: 40A35 Ideal and statistical convergence [See also]40G15statistical: 4: 40G15 Summability methods using statistical convergence [See also]40A35statistical: 5: 46N55 Applications in statistical physicsstatistical: 6: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[See also]82B43, 82C43statistical: 7: 62B15 Theory of statistical experimentsstatistical: 8: 62Qxx Statistical tablesstatistical: 9: 62Q05 Statistical tablesstatistical: 10: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXstatistical: 11: 74A25 Molecular, statistical, and kinetic theoriesstatistical: 12: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M35statistical: 13: 76F55 Statistical turbulence modeling [See also]76M35statistical: 14: 82-XX Statistical mechanics, structure of matterstatistical: 15: 82Bxx Equilibrium statistical mechanicsstatistical: 16: 82B05 Classical equilibrium statistical mechanics (general)statistical: 17: 82B10 Quantum equilibrium statistical mechanics (general)statistical: 18: 82B30 Statistical thermodynamics [See also]80-XXstatistical: 19: 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)statistical: 20: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general)statistical: 21: 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)statistical: 22: 85A35 Statistical astronomystatistical: 23: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)statistical: 24: 91B82 Statistical methods; economic indices and measuresstatistical: 25: 91G70 Statistical methods, econometricsstatistics: 1: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)statistics: 2: 35Q62 PDEs in connection with statisticsstatistics: 3: 46L53 Noncommutative probability and statisticsstatistics: 4: 46N30 Applications in probability theory and statisticsstatistics: 5: 47N30 Applications in probability theory and statisticsstatistics: 6: 62-XX Statisticsstatistics: 7: 62A86 Fuzzy analysis in statisticsstatistics: 8: 62B05 Sufficient statistics and fieldsstatistics: 9: 62G30 Order statistics; empirical distribution functionsstatistics: 10: 62G32 Statistics of extreme values; tail inferencestatistics: 11: 62H10 Distribution of statisticsstatistics: 12: 62H11 Directional data; spatial statisticsstatistics: 13: 65C60 Computational problems in statisticsstatistics: 14: 81S05 Canonical quantization, commutation relations and statisticsstatistics: 15: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXstatistics: 16: 92B10 Taxonomy, cladistics, statisticsstatistics: 17: 97Kxx Combinatorics, graph theory, probability theory, statisticsstatistics: 18: 97K40 Descriptive statisticsstatistics: 19: 97K70 Foundations and methodology of statisticsstatistics: 20: 97K80 Applied statistics
steady-state: 1: 74Gxx Equilibrium (steady-state) problemssteenrod: 1: 55S10 Steenrod algebra
steenrod-sitnikov: 1: 55N07 Steenrod-Sitnikov homologiessteepest: 1: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20steepest: 2: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
[See also]30E15stefan: 1: 80A22 Stefan problems, phase changes, etc. [See also]74Nxxstein: 1: 32E10 Stein spaces, Stein manifoldsstein: 2: 32E10 Stein spaces, Stein manifoldsstein: 3: 32Q28 Stein manifolds
steinberg: 1: 19Cxx Steinberg groups and K2
steiner: 1: 51E10 Steiner systemsstellar: 1: 85A05 Galactic and stellar dynamicsstellar: 2: 85A15 Galactic and stellar structure
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stieltjes: 1: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XXstiff: 1: 65L04 Stiff equations
stirling: 1: 11B73 Bell and Stirling numbersstochastic: 1: 15B51 Stochastic matricesstochastic: 2: 34K50 Stochastic functional-differential equations [See also]60Hxxstochastic: 3: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15stochastic: 4: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15stochastic: 5: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10stochastic: 6: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H15stochastic: 7: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H15stochastic: 8: 39A50 Stochastic difference equationsstochastic: 9: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J60stochastic: 10: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXstochastic: 11: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C65stochastic: 12: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C65stochastic: 13: 60E15 Inequalities; stochastic orderingsstochastic: 14: 60Gxx Stochastic processesstochastic: 15: 60G05 Foundations of stochastic processesstochastic: 16: 60G20 Generalized stochastic processesstochastic: 17: 60Hxx Stochastic analysis [See also]58J65stochastic: 18: 60H05 Stochastic integralsstochastic: 19: 60H07 Stochastic calculus of variations and the Malliavin calculusstochastic: 20: 60H10 Stochastic ordinary differential equations [See also]34F05stochastic: 21: 60H15 Stochastic partial differential equations [See also]35R60stochastic: 22: 60H20 Stochastic integral equationsstochastic: 23: 60H30 Applications of stochastic analysis (to PDE, etc.)stochastic: 24: 60H35 Computational methods for stochastic equations [See also]65C30stochastic: 25: 60J67 Stochastic (Schramm-)Loewner evolution (SLE)stochastic: 26: 62L20 Stochastic approximationstochastic: 27: 62Mxx Inference from stochastic processesstochastic: 28: 62M86 Inference from stochastic processes and fuzzinessstochastic: 29: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H35stochastic: 30: 65C30 Stochastic differential and integral equationsstochastic: 31: 65C35 Stochastic particle methods [See also]82C80stochastic: 32: 74S60 Stochastic methodsstochastic: 33: 76M35 Stochastic analysisstochastic: 34: 81P20 Stochastic mechanics (including stochastic electrodynamics)stochastic: 35: 81P20 Stochastic mechanics (including stochastic electrodynamics)stochastic: 36: 81S20 Stochastic quantizationstochastic: 37: 81S25 Quantum stochastic calculusstochastic: 38: 82B31 Stochastic methodsstochastic: 39: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H10stochastic: 40: 90B15 Network models, stochasticstochastic: 41: 90B36 Scheduling theory, stochastic [See also]68M20stochastic: 42: 90C15 Stochastic programmingstochastic: 43: 91A15 Stochastic gamesstochastic: 44: 91B51 Dynamic stochastic general equilibrium theorystochastic: 45: 91B70 Stochastic modelsstochastic: 46: 91G30 Interest rates (stochastic models)stochastic: 47: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)
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stochastic: 48: 93Exx Stochastic systems and controlstochastic: 49: 93E03 Stochastic systems, generalstochastic: 50: 93E15 Stochastic stabilitystochastic: 51: 93E20 Optimal stochastic controlstochastic: 52: 93E35 Stochastic learning and adaptive controlstochastic: 53: 97K60 Distributions and stochastic processes
stochasticity: 1: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D45stokes: 1: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)stokes: 2: 34M40 Stokes phenomena and connection problems (linear and nonlinear)stokes: 3: 76D07 Stokes and related (Oseen, etc.) flowsstone: 1: 06E15 Stone spaces (Boolean spaces) and related structures
stopping: 1: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60stopping: 2: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60stopping: 3: 62L15 Optimal stopping [See also]60G40, 91A60
storage: 1: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxxstorage: 2: 68P20 Information storage and retrievalstorage: 3: 90B05 Inventory, storage, reservoirs
straightening: 1: 13F50 Rings with straightening laws, Hodge algebrasstrain-rate: 1: 74Dxx Materials of strain-rate type and history type, other materials with memory (includingelastic materials with viscous damping, various viscoelastic materials)
strange: 1: 37D45 Strange attractors, chaotic dynamicsstrategies: 1: 68T20 Problem solving (heuristics, search strategies, etc.)strategies: 2: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxx
stratifiable: 1: 54E20 Stratifiable spaces, cosmic spaces, etc.stratification: 1: 76B70 Stratification effects in inviscid fluidsstratification: 2: 76D50 Stratification effects in viscous fluidsstratification: 3: 76F45 Stratification effects
stratifications: 1: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxxstratifications: 2: 57N80 Stratifications
stratified: 1: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,32S60, 58J15
stratified: 2: 58A35 Stratified sets [See also]32S60stress: 1: 74A10 Stressstress: 2: 74G70 Stress concentrations, singularitiesstress: 3: 74H35 Singularities, blowup, stress concentrations
stress-rate: 1: 74Cxx Plastic materials, materials of stress-rate and internal-variable typestresses: 1: 74B10 Linear elasticity with initial stresses
strict: 1: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
string: 1: 55P50 String topologystring: 2: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30string: 3: 83E30 String and superstring theories [See also]81T30
strings: 1: 68W32 Algorithms on stringsstrings: 2: 74K05 Stringsstrong: 1: 18D25 Strong functors, strong adjunctionsstrong: 2: 18D25 Strong functors, strong adjunctionsstrong: 3: 35D35 Strong solutionsstrong: 4: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)strong: 5: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)strong: 6: 60F15 Strong theoremsstrong: 7: 81V05 Strong interaction, including quantum chromodynamics
strongly: 1: 05E30 Association schemes, strongly regular graphsstrongly: 2: 32T15 Strongly pseudoconvex domains
structural: 1: 05C75 Structural characterization of families of graphsstructural: 2: 34D30 Structural stability and analogous concepts [See also]37C20
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structural: 3: 37C20 Generic properties, structural stabilitystructural: 4: 37F15 Expanding maps; hyperbolicity; structural stabilitystructural: 5: 70J50 Systems arising from the discretization of structural vibration problemsstructure: 1: 03F07 Structure of proofsstructure: 2: 06B05 Structure theorystructure: 3: 06D05 Structure and representation theorystructure: 4: 06E05 Structure theorystructure: 5: 08A05 Structure theorystructure: 6: 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsstructure: 7: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E40structure: 8: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial valuesstructure: 9: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10structure: 10: 11T30 Structure theorystructure: 11: 13C05 Structure, classification theoremsstructure: 12: 13M05 Structurestructure: 13: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B40structure: 14: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)structure: 15: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionstructure: 16: 16Wxx Rings and algebras with additional structurestructure: 17: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A66structure: 18: 17A60 Structure theorystructure: 19: 17B05 Structure theorystructure: 20: 17C10 Structure theorystructure: 21: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30structure: 22: 18Dxx Categories with structurestructure: 23: 20Exx Structure and classification of infinite or finite groupsstructure: 24: 20E34 General structure theoremsstructure: 25: 20G07 Structure theorystructure: 26: 20M10 General structure theorystructure: 27: 22A05 Structure of general topological groupsstructure: 28: 22A15 Structure of topological semigroupsstructure: 29: 22B05 General properties and structure of LCA groupsstructure: 30: 22B10 Structure of group algebras of LCA groupsstructure: 31: 22D05 General properties and structure of locally compact groupsstructure: 32: 22E10 General properties and structure of complex Lie groups [See also]32M05structure: 33: 22E15 General properties and structure of real Lie groupsstructure: 34: 22E20 General properties and structure of other Lie groupsstructure: 35: 22E43 Structure and representation of the Lorentz groupstructure: 36: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20structure: 37: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K30structure: 38: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50structure: 39: 37C70 Attractors and repellers, topological structurestructure: 40: 37J35 Completely integrable systems, topological structure of phase space, integration
methodsstructure: 41: 40D09 Structure of summability fieldsstructure: 42: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)structure: 43: 46B20 Geometry and structure of normed linear spacesstructure: 44: 46H20 Structure, classification of topological algebrasstructure: 45: 46J40 Structure, classification of commutative topological algebrasstructure: 46: 47A65 Structure theory
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structure: 47: 47L15 Operator algebras with symbol structurestructure: 48: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C70structure: 49: 51H30 Geometries with algebraic manifold structure [See also]14-XXstructure: 50: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)structure: 51: 62E10 Characterization and structure theorystructure: 52: 62H05 Characterization and structure theorystructure: 53: 74E15 Crystalline structurestructure: 54: 74E35 Random structurestructure: 55: 74E40 Chemical structurestructure: 56: 82-XX Statistical mechanics, structure of matterstructure: 57: 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)structure: 58: 85A15 Galactic and stellar structurestructure: 59: 91B24 Price theory and market structurestructure: 60: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)structure: 61: 93Bxx Controllability, observability, and system structurestructure: 62: 93B10 Canonical structurestructure: 63: 93B11 System structure simplificationstructure: 64: 93B12 Variable structure systems
structured: 1: 18D35 Structured objects in a category (group objects, etc.)structured: 2: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, includingde Branges-Rovnyak and other structured spaces) [See also]47B32structured: 3: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also]46E22structured: 4: 74A50 Structured surfaces and interfaces, coexistent phasesstructures: 1: 03C07 Basic properties of first-order languages and structuresstructures: 2: 03C13 Finite structures [See also]68Q15, 68Q19structures: 3: 03C15 Denumerable structuresstructures: 4: 03C64 Model theory of ordered structures; o-minimalitystructures: 5: 03D28 Other Turing degree structuresstructures: 6: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-tic and similar approaches see 03F55structures: 7: 03D50 Recursive equivalence types of sets and structures, isolsstructures: 8: 03G10 Lattices and related structures [See also]06Bxxstructures: 9: 05E18 Group actions on combinatorial structuresstructures: 10: 06-XX Order, lattices, ordered algebraic structures [See also]18B35structures: 11: 06E15 Stone spaces (Boolean spaces) and related structuresstructures: 12: 06Fxx Ordered structuresstructures: 13: 08Axx Algebraic structures [See also]03C05structures: 14: 08A72 Fuzzy algebraic structuresstructures: 15: 11N45 Asymptotic results on counting functions for algebraic and topological structuresstructures: 16: 14D07 Variation of Hodge structures [See also]32G20structures: 17: 14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)structures: 18: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,17C50, 46Kxxstructures: 19: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)[See also]16W10, 17C40, 17C50structures: 20: 17B69 Vertex operators; vertex operator algebras and related structuresstructures: 21: 17C05 Identities and free Jordan structuresstructures: 22: 17C40 Exceptional Jordan structuresstructures: 23: 17C50 Jordan structures associated with other structures [See also]16W10structures: 24: 17C50 Jordan structures associated with other structures [See also]16W10structures: 25: 17C55 Finite-dimensional structuresstructures: 26: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L70structures: 27: 17C70 Super structuresstructures: 28: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
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structures: 29: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgamsstructures: 30: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures[See also]05Bxx, 12F10, 20G40, 20H30, 51-XXstructures: 31: 20F40 Associated Lie structuresstructures: 32: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometricalstructures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40structures: 33: 22F50 Groups as automorphisms of other structuresstructures: 34: 32Gxx Deformations of analytic structuresstructures: 35: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H15structures: 36: 32G07 Deformations of special (e.g. CR) structuresstructures: 37: 32V05 CR structures, CR operators, and generalizationsstructures: 38: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawsstructures: 39: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)structures: 40: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structuresstructures: 41: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B15structures: 42: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also beassigned at least one other classification number in this section)structures: 43: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxstructures: 44: 46A17 Bornologies and related structures; Mackey convergence, etc.structures: 45: 51A15 Structures with parallelismstructures: 46: 51A45 Incidence structures imbeddable into projective geometriesstructures: 47: 51Exx Finite geometry and special incidence structuresstructures: 48: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxxstructures: 49: 51E30 Other finite incidence structures [See also]05B30structures: 50: 51Gxx Ordered geometries (ordered incidence structures, etc.)structures: 51: 51G05 Ordered geometries (ordered incidence structures, etc.)structures: 52: 51H10 Topological linear incidence structuresstructures: 53: 51H15 Topological nonlinear incidence structuresstructures: 54: 51Lxx Geometric order structures [See also]53C75structures: 55: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorialstructures, etc.) [See also]05B35, 52Cxxstructures: 56: 52C25 Rigidity and flexibility of structures [See also]70B15structures: 57: 52C45 Combinatorial complexity of geometric structures [See also]68U05structures: 58: 53B35 Hermitian and Kahlerian structures [See also]32Cxxstructures: 59: 53C15 General geometric structures on manifolds (almost complex, almost product structures,etc.)structures: 60: 53C15 General geometric structures on manifolds (almost complex, almost product structures,etc.)structures: 61: 53D30 Symplectic structures of moduli spacesstructures: 62: 54A15 Syntopogeneous structuresstructures: 63: 54Exx Spaces with richer structuresstructures: 64: 54E05 Proximity structures and generalizationsstructures: 65: 54E15 Uniform structures and generalizationsstructures: 66: 54Hxx Connections with other structures, applicationsstructures: 67: 57M50 Geometric structures on low-dimensional manifoldsstructures: 68: 57N16 Geometric structures on manifolds [See also]57M50structures: 69: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)structures: 70: 57R55 Differentiable structuresstructures: 71: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also]58-XXstructures: 72: 57Txx Homology and homotopy of topological groups and related structuresstructures: 73: 58B15 Fredholm structures [See also]47A53structures: 74: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C60structures: 75: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,58D05structures: 76: 58D27 Moduli problems for differential geometric structures
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structures: 77: 58D29 Moduli problems for topological structuresstructures: 78: 58Hxx Pseudogroups, differentiable groupoids and general structures on manifoldsstructures: 79: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,etc.) [See also]57R32structures: 80: 58H15 Deformations of structures [See also]32Gxx, 58J10structures: 81: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)structures: 82: 60Bxx Probability theory on algebraic and topological structuresstructures: 83: 68P05 Data structuresstructures: 84: 68Q87 Probability in computer science (algorithm analysis, random structures, phasetransitions, etc.) [See also]68W20, 68W40structures: 85: 74Kxx Thin bodies, structuresstructures: 86: 97H50 Ordered algebraic structures
student: 1: 97D60 Student assessment, achievement control and ratingstudent: 2: 97D70 Learning difficulties and student errorsstudent: 3: 97Q70 Student assessmentstudies: 1: 01A90 Bibliographic studiesstudies: 2: 90B90 Case-oriented studiesstudies: 3: 91A90 Experimental studiesstudies: 4: 97D10 Comprehensive works, comparative studies
sturm-liouville: 1: 34B24 Sturm-Liouville theory [See also]34Lxxsub-riemannian: 1: 53C17 Sub-Riemannian geometry
subadditivity: 1: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,26Dxx
subalgebras: 1: 08A30 Subalgebras, congruence relationssubalgebras: 2: 46H10 Ideals and subalgebrassubalgebras: 3: 46J30 Subalgebrassubalgebras: 4: 46K50 Nonselfadjoint (sub)algebras in algebras with involutionsubalgebras: 5: 47L40 Limit algebras, subalgebras of C∗-algebrassubanalytic: 1: 32B20 Semi-analytic sets and subanalytic sets [See also]14P15subbundles: 1: 58A30 Vector distributions (subbundles of the tangent bundles)
subcategories: 1: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)subdirect: 1: 08B26 Subdirect products and subdirect irreducibilitysubdirect: 2: 08B26 Subdirect products and subdirect irreducibilitysubdirect: 3: 16S60 Rings of functions, subdirect products, sheaves of rings
subdomains: 1: 32Q35 Complex manifolds as subdomains of Euclidean spacesubelliptic: 1: 35H20 Subelliptic equationssubfactors: 1: 46L37 Subfactors and their classification
subfields: 1: 74Lxx Special subfields of solid mechanicssubgraph: 1: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)subgroup: 1: 19B37 Congruence subgroup problems [See also]20H05subgroup: 2: 20E07 Subgroup theorems; subgroup growthsubgroup: 3: 20E07 Subgroup theorems; subgroup growthsubgroup: 4: 20F22 Other classes of groups defined by subgroup chains
subgroups: 1: 20B35 Subgroups of symmetric groupssubgroups: 2: 20D20 Sylow subgroups, Sylow properties, π-groups, π-structuresubgroups: 3: 20D25 Special subgroups (Frattini, Fitting, etc.)subgroups: 4: 20D30 Series and lattices of subgroupssubgroups: 5: 20D35 Subnormal subgroupssubgroups: 6: 20D40 Products of subgroupssubgroups: 7: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F22subgroups: 8: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F22subgroups: 9: 20E28 Maximal subgroupssubgroups: 10: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F20subgroups: 11: 20K27 Subgroupssubgroups: 12: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxxsubgroups: 13: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
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structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40subharmonic: 1: 31A05 Harmonic, subharmonic, superharmonic functionssubharmonic: 2: 31B05 Harmonic, subharmonic, superharmonic functionssubharmonic: 3: 31C05 Harmonic, subharmonic, superharmonic functionssubmanifolds: 1: 32C25 Analytic subsets and submanifoldssubmanifolds: 2: 32G10 Deformations of submanifolds and subspacessubmanifolds: 3: 32V40 Real submanifolds in complex manifoldssubmanifolds: 4: 53B25 Local submanifolds [See also]53C40submanifolds: 5: 53C40 Global submanifolds [See also]53B25submanifolds: 6: 53D12 Lagrangian submanifolds; Maslov indexsubmanifolds: 7: 57N40 Neighborhoods of submanifoldssubmanifolds: 8: 57R70 Critical points and critical submanifoldssubmanifolds: 9: 57R95 Realizing cycles by submanifolds
submodules: 1: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherencesubnormal: 1: 20D35 Subnormal subgroupssubnormal: 2: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F22subnormal: 3: 47B20 Subnormal operators, hyponormal operators, etc.
subordination: 1: 30C80 Maximum principle; Schwarz’s lemma, Lindelof principle, analogues and generalizations;subordination
subrecursive: 1: 03D20 Recursive functions and relations, subrecursive hierarchiessubrings: 1: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
subschemes: 1: 14Cxx Cycles and subschemessubsets: 1: 32B15 Analytic subsets of affine spacesubsets: 2: 32C25 Analytic subsets and submanifoldssubsets: 3: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D80subsonic: 1: 76Gxx General aerodynamics and subsonic flowssubsonic: 2: 76G25 General aerodynamics and subsonic flowssubspace: 1: 11J87 Schmidt Subspace Theorem and applications
subspaces: 1: 14N20 Configurations and arrangements of linear subspacessubspaces: 2: 32G10 Deformations of submanifolds and subspacessubspaces: 3: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35subspaces: 4: 47A15 Invariant subspaces [See also]47A46subspaces: 5: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.subspaces: 6: 51D25 Lattices of subspaces [See also]05B35subspaces: 7: 54B05 Subspaces
substructural: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,BCK and BCI logics) For proof-theoretic aspects see 03F52
substructural: 2: 03F52 Linear logic and other substructural logics [See also]03B47substructures: 1: 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams
subsystems: 1: 03B20 Subsystems of classical logic (including intuitionistic logic)subvarieties: 1: 14K12 Subvarieties
successive: 1: 90C55 Methods of successive quadratic programming typesuch: 1: 81Q80 Special quantum systems, such as solvable systemssuch: 2: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)sufficiency: 1: 62Bxx Sufficiency and informationsufficiency: 2: 62B86 Fuzziness, sufficiency, and information
sufficient: 1: 62B05 Sufficient statistics and fieldssum: 1: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tionsummability: 1: 40-XX Sequences, series, summabilitysummability: 2: 40Cxx General summability methodssummability: 3: 40Dxx Direct theorems on summabilitysummability: 4: 40D09 Structure of summability fieldssummability: 5: 40D15 Convergence factors and summability factors
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summability: 6: 40D20 Summability and bounded fields of methodssummability: 7: 40Fxx Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)summability: 8: 40F05 Absolute and strong summability (should also be assigned at least one other classifica-
tion number in Section 40)summability: 9: 40Gxx Special methods of summabilitysummability: 10: 40G15 Summability methods using statistical convergence [See also]40A35summability: 11: 40Hxx Functional analytic methods in summabilitysummability: 12: 40H05 Functional analytic methods in summabilitysummability: 13: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B15summability: 14: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)summability: 15: 42A24 Summability and absolute summability of Fourier and trigonometric seriessummability: 16: 42A24 Summability and absolute summability of Fourier and trigonometric seriessummability: 17: 42B08 Summabilitysummability: 18: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05summability: 19: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)summability: 20: 46A35 Summability and bases [See also]46B15summability: 21: 46B15 Summability and bases [See also]46A35
summands: 1: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions[See also]16U20, Krull dimensionsummation: 1: 34M30 Asymptotics, summation methodssummation: 2: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurinsummation formula, see 65B15summation: 3: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurinsummation formula, see 65B15summation: 4: 65B10 Summation of series
sums: 1: 11D68 Rational numbers as sums of fractionssums: 2: 11E25 Sums of squares and representations by other particular quadratic formssums: 3: 11F20 Dedekind eta function, Dedekind sumssums: 4: 11Lxx Exponential sums and character sums For finite fields, see 11Txxsums: 5: 11Lxx Exponential sums and character sums For finite fields, see 11Txxsums: 6: 11L03 Trigonometric and exponential sums, generalsums: 7: 11L05 Gauss and Kloosterman sums; generalizationssums: 8: 11L07 Estimates on exponential sumssums: 9: 11L10 Jacobsthal and Brewer sums; other complete character sumssums: 10: 11L10 Jacobsthal and Brewer sums; other complete character sumssums: 11: 11L15 Weyl sumssums: 12: 11L20 Sums over primessums: 13: 11L26 Sums over arbitrary intervalssums: 14: 11L40 Estimates on character sumssums: 15: 11T23 Exponential sumssums: 16: 11T24 Other character sums and Gauss sumssums: 17: 11T24 Other character sums and Gauss sumssums: 18: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxsums: 19: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)sums: 20: 20K25 Direct sums, direct products, etc.sums: 21: 26D15 Inequalities for sums, series and integralssums: 22: 60G50 Sums of independent random variables; random walks
sumsets: 1: 11B13 Additive bases, including sumsets [See also]05B10sumsets: 2: 11P70 Inverse problems of additive number theory, including sumsetssumsets: 3: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]
super: 1: 17B66 Lie algebras of vector fields and related (super) algebrassuper: 2: 17C70 Super structures
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super: 3: 83Exx Unified, higher-dimensional and super field theoriessuperalgebras: 1: 17A70 Superalgebrassuperalgebras: 2: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exxsuperalgebras: 3: 17B01 Identities, free Lie (super)algebrassuperalgebras: 4: 17B20 Simple, semisimple, reductive (super)algebrassuperalgebras: 5: 17B25 Exceptional (super)algebrassuperalgebras: 6: 17B30 Solvable, nilpotent (super)algebrassuperalgebras: 7: 17B35 Universal enveloping (super)algebras [See also]16S30superalgebras: 8: 17B50 Modular Lie (super)algebrassuperalgebras: 9: 17B55 Homological methods in Lie (super)algebrassuperalgebras: 10: 17B56 Cohomology of Lie (super)algebrassuperalgebras: 11: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50superalgebras: 12: 17B65 Infinite-dimensional Lie (super)algebras [See also]22E65superalgebras: 13: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrassuperalgebras: 14: 17B70 Graded Lie (super)algebrassuperalgebras: 15: 17B75 Color Lie (super)algebras
supercompactifications: 1: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)superconductors: 1: 82D55 Superconductors
superfluids: 1: 76A25 Superfluids (classical aspects)superfluids: 2: 82D50 Superfluids
supergeometry: 1: 32C11 Complex supergeometry [See also]14A22, 14M30, 58A50supergravity: 1: 83E50 Supergravity
superharmonic: 1: 31A05 Harmonic, subharmonic, superharmonic functionssuperharmonic: 2: 31B05 Harmonic, subharmonic, superharmonic functionssuperharmonic: 3: 31C05 Harmonic, subharmonic, superharmonic functionssupermanifolds: 1: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C50supermanifolds: 2: 58A50 Supermanifolds and graded manifolds [See also]14A22, 32C11supermanifolds: 3: 58C50 Analysis on supermanifolds or graded manifolds
superposed: 1: 74B15 Equations linearized about a deformed state (small deformations superposed on large)superposition: 1: 26B40 Representation and superposition of functionssuperposition: 2: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P05superprocesses: 1: 60J68 Superprocesses
supersolvable: 1: 20F16 Solvable groups, supersolvable groups [See also]20D10supersonic: 1: 76Jxx Supersonic flowssupersonic: 2: 76J20 Supersonic flows
superspaces: 1: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50and 58C50
superstring: 1: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30superstring: 2: 83E30 String and superstring theories [See also]81T30
supersymmetric: 1: 81T60 Supersymmetric field theoriessupersymmetry: 1: 81Q60 Supersymmetry and quantum mechanics
supervarieties: 1: 14M30 Supervarieties [See also]32C11, 58A50support: 1: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)
[See also]68M11surface: 1: 32S25 Surface and hypersurface singularities [See also]14J17surface: 2: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)surface: 3: 62K20 Response surface designssurface: 4: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25surface: 5: 74J15 Surface wavessurface: 6: 76B45 Capillarity (surface tension) [See also]76D45surface: 7: 76D45 Capillarity (surface tension) [See also]76B45
surfaces: 1: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and theirmodular and automorphic forms; Hilbert modular surfaces [See also]14J20
surfaces: 2: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxx
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surfaces: 3: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxsurfaces: 4: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35surfaces: 5: 14J25 Special surfaces For Hilbert modular surfaces, see 14G35surfaces: 6: 14J26 Rational and ruled surfacessurfaces: 7: 14J27 Elliptic surfacessurfaces: 8: 14J28 K3 surfaces and Enriques surfacessurfaces: 9: 14J28 K3 surfaces and Enriques surfacessurfaces: 10: 14J29 Surfaces of general typesurfaces: 11: 14J50 Automorphisms of surfaces and higher-dimensional varietiessurfaces: 12: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxsurfaces: 13: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)surfaces: 14: 14Q10 Surfaces, hypersurfacessurfaces: 15: 30Fxx Riemann surfacessurfaces: 16: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G15surfaces: 17: 30F15 Harmonic functions on Riemann surfacessurfaces: 18: 30F20 Classification theory of Riemann surfacessurfaces: 19: 30F30 Differentials on Riemann surfacessurfaces: 20: 30F50 Klein surfacessurfaces: 21: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxxsurfaces: 22: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxsurfaces: 23: 32J15 Compact surfacessurfaces: 24: 37E30 Homeomorphisms and diffeomorphisms of planes and surfacessurfaces: 25: 37E35 Flows on surfacessurfaces: 26: 49Q05 Minimal surfaces [See also]53A10, 58E12surfaces: 27: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90surfaces: 28: 51L20 Geometry of orders of surfacessurfaces: 29: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C45surfaces: 30: 53A05 Surfaces in Euclidean spacesurfaces: 31: 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-spacesurfaces: 32: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42surfaces: 33: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42surfaces: 34: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)surfaces: 35: 57M30 Wild knots and surfaces, etc., wild embeddingssurfaces: 36: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05surfaces: 37: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U07surfaces: 38: 74A50 Structured surfaces and interfaces, coexistent phasessurfaces: 39: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41surfaces: 40: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50surgery: 1: 19J25 Surgery obstructions [See also]57R67surgery: 2: 57R65 Surgery and handlebodiessurgery: 3: 57R67 Surgery obstructions, Wall groups [See also]19J25surveys: 1: 62Dxx Sampling theory, sample surveyssurveys: 2: 62D05 Sampling theory, sample surveyssurvival: 1: 62Nxx Survival analysis and censored datasurvival: 2: 62N86 Fuzziness, and survival analysis and censored data
suslin: 1: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
suspensions: 1: 55P40 Suspensionssuspensions: 2: 76T20 Suspensions
switches: 1: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxxswitching: 1: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)
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switching: 2: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30syllabuses: 1: 97B70 Syllabuses, educational standards
sylow: 1: 20D20 Sylow subgroups, Sylow properties, π-groups, π-structuresylow: 2: 20D20 Sylow subgroups, Sylow properties, π-groups, π-structure
sylvester: 1: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.symbol: 1: 47L15 Operator algebras with symbol structure
symbolic: 1: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30symbolic: 2: 37B10 Symbolic dynamics [See also]37Cxx, 37Dxxsymbolic: 3: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F10symbols: 1: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolssymbols: 2: 19C20 Symbols, presentations and stability of K2
symbols: 3: 19D45 Higher symbols, Milnor K-theorysymbols: 4: 19F15 Symbols and arithmetic [See also]11R37
symmetric: 1: 05E05 Symmetric functions and generalizationssymmetric: 2: 14M27 Compactifications; symmetric and spherical varietiessymmetric: 3: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,braided categories [See also]19D23symmetric: 4: 19D23 Symmetric monoidal categories [See also]18D10symmetric: 5: 20B30 Symmetric groupssymmetric: 6: 20B35 Subgroups of symmetric groupssymmetric: 7: 20C30 Representations of finite symmetric groupssymmetric: 8: 20C32 Representations of infinite symmetric groupssymmetric: 9: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras[See also]22E10, 22E40, 53C35, 57T15symmetric: 10: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras[See also]22E10, 22E40, 53C35, 57T15symmetric: 11: 32N15 Automorphic functions in symmetric domainssymmetric: 12: 35B07 Axially symmetric solutionssymmetric: 13: 47B25 Symmetric and selfadjoint operators (unbounded)symmetric: 14: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)symmetric: 15: 53C35 Symmetric spaces [See also]32M15, 57T15symmetric: 16: 55S15 Symmetric products, cyclic products
symmetries: 1: 34C14 Symmetries, invariantssymmetries: 2: 35B06 Symmetries, invariants, etc.symmetries: 3: 37C80 Symmetries, equivariant dynamical systemssymmetries: 4: 37G40 Symmetries, equivariant bifurcation theorysymmetries: 5: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction[See also]53D20
symmetries: 6: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawssymmetries: 7: 37L20 Symmetriessymmetries: 8: 58K70 Symmetries, equivariancesymmetries: 9: 70G65 Symmetries, Lie-group and Lie-algebra methodssymmetries: 10: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and theirbifurcations, reduction
symmetries: 11: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and theirbifurcations, reduction
symmetries: 12: 70S10 Symmetries and conservation lawssymmetries: 13: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
symmetry: 1: 11G42 Arithmetic mirror symmetry [See also]14J33symmetry: 2: 14J33 Mirror symmetry [See also]11G42, 53D37symmetry: 3: 52B15 Symmetry properties of polytopessymmetry: 4: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category[See also]14J33symmetry: 5: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category[See also]14J33
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Mathematics Subject Classification 2010
symmetry: 6: 58D19 Group actions and symmetry propertiessymmetry: 7: 58J70 Invariance and symmetry properties [See also]35A30symmetry: 8: 76M60 Symmetry analysis, Lie group and algebra methodssymmetry: 9: 81R40 Symmetry breakingsymplectic: 1: 37J05 General theory, relations with symplectic geometry and topologysymplectic: 2: 37J10 Symplectic mappings, fixed pointssymplectic: 3: 37M15 Symplectic integratorssymplectic: 4: 51A50 Polar geometry, symplectic spaces, orthogonal spacessymplectic: 5: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxxsymplectic: 6: 53D05 Symplectic manifolds, generalsymplectic: 7: 53D15 Almost contact and almost symplectic manifoldssymplectic: 8: 53D20 Momentum maps; symplectic reductionsymplectic: 9: 53D30 Symplectic structures of moduli spacessymplectic: 10: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxxsymplectic: 11: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category[See also]14J33symplectic: 12: 53D40 Floer homology and cohomology, symplectic aspectssymplectic: 13: 53D42 Symplectic field theory; contact homologysymplectic: 14: 57R17 Symplectic and contact topologysymplectic: 15: 65P10 Hamiltonian systems including symplectic integratorssymplectic: 16: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axxsymplectic: 17: 70H15 Canonical and symplectic transformationssymplectic: 18: 81S10 Geometry and quantization, symplectic methods [See also]53D50
synchronization: 1: 34D06 Synchronizationsynchronization: 2: 92B25 Biological rhythms and synchronizationsynchronization: 3: 94B50 Synchronization error-correcting codes
synthesis: 1: 43A45 Spectral synthesis on groups, semigroups, etc.synthesis: 2: 49N35 Optimal feedback synthesis [See also]93B52synthesis: 3: 93B50 Synthesis problemssynthetic: 1: 51K10 Synthetic differential geometrysynthetic: 2: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15syntopogeneous: 1: 54A15 Syntopogeneous structures
system: 1: 30B60 Completeness problems, closure of a system of functionssystem: 2: 68Mxx Computer system organizationsystem: 3: 70Fxx Dynamics of a system of particles, including celestial mechanicssystem: 4: 93A05 Axiomatic system theorysystem: 5: 93Bxx Controllability, observability, and system structuresystem: 6: 93B11 System structure simplificationsystem: 7: 93B30 System identificationsystem: 8: 93E12 System identificationsystem: 9: 97P30 System software
systems: 1: 03B22 Abstract deductive systemssystems: 2: 03D03 Thue and Post systems, etc.systems: 3: 03F50 Metamathematics of constructive systemssystems: 4: 05B07 Triple systemssystems: 5: 08-XX General algebraic systemssystems: 6: 08A02 Relational systems, laws of compositionsystems: 7: 11A07 Congruences; primitive roots; residue systemssystems: 8: 11S82 Non-Archimedean dynamical systems [See mainly]37Pxxsystems: 9: 13P15 Solving polynomial systems; resultantssystems: 10: 14C20 Divisors, linear systems, invertible sheavessystems: 11: 14H70 Relationships with integrable systemssystems: 12: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxxsystems: 13: 17B22 Root systemssystems: 14: 17B80 Applications to integrable systems
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systems: 15: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXsystems: 16: 20F29 Representations of groups as automorphism groups of algebraic systemssystems: 17: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)systems: 18: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W80systems: 19: 22A30 Other topological algebraic systems and their representationssystems: 20: 33C52 Orthogonal polynomials and functions associated with root systemssystems: 21: 33C67 Hypergeometric functions associated with root systemssystems: 22: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)systems: 23: 33D67 Basic hypergeometric functions associated with root systemssystems: 24: 34A30 Linear equations and systems, generalsystems: 25: 34A34 Nonlinear equations and systems, generalsystems: 26: 34A38 Hybrid systemssystems: 27: 34C12 Monotone systemssystems: 28: 34C20 Transformation and reduction of equations and systems, normal formssystems: 29: 34C28 Complex behavior, chaotic systems [See also]37Dxxsystems: 30: 34C40 Equations and systems on manifoldssystems: 31: 34C46 Multifrequency systemssystems: 32: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E03systems: 33: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E03systems: 34: 34K17 Transformation and reduction of equations and systems, normal formssystems: 35: 34K34 Hybrid systemssystems: 36: 34M03 Linear equations and systemssystems: 37: 35Exx Equations and systems with constant coefficients [See also]35N05systems: 38: 35Fxx General first-order equations and systemssystems: 39: 35F35 Linear first-order systemssystems: 40: 35F40 Initial value problems for linear first-order systemssystems: 41: 35F45 Boundary value problems for linear first-order systemssystems: 42: 35F46 Initial-boundary value problems for linear first-order systemssystems: 43: 35F50 Nonlinear first-order systemssystems: 44: 35F55 Initial value problems for nonlinear first-order systemssystems: 45: 35F60 Boundary value problems for nonlinear first-order systemssystems: 46: 35F61 Initial-boundary value problems for nonlinear first-order systemssystems: 47: 35Gxx General higher-order equations and systemssystems: 48: 35G35 Linear higher-order systemssystems: 49: 35G40 Initial value problems for linear higher-order systemssystems: 50: 35G45 Boundary value problems for linear higher-order systemssystems: 51: 35G46 Initial-boundary value problems for linear higher-order systemssystems: 52: 35G50 Nonlinear higher-order systemssystems: 53: 35G55 Initial value problems for nonlinear higher-order systemssystems: 54: 35G60 Boundary value problems for nonlinear higher-order systemssystems: 55: 35G61 Initial-boundary value problems for nonlinear higher-order systemssystems: 56: 35Hxx Close-to-elliptic equations and systemssystems: 57: 35Jxx Elliptic equations and systems [See also]58J10, 58J20systems: 58: 35J46 First-order elliptic systemssystems: 59: 35J47 Second-order elliptic systemssystems: 60: 35J48 Higher-order elliptic systemssystems: 61: 35J50 Variational methods for elliptic systemssystems: 62: 35J56 Boundary value problems for first-order elliptic systemssystems: 63: 35J57 Boundary value problems for second-order elliptic systemssystems: 64: 35J58 Boundary value problems for higher-order elliptic systemssystems: 65: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J40systems: 66: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J35systems: 67: 35K40 Second-order parabolic systemssystems: 68: 35K41 Higher-order parabolic systemssystems: 69: 35K45 Initial value problems for second-order parabolic systems
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systems: 70: 35K46 Initial value problems for higher-order parabolic systemssystems: 71: 35K51 Initial-boundary value problems for second-order parabolic systemssystems: 72: 35K52 Initial-boundary value problems for higher-order parabolic systemssystems: 73: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J40systems: 74: 35Lxx Hyperbolic equations and systems [See also]58J45systems: 75: 35L40 First-order hyperbolic systemssystems: 76: 35L45 Initial value problems for first-order hyperbolic systemssystems: 77: 35L50 Initial-boundary value problems for first-order hyperbolic systemssystems: 78: 35L51 Second-order hyperbolic systemssystems: 79: 35L52 Initial value problems for second-order hyperbolic systemssystems: 80: 35L53 Initial-boundary value problems for second-order hyperbolic systemssystems: 81: 35L55 Higher-order hyperbolic systemssystems: 82: 35L56 Initial value problems for higher-order hyperbolic systemssystems: 83: 35L57 Initial-boundary value problems for higher-order hyperbolic systemssystems: 84: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J40systems: 85: 35Mxx Equations and systems of special type (mixed, composite, etc.)systems: 86: 35M30 Systems of mixed typesystems: 87: 35M31 Initial value problems for systems of mixed typesystems: 88: 35M32 Boundary value problems for systems of mixed typesystems: 89: 35M33 Initial-boundary value problems for systems of mixed typesystems: 90: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J40systems: 91: 35Nxx Overdetermined systems [See also]58Hxx, 58J10, 58J15systems: 92: 35N05 Overdetermined systems with constant coefficientssystems: 93: 35N10 Overdetermined systems with variable coefficientssystems: 94: 35Q70 PDEs in connection with mechanics of particles and systemssystems: 95: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XXsystems: 96: 37A60 Dynamical systems in statistical mechanics [See also]82Cxxsystems: 97: 37B55 Nonautonomous dynamical systemssystems: 98: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxxsystems: 99: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemssystems: 100: 37C45 Dimension theory of dynamical systemssystems: 101: 37C60 Nonautonomous smooth dynamical systems [See also]37B55systems: 102: 37C80 Symmetries, equivariant dynamical systemssystems: 103: 37Dxx Dynamical systems with hyperbolic behaviorsystems: 104: 37D15 Morse-Smale systemssystems: 105: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)systems: 106: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)systems: 107: 37D30 Partially hyperbolic systems and dominated splittingssystems: 108: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
etc.)systems: 109: 37D50 Hyperbolic systems with singularities (billiards, etc.)systems: 110: 37Exx Low-dimensional dynamical systemssystems: 111: 37Fxx Complex dynamical systems [See also]30D05, 32H50systems: 112: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemssystems: 113: 37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcationssystems: 114: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exxsystems: 115: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxxsystems: 116: 37J35 Completely integrable systems, topological structure of phase space, integration
methodssystems: 117: 37J55 Contact systems [See also]53D10systems: 118: 37J60 Nonholonomic dynamical systems [See also]70F25
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systems: 119: 37Kxx Infinite-dimensional Hamiltonian systems [See also]35Axx, 35Qxxsystems: 120: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,
hierarchies (KdV, KP, Toda, etc.)systems: 121: 37K15 Integration of completely integrable systems by inverse spectral and scattering methodssystems: 122: 37K55 Perturbations, KAM for infinite-dimensional systemssystems: 123: 37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and
metricssystems: 124: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxxsystems: 125: 37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systemssystems: 126: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H15systems: 127: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxsystems: 128: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxxsystems: 129: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A10systems: 130: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxxsystems: 131: 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity,
laser physics)systems: 132: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XXsystems: 133: 37N30 Dynamical systems in numerical analysissystems: 134: 37N35 Dynamical systems in controlsystems: 135: 37N40 Dynamical systems in optimization and economicssystems: 136: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A45systems: 137: 37P50 Dynamical systems on Berkovich spacessystems: 138: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05systems: 139: 39B72 Systems of functional equations and inequalitiessystems: 140: 41A50 Best approximation, Chebyshev systemssystems: 141: 42C40 Wavelets and other special systemssystems: 142: 45Fxx Systems of linear integral equationssystems: 143: 45F05 Systems of nonsingular linear integral equationssystems: 144: 45F15 Systems of singular linear integral equationssystems: 145: 45G15 Systems of nonlinear integral equationssystems: 146: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H20systems: 147: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.systems: 148: 47Cxx Individual linear operators as elements of algebraic systemssystems: 149: 47N70 Applications in systems theory, circuits, and control theorysystems: 150: 51Dxx Geometric closure systemssystems: 151: 51E10 Steiner systemssystems: 152: 54H10 Topological representations of algebraic systems [See also]22-XXsystems: 153: 55S45 Postnikov systems, k-invariantssystems: 154: 58A15 Exterior differential systems (Cartan theory)systems: 155: 58A17 Pfaffian systemssystems: 156: 65F05 Direct methods for linear systems and matrix inversionsystems: 157: 65F10 Iterative methods for linear systems [See also]65N22systems: 158: 65F20 Overdetermined systems, pseudoinversessystems: 159: 65H10 Systems of equationssystems: 160: 65Pxx Numerical problems in dynamical systems [See also]37Mxxsystems: 161: 65P10 Hamiltonian systems including symplectic integratorssystems: 162: 68M14 Distributed systemssystems: 163: 68N25 Operating systemssystems: 164: 68Q42 Grammars and rewriting systemssystems: 165: 68T05 Learning and adaptive systems [See also]68Q32, 91E40systems: 166: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)systems: 167: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)
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systems: 168: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)systems: 169: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)
[See also]68M11systems: 170: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XXsystems: 171: 70Exx Dynamics of a rigid body and of multibody systemssystems: 172: 70E55 Dynamics of multibody systemssystems: 173: 70F20 Holonomic systemssystems: 174: 70F25 Nonholonomic systemssystems: 175: 70F45 Infinite particle systemssystems: 176: 70G60 Dynamical systems methodssystems: 177: 70H06 Completely integrable systems and methods of integrationsystems: 178: 70H07 Nonintegrable systemssystems: 179: 70H08 Nearly integrable Hamiltonian systems, KAM theorysystems: 180: 70J50 Systems arising from the discretization of structural vibration problemssystems: 181: 70K70 Systems with slow and fast motionssystems: 182: 70Qxx Control of mechanical systems [See also]60Gxx, 60Jxxsystems: 183: 70Q05 Control of mechanical systemssystems: 184: 76F20 Dynamical systems approach to turbulence [See also]37-XXsystems: 185: 81Q80 Special quantum systems, such as solvable systemssystems: 186: 81Q80 Special quantum systems, such as solvable systemssystems: 187: 81R12 Relations with integrable systems [See also]17Bxx, 37J35systems: 188: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C31systems: 189: 81U15 Exactly and quasi-solvable systemssystems: 190: 81Vxx Applications to specific physical systemssystems: 191: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphssystems: 192: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphssystems: 193: 82B21 Continuum models (systems of particles, etc.)systems: 194: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)systems: 195: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphssystems: 196: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphssystems: 197: 82C21 Dynamic continuum models (systems of particles, etc.)systems: 198: 82C22 Interacting particle systems [See also]60K35systems: 199: 82C44 Dynamics of disordered systems (random Ising systems, etc.)systems: 200: 82C44 Dynamics of disordered systems (random Ising systems, etc.)systems: 201: 82Dxx Applications to specific types of physical systemssystems: 202: 91B74 Models of real-world systemssystems: 203: 91D35 Manpower systems [See also]91B40, 90B70systems: 204: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)systems: 205: 92C42 Systems biology, networkssystems: 206: 93-XX Systems theory; control For optimal control, see 49-XXsystems: 207: 93A10 General systemssystems: 208: 93A13 Hierarchical systemssystems: 209: 93A14 Decentralized systemssystems: 210: 93A15 Large scale systemssystems: 211: 93A30 Mathematical modeling (models of systems, model-matching, etc.)systems: 212: 93B12 Variable structure systemssystems: 213: 93B20 Minimal systems representationssystems: 214: 93Cxx Control systemssystems: 215: 93C05 Linear systemssystems: 216: 93C10 Nonlinear systemssystems: 217: 93C15 Systems governed by ordinary differential equations [See also]34H05systems: 218: 93C20 Systems governed by partial differential equationssystems: 219: 93C23 Systems governed by functional-differential equations [See also]34K35systems: 220: 93C25 Systems in abstract spacessystems: 221: 93C30 Systems governed by functional relations other than differential equations (such as
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hybrid and switching systems)systems: 222: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)systems: 223: 93C35 Multivariable systemssystems: 224: 93C42 Fuzzy control systemssystems: 225: 93C55 Discrete-time systemssystems: 226: 93C57 Sampled-data systemssystems: 227: 93C62 Digital systemssystems: 228: 93C65 Discrete event systemssystems: 229: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q05systems: 230: 93D10 Popov-type stability of feedback systemssystems: 231: 93D15 Stabilization of systems by feedbacksystems: 232: 93Exx Stochastic systems and controlsystems: 233: 93E03 Stochastic systems, generalsystems: 234: 97Bxx Educational policy and systemssystems: 235: 97R50 Data bases, information systemssyzygies: 1: 13D02 Syzygies, resolutions, complexessyzygies: 2: 16E05 Syzygies, resolutions, complexes
szego: 1: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)tables: 1: 11Y70 Values of arithmetic functions; tablestables: 2: 62H17 Contingency tablestables: 3: 62Qxx Statistical tablestables: 4: 62Q05 Statistical tablestables: 5: 65Axx Tablestables: 6: 65A05 Tablestables: 7: 65D20 Computation of special functions, construction of tables [See also]33F05
tail: 1: 62G32 Statistics of extreme values; tail inferencetaking: 1: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxtaking: 2: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)tame: 1: 16G60 Representation type (finite, tame, wild, etc.)tame: 2: 46A61 Graded Frechet spaces and tame operators
tameness: 1: 57N45 Flatness and tamenesstangent: 1: 58A30 Vector distributions (subbundles of the tangent bundles)
tauberian: 1: 11M45 Tauberian theorems [See also]40E05tauberian: 2: 40D10 Tauberian constants and oscillation limitstauberian: 3: 40E05 Tauberian theorems, generaltauberian: 4: 40E20 Tauberian constants
taxation: 1: 91B64 Macro-economic models (monetary models, models of taxation)taxonomy: 1: 92B10 Taxonomy, cladistics, statistics
taylor: 1: 30K05 Universal Taylor seriestaylor: 2: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
teacher: 1: 97B50 Teacher education For research aspects, see 97C70teachers’: 1: 97U30 Teachers’ manuals and planning aidsteaching: 1: 97D40 Teaching methods and classroom techniquesteaching: 2: 97D50 Teaching problem solving and heuristic strategies For research aspects, see 97Cxxteaching: 3: 97D80 Teaching units and draft lessonsteaching: 4: 97Q20 Affective aspects in teaching computer scienceteaching: 5: 97Q60 Teaching methods and classroom techniquesteaching: 6: 97Q80 Teaching units
teaching-learning: 1: 97C70 Teaching-learning processestechnical: 1: 78A55 Technical applications
techniques: 1: 14N05 Projective techniques [See also]51N35techniques: 2: 16W70 Filtered rings; filtrational and graded techniquestechniques: 3: 32A65 Banach algebra techniques [See mainly]46Jxxtechniques: 4: 32A70 Functional analysis techniques [See mainly]46Exx
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techniques: 5: 34M25 Formal solutions, transform techniquestechniques: 6: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytictechniques in dynamical systemstechniques: 7: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07techniques: 8: 65Kxx Mathematical programming, optimization and variational techniquestechniques: 9: 65K10 Optimization and variational techniques [See also]49Mxx, 93B40techniques: 10: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,etc.)techniques: 11: 78M12 Finite volume methods, finite integration techniquestechniques: 12: 81Q20 Semiclassical techniques, including WKB and Maslov methodstechniques: 13: 93B51 Design techniques (robust design, computer-aided design, etc.)techniques: 14: 97D40 Teaching methods and classroom techniquestechniques: 15: 97P50 Programming techniquestechniques: 16: 97Q60 Teaching methods and classroom techniques
technological: 1: 97U70 Technological tools, calculatorstechnology: 1: 68T42 Agent technologytechnology: 2: 97M50 Physics, astronomy, technology, engineeringtechnology: 3: 97Uxx Educational material and media, educational technologyteichmuller: 1: 30F60 Teichmuller theory [See also]32G15teichmuller: 2: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxxteichmuller: 3: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups asdynamical systems
temporal: 1: 03B44 Temporal logictemporal: 2: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F45tension: 1: 76B45 Capillarity (surface tension) [See also]76D45tension: 2: 76D45 Capillarity (surface tension) [See also]76B45tensor: 1: 15A69 Multilinear algebra, tensor productstensor: 2: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L24tensor: 3: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20tensor: 4: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L20tensor: 5: 46L06 Tensor products of C∗-algebrastensor: 6: 46M05 Tensor products [See also]46A32, 46B28, 47A80tensor: 7: 47A80 Tensor products of operators [See also]46M05tensor: 8: 53A45 Vector and tensor analysis
tensors: 1: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx
term-rewriting: 1: 16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)terms: 1: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variableterms: 2: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variableternary: 1: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesternary: 2: 17A40 Ternary compositionsternary: 3: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
tessellation: 1: 05B45 Tessellation and tiling problems [See also]52C20, 52C22test: 1: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E35testing: 1: 62F03 Hypothesis testingtesting: 2: 62G10 Hypothesis testingtesting: 3: 62H15 Hypothesis testingtesting: 4: 62M02 Markov processes: hypothesis testingtesting: 5: 62M07 Non-Markovian processes: hypothesis testingtesting: 6: 62N03 Testingtesting: 7: 62N05 Reliability and life testing [See also]90B25
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testing: 8: 68M15 Reliability, testing and fault tolerance [See also]94C12testing: 9: 94C12 Fault detection; testing
tests: 1: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)
tests: 2: 62F05 Asymptotic properties of teststext: 1: 68U15 Text processing; mathematical typography
textbook: 1: 97U20 Textbooks. Textbook researchtextbooks: 1: 97U20 Textbooks. Textbook research
texture: 1: 74E25 Texturethan: 1: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesthan: 2: 11E76 Forms of degree higher than twothan: 3: 16R40 Identities other than those of matrices over commutative ringsthan: 4: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxxthan: 5: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)than: 6: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P05than: 7: 47A30 Norms (inequalities, more than one norm, etc.)than: 8: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theorythan: 9: 49J21 Optimal control problems involving relations other than differential equationsthan: 10: 49K21 Problems involving relations other than differential equationsthan: 11: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C90than: 12: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesthan: 13: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriesthan: 14: 93C30 Systems governed by functional relations other than differential equations (such as
hybrid and switching systems)that: 1: 68-XX Computer science For papers involving machine computations and programs in a
specific mathematical area, see Section–04 in that areathe: 1: 11D07 The Frobenius problemthe: 2: 32C55 The Levi problem in complex spaces; generalizationsthe: 3: 32E40 The Levi problem
their: 1: 03E04 Ordered sets and their cofinalities; pcf theorytheir: 2: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J20their: 3: 11F55 Other groups and their modular and automorphic forms (several variables)their: 4: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxxtheir: 5: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxxtheir: 6: 13A18 Valuations and their generalizations [See also]12J20their: 7: 13F05 Dedekind, Prufer, Krull and Mori rings and their generalizationstheir: 8: 13N10 Rings of differential operators and their modules [See also]16S32, 32C38their: 9: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05their: 10: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxtheir: 11: 15B48 Positive matrices and their generalizations; cones of matricestheir: 12: 16T05 Hopf algebras and their applications [See also]16S40, 57T05their: 13: 20C05 Group rings of finite groups and their modules [See also]16S34their: 14: 20C07 Group rings of infinite groups and their modules [See also]16S34their: 15: 20C08 Hecke algebras and their representationstheir: 16: 20D05 Finite simple groups and their classificationtheir: 17: 20F24 FC-groups and their generalizationstheir: 18: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxxtheir: 19: 20G25 Linear algebraic groups over local fields and their integers
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their: 20: 20G30 Linear algebraic groups over global fields and their integerstheir: 21: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R50their: 22: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxxtheir: 23: 22A30 Other topological algebraic systems and their representationstheir: 24: 22Dxx Locally compact groups and their algebrastheir: 25: 22E46 Semisimple Lie groups and their representationstheir: 26: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H05their: 27: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J15their: 28: 37G35 Attractors and their bifurcationstheir: 29: 37L30 Attractors and their dimensions, Lyapunov exponentstheir: 30: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionstheir: 31: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)their: 32: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exxtheir: 33: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J10their: 34: 46L37 Subfactors and their classificationtheir: 35: 47Dxx Groups and semigroups of linear operators, their generalizations and applicationstheir: 36: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxxtheir: 37: 51M30 Line geometries and their generalizations [See also]53A25their: 38: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M15their: 39: 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their
bifurcations, reductiontheir: 40: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E70their: 41: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
them: 1: 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions)them: 2: 33D60 Basic hypergeometric integrals and functions defined by them
theorem: 1: 11J87 Schmidt Subspace Theorem and applicationstheorem: 2: 12E25 Hilbertian fields; Hilbert’s irreducibility theoremtheorem: 3: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericitytheorem: 4: 57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericitytheorem: 5: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B35
theorems: 1: 03F05 Cut-elimination and normal-form theoremstheorems: 2: 11H60 Mean value and transfer theoremstheorems: 3: 11M45 Tauberian theorems [See also]40E05theorems: 4: 11P32 Goldbach-type theorems; other additive questions involving primestheorems: 5: 11R45 Density theoremstheorems: 6: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15theorems: 7: 13C05 Structure, classification theoremstheorems: 8: 13D22 Homological conjectures (intersection theorems)theorems: 9: 14C40 Riemann-Roch theorems [See also]19E20, 19L10theorems: 10: 14F17 Vanishing theorems [See also]32L20theorems: 11: 18B15 Embedding theorems, universal categories [See also]18E20theorems: 12: 18E20 Embedding theorems [See also]18B15theorems: 13: 19L10 Riemann-Roch theorems, Chern characterstheorems: 14: 20B10 Characterization theorems
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theorems: 15: 20E07 Subgroup theorems; subgroup growththeorems: 16: 20E34 General structure theoremstheorems: 17: 22D35 Duality theoremstheorems: 18: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15theorems: 19: 26B10 Implicit function theorems, Jacobians, transformations with several variablestheorems: 20: 30C25 Covering theorems in conformal mapping theorytheorems: 21: 30H80 Corona theoremstheorems: 22: 31A20 Boundary behavior (theorems of Fatou type, etc.)theorems: 23: 32B05 Analytic algebras and generalizations, preparation theoremstheorems: 24: 32C37 Duality theoremstheorems: 25: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)theorems: 26: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see
32A22theorems: 27: 32H35 Proper mappings, finiteness theoremstheorems: 28: 32J10 Algebraic dependence theoremstheorems: 29: 32L20 Vanishing theoremstheorems: 30: 32Q40 Embedding theoremstheorems: 31: 32Q57 Classification theoremstheorems: 32: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantstheorems: 33: 35A10 Cauchy-Kovalevskaya theoremstheorems: 34: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.theorems: 35: 35B53 Liouville theorems, Phragmen-Lindelof theoremstheorems: 36: 35B53 Liouville theorems, Phragmen-Lindelof theoremstheorems: 37: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35theorems: 38: 40Dxx Direct theorems on summabilitytheorems: 39: 40D05 General theoremstheorems: 40: 40D25 Inclusion and equivalence theoremstheorems: 41: 40Exx Inversion theoremstheorems: 42: 40E05 Tauberian theorems, generaltheorems: 43: 40E15 Lacunary inversion theoremstheorems: 44: 41A27 Inverse theoremstheorems: 45: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
[See also]46M10theorems: 46: 46A30 Open mapping and closed graph theorems; completeness (including B-, Br-
completeness)theorems: 47: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremstheorems: 48: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremstheorems: 49: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C30theorems: 50: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A35theorems: 51: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C15theorems: 52: 51A20 Configuration theoremstheorems: 53: 51L15 n-vertex theorems via direct methodstheorems: 54: 52A35 Helly-type theorems and geometric transversal theorytheorems: 55: 54H25 Fixed-point and coincidence theorems [See also]47H10, 55M20theorems: 56: 55N40 Axioms for homology theory and uniqueness theoremstheorems: 57: 55U20 Universal coefficient theorems, Bockstein operatortheorems: 58: 58C15 Implicit function theorems; global Newton methodstheorems: 59: 58C30 Fixed point theorems on manifolds [See also]47H10theorems: 60: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80theorems: 61: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)theorems: 62: 60Fxx Limit theorems [See also]28Dxx, 60B12theorems: 63: 60F05 Central limit and other weak theoremstheorems: 64: 60F15 Strong theorems
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Mathematics Subject Classification 2010
theorems: 65: 60F17 Functional limit theorems; invariance principlestheorems: 66: 60F25 Lp-limit theoremstheorems: 67: 94A24 Coding theorems (Shannon theory)
theoretical: 1: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxxtheoretical: 2: 34K07 Theoretical approximation of solutionstheoretical: 3: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxtheoretical: 4: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxxtheoretical: 5: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxxtheoretical: 6: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoreticalaspects, see 68U20 and 60H35theoretical: 7: 97D20 Philosophical and theoretical contributions (maths didactics)
theories: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F10theories: 2: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F35theories: 3: 03C35 Categoricity and completeness of theoriestheories: 4: 03C65 Models of other mathematical theoriestheories: 5: 03E70 Nonclassical and second-order set theoriestheories: 6: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxtheories: 7: 18Cxx Categories and theoriestheories: 8: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30theories: 9: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30theories: 10: 18E40 Torsion theories, radicals [See also]13D30, 16S90theories: 11: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J22theories: 12: 19E20 Relations with cohomology theories [See also]14Fxxtheories: 13: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J20theories: 14: 49Jxx Existence theoriestheories: 15: 49Lxx Hamilton-Jacobi theories, including dynamic programmingtheories: 16: 55Nxx Homology and cohomology theories [See also]57Txxtheories: 17: 55N20 Generalized (extraordinary) homology and cohomology theoriestheories: 18: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R90theories: 19: 55N35 Other homology theoriestheories: 20: 57R56 Topological quantum field theoriestheories: 21: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M20theories: 22: 70H09 Perturbation theoriestheories: 23: 70H50 Higher-order theoriestheories: 24: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XXtheories: 25: 70S15 Yang-Mills and other gauge theoriestheories: 26: 70S20 More general nonquantum field theoriestheories: 27: 74A25 Molecular, statistical, and kinetic theoriestheories: 28: 74A45 Theories of fracture and damagetheories: 29: 74A55 Theories of friction (tribology)theories: 30: 74A60 Micromechanical theoriestheories: 31: 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic
materials)theories: 32: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)theories: 33: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)theories: 34: 74C15 Large-strain, rate-independent theories (including nonlinear plasticity)theories: 35: 74C20 Large-strain, rate-dependent theoriestheories: 36: 81Q15 Perturbation theories for operators and differential equationstheories: 37: 81Txx Quantum field theory; related classical field theories [See also]70Sxxtheories: 38: 81T10 Model quantum field theoriestheories: 39: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E15theories: 40: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30theories: 41: 81T40 Two-dimensional field theories, conformal field theories, etc.theories: 42: 81T40 Two-dimensional field theories, conformal field theories, etc.theories: 43: 81T45 Topological field theories [See also]57R56, 58Dxx
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theories: 44: 81T60 Supersymmetric field theoriestheories: 45: 81V22 Unified theoriestheories: 46: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriestheories: 47: 83Dxx Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriestheories: 48: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriestheories: 49: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field
theoriestheories: 50: 83Exx Unified, higher-dimensional and super field theoriestheories: 51: 83E15 Kaluza-Klein and other higher-dimensional theoriestheories: 52: 83E30 String and superstring theories [See also]81T30theories: 53: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)theories: 54: 97C30 Cognitive processes, learning theories
theory: 1: 00A71 Theory of mathematical modelingtheory: 2: 03B15 Higher-order logic and type theorytheory: 3: 03Cxx Model theorytheory: 4: 03C45 Classification theory, stability and related concepts [See also]03C48theory: 5: 03C55 Set-theoretic model theorytheory: 6: 03C57 Effective and recursion-theoretic model theory [See also]03D45theory: 7: 03C62 Models of arithmetic and set theory [See also]03Hxxtheory: 8: 03C64 Model theory of ordered structures; o-minimalitytheory: 9: 03C68 Other classical first-order model theorytheory: 10: 03C85 Second- and higher-order model theorytheory: 11: 03C95 Abstract model theorytheory: 12: 03C98 Applications of model theory [See also]03C60theory: 13: 03Dxx Computability and recursion theorytheory: 14: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionis-
tic and similar approaches see 03F55theory: 15: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.theory: 16: 03D65 Higher-type and set recursion theorytheory: 17: 03D75 Abstract and axiomatic computability and recursion theorytheory: 18: 03D80 Applications of computability and recursion theorytheory: 19: 03Exx Set theorytheory: 20: 03E04 Ordered sets and their cofinalities; pcf theorytheory: 21: 03E05 Other combinatorial set theorytheory: 22: 03E15 Descriptive set theory [See also]28A05, 54H05theory: 23: 03E20 Other classical set theory (including functions, relations, and set algebra)theory: 24: 03E30 Axiomatics of classical set theory and its fragmentstheory: 25: 03E72 Fuzzy set theorytheory: 26: 03E75 Applications of set theorytheory: 27: 03Fxx Proof theory and constructive mathematicstheory: 28: 03F03 Proof theory, generaltheory: 29: 03F10 Functionals in proof theorytheory: 30: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C30theory: 31: 05Bxx Designs and configurations For applications of design theory, see 94C30theory: 32: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C15theory: 33: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
57M25theory: 34: 05C30 Enumeration in graph theorytheory: 35: 05C55 Generalized Ramsey theory [See also]05D10theory: 36: 05C72 Fractional graph theory, fuzzy graph theorytheory: 37: 05C72 Fractional graph theory, fuzzy graph theorytheory: 38: 05D05 Extremal set theory
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theory: 39: 05D10 Ramsey theory [See also]05C55theory: 40: 05D15 Transversal (matching) theorytheory: 41: 05E10 Combinatorial aspects of representation theory [See also]20C30theory: 42: 06B05 Structure theorytheory: 43: 06B15 Representation theorytheory: 44: 06D05 Structure and representation theorytheory: 45: 06E05 Structure theorytheory: 46: 08A05 Structure theorytheory: 47: 11-XX Number theorytheory: 48: 11Axx Elementary number theory For analogues in number fields, see 11R04theory: 49: 11B75 Other combinatorial number theorytheory: 50: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)theory: 51: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24theory: 52: 11E95 p-adic theorytheory: 53: 11F72 Spectral theory; Selberg trace formulatheory: 54: 11F85 p-adic theory, local fields [See also]14G20, 22E50theory: 55: 11G32 Dessins d’enfants, Belyı theorytheory: 56: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F05theory: 57: 11Hxx Geometry of numbers For applications in coding theory, see 94B75theory: 58: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)theory: 59: 11H71 Relations with coding theorytheory: 60: 11Jxx Diophantine approximation, transcendental number theory [See also]11K60theory: 61: 11J81 Transcendence (general theory)theory: 62: 11J83 Metric theorytheory: 63: 11J89 Transcendence theory of elliptic and abelian functionstheory: 64: 11J91 Transcendence theory of other special functionstheory: 65: 11J93 Transcendence theory of Drinfel′d and t-modulestheory: 66: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)theory: 67: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmstheory: 68: 11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithmstheory: 69: 11K06 General theory of distribution modulo 1 [See also]11J71theory: 70: 11K50 Metric theory of continued fractions [See also]11A55, 11J70theory: 71: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
[See also]11N99, 28Dxxtheory: 72: 11Mxx Zeta and L-functions: analytic theorytheory: 73: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulastheory: 74: 11Nxx Multiplicative number theorytheory: 75: 11N30 Turan theory [See also]30Bxxtheory: 76: 11Pxx Additive number theory; partitionstheory: 77: 11P70 Inverse problems of additive number theory, including sumsetstheory: 78: 11P81 Elementary theory of partitions [See also]05A17theory: 79: 11P82 Analytic theory of partitionstheory: 80: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G15theory: 81: 11R23 Iwasawa theorytheory: 82: 11R32 Galois theorytheory: 83: 11R37 Class field theorytheory: 84: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E55theory: 85: 11R47 Other analytic theory [See also]11Nxxtheory: 86: 11R58 Arithmetic theory of algebraic function fields [See also]14-XXtheory: 87: 11Sxx Algebraic number theory: local and p-adic fieldstheory: 88: 11S15 Ramification and extension theorytheory: 89: 11S20 Galois theorytheory: 90: 11S31 Class field theory; p-adic formal groups [See also]14L05theory: 91: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E50theory: 92: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)
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theory: 93: 11S85 Other nonanalytic theorytheory: 94: 11T30 Structure theorytheory: 95: 11T55 Arithmetic theory of polynomial rings over finite fieldstheory: 96: 11T71 Algebraic coding theory; cryptographytheory: 97: 11U09 Model theory [See also]03Cxxtheory: 98: 11Yxx Computational number theory [See also]11-04theory: 99: 11Y40 Algebraic number theory computationstheory: 100: 11Zxx Miscellaneous applications of number theorytheory: 101: 11Z05 Miscellaneous applications of number theorytheory: 102: 12-XX Field theory and polynomialstheory: 103: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15theory: 104: 12Exx General field theorytheory: 105: 12F10 Separable extensions, Galois theorytheory: 106: 12F12 Inverse Galois theorytheory: 107: 12Gxx Homological methods (field theory)theory: 108: 12J20 General valuation theory [See also]13A18theory: 109: 12L12 Model theory [See also]03C60theory: 110: 12Yxx Computational aspects of field theory and polynomialstheory: 111: 12Y05 Computational aspects of field theory and polynomialstheory: 112: 13Axx General commutative ring theorytheory: 113: 13A15 Ideals; multiplicative ideal theorytheory: 114: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L24theory: 115: 13B02 Extension theorytheory: 116: 13B05 Galois theorytheory: 117: 13Cxx Theory of modules and idealstheory: 118: 13C15 Dimension theory, depth, related rings (catenary, etc.)theory: 119: 13D30 Torsion theory [See also]13C12, 18E40theory: 120: 13H15 Multiplicity theory and related topics [See also]14C17theory: 121: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)theory: 122: 14Bxx Local theorytheory: 123: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10theory: 124: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H15theory: 125: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecturetheory: 126: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxtheory: 127: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxtheory: 128: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S45theory: 129: 14E30 Minimal model program (Mori theory, extremal rays)theory: 130: 14Fxx (Co)homology theory [See also]13Dxxtheory: 131: 14F35 Homotopy theory; fundamental groups [See also]14H30theory: 132: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E15theory: 133: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)theory: 134: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30theory: 135: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B40theory: 136: 14H51 Special divisors (gonality, Brill-Noether theory)theory: 137: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G32theory: 138: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxtheory: 139: 14J10 Families, moduli, classification: algebraic theorytheory: 140: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13theory: 141: 14K05 Algebraic theorytheory: 142: 14K20 Analytic theory; abelian integrals and differentialstheory: 143: 14L24 Geometric invariant theory [See also]13A50
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theory: 144: 15-XX Linear and multilinear algebra; matrix theorytheory: 145: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05theory: 146: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L24theory: 147: 16D10 General module theorytheory: 148: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and dualitytheory: 149: 16Gxx Representation theory of rings and algebrastheory: 150: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G30theory: 151: 16R30 Trace rings and invariant theorytheory: 152: 16W22 Actions of groups and semigroups; invariant theorytheory: 153: 17A01 General theorytheory: 154: 17A60 Structure theorytheory: 155: 17A65 Radical theorytheory: 156: 17B05 Structure theorytheory: 157: 17B10 Representations, algebraic theory (weights)theory: 158: 17B15 Representations, analytic theorytheory: 159: 17C10 Structure theorytheory: 160: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
theory: 161: 18Axx General theory of categories and functorstheory: 162: 19Fxx K-theory in number theory [See also]11R70, 11S70theory: 163: 19F05 Generalized class field theory [See also]11G45theory: 164: 19K35 Kasparov theory (KK-theory) [See also]58J22theory: 165: 19K56 Index theory [See also]58J20, 58J22theory: 166: 20-XX Group theory and generalizationstheory: 167: 20A15 Applications of logic to group theorytheory: 168: 20B05 General theory for finite groupstheory: 169: 20B07 General theory for infinite groupstheory: 170: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)theory: 171: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F17theory: 172: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05theory: 173: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxxtheory: 174: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
theory: 175: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
theory: 176: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46,22E47, 22E50, 22E55
theory: 177: 20G05 Representation theorytheory: 178: 20G07 Structure theorytheory: 179: 20G10 Cohomology theorytheory: 180: 20Jxx Connections with homological algebra and category theorytheory: 181: 20J05 Homological methods in group theorytheory: 182: 20M10 General structure theorytheory: 183: 20M11 Radical theorytheory: 184: 20M12 Ideal theorytheory: 185: 20M13 Arithmetic theory of monoidstheory: 186: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50theory: 187: 20M50 Connections of semigroups with homological algebra and category theory
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theory: 188: 20Pxx Probabilistic methods in group theory [See also]60Bxxtheory: 189: 20P05 Probabilistic methods in group theory [See also]60Bxxtheory: 190: 22D40 Ergodic theory on groups [See also]28Dxxtheory: 191: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G05theory: 192: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxxtheory: 193: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20theory: 194: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15theory: 195: 28Axx Classical measure theorytheory: 196: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A24theory: 197: 28A51 Lifting theory [See also]46G15theory: 198: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15theory: 199: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measurestheory: 200: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G10theory: 201: 28Exx Miscellaneous topics in measure theorytheory: 202: 28E05 Nonstandard measure theory [See also]03H05, 26E35theory: 203: 28E10 Fuzzy measure theory [See also]03E72, 26E50, 94D05theory: 204: 28E15 Other connections with logic and set theorytheory: 205: 30Cxx Geometric function theorytheory: 206: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10theory: 207: 30C25 Covering theorems in conformal mapping theorytheory: 208: 30C30 Numerical methods in conformal mapping theory [See also]65E05theory: 209: 30C35 General theory of conformal mappingstheory: 210: 30C55 General theory of univalent and multivalent functionstheory: 211: 30D20 Entire functions, general theorytheory: 212: 30D30 Meromorphic functions, general theorytheory: 213: 30D35 Distribution of values, Nevanlinna theorytheory: 214: 30F20 Classification theory of Riemann surfacestheory: 215: 30F25 Ideal boundary theorytheory: 216: 30F60 Teichmuller theory [See also]32G15theory: 217: 30Gxx Generalized function theorytheory: 218: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05theory: 219: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H05theory: 220: 30G12 Finely holomorphic functions and topological function theorytheory: 221: 30Jxx Function theory on the disctheory: 222: 31-XX Potential theory For probabilistic potential theory, see 60J45theory: 223: 31-XX Potential theory For probabilistic potential theory, see 60J45theory: 224: 31Axx Two-dimensional theorytheory: 225: 31Bxx Higher-dimensional theorytheory: 226: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14theory: 227: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A14theory: 228: 31C20 Discrete potential theory and numerical methodstheory: 229: 31C35 Martin boundary theory [See also]60J50theory: 230: 31C40 Fine potential theorytheory: 231: 31C45 Other generalizations (nonlinear potential theory, etc.)theory: 232: 31Dxx Axiomatic potential theorytheory: 233: 31D05 Axiomatic potential theorytheory: 234: 31Exx Potential theory on metric spacestheory: 235: 31E05 Potential theory on metric spacestheory: 236: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
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see 32H25, 32H30theory: 237: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H30theory: 238: 32A27 Local theory of residues [See also]32C30theory: 239: 32A30 Other generalizations of function theory of one complex variable (should also be
assigned at least one classification number from Section 30) For functions of several hypercomplex variables, see30G35
theory: 240: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A27theory: 241: 32E05 Holomorphically convex complex spaces, reduction theorytheory: 242: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxxtheory: 243: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22theory: 244: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxxtheory: 245: 32L25 Twistor theory, double fibrations [See also]53C28theory: 246: 32N05 General theory of automorphic functions of several complex variablestheory: 247: 32Q25 Calabi-Yau theory [See also]14J30theory: 248: 32S20 Global theory of singularities; cohomological properties [See also]14E15theory: 249: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D07theory: 250: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45theory: 251: 32Uxx Pluripotential theorytheory: 252: 32U15 General pluripotential theorytheory: 253: 32U20 Capacity theory and generalizationstheory: 254: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
theory: 255: 34Axx General theorytheory: 256: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XXtheory: 257: 34B20 Weyl theory and its generalizationstheory: 258: 34B24 Sturm-Liouville theory [See also]34Lxxtheory: 259: 34Cxx Qualitative theory [See also]37-XXtheory: 260: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)theory: 261: 34C10 Oscillation theory, zeros, disconjugacy and comparison theorytheory: 262: 34C10 Oscillation theory, zeros, disconjugacy and comparison theorytheory: 263: 34Dxx Stability theory [See also]37C75, 93Dxxtheory: 264: 34Exx Asymptotic theorytheory: 265: 34E15 Singular perturbations, general theorytheory: 266: 34E20 Singular perturbations, turning point theory, WKB methodstheory: 267: 34K05 General theorytheory: 268: 34K08 Spectral theory of functional-differential operatorstheory: 269: 34K11 Oscillation theorytheory: 270: 34K18 Bifurcation theorytheory: 271: 34K20 Stability theorytheory: 272: 34K25 Asymptotic theorytheory: 273: 34L05 General spectral theorytheory: 274: 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctionstheory: 275: 34L25 Scattering theory, inverse scatteringtheory: 276: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J15theory: 277: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J72theory: 278: 35E20 General theorytheory: 279: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F05theory: 280: 35P05 General topics in linear spectral theorytheory: 281: 35P25 Scattering theory [See also]47A40theory: 282: 35P30 Nonlinear eigenvalue problems, nonlinear spectral theory
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theory: 283: 35Q60 PDEs in connection with optics and electromagnetic theorytheory: 284: 35Q75 PDEs in connection with relativity and gravitational theorytheory: 285: 35Q91 PDEs in connection with game theory, economics, social and behavioral sciencestheory: 286: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XXtheory: 287: 37Axx Ergodic theory [See also]28Dxxtheory: 288: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35theory: 289: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A35theory: 290: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxtheory: 291: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10theory: 292: 37A55 Relations with the theory of C∗-algebras [See mainly]46L55theory: 293: 37B30 Index theory, Morse-Conley indicestheory: 294: 37B45 Continua theory in dynamicstheory: 295: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxxtheory: 296: 37C25 Fixed points, periodic points, fixed-point index theorytheory: 297: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxxtheory: 298: 37C45 Dimension theory of dynamical systemstheory: 299: 37C75 Stability theorytheory: 300: 37D10 Invariant manifold theorytheory: 301: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)theory: 302: 37F30 Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as
dynamical systemstheory: 303: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K18theory: 304: 37G40 Symmetries, equivariant bifurcation theorytheory: 305: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxtheory: 306: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axxtheory: 307: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxxtheory: 308: 37H20 Bifurcation theory [See also]37Gxxtheory: 309: 37J05 General theory, relations with symplectic geometry and topologytheory: 310: 37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol′d diffusiontheory: 311: 37K40 Soliton theory, asymptotic behavior of solutionstheory: 312: 37L05 General theory, nonlinear semigroups, evolution equationstheory: 313: 37L10 Normal forms, center manifold theory, bifurcation theorytheory: 314: 37L10 Normal forms, center manifold theory, bifurcation theorytheory: 315: 37M25 Computational methods for ergodic theory (approximation of invariant measures,
computation of Lyapunov exponents, entropy)theory: 316: 39A05 General theorytheory: 317: 39A21 Oscillation theorytheory: 318: 39A28 Bifurcation theorytheory: 319: 39A30 Stability theorytheory: 320: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XXtheory: 321: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
theory: 322: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
theory: 323: 41A65 Abstract approximation theory (approximation in normed linear spaces and otherabstract spaces)
theory: 324: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30
theory: 325: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localization
theory: 326: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30
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theory: 327: 42B25 Maximal functions, Littlewood-Paley theorytheory: 328: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45theory: 329: 45M10 Stability theorytheory: 330: 46A03 General theory of locally convex spacestheory: 331: 46A20 Duality theorytheory: 332: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07theory: 333: 46B03 Isomorphic theory (including renorming) of Banach spacestheory: 334: 46B04 Isometric theory of Banach spacestheory: 335: 46B06 Asymptotic theory of Banach spaces [See also]52A23theory: 336: 46B07 Local theory of Banach spacestheory: 337: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07theory: 338: 46B09 Probabilistic methods in Banach space theory [See also]60Bxxtheory: 339: 46B25 Classical Banach spaces in the general theorytheory: 340: 46G15 Functional analytic lifting theory [See also]28A51theory: 341: 46H05 General theory of topological algebrastheory: 342: 46J05 General theory of commutative topological algebrastheory: 343: 46K05 General theory of topological algebras with involutiontheory: 344: 46L05 General theory of C∗-algebrastheory: 345: 46L10 General theory of von Neumann algebrastheory: 346: 46L45 Decomposition theory for C∗-algebrastheory: 347: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J22theory: 348: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J22theory: 349: 46Mxx Methods of category theory in functional analysis [See also]18-XXtheory: 350: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxtheory: 351: 46N30 Applications in probability theory and statisticstheory: 352: 47-XX Operator theorytheory: 353: 47Axx General theory of linear operatorstheory: 354: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)theory: 355: 47A35 Ergodic theory [See also]28Dxx, 37Axxtheory: 356: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxxtheory: 357: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q15theory: 358: 47A58 Operator approximation theorytheory: 359: 47A65 Structure theorytheory: 360: 47A67 Representation theorytheory: 361: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)theory: 362: 47H11 Degree theory [See also]55M25, 58C30theory: 363: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R05theory: 364: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E09theory: 365: 47Nxx Miscellaneous applications of operator theory [See also]46Nxxtheory: 366: 47N30 Applications in probability theory and statisticstheory: 367: 47N70 Applications in systems theory, circuits, and control theorytheory: 368: 47N70 Applications in systems theory, circuits, and control theorytheory: 369: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxxtheory: 370: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theorytheory: 371: 47S10 Operator theory over fields other than R, C or the quaternions; non-Archimedean
operator theorytheory: 372: 47S20 Nonstandard operator theory [See also]03H05theory: 373: 47S30 Constructive operator theory [See also]03F60theory: 374: 47S40 Fuzzy operator theory [See also]03E72theory: 375: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E70theory: 376: 49N15 Duality theorytheory: 377: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C35
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theory: 378: 51A05 General theory and projective geometriestheory: 379: 51B05 General theorytheory: 380: 51H05 General theorytheory: 381: 51J05 General theorytheory: 382: 51K05 General theorytheory: 383: 52A23 Asymptotic theory of convex bodies [See also]46B06theory: 384: 52A35 Helly-type theorems and geometric transversal theorytheory: 385: 53A55 Differential invariants (local theory), geometric objectstheory: 386: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxxtheory: 387: 53C05 Connections, general theorytheory: 388: 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)theory: 389: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxxtheory: 390: 53D42 Symplectic field theory; contact homologytheory: 391: 54C56 Shape theory [See also]55P55, 57N25theory: 392: 54F45 Dimension theory [See also]55M10theory: 393: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05theory: 394: 55M10 Dimension theory [See also]54F45theory: 395: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17theory: 396: 55N10 Singular theorytheory: 397: 55N40 Axioms for homology theory and uniqueness theoremstheory: 398: 55Pxx Homotopy theory For simple homotopy type, see 57Q10theory: 399: 55P42 Stable homotopy theory, spectratheory: 400: 55P55 Shape theory [See also]54C56, 55Q07theory: 401: 55P57 Proper homotopy theorytheory: 402: 55P62 Rational homotopy theorytheory: 403: 55P91 Equivariant homotopy theory [See also]19L47theory: 404: 55P92 Relations between equivariant and nonequivariant homotopy theorytheory: 405: 55S35 Obstruction theorytheory: 406: 55Uxx Applied homological algebra and category theory [See also]18Gxxtheory: 407: 55U35 Abstract and axiomatic homotopy theorytheory: 408: 55U40 Topological categories, foundations of homotopy theorytheory: 409: 57M07 Topological methods in group theorytheory: 410: 57M15 Relations with graph theory [See also]05Cxxtheory: 411: 57R30 Foliations; geometric theorytheory: 412: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q15theory: 413: 58Axx General theory of differentiable manifolds [See also]32Cxxtheory: 414: 58A12 de Rham theory [See also]14Fxxtheory: 415: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S35theory: 416: 58A15 Exterior differential systems (Cartan theory)theory: 417: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G05theory: 418: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E07theory: 419: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)theory: 420: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)theory: 421: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)theory: 422: 58E07 Abstract bifurcation theorytheory: 423: 58E09 Group-invariant bifurcation theorytheory: 424: 58E10 Applications to the theory of geodesics (problems in one independent variable)theory: 425: 58E25 Applications to control theory [See also]49-XX, 93-XXtheory: 426: 58J05 Elliptic equations on manifolds, general theory [See also]35-XXtheory: 427: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L80theory: 428: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxx
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theory: 429: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicitytheory: 430: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicitytheory: 431: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XXtheory: 432: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XXtheory: 433: 58K30 Global theorytheory: 434: 58K35 Catastrophe theorytheory: 435: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XXtheory: 436: 60Axx Foundations of probability theorytheory: 437: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxtheory: 438: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxxtheory: 439: 60Bxx Probability theory on algebraic and topological structurestheory: 440: 60B11 Probability theory on linear topological spaces [See also]28C20theory: 441: 60Exx Distribution theory [See also]62Exx, 62Hxxtheory: 442: 60E05 Distributions: general theorytheory: 443: 60G07 General theory of processestheory: 444: 60G25 Prediction theory [See also]62M20theory: 445: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60theory: 446: 60G70 Extreme value theory; extremal processestheory: 447: 60H40 White noise theorytheory: 448: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40theory: 449: 60J45 Probabilistic potential theory [See also]31Cxx, 31D05theory: 450: 60J50 Boundary theorytheory: 451: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxtheory: 452: 60K05 Renewal theorytheory: 453: 60K10 Applications (reliability, demand theory, etc.)theory: 454: 60K25 Queueing theory [See also]68M20, 90B22theory: 455: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C43theory: 456: 62B15 Theory of statistical experimentstheory: 457: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35theory: 458: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A35theory: 459: 62C86 Decision theory and fuzzinesstheory: 460: 62Dxx Sampling theory, sample surveystheory: 461: 62D05 Sampling theory, sample surveystheory: 462: 62Exx Distribution theory [See also]60Exxtheory: 463: 62E10 Characterization and structure theorytheory: 464: 62E15 Exact distribution theorytheory: 465: 62E20 Asymptotic distribution theorytheory: 466: 62H05 Characterization and structure theorytheory: 467: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxxtheory: 468: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30theory: 469: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30theory: 470: 65J05 General theorytheory: 471: 68Pxx Theory of datatheory: 472: 68P15 Database theorytheory: 473: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxtheory: 474: 68Qxx Theory of computingtheory: 475: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32theory: 476: 68Q32 Computational learning theory [See also]68T05theory: 477: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M35
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theory: 478: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C35theory: 479: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxxtheory: 480: 70H08 Nearly integrable Hamiltonian systems, KAM theorytheory: 481: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxxtheory: 482: 70Jxx Linear vibration theorytheory: 483: 74A20 Theory of constitutive functionstheory: 484: 76B03 Existence, uniqueness, and regularity theory [See also]35Q35theory: 485: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingtheory: 486: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and
hydrofoil theory, sloshingtheory: 487: 76D03 Existence, uniqueness, and regularity theory [See also]35Q30theory: 488: 76D08 Lubrication theorytheory: 489: 76D10 Boundary-layer theory, separation and reattachment, higher-order effectstheory: 490: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q30theory: 491: 76N20 Boundary-layer theorytheory: 492: 78-XX Optics, electromagnetic theory For quantum optics, see 81V80theory: 493: 78A25 Electromagnetic theory, generaltheory: 494: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)theory: 495: 81-XX Quantum theorytheory: 496: 81P15 Quantum measurement theorytheory: 497: 81Qxx General mathematical topics and methods in quantum theorytheory: 498: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysistheory: 499: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysistheory: 500: 81Q12 Non-selfadjoint operator theory in quantum theorytheory: 501: 81Q12 Non-selfadjoint operator theory in quantum theorytheory: 502: 81Rxx Groups and algebras in quantum theorytheory: 503: 81Txx Quantum field theory; related classical field theories [See also]70Sxxtheory: 504: 81T05 Axiomatic quantum field theory; operator algebrastheory: 505: 81T08 Constructive quantum field theorytheory: 506: 81T20 Quantum field theory on curved space backgroundstheory: 507: 81T25 Quantum field theory on latticestheory: 508: 81T28 Thermal quantum field theory [See also]82B30theory: 509: 81T70 Quantization in field theory; cohomological methods [See also]58D29theory: 510: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A40theory: 511: 81U05 2-body potential scattering theory [See also]34E20 for WKB methodstheory: 512: 81U10 n-body potential scattering theorytheory: 513: 81U20 S-matrix theory, etc.theory: 514: 81U30 Dispersion theory, dispersion relationstheory: 515: 81V25 Other elementary particle theorytheory: 516: 81V70 Many-body theory; quantum Hall effecttheory: 517: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E20theory: 518: 82B40 Kinetic theory of gasestheory: 519: 82C35 Irreversible thermodynamics, including Onsager-Machlup theorytheory: 520: 82C40 Kinetic theory of gasestheory: 521: 82D25 Crystals For crystallographic group theory, see 20H15theory: 522: 82D75 Nuclear reactor theory; neutron transporttheory: 523: 83-XX Relativity and gravitational theorytheory: 524: 83C47 Methods of quantum field theory [See also]81T20theory: 525: 90B35 Scheduling theory, deterministic [See also]68M20theory: 526: 90B36 Scheduling theory, stochastic [See also]68M20theory: 527: 90B40 Search theorytheory: 528: 90B70 Theory of organizations, manpower planning [See also]91D35theory: 529: 91-XX Game theory, economics, social and behavioral sciencestheory: 530: 91Axx Game theory
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theory: 531: 91A30 Utility theory for games [See also]91B16theory: 532: 91A35 Decision theory for games [See also]62Cxx, 91B06, 90B50theory: 533: 91A44 Games involving topology or set theorytheory: 534: 91A80 Applications of game theorytheory: 535: 91B06 Decision theory [See also]62Cxx, 90B50, 91A35theory: 536: 91B12 Voting theorytheory: 537: 91B16 Utility theorytheory: 538: 91B24 Price theory and market structuretheory: 539: 91B30 Risk theory, insurancetheory: 540: 91B38 Production theory, theory of the firmtheory: 541: 91B38 Production theory, theory of the firmtheory: 542: 91B42 Consumer behavior, demand theorytheory: 543: 91B50 General equilibrium theorytheory: 544: 91B51 Dynamic stochastic general equilibrium theorytheory: 545: 91C05 Measurement theorytheory: 546: 91G10 Portfolio theorytheory: 547: 93-XX Systems theory; control For optimal control, see 49-XXtheory: 548: 93A05 Axiomatic system theorytheory: 549: 94A05 Communication theory [See also]60G35, 90B18theory: 550: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)theory: 551: 94A13 Detection theorytheory: 552: 94A15 Information theory, general [See also]62B10, 81P45theory: 553: 94A20 Sampling theorytheory: 554: 94A24 Coding theorems (Shannon theory)theory: 555: 94A34 Rate-distortion theorytheory: 556: 94A50 Theory of questionnairestheory: 557: 94Bxx Theory of error-correcting codes and error-detecting codestheory: 558: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71theory: 559: 94C05 Analytic circuit theorytheory: 560: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E30theory: 561: 94C15 Applications of graph theory [See also]05Cxx, 68R10theory: 562: 94C30 Applications of design theory [See also]05Bxxtheory: 563: 97E60 Sets, relations, set theorytheory: 564: 97Fxx Arithmetic, number theorytheory: 565: 97F60 Number theorytheory: 566: 97Kxx Combinatorics, graph theory, probability theory, statisticstheory: 567: 97Kxx Combinatorics, graph theory, probability theory, statisticstheory: 568: 97K30 Graph theorytheory: 569: 97K50 Probability theorytheory: 570: 97N20 Rounding, estimation, theory of errorstheory: 571: 97P20 Theory of computer science
thereon: 1: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;for analysis thereon, see 43A80, 43A85, 43A90
thermal: 1: 74F05 Thermal effectsthermal: 2: 81T28 Thermal quantum field theory [See also]82B30
thermodynamic: 1: 37D35 Thermodynamic formalism, variational principles, equilibrium statesthermodynamics: 1: 35Q79 PDEs in connection with classical thermodynamics and heat transferthermodynamics: 2: 74A15 Thermodynamicsthermodynamics: 3: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15thermodynamics: 4: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15thermodynamics: 5: 80Axx Thermodynamics and heat transferthermodynamics: 6: 80A10 Classical thermodynamics, including relativisticthermodynamics: 7: 80A17 Thermodynamics of continua [See also]74A15thermodynamics: 8: 82B30 Statistical thermodynamics [See also]80-XXthermodynamics: 9: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E20thermodynamics: 10: 82C35 Irreversible thermodynamics, including Onsager-Machlup theory
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theses: 1: 97A70 Theses and postdoctoral thesestheses: 2: 97A70 Theses and postdoctoral thesestheta: 1: 11F27 Theta series; Weil representation; theta correspondencestheta: 2: 11F27 Theta series; Weil representation; theta correspondencestheta: 3: 14H42 Theta functions; Schottky problem [See also]14K25, 32G20theta: 4: 14K25 Theta functions [See also]14H42thin: 1: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)thin: 2: 74Kxx Thin bodies, structuresthin: 3: 74K35 Thin filmsthin: 4: 76A20 Thin fluid films
third: 1: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)this: 1: 40B05 Multiple sequences and series (should also be assigned at least one other classification
number in this section)this: 2: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)this: 3: 41A63 Multidimensional problems (should also be assigned at least one other classification
number in this section)this: 4: 62E86 Fuzziness in connection with the topics on distributions in this sectionthis: 5: 78A97 Mathematically heuristic optics and electromagnetic theory (must also be assigned at
least one other classification number in this section)this: 6: 92Fxx Other natural sciences (should also be assigned at least one other classification number
in this section)those: 1: 16R40 Identities other than those of matrices over commutative ringsthose: 2: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
three: 1: 76T30 Three or more component flowsthree-body: 1: 70F07 Three-body problems
three-dimensional: 1: 52B10 Three-dimensional polytopesthrough: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 86through: 2: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
thue: 1: 03D03 Thue and Post systems, etc.thue-mahler: 1: 11D59 Thue-Mahler equations
tight: 1: 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p;tight closure [See also]13B22
tight: 2: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,57R40, 57R42
tiling: 1: 05B45 Tessellation and tiling problems [See also]52C20, 52C22tiling: 2: 37B50 Multi-dimensional shifts of finite type, tiling dynamics
tilings: 1: 52C20 Tilings in 2 dimensions [See also]05B45, 51M20tilings: 2: 52C22 Tilings in n dimensions [See also]05B45, 51M20tilings: 3: 52C23 Quasicrystals, aperiodic tilings
time: 1: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scalesor measure chains see 34N05
time: 2: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scalesor measure chains see 34N05
time: 3: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scalessee 26E70
time: 4: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scalessee 26E70
time: 5: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales ormeasure chains, see 26E70
time: 6: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales ormeasure chains, see 26E70
time: 7: 37M10 Time series analysistime: 8: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N05
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time: 9: 60J55 Local time and additive functionalstime: 10: 62M10 Time series, auto-correlation, regression, etc. [See also]91B84time: 11: 91B84 Economic time series analysis [See also]62M10
time-dependent: 1: 35Q41 Time-dependent Schrodinger equations, Dirac equationstime-dependent: 2: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemstime-dependent: 3: 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)time-dependent: 4: 82C43 Time-dependent percolation [See also]60K35
time-scale: 1: 93C70 Time-scale analysis and singular perturbationstimes: 1: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60
timing: 1: 91A55 Games of timingto: 1: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F35to: 2: 11B37 Recurrences For applications to special functions, see 33-XXto: 3: 11F22 Relationship to Lie algebras and finite simple groupsto: 4: 11F52 Modular forms associated to Drinfel′d modulesto: 5: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesto: 6: 11J04 Homogeneous approximation to one numberto: 7: 11J68 Approximation to algebraic numbersto: 8: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulasto: 9: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxxto: 10: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C10to: 11: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxxto: 12: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxxto: 13: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)to: 14: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)to: 15: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B40to: 16: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J05to: 17: 17B80 Applications to integrable systemsto: 18: 17B81 Applications to physicsto: 19: 17C90 Applications to physicsto: 20: 18A15 Foundations, relations to logic and deductive systems [See also]03-XXto: 21: 19J35 Obstructions to group actionsto: 22: 20A15 Applications of logic to group theoryto: 23: 20C35 Applications of group representations to physicsto: 24: 20F38 Other groups related to topology or analysisto: 25: 20G45 Applications to physicsto: 26: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxxto: 27: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R10to: 28: 28A25 Integration with respect to measures and other set functionsto: 29: 32C81 Applications to physicsto: 30: 32G81 Applications to physicsto: 31: 32J81 Applications to physicsto: 32: 32L81 Applications to physicsto: 33: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxxto: 34: 35J67 Boundary values of solutions to elliptic equationsto: 35: 37J30 Obstructions to integrability (nonintegrability criteria)to: 36: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15to: 37: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C10
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to: 38: 46N20 Applications to differential and integral equationsto: 39: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20to: 40: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxxto: 41: 47L90 Applications of operator algebras to physicsto: 42: 47N20 Applications to differential and integral equationsto: 43: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)to: 44: 49K30 Optimal solutions belonging to restricted classesto: 45: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxxto: 46: 53B50 Applications to physicsto: 47: 53C80 Applications to physicsto: 48: 53Zxx Applications to physicsto: 49: 53Z05 Applications to physicsto: 50: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XXto: 51: 58A03 Topos-theoretic approach to differentiable manifoldsto: 52: 58E10 Applications to the theory of geodesics (problems in one independent variable)to: 53: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05to: 54: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.to: 55: 58E17 Pareto optimality, etc., applications to economics [See also]90C29to: 56: 58E25 Applications to control theory [See also]49-XX, 93-XXto: 57: 58Zxx Applications to physicsto: 58: 58Z05 Applications to physicsto: 59: 60H30 Applications of stochastic analysis (to PDE, etc.)to: 60: 62E17 Approximations to distributions (nonasymptotic)to: 61: 62P05 Applications to actuarial sciences and financial mathematicsto: 62: 62P10 Applications to biology and medical sciencesto: 63: 62P12 Applications to environmental and related topicsto: 64: 62P15 Applications to psychologyto: 65: 62P20 Applications to economics [See also]91Bxxto: 66: 62P25 Applications to social sciencesto: 67: 62P35 Applications to physicsto: 68: 65B05 Extrapolation to the limit, deferred correctionsto: 69: 65Zxx Applications to physicsto: 70: 65Z05 Applications to physicsto: 71: 68Rxx Discrete mathematics in relation to computer scienceto: 72: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D45to: 73: 76F06 Transition to turbulenceto: 74: 76F20 Dynamical systems approach to turbulence [See also]37-XXto: 75: 81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other
equations of quantum mechanicsto: 76: 81Vxx Applications to specific physical systemsto: 77: 82Dxx Applications to specific types of physical systemsto: 78: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)to: 79: 91B80 Applications of statistical and quantum mechanics to economics (econophysics)to: 80: 92D15 Problems related to evolution
toda: 1: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,hierarchies (KdV, KP, Toda, etc.)
toeplitz: 1: 15B05 Toeplitz, Cauchy, and related matricestoeplitz: 2: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35
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toeplitz: 3: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 forother integral operators; see also 32A25, 32M15
toeplitz: 4: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)tolerance: 1: 62F25 Tolerance and confidence regionstolerance: 2: 62G15 Tolerance and confidence regionstolerance: 3: 68M15 Reliability, testing and fault tolerance [See also]94C12
tools: 1: 97U70 Technological tools, calculatorstopics: 1: 00Axx General and miscellaneous specific topicstopics: 2: 03C10 Quantifier elimination, model completeness and related topicstopics: 3: 03C48 Abstract elementary classes and related topics [See also]03C45topics: 4: 05A30 q-calculus and related topics [See also]33Dxxtopics: 5: 06D72 Fuzzy lattices (soft algebras) and related topicstopics: 6: 13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related
topicstopics: 7: 13Bxx Ring extensions and related topicstopics: 8: 13H15 Multiplicity theory and related topics [See also]14C17topics: 9: 16Txx Hopf algebras, quantum groups and related topicstopics: 10: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
topics: 11: 26Exx Miscellaneous topics [See also]58Cxxtopics: 12: 28Exx Miscellaneous topics in measure theorytopics: 13: 30Dxx Entire and meromorphic functions, and related topicstopics: 14: 30Exx Miscellaneous topics of analysis in the complex domaintopics: 15: 33C80 Connections with groups and algebras, and related topicstopics: 16: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and
related topicstopics: 17: 35Axx General topicstopics: 18: 35P05 General topics in linear spectral theorytopics: 19: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H15topics: 20: 39A12 Discrete version of topics in analysistopics: 21: 39B82 Stability, separation, extension, and related topics [See also]46A22topics: 22: 49Nxx Miscellaneous topicstopics: 23: 51D30 Continuous geometries and related topics [See also]06Cxxtopics: 24: 52A39 Mixed volumes and related topicstopics: 25: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxxtopics: 26: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxtopics: 27: 62Axx Foundational and philosophical topicstopics: 28: 62A01 Foundations and philosophical topicstopics: 29: 62B10 Information-theoretic topics [See also]94A17topics: 30: 62E86 Fuzziness in connection with the topics on distributions in this sectiontopics: 31: 62P12 Applications to environmental and related topicstopics: 32: 68M11 Internet topics [See also]68U35topics: 33: 81Qxx General mathematical topics and methods in quantum theorytopics: 34: 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in
general)topics: 35: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XXtopics: 36: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxxtopics: 37: 92Cxx Physiological, cellular and medical topicstopoi: 1: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C10topoi: 2: 18B25 Topoi [See also]03G30
topological: 1: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,57M25topological: 2: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A26topological: 3: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H12topological: 4: 06D22 Frames, locales For topological questions see 54-XX
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topological: 5: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H12topological: 6: 11N45 Asymptotic results on counting functions for algebraic and topological structurestopological: 7: 12Jxx Topological fieldstopological: 8: 12J17 Topological semifieldstopological: 9: 13Jxx Topological rings and modules [See also]16W60, 16W80topological: 10: 13J20 Global topological ringstopological: 11: 14F45 Topological propertiestopological: 12: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxxtopological: 13: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, forassociative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topologytopological: 14: 18B30 Categories of topological spaces and continuous mappings [See also]54-XXtopological: 15: 19Lxx Topological K-theory [See also]55N15, 55R50, 55S25topological: 16: 20K45 Topological methods [See also]22A05, 22B05topological: 17: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05topological: 18: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For setswith a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05topological: 19: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.For abstract harmonic analysis, see 43-XXtopological: 20: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see12Jxx, 13Jxx, 16W80topological: 21: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see12Jxx, 13Jxx, 16W80topological: 22: 22A05 Structure of general topological groupstopological: 23: 22A10 Analysis on general topological groupstopological: 24: 22A15 Structure of topological semigroupstopological: 25: 22A20 Analysis on topological semigroupstopological: 26: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H05topological: 27: 22A25 Representations of general topological groups and semigroupstopological: 28: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F30topological: 29: 22A30 Other topological algebraic systems and their representationstopological: 30: 22F05 General theory of group and pseudogroup actions For topological properties of spaceswith an action, see 57S20topological: 31: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,invariant measures [See also]22Axx, 43A05topological: 32: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)topological: 33: 30G12 Finely holomorphic functions and topological function theorytopological: 34: 32F27 Topological consequences of geometric convexitytopological: 35: 32Q55 Topological aspects of complex manifoldstopological: 36: 32S15 Equisingularity (topological and analytic) [See also]14E15topological: 37: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantstopological: 38: 32S50 Topological aspects: Lefschetz theorems, topological classification, invariantstopological: 39: 35A16 Topological and monotonicity methodstopological: 40: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,32S60, 58J15topological: 41: 37Bxx Topological dynamics [See also]54H20topological: 42: 37B40 Topological entropytopological: 43: 37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classificationtopological: 44: 37C70 Attractors and repellers, topological structuretopological: 45: 37J35 Completely integrable systems, topological structure of phase space, integrationmethodstopological: 46: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exxtopological: 47: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exxtopological: 48: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
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58Bxxtopological: 49: 46Axx Topological linear spaces and related structures For function spaces, see 46Exxtopological: 50: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,quasi-Banach spaces, etc.)topological: 51: 46A32 Spaces of linear operators; topological tensor products; approximation properties[See also]46B28, 46M05, 47L05, 47L20topological: 52: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42topological: 53: 46A50 Compactness in topological linear spaces; angelic spaces, etc.topological: 54: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A07topological: 55: 46A63 Topological invariants ((DN), (Ω), etc.)topological: 56: 46E10 Topological linear spaces of continuous, differentiable or analytic functionstopological: 57: 46F05 Topological linear spaces of test functions, distributions and ultradistributions[See also]46E10, 46E35topological: 58: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,convolution algebras and measure algebras, see 43A10, 43A20topological: 59: 46H05 General theory of topological algebrastopological: 60: 46H15 Representations of topological algebrastopological: 61: 46H20 Structure, classification of topological algebrastopological: 62: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or16-XX)topological: 63: 46H30 Functional calculus in topological algebras [See also]47A60topological: 64: 46H35 Topological algebras of operators [See mainly]47Lxxtopological: 65: 46H70 Nonassociative topological algebras [See also]46K70, 46L70topological: 66: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E25topological: 67: 46J05 General theory of commutative topological algebrastopological: 68: 46J25 Representations of commutative topological algebrastopological: 69: 46J40 Structure, classification of commutative topological algebrastopological: 70: 46Kxx Topological (rings and) algebras with an involution [See also]16W10topological: 71: 46K05 General theory of topological algebras with involutiontopological: 72: 46K10 Representations of topological algebras with involutiontopological: 73: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L70topological: 74: 46M35 Abstract interpolation of topological vector spaces [See also]46B70topological: 75: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topologicalvector spacestopological: 76: 47L10 Algebras of operators on Banach spaces and other topological linear spacestopological: 77: 51Hxx Topological geometrytopological: 78: 51H10 Topological linear incidence structurestopological: 79: 51H15 Topological nonlinear incidence structurestopological: 80: 51H20 Topological geometries on manifolds [See also]57-XXtopological: 81: 52A07 Convex sets in topological vector spaces [See also]46A55topological: 82: 53C23 Global geometric and topological methods (a la Gromov); differential geometric analysison metric spacestopological: 83: 54A05 Topological spaces and generalizations (closure spaces, etc.)topological: 84: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)topological: 85: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially orderedspaces [See also]06B30, 06F30topological: 86: 54F65 Topological characterizations of particular spacestopological: 87: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)[See also]03E15, 26A21, 28A05topological: 88: 54H10 Topological representations of algebraic systems [See also]22-XXtopological: 89: 54H11 Topological groups [See also]22A05topological: 90: 54H12 Topological lattices, etc. [See also]06B30, 06F30topological: 91: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80topological: 92: 54H20 Topological dynamics [See also]28Dxx, 37Bxxtopological: 93: 55U40 Topological categories, foundations of homotopy theorytopological: 94: 57M07 Topological methods in group theorytopological: 95: 57Nxx Topological manifolds
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topological: 96: 57N17 Topology of topological vector spacestopological: 97: 57R56 Topological quantum field theoriestopological: 98: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D05topological: 99: 57S05 Topological properties of groups of homeomorphisms or diffeomorphismstopological: 100: 57Txx Homology and homotopy of topological groups and related structurestopological: 101: 57T20 Homotopy groups of topological groups and homogeneous spacestopological: 102: 58B05 Homotopy and topological questionstopological: 103: 58D29 Moduli problems for topological structurestopological: 104: 58K15 Topological properties of mappingstopological: 105: 58K45 Singularities of vector fields, topological aspectstopological: 106: 58K65 Topological invariantstopological: 107: 60Bxx Probability theory on algebraic and topological structurestopological: 108: 60B05 Probability measures on topological spacestopological: 109: 60B11 Probability theory on linear topological spaces [See also]28C20topological: 110: 70G40 Topological and differential-topological methodstopological: 111: 74P15 Topological methodstopological: 112: 81T45 Topological field theories [See also]57R56, 58Dxxtopologies: 1: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H12topologies: 2: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H12topologies: 3: 14F20 Etale and other Grothendieck topologies and (co)homologiestopologies: 4: 18F10 Grothendieck topologies [See also]14F20topologies: 5: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)topologies: 6: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)topologies: 7: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices oftopologies)topologies: 8: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices oftopologies)topologies: 9: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices oftopologies)
topology: 1: 11B05 Density, gaps, topologytopology: 2: 11F23 Relations with algebraic geometry and topologytopology: 3: 14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)topology: 4: 14P25 Topology of real algebraic varietiestopology: 5: 19Jxx Obstructions from topologytopology: 6: 20F38 Other groups related to topology or analysistopology: 7: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A90topology: 8: 26A03 Foundations: limits and generalizations, elementary topology of the linetopology: 9: 32C18 Topology of analytic spacestopology: 10: 37F20 Combinatorics and topologytopology: 11: 37J05 General theory, relations with symplectic geometry and topologytopology: 12: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxxtopology: 13: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)topology: 14: 46L85 Noncommutative topology [See also]58B32, 58B34, 58J22topology: 15: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxtopology: 16: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axxtopology: 17: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxtopology: 18: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxxtopology: 19: 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of
topologies)topology: 20: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
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topology: 21: 54A40 Fuzzy topology [See also]03E72topology: 22: 54Jxx Nonstandard topology [See also]03H05topology: 23: 54J05 Nonstandard topology [See also]03H05topology: 24: 55-XX Algebraic topologytopology: 25: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxxtopology: 26: 55P50 String topologytopology: 27: 55R70 Fibrewise topologytopology: 28: 57Mxx Low-dimensional topologytopology: 29: 57N05 Topology of E2, 2-manifoldstopology: 30: 57N10 Topology of general 3-manifolds [See also]57Mxxtopology: 31: 57N12 Topology of E3 and S3 [See also]57M40topology: 32: 57N13 Topology of E4, 4-manifolds [See also]14Jxx, 32Jxxtopology: 33: 57N15 Topology of En, n-manifolds (4 < n <∞)topology: 34: 57N17 Topology of topological vector spacestopology: 35: 57N20 Topology of infinite-dimensional manifolds [See also]58Bxxtopology: 36: 57N65 Algebraic topology of manifoldstopology: 37: 57Q05 General topology of complexestopology: 38: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxxtopology: 39: 57R17 Symplectic and contact topologytopology: 40: 57R18 Topology and geometry of orbifoldstopology: 41: 57R19 Algebraic topology on manifoldstopology: 42: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxxtopology: 43: 57R91 Equivariant algebraic topology of manifoldstopology: 44: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S40topology: 45: 91A44 Games involving topology or set theorytopology: 46: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)topology: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
topos-theoretic: 1: 58A03 Topos-theoretic approach to differentiable manifoldstor: 1: 13D07 Homological functors on modules (Tor, Ext, etc.)tor: 2: 16E30 Homological functors on modules (Tor, Ext, etc.)tor: 3: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U25
torelli: 1: 14C34 Torelli problem [See also]32G20tori: 1: 70K43 Quasi-periodic motions and invariant tori
toric: 1: 14M25 Toric varieties, Newton polyhedra [See also]52B20toroidal: 1: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebrastorsion: 1: 13C12 Torsion modules and idealstorsion: 2: 13D30 Torsion theory [See also]13C12, 18E40torsion: 3: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxxtorsion: 4: 18E40 Torsion theories, radicals [See also]13D30, 16S90torsion: 5: 19J10 Whitehead (and related) torsiontorsion: 6: 20K10 Torsion groups, primary groups and generalized primary groupstorsion: 7: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28torsion: 8: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28torsion: 9: 58J52 Determinants and determinant bundles, analytic torsion
torsion-free: 1: 20K15 Torsion-free groups, finite ranktorsion-free: 2: 20K20 Torsion-free groups, infinite rank
total: 1: 06A05 Total ordertotally: 1: 11R80 Totally real fields [See also]12J15
toughness: 1: 05C42 Density (toughness, etc.)tournaments: 1: 05C20 Directed graphs (digraphs), tournaments
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Mathematics Subject Classification 2010
towers: 1: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,Galois theory)
trace: 1: 11F72 Spectral theory; Selberg trace formulatrace: 2: 16R30 Trace rings and invariant theorytrace: 3: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace
theoremstraces: 1: 19K14 K0 as an ordered group, tracestrade: 1: 91B60 Trade modelstraffic: 1: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxxtraffic: 2: 90B20 Traffic problems
training: 1: 97M20 Mathematics in vocational training and career educationtrajectories: 1: 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)trajectories: 2: 37G20 Hyperbolic singular points with homoclinic trajectoriestrajectories: 3: 70K42 Equilibria and periodic trajectoriestrajectories: 4: 70K44 Homoclinic and heteroclinic trajectories
transcendence: 1: 11J81 Transcendence (general theory)transcendence: 2: 11J82 Measures of irrationality and of transcendencetranscendence: 3: 11J89 Transcendence theory of elliptic and abelian functionstranscendence: 4: 11J91 Transcendence theory of other special functionstranscendence: 5: 11J93 Transcendence theory of Drinfel′d and t-modulestranscendental: 1: 11Jxx Diophantine approximation, transcendental number theory [See also]11K60transcendental: 2: 12F20 Transcendental extensionstranscendental: 3: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecturetranscendental: 4: 32J25 Transcendental methods of algebraic geometry [See also]14C30transcendental: 5: 65Hxx Nonlinear algebraic or transcendental equations
transfer: 1: 11H60 Mean value and transfer theoremstransfer: 2: 35Q79 PDEs in connection with classical thermodynamics and heat transfertransfer: 3: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemstransfer: 4: 55R12 Transfertransfer: 5: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15transfer: 6: 80Axx Thermodynamics and heat transfertransfer: 7: 80A20 Heat and mass transfer, heat flowtransfer: 8: 85A25 Radiative transfer
transform: 1: 34M25 Formal solutions, transform techniquestransform: 2: 35A22 Transform methods (e.g. integral transforms)transform: 3: 44A10 Laplace transformtransform: 4: 44A12 Radon transform [See also]92C55
transformation: 1: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.For abstract harmonic analysis, see 43-XX
transformation: 2: 22Fxx Noncompact transformation groupstransformation: 3: 34C20 Transformation and reduction of equations and systems, normal formstransformation: 4: 34K17 Transformation and reduction of equations and systems, normal formstransformation: 5: 51N25 Analytic geometry with other transformation groupstransformation: 6: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxxtransformation: 7: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D05transformation: 8: 57S17 Finite transformation groupstransformation: 9: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22transformation: 10: 97G50 Transformation geometry
transformations: 1: 15A04 Linear transformations, semilinear transformationstransformations: 2: 15A04 Linear transformations, semilinear transformationstransformations: 3: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H15transformations: 4: 26B10 Implicit function theorems, Jacobians, transformations with several variablestransformations: 5: 28D05 Measure-preserving transformationstransformations: 6: 28D10 One-parameter continuous families of measure-preserving transformationstransformations: 7: 28D15 General groups of measure-preserving transformations
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transformations: 8: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.[See also]44-XX
transformations: 9: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J72transformations: 10: 37A05 Measure-preserving transformationstransformations: 11: 37A10 One-parameter continuous families of measure-preserving transformationstransformations: 12: 37A15 General groups of measure-preserving transformations [See mainly]22Fxxtransformations: 13: 37A40 Nonsingular (and infinite-measure preserving) transformationstransformations: 14: 37B05 Transformations and group actions with special properties (minimality, distality,
proximality, etc.)transformations: 15: 37K35 Lie-Backlund and other transformationstransformations: 16: 42C20 Other transformations of harmonic typetransformations: 17: 53D22 Canonical transformationstransformations: 18: 55M35 Finite groups of transformations (including Smith theory) [See also]57S17transformations: 19: 57S15 Compact Lie groups of differentiable transformationstransformations: 20: 57S20 Noncompact Lie groups of transformationstransformations: 21: 57S30 Discontinuous groups of transformationstransformations: 22: 70H15 Canonical and symplectic transformationstransformations: 23: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C26transformations: 24: 74N10 Displacive transformationstransformations: 25: 74N25 Transformations involving diffusiontransformations: 26: 93B17 Transformations
transformers: 1: 47B49 Transformers, preservers (operators on spaces of operators)transforms: 1: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.[See also]44-XXtransforms: 2: 35A22 Transform methods (e.g. integral transforms)transforms: 3: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typetransforms: 4: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typetransforms: 5: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typetransforms: 6: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typetransforms: 7: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groupstransforms: 8: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.transforms: 9: 43A32 Other transforms and operators of Fourier typetransforms: 10: 43A50 Convergence of Fourier series and of inverse transformstransforms: 11: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 12: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 13: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 14: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 15: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 16: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10transforms: 17: 44A05 General transforms [See also]42A38transforms: 18: 44A15 Special transforms (Legendre, Hilbert, etc.)transforms: 19: 44A20 Transforms of special functionstransforms: 20: 44A30 Multiple transformstransforms: 21: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XXtransforms: 22: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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transforms: 23: 60E10 Characteristic functions; other transformstransforms: 24: 65Rxx Integral equations, integral transformstransforms: 25: 65R10 Integral transformstransforms: 26: 65T50 Discrete and fast Fourier transformstransition: 1: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D07transition: 2: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)transition: 3: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D45transition: 4: 76F06 Transition to turbulence
transitions: 1: 68Q87 Probability in computer science (algorithm analysis, random structures, phasetransitions, etc.) [See also]68W20, 68W40transitions: 2: 82B26 Phase transitions (general)transitions: 3: 82C26 Dynamic and nonequilibrium phase transitions (general)transitive: 1: 20B20 Multiply transitive finite groupstransitive: 2: 20B22 Multiply transitive infinite groups
translation: 1: 51A40 Translation planes and spreadstranslations: 1: 00B50 Volumes of selected translationstranslations: 2: 00B55 Miscellaneous volumes of translationstranslations: 3: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60
transonic: 1: 76Hxx Transonic flowstransonic: 2: 76H05 Transonic flowstransport: 1: 76F25 Turbulent transport, mixingtransport: 2: 82C70 Transport processestransport: 3: 82D75 Nuclear reactor theory; neutron transport
transportation: 1: 90B06 Transportation, logisticstransportation: 2: 90C08 Special problems of linear programming (transportation, multi-index, etc.)
transversal: 1: 05D15 Transversal (matching) theorytransversal: 2: 52A35 Helly-type theorems and geometric transversal theory
transversality: 1: 57N75 General position and transversalitytransversality: 2: 57Q65 General position and transversality
traps: 1: 78A37 Ion trapstraveling: 1: 35C07 Traveling wave solutions
treatment: 1: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05treatment: 2: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxxtreatment: 3: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,Veronesians and their generalizations) [See also]14M15treatment: 4: 74Exx Material properties given special treatmenttreatment: 5: 91Fxx Other social and behavioral sciences (mathematical treatment)
trees: 1: 05C05 Treestrees: 2: 20E08 Groups acting on trees [See also]20F65trees: 3: 37E25 Maps of trees and graphs
trellis: 1: 94B12 Combined modulation schemes (including trellis codes)triad: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxtriangulated: 1: 18E30 Derived categories, triangulated categories
triangulating: 1: 57Q15 Triangulating manifoldstriangulating: 2: 57R05 Triangulatingtriangulation: 1: 32B25 Triangulation and related questions
tribology: 1: 74A55 Theories of friction (tribology)trichotomy: 1: 34D09 Dichotomy, trichotomytridiagonal: 1: 47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
trigonometric: 1: 11L03 Trigonometric and exponential sums, generaltrigonometric: 2: 26D05 Inequalities for trigonometric functions and polynomialstrigonometric: 3: 33B10 Exponential and trigonometric functionstrigonometric: 4: 35C09 Trigonometric solutionstrigonometric: 5: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical
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approximation, see 65Dxxtrigonometric: 6: 41Axx Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
trigonometric: 7: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
trigonometric: 8: 42A05 Trigonometric polynomials, inequalities, extremal problemstrigonometric: 9: 42A10 Trigonometric approximationtrigonometric: 10: 42A15 Trigonometric interpolationtrigonometric: 11: 42A20 Convergence and absolute convergence of Fourier and trigonometric seriestrigonometric: 12: 42A24 Summability and absolute summability of Fourier and trigonometric seriestrigonometric: 13: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)trigonometric: 14: 42A55 Lacunary series of trigonometric and other functions; Riesz productstrigonometric: 15: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann
theory, localizationtrigonometric: 16: 42A70 Trigonometric moment problemstrigonometric: 17: 65T40 Trigonometric approximation and interpolationtrigonometry: 1: 97G60 Plane and spherical trigonometry
triple: 1: 05B07 Triple systemstriple: 2: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxtriple: 3: 45F10 Dual, triple, etc., integral and series equations
triples: 1: 17Cxx Jordan algebras (algebras, triples and pairs)triples: 2: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxtriples: 3: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxxtropical: 1: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B20tropical: 2: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B20
tsev: 1: 08B05 Equational logic, Mal′cev (Mal′tsev) conditionstsev: 2: 17D10 Mal′cev (Mal′tsev) rings and algebrastube: 1: 32A07 Special domains (Reinhardt, Hartogs, circular, tube)
turan: 1: 11N30 Turan theory [See also]30Bxxturbulence: 1: 76Fxx Turbulence [See also]37-XX, 60Gxx, 60Jxxturbulence: 2: 76F05 Isotropic turbulence; homogeneous turbulenceturbulence: 3: 76F05 Isotropic turbulence; homogeneous turbulenceturbulence: 4: 76F06 Transition to turbulenceturbulence: 5: 76F20 Dynamical systems approach to turbulence [See also]37-XXturbulence: 6: 76F35 Convective turbulence [See also]76E15, 76Rxxturbulence: 7: 76F55 Statistical turbulence modeling [See also]76M35turbulence: 8: 76F65 Direct numerical and large eddy simulation of turbulenceturbulent: 1: 76F25 Turbulent transport, mixingturbulent: 2: 76F40 Turbulent boundary layersturbulent: 3: 76F70 Control of turbulent flows
turing: 1: 03D10 Turing machines and related notions [See also]68Q05turing: 2: 03D28 Other Turing degree structuresturing: 3: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P68
turning: 1: 34E20 Singular perturbations, turning point theory, WKB methodsturning: 2: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20twenty-first: 1: 01A61 Twenty-first century
twist: 1: 37E40 Twist mapstwisted: 1: 16S35 Twisted and skew group rings, crossed productstwisted: 2: 19L50 Twisted K-theory; differential K-theorytwistor: 1: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxtwistor: 2: 32L25 Twistor theory, double fibrations [See also]53C28
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twistor: 3: 53C28 Twistor methods [See also]32L25twistor: 4: 81R25 Spinor and twistor methods [See also]32L25twistor: 5: 83C60 Spinor and twistor methods; Newman-Penrose formalism
two: 1: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablestwo: 2: 11E76 Forms of degree higher than twotwo: 3: 49J10 Free problems in two or more independent variablestwo: 4: 49K10 Free problems in two or more independent variablestwo: 5: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05two-body: 1: 70F05 Two-body problems
two-dimensional: 1: 31Axx Two-dimensional theorytwo-dimensional: 2: 57M20 Two-dimensional complexestwo-dimensional: 3: 81T40 Two-dimensional field theories, conformal field theories, etc.
two-norm: 1: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)two-phase: 1: 76Txx Two-phase and multiphase flowstwo-phase: 2: 76T10 Liquid-gas two-phase flows, bubbly flowstwo-phase: 3: 76T15 Dusty-gas two-phase flows
type: 1: 03B15 Higher-order logic and type theorytype: 2: 11P84 Partition identities; identities of Rogers-Ramanujan typetype: 3: 14J29 Surfaces of general typetype: 4: 16G60 Representation type (finite, tame, wild, etc.)type: 5: 20C33 Representations of finite groups of Lie typetype: 6: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxxtype: 7: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XXtype: 8: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exxtype: 9: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)type: 10: 31A20 Boundary behavior (theorems of Fatou type, etc.)type: 11: 32Kxx Generalizations of analytic spaces (should also be assigned at least one other classifica-
tion number from Section 32 describing the type of problem)type: 12: 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)type: 13: 32P05 Non-Archimedean analysis (should also be assigned at least one other classification
number from Section 32 describing the type of problem)type: 14: 32T25 Finite type domainstype: 15: 32V35 Finite type conditions on CR manifoldstype: 16: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionstype: 17: 35Mxx Equations and systems of special type (mixed, composite, etc.)type: 18: 35M10 Equations of mixed typetype: 19: 35M11 Initial value problems for equations of mixed typetype: 20: 35M12 Boundary value problems for equations of mixed typetype: 21: 35M13 Initial-boundary value problems for equations of mixed typetype: 22: 35M30 Systems of mixed typetype: 23: 35M31 Initial value problems for systems of mixed typetype: 24: 35M32 Boundary value problems for systems of mixed typetype: 25: 35M33 Initial-boundary value problems for systems of mixed typetype: 26: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J40type: 27: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40type: 28: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J40type: 29: 37B50 Multi-dimensional shifts of finite type, tiling dynamicstype: 30: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typetype: 31: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier typetype: 32: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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type: 33: 42C20 Other transformations of harmonic typetype: 34: 43A32 Other transforms and operators of Fourier typetype: 35: 45E05 Integral equations with kernels of Cauchy type [See also]35J15type: 36: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35type: 37: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B35type: 38: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
[See also]46M10type: 39: 49M20 Methods of relaxation typetype: 40: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxxtype: 41: 55Pxx Homotopy theory For simple homotopy type, see 57Q10type: 42: 55P15 Classification of homotopy typetype: 43: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28type: 44: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C43type: 45: 74Cxx Plastic materials, materials of stress-rate and internal-variable typetype: 46: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)type: 47: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)type: 48: 90C52 Methods of reduced gradient typetype: 49: 90C53 Methods of quasi-Newton typetype: 50: 90C55 Methods of successive quadratic programming type
types: 1: 03D50 Recursive equivalence types of sets and structures, isolstypes: 2: 13C13 Other special typestypes: 3: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05types: 4: 26D07 Inequalities involving other types of functionstypes: 5: 37E15 Combinatorial dynamics (types of periodic orbits)types: 6: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)types: 7: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxxtypes: 8: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J40types: 9: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K21types: 10: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)types: 11: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxxtypes: 12: 54Cxx Maps and general types of spaces defined by mapstypes: 13: 55N05 Cech typestypes: 14: 55Q70 Homotopy groups of special types [See also]55N05, 55N07types: 15: 57R90 Other types of cobordism [See also]55N22types: 16: 68Q65 Abstract data types; algebraic specification [See also]18C50types: 17: 82Dxx Applications to specific types of physical systemstypes: 18: 91B52 Special types of equilibriatypes: 19: 91B54 Special types of economiestypes: 20: 94B60 Other types of codes
typography: 1: 68U15 Text processing; mathematical typographyufds: 1: 16U30 Divisibility, noncommutative UFDs
ultradistributions: 1: 46F05 Topological linear spaces of test functions, distributions and ultradistributions[See also]46E10, 46E35
ultradistributions: 2: 46F20 Distributions and ultradistributions as boundary values of analytic functions[See also]30D40, 30E25, 32A40ultrafilters: 1: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)[See also]03Exx For ultrafilters, see 54D80ultrafilters: 2: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)
ultraparabolic: 1: 35K70 Ultraparabolic equations, pseudoparabolic equations, etc.ultraproduct: 1: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07
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ultraproducts: 1: 03C20 Ultraproducts and related constructionsultraproducts: 2: 11U07 Ultraproducts [See also]03C20ultraproducts: 3: 12L10 Ultraproducts [See also]03C20ultraproducts: 4: 46M07 Ultraproducts [See also]46B08, 46S20
umbral: 1: 05A40 Umbral calculusunary: 1: 08A60 Unary algebras
unbounded: 1: 47B25 Symmetric and selfadjoint operators (unbounded)unbounded: 2: 47L60 Algebras of unbounded operators; partial algebras of operatorsuncertainty: 1: 68T37 Reasoning under uncertainty
undecidability: 1: 03D35 Undecidability and degrees of sets of sentencesunder: 1: 16Sxx Rings and algebras arising under various constructionsunder: 2: 62F30 Inference under constraintsunder: 3: 68T37 Reasoning under uncertainty
understanding: 1: 68T45 Machine vision and scene understandingunicoherence: 1: 54F55 Unicoherence, multicoherence
unified: 1: 81V22 Unified theoriesunified: 2: 83Exx Unified, higher-dimensional and super field theories
uniform: 1: 54E15 Uniform structures and generalizationsuniformity: 1: 11B30 Arithmetic combinatorics; higher degree uniformity
uniformization: 1: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G15uniformization: 2: 32Q30 Uniformization
uniformly: 1: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)unilateral: 1: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J40unilateral: 2: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J40unilateral: 3: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J40unilateral: 4: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J40unilateral: 5: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J40unilateral: 6: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J40unilateral: 7: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J40unilateral: 8: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J40unilateral: 9: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J40unimodular: 1: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F20
unique: 1: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicityuniqueness: 1: 32H12 Boundary uniqueness of mappingsuniqueness: 2: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuationof solutionsuniqueness: 3: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,bounds, Hilbert’s 16th problem and ramifications)uniqueness: 4: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenessuniqueness: 5: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenessuniqueness: 6: 35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniquenessuniqueness: 7: 41A52 Uniqueness of best approximationuniqueness: 8: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localizationuniqueness: 9: 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemanntheory, localizationuniqueness: 10: 42C25 Uniqueness and localization for orthogonal seriesuniqueness: 11: 55N40 Axioms for homology theory and uniqueness theorems
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uniqueness: 12: 74G30 Uniqueness of solutionsuniqueness: 13: 74H25 Uniqueness of solutionsuniqueness: 14: 76B03 Existence, uniqueness, and regularity theory [See also]35Q35uniqueness: 15: 76D03 Existence, uniqueness, and regularity theory [See also]35Q30uniqueness: 16: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q30unirational: 1: 14M20 Rational and unirational varieties [See also]14E08
unitary: 1: 22D10 Unitary representations of locally compact groupsunitary: 2: 51F25 Orthogonal and unitary groups [See also]20H05
units: 1: 11G16 Elliptic and modular units [See also]11R27units: 2: 11R27 Units and factorizationunits: 3: 16U60 Units, groups of unitsunits: 4: 16U60 Units, groups of unitsunits: 5: 97D80 Teaching units and draft lessonsunits: 6: 97F70 Measures and unitsunits: 7: 97Q80 Teaching units
univalent: 1: 30C45 Special classes of univalent and multivalent functions (starlike, convex, boundedrotation, etc.)
univalent: 2: 30C50 Coefficient problems for univalent and multivalent functionsunivalent: 3: 30C55 General theory of univalent and multivalent functionsuniversal: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C05universal: 2: 08A70 Applications of universal algebra in computer scienceuniversal: 3: 14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers,
Galois theory)universal: 4: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)universal: 5: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B35universal: 6: 17B35 Universal enveloping (super)algebras [See also]16S30universal: 7: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)universal: 8: 18B15 Embedding theorems, universal categories [See also]18E20universal: 9: 30Kxx Universal holomorphic functionsuniversal: 10: 30K05 Universal Taylor seriesuniversal: 11: 30K10 Universal Dirichlet seriesuniversal: 12: 30K15 Bounded universal functionsuniversal: 13: 55U20 Universal coefficient theorems, Bockstein operator
universality: 1: 30K20 Compositional universalityuniversality: 2: 37E20 Universality, renormalization [See also]37F25universities: 1: 01A73 Universities
unknowns: 1: 47A50 Equations and inequalities involving linear operators, with vector unknownsunknowns: 2: 47A62 Equations involving linear operators, with operator unknowns
up: 1: 13B21 Integral dependence; going up, going downupper: 1: 11T60 Finite upper half-planesupper: 2: 34L15 Eigenvalues, estimation of eigenvalues, upper and lower boundsupper: 3: 35P15 Estimation of eigenvalues, upper and lower boundsurban: 1: 91D10 Models of societies, social and urban evolution
uryson: 1: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)[See also]45Gxx, 45P05
use: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)use: 2: 65J10 Equations with linear operators (do not use 65Fxx)use: 3: 65J15 Equations with nonlinear operators (do not use 65Hxx)
user: 1: 97R70 User programs, administrative applicationsusing: 1: 40G15 Summability methods using statistical convergence [See also]40A35using: 2: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J52
utility: 1: 91A30 Utility theory for games [See also]91B16utility: 2: 91B16 Utility theory
vagueness: 1: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D05valuation: 1: 12J20 General valuation theory [See also]13A18valuation: 2: 13F30 Valuation rings [See also]13A18
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valuations: 1: 11J61 Approximation in non-Archimedean valuationsvaluations: 2: 13A18 Valuations and their generalizations [See also]12J20valuations: 3: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxxvaluations: 4: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)
value: 1: 11H60 Mean value and transfer theoremsvalue: 2: 30E25 Boundary value problems [See also]45Exxvalue: 3: 31A25 Boundary value and inverse problemsvalue: 4: 31B20 Boundary value and inverse problemsvalue: 5: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A22value: 6: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation
of solutionsvalue: 7: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxxvalue: 8: 34B05 Linear boundary value problemsvalue: 9: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parametervalue: 10: 34B08 Parameter dependent boundary value problemsvalue: 11: 34B10 Nonlocal and multipoint boundary value problemsvalue: 12: 34B15 Nonlinear boundary value problemsvalue: 13: 34B16 Singular nonlinear boundary value problemsvalue: 14: 34B18 Positive solutions of nonlinear boundary value problemsvalue: 15: 34B37 Boundary value problems with impulsesvalue: 16: 34B40 Boundary value problems on infinite intervalsvalue: 17: 34B45 Boundary value problems on graphs and networksvalue: 18: 34K10 Boundary value problemsvalue: 19: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.value: 20: 35E15 Initial value problemsvalue: 21: 35F10 Initial value problems for linear first-order equationsvalue: 22: 35F15 Boundary value problems for linear first-order equationsvalue: 23: 35F16 Initial-boundary value problems for linear first-order equationsvalue: 24: 35F25 Initial value problems for nonlinear first-order equationsvalue: 25: 35F30 Boundary value problems for nonlinear first-order equationsvalue: 26: 35F31 Initial-boundary value problems for nonlinear first-order equationsvalue: 27: 35F40 Initial value problems for linear first-order systemsvalue: 28: 35F45 Boundary value problems for linear first-order systemsvalue: 29: 35F46 Initial-boundary value problems for linear first-order systemsvalue: 30: 35F55 Initial value problems for nonlinear first-order systemsvalue: 31: 35F60 Boundary value problems for nonlinear first-order systemsvalue: 32: 35F61 Initial-boundary value problems for nonlinear first-order systemsvalue: 33: 35G10 Initial value problems for linear higher-order equationsvalue: 34: 35G15 Boundary value problems for linear higher-order equationsvalue: 35: 35G16 Initial-boundary value problems for linear higher-order equationsvalue: 36: 35G25 Initial value problems for nonlinear higher-order equationsvalue: 37: 35G30 Boundary value problems for nonlinear higher-order equationsvalue: 38: 35G31 Initial-boundary value problems for nonlinear higher-order equationsvalue: 39: 35G40 Initial value problems for linear higher-order systemsvalue: 40: 35G45 Boundary value problems for linear higher-order systemsvalue: 41: 35G46 Initial-boundary value problems for linear higher-order systemsvalue: 42: 35G55 Initial value problems for nonlinear higher-order systemsvalue: 43: 35G60 Boundary value problems for nonlinear higher-order systemsvalue: 44: 35G61 Initial-boundary value problems for nonlinear higher-order systemsvalue: 45: 35J25 Boundary value problems for second-order elliptic equationsvalue: 46: 35J40 Boundary value problems for higher-order elliptic equationsvalue: 47: 35J56 Boundary value problems for first-order elliptic systemsvalue: 48: 35J57 Boundary value problems for second-order elliptic systemsvalue: 49: 35J58 Boundary value problems for higher-order elliptic systemsvalue: 50: 35J65 Nonlinear boundary value problems for linear elliptic equationsvalue: 51: 35J66 Nonlinear boundary value problems for nonlinear elliptic equations
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value: 52: 35K15 Initial value problems for second-order parabolic equationsvalue: 53: 35K20 Initial-boundary value problems for second-order parabolic equationsvalue: 54: 35K30 Initial value problems for higher-order parabolic equationsvalue: 55: 35K35 Initial-boundary value problems for higher-order parabolic equationsvalue: 56: 35K45 Initial value problems for second-order parabolic systemsvalue: 57: 35K46 Initial value problems for higher-order parabolic systemsvalue: 58: 35K51 Initial-boundary value problems for second-order parabolic systemsvalue: 59: 35K52 Initial-boundary value problems for higher-order parabolic systemsvalue: 60: 35K60 Nonlinear initial value problems for linear parabolic equationsvalue: 61: 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equationsvalue: 62: 35L03 Initial value problems for first-order hyperbolic equationsvalue: 63: 35L04 Initial-boundary value problems for first-order hyperbolic equationsvalue: 64: 35L15 Initial value problems for second-order hyperbolic equationsvalue: 65: 35L20 Initial-boundary value problems for second-order hyperbolic equationsvalue: 66: 35L30 Initial value problems for higher-order hyperbolic equationsvalue: 67: 35L35 Initial-boundary value problems for higher-order hyperbolic equationsvalue: 68: 35L45 Initial value problems for first-order hyperbolic systemsvalue: 69: 35L50 Initial-boundary value problems for first-order hyperbolic systemsvalue: 70: 35L52 Initial value problems for second-order hyperbolic systemsvalue: 71: 35L53 Initial-boundary value problems for second-order hyperbolic systemsvalue: 72: 35L56 Initial value problems for higher-order hyperbolic systemsvalue: 73: 35L57 Initial-boundary value problems for higher-order hyperbolic systemsvalue: 74: 35M11 Initial value problems for equations of mixed typevalue: 75: 35M12 Boundary value problems for equations of mixed typevalue: 76: 35M13 Initial-boundary value problems for equations of mixed typevalue: 77: 35M31 Initial value problems for systems of mixed typevalue: 78: 35M32 Boundary value problems for systems of mixed typevalue: 79: 35M33 Initial-boundary value problems for systems of mixed typevalue: 80: 35N20 Overdetermined initial value problemsvalue: 81: 35N25 Overdetermined boundary value problemsvalue: 82: 35N30 Overdetermined initial-boundary value problemsvalue: 83: 35S10 Initial value problems for pseudodifferential operatorsvalue: 84: 35S11 Initial-boundary value problems for pseudodifferential operatorsvalue: 85: 35S15 Boundary value problems for pseudodifferential operatorsvalue: 86: 58J32 Boundary value problems on manifoldsvalue: 87: 58J47 Propagation of singularities; initial value problemsvalue: 88: 60G70 Extreme value theory; extremal processesvalue: 89: 65L05 Initial value problemsvalue: 90: 65L10 Boundary value problemsvalue: 91: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsvalue: 92: 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value
problemsvalue: 93: 65Nxx Partial differential equations, boundary value problems
valued: 1: 12J10 Valued fieldsvalued: 2: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S10valued: 3: 17A80 Valued algebrasvalued: 4: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxvalued: 5: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)valued: 6: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C60valued: 7: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C60values: 1: 11F67 Special values of automorphic L-series, periods of modular forms, cohomology, modular
symbolsvalues: 2: 11M32 Multiple Dirichlet series and zeta functions and multizeta valuesvalues: 3: 11N32 Primes represented by polynomials; other multiplicative structure of polynomial values
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values: 4: 11N64 Other results on the distribution of values or the characterization of arithmetic functionsvalues: 5: 11Y70 Values of arithmetic functions; tablesvalues: 6: 15A18 Eigenvalues, singular values, and eigenvectorsvalues: 7: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxxvalues: 8: 28Bxx Set functions, measures and integrals with values in abstract spacesvalues: 9: 28B15 Set functions, measures and integrals with values in ordered spacesvalues: 10: 30D35 Distribution of values, Nevanlinna theoryvalues: 11: 35J67 Boundary values of solutions to elliptic equationsvalues: 12: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15values: 13: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)values: 14: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A40values: 15: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)values: 16: 62G32 Statistics of extreme values; tail inference
van: 1: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M05vanishing: 1: 14F17 Vanishing theorems [See also]32L20vanishing: 2: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxvanishing: 3: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)vanishing: 4: 32L20 Vanishing theoremsvanishing: 5: 32S30 Deformations of singularities; vanishing cycles [See also]14B07
variable: 1: 11F12 Automorphic forms, one variablevariable: 2: 11F25 Hecke-Petersson operators, differential operators (one variable)variable: 3: 11F66 Langlands L-functions; one variable Dirichlet series and functional equationsvariable: 4: 26Axx Functions of one variablevariable: 5: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A15variable: 6: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XXvariable: 7: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35variable: 8: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablevariable: 9: 33D15 Basic hypergeometric functions in one variable, rϕs
variable: 10: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basichypergeometric functions in one variable
variable: 11: 35N10 Overdetermined systems with variable coefficientsvariable: 12: 42Axx Harmonic analysis in one variablevariable: 13: 49J05 Free problems in one independent variablevariable: 14: 49K05 Free problems in one independent variablevariable: 15: 58E10 Applications to the theory of geodesics (problems in one independent variable)variable: 16: 70Pxx Variable mass, rocketsvariable: 17: 70P05 Variable mass, rocketsvariable: 18: 74S70 Complex variable methodsvariable: 19: 93B12 Variable structure systems
variables: 1: 11D72 Equations in many variables [See also]11P55variables: 2: 11D79 Congruences in many variablesvariables: 3: 11E20 General ternary and quaternary quadratic forms; forms of more than two variablesvariables: 4: 11F55 Other groups and their modular and automorphic forms (several variables)variables: 5: 11F60 Hecke-Petersson operators, differential operators (several variables)variables: 6: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl
group multiple Dirichlet seriesvariables: 7: 15A54 Matrices over function rings in one or more variablesvariables: 8: 26Bxx Functions of several variables
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variables: 9: 26B10 Implicit function theorems, Jacobians, transformations with several variablesvariables: 10: 26B35 Special properties of functions of several variables, Holder conditions, etc.variables: 11: 30G35 Functions of hypercomplex variables and generalized variablesvariables: 12: 30G35 Functions of hypercomplex variables and generalized variablesvariables: 13: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B12variables: 14: 32Axx Holomorphic functions of several complex variablesvariables: 15: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G35variables: 16: 32A50 Harmonic analysis of several complex variables [See mainly]43-XXvariables: 17: 32N05 General theory of automorphic functions of several complex variablesvariables: 18: 32Wxx Differential operators in several variablesvariables: 19: 32W25 Pseudodifferential operators in several complex variablesvariables: 20: 32W30 Heat kernels in several complex variablesvariables: 21: 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special
functions in one variablevariables: 22: 33C70 Other hypergeometric functions and integrals in several variablesvariables: 23: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic
hypergeometric functions in one variablevariables: 24: 33D70 Other basic hypergeometric functions and integrals in several variablesvariables: 25: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25variables: 26: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F30variables: 27: 46E39 Sobolev (and similar kinds of) spaces of functions of discrete variablesvariables: 28: 49J10 Free problems in two or more independent variablesvariables: 29: 49K10 Free problems in two or more independent variablesvariables: 30: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q05variables: 31: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.variables: 32: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)variables: 33: 60G50 Sums of independent random variables; random walksvariables: 34: 97I60 Functions of several variablesvariance: 1: 62J10 Analysis of variance and covariancevariants: 1: 11P05 Waring’s problem and variantsvariants: 2: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)
variation: 1: 14D07 Variation of Hodge structures [See also]32G20variation: 2: 26A45 Functions of bounded variation, generalizationsvariation: 3: 26B30 Absolutely continuous functions, functions of bounded variationvariation: 4: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K30variational: 1: 30C70 Extremal problems for conformal and quasiconformal mappings, variational methodsvariational: 2: 35A15 Variational methodsvariational: 3: 35J20 Variational methods for second-order elliptic equationsvariational: 4: 35J35 Variational methods for higher-order elliptic equationsvariational: 5: 35J50 Variational methods for elliptic systemsvariational: 6: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities[See also]35R35, 49J40variational: 7: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities[See also]35R35, 49J40variational: 8: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J40variational: 9: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities[See also]35R35, 49J40variational: 10: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities[See also]35R35, 49J40variational: 11: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J40variational: 12: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
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[See also]35R35, 49J40variational: 13: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variationalinequalities [See also]35R35, 49J40variational: 14: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,49J40variational: 15: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,49J40variational: 16: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type[See also]35R35, 49J40variational: 17: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J40variational: 18: 37D35 Thermodynamic formalism, variational principles, equilibrium statesvariational: 19: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoreticmethodsvariational: 20: 37K05 Hamiltonian structures, symmetries, variational principles, conservation lawsvariational: 21: 47J20 Variational and other types of inequalities involving nonlinear operators (general)[See also]49J40variational: 22: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K21variational: 23: 47J30 Variational methods [See also]58Exxvariational: 24: 49J40 Variational methods including variational inequalities [See also]47J20variational: 25: 49J40 Variational methods including variational inequalities [See also]47J20variational: 26: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C06variational: 27: 49Q20 Variational problems in a geometric measure-theoretic settingvariational: 28: 49Rxx Variational methods for eigenvalues of operators [See also]47A75variational: 29: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also beassigned at least one other classification number in Section 49)variational: 30: 49Sxx Variational principles of physicsvariational: 31: 49S05 Variational principles of physics (should also be assigned at least one other classificationnumber in section 49)variational: 32: 58Exx Variational problems in infinite-dimensional spacesvariational: 33: 58E30 Variational principlesvariational: 34: 58E35 Variational inequalities (global problems)variational: 35: 65Kxx Mathematical programming, optimization and variational techniquesvariational: 36: 65K10 Optimization and variational techniques [See also]49Mxx, 93B40variational: 37: 65K15 Numerical methods for variational inequalities and related problemsvariational: 38: 70G75 Variational methodsvariational: 39: 70H30 Other variational principlesvariational: 40: 76M30 Variational methodsvariational: 41: 78M30 Variational methodsvariational: 42: 80M30 Variational methodsvariational: 43: 90C33 Complementarity and equilibrium problems and variational inequalities (finitedimensions)variations: 1: 11K36 Well-distributed sequences and other variationsvariations: 2: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XXvariations: 3: 60H07 Stochastic calculus of variations and the Malliavin calculusvariations: 4: 91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE,
SPDE, dynamical systems)varieties: 1: 06B20 Varieties of latticesvarieties: 2: 08Bxx Varieties [See also]03C05varieties: 3: 08B15 Lattices of varietiesvarieties: 4: 11G10 Abelian varieties of dimension > 1 [See also]14Kxxvarieties: 5: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K22varieties: 6: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G35varieties: 7: 11G25 Varieties over finite and local fields [See also]14G15, 14G20varieties: 8: 11G35 Varieties over global fields [See also]14G25varieties: 9: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10
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Mathematics Subject Classification 2010
varieties: 10: 11J95 Results involving abelian varietiesvarieties: 11: 14A10 Varieties and morphismsvarieties: 12: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G18varieties: 13: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P30varieties: 14: 14H40 Jacobians, Prym varieties [See also]32G20varieties: 15: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxxvarieties: 16: 14J45 Fano varietiesvarieties: 17: 14J50 Automorphisms of surfaces and higher-dimensional varietiesvarieties: 18: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxvarieties: 19: 14Kxx Abelian varieties and schemesvarieties: 20: 14L10 Group varietiesvarieties: 21: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M17varieties: 22: 14Mxx Special varietiesvarieties: 23: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H10varieties: 24: 14M12 Determinantal varieties [See also]13C40varieties: 25: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M35varieties: 26: 14M20 Rational and unirational varieties [See also]14E08varieties: 27: 14M22 Rationally connected varietiesvarieties: 28: 14M25 Toric varieties, Newton polyhedra [See also]52B20varieties: 29: 14M27 Compactifications; symmetric and spherical varietiesvarieties: 30: 14N25 Varieties of low degreevarieties: 31: 14P25 Topology of real algebraic varietiesvarieties: 32: 14Q15 Higher-dimensional varietiesvarieties: 33: 14R05 Classification of affine varietiesvarieties: 34: 14R20 Group actions on affine varieties [See also]13A50, 14L30varieties: 35: 16R10 T -ideals, identities, varieties of rings and algebrasvarieties: 36: 17B08 Coadjoint orbits; nilpotent varietiesvarieties: 37: 20E10 Quasivarieties and varieties of groupsvarieties: 38: 20M07 Varieties and pseudovarieties of semigroupsvarieties: 39: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D07varieties: 40: 37P55 Arithmetic dynamics on general algebraic varietiesvarieties: 41: 55R80 Discriminantal varieties, configuration spacesvarious: 1: 16Sxx Rings and algebras arising under various constructionsvarious: 2: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)varying: 1: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A48vector: 1: 11S90 Prehomogeneous vector spacesvector: 2: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G13vector: 3: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txxvector: 4: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F05vector: 5: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxxvector: 6: 15A03 Vector spaces, linear dependence, rankvector: 7: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L24vector: 8: 17B66 Lie algebras of vector fields and related (super) algebrasvector: 9: 26B12 Calculus of vector functionsvector: 10: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N30vector: 11: 32M25 Complex vector fieldsvector: 12: 32S65 Singularities of holomorphic vector fields and foliationsvector: 13: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness,
bounds, Hilbert’s 16th problem and ramifications)vector: 14: 37C10 Vector fields, flows, ordinary differential equations
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vector: 15: 37C27 Periodic orbits of vector fields and flowsvector: 16: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxxvector: 17: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B42vector: 18: 46M35 Abstract interpolation of topological vector spaces [See also]46B70vector: 19: 47A50 Equations and inequalities involving linear operators, with vector unknownsvector: 20: 47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological
vector spacesvector: 21: 52A07 Convex sets in topological vector spaces [See also]46A55vector: 22: 53A45 Vector and tensor analysisvector: 23: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
[See also]32Q20vector: 24: 55R25 Sphere bundles and vector bundlesvector: 25: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XXvector: 26: 57N17 Topology of topological vector spacesvector: 27: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxxvector: 28: 57R25 Vector fields, frame fieldsvector: 29: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B05vector: 30: 58A30 Vector distributions (subbundles of the tangent bundles)vector: 31: 58K45 Singularities of vector fields, topological aspectsvector: 32: 93D30 Scalar and vector Lyapunov functionsvector: 33: 97G70 Analytic geometry. Vector algebra
vector-: 1: 46E40 Spaces of vector- and operator-valued functionsvector-valued: 1: 28B05 Vector-valued set functions, measures and integrals [See also]46G10vector-valued: 2: 46G10 Vector-valued measures and integration [See also]28Bxx, 46B22vector-valued: 3: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
vectors: 1: 13F35 Witt vectors and related ringsvectors: 2: 37E45 Rotation numbers and vectorsvectors: 3: 47A16 Cyclic vectors, hypercyclic and chaotic operators
vekua: 1: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)verbal: 1: 97C50 Language and verbal communities
verification: 1: 65G20 Algorithms with automatic result verificationverification: 2: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,requirements, etc.)verification: 3: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70
verma: 1: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,etc.) [See also]17B10
veronesians: 1: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,Veronesians and their generalizations) [See also]14M15
version: 1: 39A12 Discrete version of topics in analysisversions: 1: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxxvertex: 1: 05C07 Vertex degrees [See also]05E30vertex: 2: 17B69 Vertex operators; vertex operator algebras and related structuresvertex: 3: 17B69 Vertex operators; vertex operator algebras and related structuresvessels: 1: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.via: 1: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
representing set functions and measuresvia: 2: 51L15 n-vertex theorems via direct methods
vibration: 1: 70Jxx Linear vibration theoryvibration: 2: 70J50 Systems arising from the discretization of structural vibration problems
vibrations: 1: 70Lxx Random vibrations [See also]74H50vibrations: 2: 70L05 Random vibrations [See also]74H50vibrations: 3: 74H45 Vibrationsvibrations: 4: 74H50 Random vibrations
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Mathematics Subject Classification 2010
viewed: 1: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XXviewed: 2: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
20L05, 20Mxxvirasoro: 1: 17B68 Virasoro and related algebrasvirasoro: 2: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70viscoelastic: 1: 74Dxx Materials of strain-rate type and history type, other materials with memory (includingelastic materials with viscous damping, various viscoelastic materials)viscoelastic: 2: 76A10 Viscoelastic fluids
viscoplasticity: 1: 74C10 Small-strain, rate-dependent theories (including theories of viscoplasticity)viscosity: 1: 35D40 Viscosity solutionsviscosity: 2: 49L25 Viscosity solutions
viscous: 1: 74Dxx Materials of strain-rate type and history type, other materials with memory (includingelastic materials with viscous damping, various viscoelastic materials)
viscous: 2: 76Dxx Incompressible viscous fluidsviscous: 3: 76D17 Viscous vortex flowsviscous: 4: 76D50 Stratification effects in viscous fluids
viscous-inviscid: 1: 76D09 Viscous-inviscid interactionviscous-inviscid: 2: 76N17 Viscous-inviscid interaction
vision: 1: 65D19 Computational issues in computer and robotic visionvision: 2: 68T45 Machine vision and scene understandingvisual: 1: 00A66 Mathematics and visual arts, visualization
visualization: 1: 00A66 Mathematics and visual arts, visualizationvisualization: 2: 76M27 Visualization algorithms
vlasov-like: 1: 35Q83 Vlasov-like equationsvlsi: 1: 68W35 VLSI algorithms
vmoa: 1: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),vanishing mean oscillation (VMOA)) [See also]46Exxvocational: 1: 97B30 Vocational educationvocational: 2: 97M20 Mathematics in vocational training and career education
vojta: 1: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)volterra: 1: 45Dxx Volterra integral equations [See also]34A12volterra: 2: 45D05 Volterra integral equations [See also]34A12volume: 1: 26B15 Integration: length, area, volume [See also]28A75, 51M25volume: 2: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q15volume: 3: 51M25 Length, area and volume [See also]26B15volume: 4: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q20volume: 5: 65M08 Finite volume methodsvolume: 6: 65N08 Finite volume methodsvolume: 7: 74S10 Finite volume methodsvolume: 8: 76M12 Finite volume methodsvolume: 9: 78M12 Finite volume methods, finite integration techniquesvolume: 10: 80M12 Finite volume methods
volumes: 1: 00B50 Volumes of selected translationsvolumes: 2: 00B55 Miscellaneous volumes of translationsvolumes: 3: 52A39 Mixed volumes and related topicsvolumes: 4: 97G30 Areas and volumes
von: 1: 16E50 von Neumann regular rings and generalizationsvon: 2: 46L10 General theory of von Neumann algebrasvon: 3: 47C15 Operators in C∗- or von Neumann algebras
vortex: 1: 76B47 Vortex flowsvortex: 2: 76D17 Viscous vortex flowsvortex: 3: 76M23 Vortex methodsvoting: 1: 91B12 Voting theory
vries: 1: 35Q53 KdV-like equations (Korteweg-de Vries) [See also]37K10wakes: 1: 76D25 Wakes and jets
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Mathematics Subject Classification 2010
walks: 1: 05C81 Random walks on graphswalks: 2: 60G50 Sums of independent random variables; random walkswalks: 3: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41walks: 4: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50
wall: 1: 57Q12 Wall finiteness obstruction for CW-complexeswall: 2: 57R67 Surgery obstructions, Wall groups [See also]19J25
walsh: 1: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,etc.)
waring’s: 1: 11P05 Waring’s problem and variantswater: 1: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30water: 2: 76Z10 Biopropulsion in water and in air
water-entry: 1: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil andhydrofoil theory, sloshing
wave: 1: 33E10 Lame, Mathieu, and spheroidal wave functionswave: 2: 33E15 Other wave functionswave: 3: 35A18 Wave front setswave: 4: 35C07 Traveling wave solutionswave: 5: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxxwave: 6: 35L05 Wave equationwave: 7: 74J20 Wave scatteringwave: 8: 81R20 Covariant wave equationswave: 9: 82D77 Quantum wave guides, quantum wires [See also]78A50
wave-guides: 1: 78A50 Antennas, wave-guideswaveguides: 1: 81Q37 Quantum dots, waveguides, ratchets, etc.
wavelets: 1: 42C40 Wavelets and other special systemswavelets: 2: 65T60 Wavelets
waves: 1: 74Jxx Waveswaves: 2: 74J05 Linear waveswaves: 3: 74J10 Bulk waveswaves: 4: 74J15 Surface waveswaves: 5: 74J30 Nonlinear waveswaves: 6: 74J35 Solitary waveswaves: 7: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30waves: 8: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30waves: 9: 76B20 Ship waveswaves: 10: 76B25 Solitary waves [See also]35C11waves: 11: 76B55 Internal waveswaves: 12: 76B60 Atmospheric waves [See also]86A10waves: 13: 76B65 Rossby waves [See also]86A05, 86A10waves: 14: 76D33 Waveswaves: 15: 76Lxx Shock waves and blast waves [See also]35L67waves: 16: 76Lxx Shock waves and blast waves [See also]35L67waves: 17: 76L05 Shock waves and blast waves [See also]35L67waves: 18: 76L05 Shock waves and blast waves [See also]35L67waves: 19: 78A20 Space charge waveswaves: 20: 78A40 Waves and radiationwaves: 21: 83C35 Gravitational wavesweak: 1: 35D30 Weak solutionsweak: 2: 54C08 Weak and generalized continuityweak: 3: 60F05 Central limit and other weak theoremsweak: 4: 81V15 Weak interactionweak: 5: 83C25 Approximation procedures, weak fields
weakly: 1: 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries
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Mathematics Subject Classification 2010
weakly: 2: 47L45 Dual algebras; weakly closed singly generated operator algebraswebs: 1: 14C21 Pencils, nets, webs [See also]53A60webs: 2: 53A60 Geometry of webs [See also]14C21, 20N05
wedges: 1: 55Q20 Homotopy groups of wedges, joins, and simple spacesweierstrass: 1: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxx
weight: 1: 11F11 Holomorphic modular forms of integral weightweight: 2: 11F37 Forms of half-integer weight; nonholomorphic modular formsweight: 3: 74P05 Compliance or weight optimization
weighted: 1: 05C22 Signed and weighted graphsweighted: 2: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
weights: 1: 17B10 Representations, algebraic theory (weights)weil: 1: 11F27 Theta series; Weil representation; theta correspondences
welfare: 1: 91B15 Welfare economicswell-bounded: 1: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
well-distributed: 1: 11K36 Well-distributed sequences and other variationswell-posedness: 1: 49K40 Sensitivity, stability, well-posedness [See also]90C31
weyl: 1: 11F68 Dirichlet series in several complex variables associated to automorphic forms; Weylgroup multiple Dirichlet series
weyl: 2: 11L15 Weyl sumsweyl: 3: 34B20 Weyl theory and its generalizations
when: 1: 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)which: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05which: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05white: 1: 60H40 White noise theory
whitehead: 1: 19Bxx Whitehead groups and K1
whitehead: 2: 19J10 Whitehead (and related) torsionwhitehead: 3: 55Q15 Whitehead products and generalizationswhitehead: 4: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.[See also]19B28whittaker: 1: 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1
whose: 1: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,including analytic and meromorphic ones)
widths: 1: 41A46 Approximation by arbitrary nonlinear expressions; widths and entropywiener: 1: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11wiener-hopf: 1: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopftype) [See also]47B35
wiener-hopf: 2: 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations)wiener-hopf: 3: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 forother integral operators; see also 32A25, 32M15
wigner: 1: 81S30 Phase-space methods including Wigner distributions, etc.wild: 1: 16G60 Representation type (finite, tame, wild, etc.)wild: 2: 57M30 Wild knots and surfaces, etc., wild embeddingswild: 3: 57M30 Wild knots and surfaces, etc., wild embeddings
winding: 1: 55M25 Degree, winding numberwires: 1: 82D77 Quantum wave guides, quantum wires [See also]78A50with: 1: 03C50 Models with special properties (saturated, rigid, etc.)with: 2: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B48with: 3: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R15with: 4: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45with: 5: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)with: 6: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
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22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45with: 7: 11F23 Relations with algebraic geometry and topologywith: 8: 11G55 Polylogarithms and relations with K-theorywith: 9: 11H71 Relations with coding theorywith: 10: 11M50 Relations with random matriceswith: 11: 11M55 Relations with noncommutative geometrywith: 12: 11N25 Distribution of integers with specified multiplicative constraintswith: 13: 11N60 Distribution functions associated with additive and positive multiplicative functionswith: 14: 11Uxx Connections with logicwith: 15: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxwith: 16: 12Lxx Connections with logicwith: 17: 13F50 Rings with straightening laws, Hodge algebraswith: 18: 14H70 Relationships with integrable systemswith: 19: 14H81 Relationships with physicswith: 20: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G13with: 21: 14J81 Relationships with physicswith: 22: 16Rxx Rings with polynomial identitywith: 23: 16T30 Connections with combinatoricswith: 24: 16Wxx Rings and algebras with additional structurewith: 25: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxxwith: 26: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50with: 27: 17C50 Jordan structures associated with other structures [See also]16W10with: 28: 18C20 Algebras and Kleisli categories associated with monadswith: 29: 18Dxx Categories with structurewith: 30: 19E20 Relations with cohomology theories [See also]14Fxxwith: 31: 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann
extensions, and generalizationswith: 32: 20E42 Groups with a BN -pair; buildings [See also]51E24with: 33: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70with: 34: 20Jxx Connections with homological algebra and category theorywith: 35: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05with: 36: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05with: 37: 20M50 Connections of semigroups with homological algebra and category theorywith: 38: 20N02 Sets with a single binary operation (groupoids)with: 39: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S20with: 40: 26A30 Singular functions, Cantor functions, functions with other special propertieswith: 41: 26B10 Implicit function theorems, Jacobians, transformations with several variableswith: 42: 28A25 Integration with respect to measures and other set functionswith: 43: 28Bxx Set functions, measures and integrals with values in abstract spaceswith: 44: 28B15 Set functions, measures and integrals with values in ordered spaceswith: 45: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D20with: 46: 28E15 Other connections with logic and set theorywith: 47: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10with: 48: 31A35 Connections with differential equationswith: 49: 31B35 Connections with differential equationswith: 50: 32Mxx Complex spaces with a group of automorphismswith: 51: 32S22 Relations with arrangements of hyperplanes [See also]52C35with: 52: 32S40 Monodromy; relations with differential equations and D-modules
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with: 53: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q45with: 54: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
with: 55: 33C52 Orthogonal polynomials and functions associated with root systemswith: 56: 33C67 Hypergeometric functions associated with root systemswith: 57: 33C80 Connections with groups and algebras, and related topicswith: 58: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)with: 59: 33D67 Basic hypergeometric functions associated with root systemswith: 60: 33D80 Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and
related topicswith: 61: 34A37 Differential equations with impulseswith: 62: 34B07 Linear boundary value problems with nonlinear dependence on the spectral parameterwith: 63: 34B37 Boundary value problems with impulseswith: 64: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)with: 65: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E03with: 66: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E03with: 67: 34K37 Functional-differential equations with fractional derivativeswith: 68: 34K45 Equations with impulseswith: 69: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M50with: 70: 35Exx Equations and systems with constant coefficients [See also]35N05with: 71: 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacianwith: 72: 35J92 Quasilinear elliptic equations with p-Laplacianwith: 73: 35J93 Quasilinear elliptic equations with mean curvature operatorwith: 74: 35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacianwith: 75: 35K92 Quasilinear parabolic equations with p-Laplacianwith: 76: 35K93 Quasilinear parabolic equations with mean curvature operatorwith: 77: 35N05 Overdetermined systems with constant coefficientswith: 78: 35N10 Overdetermined systems with variable coefficientswith: 79: 35Q35 PDEs in connection with fluid mechanicswith: 80: 35Q40 PDEs in connection with quantum mechanicswith: 81: 35Q60 PDEs in connection with optics and electromagnetic theorywith: 82: 35Q62 PDEs in connection with statisticswith: 83: 35Q68 PDEs in connection with computer sciencewith: 84: 35Q70 PDEs in connection with mechanics of particles and systemswith: 85: 35Q74 PDEs in connection with mechanics of deformable solidswith: 86: 35Q75 PDEs in connection with relativity and gravitational theorywith: 87: 35Q79 PDEs in connection with classical thermodynamics and heat transferwith: 88: 35Q82 PDEs in connection with statistical mechanicswith: 89: 35Q85 PDEs in connection with astronomy and astrophysicswith: 90: 35Q86 PDEs in connection with geophysicswith: 91: 35Q90 PDEs in connection with mathematical programmingwith: 92: 35Q91 PDEs in connection with game theory, economics, social and behavioral scienceswith: 93: 35Q92 PDEs in connection with biology and other natural scienceswith: 94: 35Q93 PDEs in connection with control and optimizationwith: 95: 35Q94 PDEs in connection with information and communicationwith: 96: 35R05 Partial differential equations with discontinuous coefficients or datawith: 97: 35R06 Partial differential equations with measurewith: 98: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H15with: 99: 35R70 Partial differential equations with multivalued right-hand sideswith: 100: 37A45 Relations with number theory and harmonic analysis [See also]11Kxxwith: 101: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G10with: 102: 37A55 Relations with the theory of C∗-algebras [See mainly]46L55with: 103: 37B05 Transformations and group actions with special properties (minimality, distality,
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proximality, etc.)with: 104: 37Dxx Dynamical systems with hyperbolic behaviorwith: 105: 37D50 Hyperbolic systems with singularities (billiards, etc.)with: 106: 37G20 Hyperbolic singular points with homoclinic trajectorieswith: 107: 37G25 Bifurcations connected with nontransversal intersectionwith: 108: 37J05 General theory, relations with symplectic geometry and topologywith: 109: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H70with: 110: 37K25 Relations with differential geometrywith: 111: 37K30 Relations with infinite-dimensional Lie algebras and other algebraic structureswith: 112: 39B52 Equations for functions with more general domains and/or rangeswith: 113: 41A29 Approximation with constraintswith: 114: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier
series For automorphic theory, see mainly 11F30with: 115: 45E05 Integral equations with kernels of Cauchy type [See also]35J15with: 116: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)with: 117: 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with
semidefinite inner product)with: 118: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50with: 119: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B32with: 120: 46F10 Operations with distributionswith: 121: 46Kxx Topological (rings and) algebras with an involution [See also]16W10with: 122: 46K05 General theory of topological algebras with involutionwith: 123: 46K10 Representations of topological algebras with involutionwith: 124: 46K50 Nonselfadjoint (sub)algebras in algebras with involutionwith: 125: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L70with: 126: 47A50 Equations and inequalities involving linear operators, with vector unknownswith: 127: 47A62 Equations involving linear operators, with operator unknownswith: 128: 47B50 Operators on spaces with an indefinite metric [See also]46C50with: 129: 47J40 Equations with hysteresis operators [See also]34C55, 74N30with: 130: 47L15 Operator algebras with symbol structurewith: 131: 49N30 Problems with incomplete information [See also]93C41with: 132: 51A15 Structures with parallelismwith: 133: 51D10 Abstract geometries with exchange axiomwith: 134: 51D15 Abstract geometries with parallelismwith: 135: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C70with: 136: 51H30 Geometries with algebraic manifold structure [See also]14-XXwith: 137: 51N25 Analytic geometry with other transformation groupswith: 138: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxxwith: 139: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C42with: 140: 53C50 Lorentz manifolds, manifolds with indefinite metricswith: 141: 54Exx Spaces with richer structureswith: 142: 54Hxx Connections with other structures, applicationswith: 143: 55N25 Homology with local coefficients, equivariant cohomologywith: 144: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)with: 145: 55R55 Fiberings with singularitieswith: 146: 57M15 Relations with graph theory [See also]05Cxxwith: 147: 58J15 Relations with hyperfunctionswith: 148: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)with: 149: 60G42 Martingales with discrete parameterwith: 150: 60G44 Martingales with continuous parameterwith: 151: 60G51 Processes with independent increments; Levy processeswith: 152: 62E86 Fuzziness in connection with the topics on distributions in this section
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with: 153: 65G20 Algorithms with automatic result verificationwith: 154: 65J10 Equations with linear operators (do not use 65Fxx)with: 155: 65J15 Equations with nonlinear operators (do not use 65Hxx)with: 156: 70E17 Motion of a rigid body with a fixed pointwith: 157: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25with: 158: 70F40 Problems with frictionwith: 159: 70K70 Systems with slow and fast motionswith: 160: 74B10 Linear elasticity with initial stresseswith: 161: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)with: 162: 74Dxx Materials of strain-rate type and history type, other materials with memory (including
elastic materials with viscous damping, various viscoelastic materials)with: 163: 74Fxx Coupling of solid mechanics with other effectswith: 164: 81R12 Relations with integrable systems [See also]17Bxx, 37J35with: 165: 83C20 Classes of solutions; algebraically special solutions, metrics with symmetrieswith: 166: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)with: 167: 91A13 Games with infinitely many playerswith: 168: 93C41 Problems with incomplete informationwith: 169: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10with: 170: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E10without: 1: 52A05 Convex sets without dimension restrictions
witt: 1: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G24witt: 2: 13F35 Witt vectors and related ringswitt: 3: 19G12 Witt groups of rings [See also]11E81wkb: 1: 34E20 Singular perturbations, turning point theory, WKB methodswkb: 2: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E20wkb: 3: 78A45 Diffraction, scattering [See also]34E20 for WKB methodswkb: 4: 81Q20 Semiclassical techniques, including WKB and Maslov methodswkb: 5: 81U05 2-body potential scattering theory [See also]34E20 for WKB methods
word: 1: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R15word: 2: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F10word: 3: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R15word: 4: 20A10 Metamathematical considerations For word problems, see 20F10word: 5: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70word: 6: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F10words: 1: 05A05 Permutations, words, matriceswords: 2: 68R15 Combinatorics on wordswork: 1: 11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.)
works: 1: 00A20 Dictionaries and other general reference worksworks: 2: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B60works: 3: 97A10 Comprehensive works, reference booksworks: 4: 97C10 Comprehensive worksworks: 5: 97D10 Comprehensive works, comparative studiesworks: 6: 97E10 Comprehensive worksworks: 7: 97F10 Comprehensive worksworks: 8: 97G10 Comprehensive worksworks: 9: 97H10 Comprehensive worksworks: 10: 97I10 Comprehensive worksworks: 11: 97K10 Comprehensive worksworks: 12: 97N10 Comprehensive worksworks: 13: 97P10 Comprehensive worksworks: 14: 97Q10 Comprehensive works
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works: 15: 97R10 Comprehensive works, collections of programsworks: 16: 97U10 Comprehensive worksworld: 1: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D30worm: 1: 32T20 Worm domains
wreath: 1: 20E22 Extensions, wreath products, and other compositions [See also]20J05yang-baxter: 1: 16T25 Yang-Baxter equations
yang-mills: 1: 58E15 Application to extremal problems in several variables; Yang-Mills functionals[See also]81T13, etc.yang-mills: 2: 70S15 Yang-Mills and other gauge theoriesyang-mills: 3: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E15zeilberger: 1: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30
zero: 1: 32A60 Zero sets of holomorphic functionszero: 2: 93B55 Pole and zero placement problems
zero-one: 1: 60F20 Zero-one lawszeros: 1: 11M20 Real zeros of L(s, χ); results on L(1, χ)zeros: 2: 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheseszeros: 3: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C15zeros: 4: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H05zeros: 5: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10zeros: 6: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10zeros: 7: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)zeros: 8: 34C10 Oscillation theory, zeros, disconjugacy and comparison theoryzeros: 9: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.zeta: 1: 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and
functions)zeta: 2: 11Mxx Zeta and L-functions: analytic theoryzeta: 3: 11M32 Multiple Dirichlet series and zeta functions and multizeta valueszeta: 4: 11M35 Hurwitz and Lerch zeta functionszeta: 5: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulaszeta: 6: 11M38 Zeta and L-functions in characteristic pzeta: 7: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72zeta: 8: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F27zeta: 9: 11R52 Quaternion and other division algebras: arithmetic, zeta functionszeta: 10: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxxzeta: 11: 11S40 Zeta functions and L-functions [See also]11M41, 19F27zeta: 12: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxxzeta: 13: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G10zeta: 14: 37C30 Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic
techniques in dynamical systemszeta-functions: 1: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyer
conjecture)zonoids: 1: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxx lukasiewicz: 1: 03G20 Lukasiewicz and Post algebras [See also]06D25, 06D30 lukasiewicz: 2: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G20
e.g.: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,03G25, 06E25
e.g.: 2: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,cyclic, dihedral, etc.)
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e.g.: 3: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)[See also]13A05, 14M05
e.g.: 4: 13P10 Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)e.g.: 5: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)e.g.: 6: 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne
(co)homologies)e.g.: 7: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)e.g.: 8: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)e.g.: 9: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G30e.g.: 10: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C10e.g.: 11: 32A26 Integral representations, constructed kernels (e.g. Cauchy, Fantappie-type kernels)e.g.: 12: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exxe.g.: 13: 32G07 Deformations of special (e.g. CR) structurese.g.: 14: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxxe.g.: 15: 35A22 Transform methods (e.g. integral transforms)e.g.: 16: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D25e.g.: 17: 39A20 Multiplicative and other generalized difference equations, e.g. of Lyness typee.g.: 18: 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)e.g.: 19: 57M12 Special coverings, e.g. branchede.g.: 20: 58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicitye.g.: 21: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A22e.g.: 22: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E30etc.: 1: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)etc.: 2: 01A15 Indigenous European cultures (pre-Greek, etc.)etc.: 3: 03C50 Models with special properties (saturated, rigid, etc.)etc.: 4: 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)etc.: 5: 03D03 Thue and Post systems, etc.etc.: 6: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R15etc.: 7: 03D60 Computability and recursion theory on ordinals, admissible sets, etc.etc.: 8: 03H10 Other applications of nonstandard models (economics, physics, etc.)etc.: 9: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B13etc.: 10: 05B20 Matrices (incidence, Hadamard, etc.)etc.: 11: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F65etc.: 12: 05C42 Density (toughness, etc.)etc.: 13: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)etc.: 14: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)etc.: 15: 05C60 Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph
embedding, etc.)etc.: 16: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R10etc.: 17: 05C76 Graph operations (line graphs, products, etc.)etc.: 18: 05C78 Graph labelling (graceful graphs, bandwidth, etc.)etc.: 19: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F45etc.: 20: 11F32 Modular correspondences, etc.etc.: 21: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L05etc.: 22: 11H55 Quadratic forms (reduction theory, extreme forms, etc.)etc.: 23: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,
etc. [See also]11A63etc.: 24: 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory,
Dirichlet series, Eisenstein series, etc. Explicit formulas
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etc.: 25: 11R09 Polynomials (irreducibility, etc.)etc.: 26: 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)etc.: 27: 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)etc.: 28: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exxetc.: 29: 12E05 Polynomials (irreducibility, etc.)etc.: 30: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)etc.: 31: 13C15 Dimension theory, depth, related rings (catenary, etc.)etc.: 32: 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen,
cyclic, dihedral, etc.)etc.: 33: 13D07 Homological functors on modules (Tor, Ext, etc.)etc.: 34: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M05etc.: 35: 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization,
etc.)etc.: 36: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D10etc.: 37: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B40etc.: 38: 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)etc.: 39: 15B33 Matrices over special rings (quaternions, finite fields, etc.)etc.: 40: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D50etc.: 41: 16E30 Homological functors on modules (Tor, Ext, etc.)etc.: 42: 16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)etc.: 43: 16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.etc.: 44: 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-
Macaulay rings, etc.)etc.: 45: 16G60 Representation type (finite, tame, wild, etc.)etc.: 46: 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)etc.: 47: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherenceetc.: 48: 16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of
inverses, etc.)etc.: 49: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C50etc.: 50: 18A22 Special properties of functors (faithful, full, etc.)etc.: 51: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products,
equalizers, kernels, ends and coends, etc.)etc.: 52: 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)etc.: 53: 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)etc.: 54: 18D35 Structured objects in a category (group objects, etc.)etc.: 55: 20D25 Special subgroups (Frattini, Fitting, etc.)etc.: 56: 20K25 Direct sums, direct products, etc.etc.: 57: 20K30 Automorphisms, homomorphisms, endomorphisms, etc.etc.: 58: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H15etc.: 59: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T50etc.: 60: 20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)etc.: 61: 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type
I representations, etc.)etc.: 62: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B10etc.: 63: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
etc.: 64: 26B20 Integral formulas (Stokes, Gauss, Green, etc.)etc.: 65: 26B35 Special properties of functions of several variables, Holder conditions, etc.etc.: 66: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exxetc.: 67: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H05etc.: 68: 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.),
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representing set functions and measuresetc.: 69: 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)etc.: 70: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B11etc.: 71: 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded
rotation, etc.)etc.: 72: 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)etc.: 73: 31A20 Boundary behavior (theorems of Fatou type, etc.)etc.: 74: 31C45 Other generalizations (nonlinear potential theory, etc.)etc.: 75: 32A25 Integral representations; canonical kernels (Szego, Bergman, etc.)etc.: 76: 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.)etc.: 77: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functionsetc.: 78: 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)etc.: 79: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald
polynomials, etc.)etc.: 80: 33E50 Special functions in characteristic p (gamma functions, etc.)etc.: 81: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W30etc.: 82: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XXetc.: 83: 34B30 Special equations (Mathieu, Hill, Bessel, etc.)etc.: 84: 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of
Abelian integrals, etc.)etc.: 85: 34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)etc.: 86: 34M50 Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)etc.: 87: 35B05 Oscillation, zeros of solutions, mean value theorems, etc.etc.: 88: 35B06 Symmetries, invariants, etc.etc.: 89: 35K70 Ultraparabolic equations, pseudoparabolic equations, etc.etc.: 90: 35Mxx Equations and systems of special type (mixed, composite, etc.)etc.: 91: 35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.etc.: 92: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J15etc.: 93: 37B05 Transformations and group actions with special properties (minimality, distality,
proximality, etc.)etc.: 94: 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)etc.: 95: 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)etc.: 96: 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)etc.: 97: 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows,
etc.)etc.: 98: 37D50 Hyperbolic systems with singularities (billiards, etc.)etc.: 99: 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures,
hierarchies (KdV, KP, Toda, etc.)etc.: 100: 37L65 Special approximation methods (nonlinear Galerkin, etc.)etc.: 101: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxxetc.: 102: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B15etc.: 103: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
[See also]30E15etc.: 104: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)etc.: 105: 42B20 Singular and oscillatory integrals (Calderon-Zygmund, etc.)etc.: 106: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions,
etc.)etc.: 107: 43A05 Measures on groups and semigroups, etc.etc.: 108: 43A07 Means on groups, semigroups, etc.; amenable groupsetc.: 109: 43A10 Measure algebras on groups, semigroups, etc.etc.: 110: 43A15 Lp-spaces and other function spaces on groups, semigroups, etc.
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etc.: 111: 43A20 L1-algebras on groups, semigroups, etc.etc.: 112: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.etc.: 113: 43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.etc.: 114: 43A35 Positive definite functions on groups, semigroups, etc.etc.: 115: 43A45 Spectral synthesis on groups, semigroups, etc.etc.: 116: 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)etc.: 117: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05etc.: 118: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent
functions, distal functions, etc.); almost automorphic functionsetc.: 119: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E45etc.: 120: 44A15 Special transforms (Legendre, Hilbert, etc.)etc.: 121: 45F10 Dual, triple, etc., integral and series equationsetc.: 122: 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz
spaces, Montel spaces, etc.)etc.: 123: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M40etc.: 124: 46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces,
quasi-Banach spaces, etc.)etc.: 125: 46A17 Bornologies and related structures; Mackey convergence, etc.etc.: 126: 46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a
metric taking values in an ordered structure more general than R, etc.)etc.: 127: 46A50 Compactness in topological linear spaces; angelic spaces, etc.etc.: 128: 46A63 Topological invariants ((DN), (Ω), etc.)etc.: 129: 46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-
Saks spaces, etc.)etc.: 130: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M35etc.: 131: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B50etc.: 132: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)etc.: 133: 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces,
Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)etc.: 134: 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)etc.: 135: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)
[See also]22D25, 47Lxxetc.: 136: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20etc.: 137: 46M18 Homological methods (exact sequences, right inverses, lifting, etc.)etc.: 138: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxxetc.: 139: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXetc.: 140: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XXetc.: 141: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)etc.: 142: 47A13 Several-variable operator theory (spectral, Fredholm, etc.)etc.: 143: 47A30 Norms (inequalities, more than one norm, etc.)etc.: 144: 47A46 Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.etc.: 145: 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions,
realizations, etc.etc.: 146: 47A56 Functions whose values are linear operators (operator and matrix valued functions, etc.,
including analytic and meromorphic ones)etc.: 147: 47A64 Operator means, shorted operators, etc.etc.: 148: 47B06 Riesz operators; eigenvalue distributions; approximation numbers, s-numbers,
Kolmogorov numbers, entropy numbers, etc. of operatorsetc.: 149: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L20etc.: 150: 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)etc.: 151: 47B20 Subnormal operators, hyponormal operators, etc.
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etc.: 152: 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)etc.: 153: 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.etc.: 154: 47B44 Accretive operators, dissipative operators, etc.etc.: 155: 47B47 Commutators, derivations, elementary operators, etc.etc.: 156: 47H06 Accretive operators, dissipative operators, etc.etc.: 157: 47H08 Measures of noncompactness and condensing mappings, K-set contractions, etc.etc.: 158: 47H09 Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.etc.: 159: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P05etc.: 160: 47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)etc.: 161: 49J30 Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls,
etc.)etc.: 162: 51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)etc.: 163: 51C05 Ring geometry (Hjelmslev, Barbilian, etc.)etc.: 164: 51Gxx Ordered geometries (ordered incidence structures, etc.)etc.: 165: 51G05 Ordered geometries (ordered incidence structures, etc.)etc.: 166: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxxetc.: 167: 52A30 Variants of convex sets (star-shaped, (m,n)-convex, etc.)etc.: 168: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxxetc.: 169: 52B12 Special polytopes (linear programming, centrally symmetric, etc.)etc.: 170: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxxetc.: 171: 52B45 Dissections and valuations (Hilbert’s third problem, etc.)etc.: 172: 53C15 General geometric structures on manifolds (almost complex, almost product structures,
etc.)etc.: 173: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)etc.: 174: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R42etc.: 175: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.)etc.: 176: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axxetc.: 177: 53C70 Direct methods (G-spaces of Busemann, etc.)etc.: 178: 54A05 Topological spaces and generalizations (closure spaces, etc.)etc.: 179: 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)etc.: 180: 54C10 Special maps on topological spaces (open, closed, perfect, etc.)etc.: 181: 54D10 Lower separation axioms (T0–T3, etc.)etc.: 182: 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise
normal, etc.)etc.: 183: 54D20 Noncompact covering properties (paracompact, Lindelof, etc.)etc.: 184: 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)etc.: 185: 54D80 Special constructions of spaces (spaces of ultrafilters, etc.)etc.: 186: 54E18 p-spaces, M -spaces, σ-spaces, etc.etc.: 187: 54E20 Stratifiable spaces, cosmic spaces, etc.etc.: 188: 54G05 Extremally disconnected spaces, F -spaces, etc.etc.: 189: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A05etc.: 190: 54H12 Topological lattices, etc. [See also]06B30, 06F30etc.: 191: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W80etc.: 192: 55P43 Spectra with additional structure (E∞, A∞, ring spectra, etc.)etc.: 193: 57M30 Wild knots and surfaces, etc., wild embeddingsetc.: 194: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B28etc.: 195: 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)etc.: 196: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G05etc.: 197: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T12etc.: 198: 58D30 Applications (in quantum mechanics (Feynman path integrals), relativity, fluid
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dynamics, etc.)etc.: 199: 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-
Shnirel′man) theory, etc.)etc.: 200: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.etc.: 201: 58E17 Pareto optimality, etc., applications to economics [See also]90C29etc.: 202: 58E20 Harmonic maps [See also]53C43, etc.etc.: 203: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R32etc.: 204: 58J60 Relations with special manifold structures (Riemannian, Finsler, etc.)etc.: 205: 60H30 Applications of stochastic analysis (to PDE, etc.)etc.: 206: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E40etc.: 207: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxxetc.: 208: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)etc.: 209: 60K10 Applications (reliability, demand theory, etc.)etc.: 210: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxxetc.: 211: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxxetc.: 212: 62H20 Measures of association (correlation, canonical correlation, etc.)etc.: 213: 62M10 Time series, auto-correlation, regression, etc. [See also]91B84etc.: 214: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30etc.: 215: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C30etc.: 216: 65M75 Probabilistic methods, particle methods, etc.etc.: 217: 65M80 Fundamental solutions, Green’s function methods, etc.etc.: 218: 65N75 Probabilistic methods, particle methods, etc.etc.: 219: 65N80 Fundamental solutions, Green’s function methods, etc.etc.: 220: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M07etc.: 221: 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic,
etc.)etc.: 222: 68N30 Mathematical aspects of software engineering (specification, verification, metrics,
requirements, etc.)etc.: 223: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axxetc.: 224: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P68etc.: 225: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q85etc.: 226: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q19etc.: 227: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q15etc.: 228: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D32etc.: 229: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B70etc.: 230: 68Q85 Models and methods for concurrent and distributed computing (process algebras,
bisimulation, transition nets, etc.)etc.: 231: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W40etc.: 232: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B35etc.: 233: 68T20 Problem solving (heuristics, search strategies, etc.)etc.: 234: 68T35 Languages and software systems (knowledge-based systems, expert systems, etc.)etc.: 235: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)
[See also]68M11etc.: 236: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx
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etc.: 237: 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)etc.: 238: 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)etc.: 239: 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series,
etc.)etc.: 240: 74K10 Rods (beams, columns, shafts, arches, rings, etc.)etc.: 241: 76D07 Stokes and related (Oseen, etc.) flowsetc.: 242: 80A22 Stefan problems, phase changes, etc. [See also]74Nxxetc.: 243: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.etc.: 244: 81Q37 Quantum dots, waveguides, ratchets, etc.etc.: 245: 81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.etc.: 246: 81S30 Phase-space methods including Wigner distributions, etc.etc.: 247: 81T40 Two-dimensional field theories, conformal field theories, etc.etc.: 248: 81U20 S-matrix theory, etc.etc.: 249: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphsetc.: 250: 82B21 Continuum models (systems of particles, etc.)etc.: 251: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C41etc.: 252: 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)etc.: 253: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T80etc.: 254: 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphsetc.: 255: 82C21 Dynamic continuum models (systems of particles, etc.)etc.: 256: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H10etc.: 257: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G50etc.: 258: 82C44 Dynamics of disordered systems (random Ising systems, etc.)etc.: 259: 82C80 Numerical methods (Monte Carlo, series resummation, etc.)etc.: 260: 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)etc.: 261: 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)etc.: 262: 83C75 Space-time singularities, cosmic censorship, etc.etc.: 263: 90C08 Special problems of linear programming (transportation, multi-index, etc.)etc.: 264: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N75etc.: 265: 91B26 Market models (auctions, bargaining, bidding, selling, etc.)etc.: 266: 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)etc.: 267: 92C17 Cell movement (chemotaxis, etc.)etc.: 268: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A30etc.: 269: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)etc.: 270: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A32etc.: 271: 93A30 Mathematical modeling (models of systems, model-matching, etc.)etc.: 272: 93B51 Design techniques (robust design, computer-aided design, etc.)etc.: 273: 93C83 Control problems involving computers (process control, etc.)etc.: 274: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q05etc.: 275: 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp, lp, etc.)etc.: 276: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U10etc.: 277: 94A12 Signal theory (characterization, reconstruction, filtering, etc.)etc.: 278: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius,
etc.) [See also]11H31, 11H71i.e.: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05i.e.: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05i.e.: 3: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxxp.i.: 1: 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
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00B60: 1: 01A75 Collected or selected works; reprintings or translations of classics [See also]00B6001-00: 1: 97A50 Bibliographies [See also]01-00
01-XX: 1: 97A30 History of mathematics and mathematics education [See also]01-XX01A75: 1: 00B60 Collections of reprinted articles [See also]01A7503-XX: 1: 18A15 Foundations, relations to logic and deductive systems [See also]03-XX03-XX: 2: 18B05 Category of sets, characterizations [See also]03-XX03A05: 1: 00A30 Philosophy of mathematics [See also]03A0503B25: 1: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7003B25: 1: 11U05 Decidability [See also]03B2503B25: 2: 12L05 Decidability [See also]03B2503B30: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S3003B30: 1: 03F35 Second- and higher-order arithmetic and fragments [See also]03B3003B35: 1: 68T15 Theorem proving (deduction, resolution, etc.) [See also]03B3503B40: 1: 68N18 Functional programming and lambda calculus [See also]03B4003B42: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B4803B45: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E2503B47: 1: 03F52 Linear logic and other substructural logics [See also]03B4703B52: 1: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1003B52: 2: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1003B65: 1: 91F20 Linguistics [See also]03B65, 68T5003B65: 1: 68T50 Natural language processing [See also]03B6503B70: 1: 68Q55 Semantics [See also]03B70, 06B35, 18C5003B70: 1: 68Q60 Specification and verification (program logics, model checking, etc.) [See also]03B7003C05: 1: 18C05 Equational categories [See also]03C05, 08C0503C05: 1: 08Axx Algebraic structures [See also]03C0503C05: 2: 08Bxx Varieties [See also]03C0503C13: 1: 68Q19 Descriptive complexity and finite models [See also]03C1303C20: 1: 11U07 Ultraproducts [See also]03C2003C20: 2: 12L10 Ultraproducts [See also]03C2003C45: 1: 20F11 Groups of finite Morley rank [See also]03C45, 03C6003C45: 1: 03C48 Abstract elementary classes and related topics [See also]03C4503C48: 1: 03C45 Classification theory, stability and related concepts [See also]03C4803C57: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionistic
and similar approaches see 03F5503C60: 1: 03C98 Applications of model theory [See also]03C6003C60: 2: 12L12 Model theory [See also]03C6003C62: 1: 03Hxx Nonstandard models [See also]03C6203Cxx: 1: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C6003Cxx: 2: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxx03Cxx: 3: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxx03Cxx: 1: 11U09 Model theory [See also]03Cxx03Cxx: 2: 16B70 Applications of logic [See also]03Cxx03D05: 1: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxx03D05: 2: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T5003D05: 3: 68Q45 Formal languages and automata [See also]03D05, 68Q70, 94A4503D10: 1: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P6803D15: 1: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q1903D32: 1: 68Q30 Algorithmic information theory (Kolmogorov complexity, etc.) [See also]03D3203D40: 1: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F1003D40: 2: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R1503D40: 3: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F10
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03D45: 1: 03C57 Effective and recursion-theoretic model theory [See also]03D4503D45: 2: 03F65 Other constructive mathematics [See also]03D4503E15: 1: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H0503E15: 2: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H0503E15: 3: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
[See also]03E15, 26A21, 28A0503E35: 1: 54A35 Consistency and independence results [See also]03E3503E50: 1: 03E57 Generic absoluteness and forcing axioms [See also]03E5003E57: 1: 03E50 Continuum hypothesis and Martin’s axiom [See also]03E5703E72: 1: 26E50 Fuzzy real analysis [See also]03E72, 28E1003E72: 2: 28E10 Fuzzy measure theory [See also]03E72, 26E50, 94D0503E72: 1: 20N25 Fuzzy groups [See also]03E7203E72: 2: 46S40 Fuzzy functional analysis [See also]03E7203E72: 3: 47S40 Fuzzy operator theory [See also]03E7203E72: 4: 54A40 Fuzzy topology [See also]03E7203Exx: 1: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D8003F35: 1: 03B30 Foundations of classical theories (including reverse mathematics) [See also]03F3503F45: 1: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F3503F60: 1: 26E40 Constructive real analysis [See also]03F6003F60: 2: 46S30 Constructive functional analysis [See also]03F6003F60: 3: 47S30 Constructive operator theory [See also]03F6003G05: 1: 06Exx Boolean algebras (Boolean rings) [See also]03G0503G10: 1: 06Bxx Lattices [See also]03G1003G12: 1: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P1003G12: 2: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C1503G20: 1: 06D25 Post algebras [See also]03G2003G20: 2: 06D30 De Morgan algebras, Lukasiewicz algebras [See also]03G2003G25: 1: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F4503G25: 1: 06D20 Heyting algebras [See also]03G2503G25: 2: 06F35 BCK-algebras, BCI-algebras [See also]03G2503G30: 1: 18B25 Topoi [See also]03G3003G30: 2: 18C10 Theories (e.g. algebraic theories), structure, and semantics [See also]03G3003H05: 1: 26E35 Nonstandard analysis [See also]03H05, 28E05, 54J0503H05: 2: 28E05 Nonstandard measure theory [See also]03H05, 26E3503H05: 1: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H0503H05: 2: 46S20 Nonstandard functional analysis [See also]03H0503H05: 3: 47S20 Nonstandard operator theory [See also]03H0503H05: 4: 54Jxx Nonstandard topology [See also]03H0503H05: 5: 54J05 Nonstandard topology [See also]03H0503H15: 1: 11U10 Nonstandard arithmetic [See also]03H1503H15: 2: 12L15 Nonstandard arithmetic [See also]03H1503Hxx: 1: 03C62 Models of arithmetic and set theory [See also]03Hxx05A10: 1: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A3005A17: 1: 11P81 Elementary theory of partitions [See also]05A1705B05: 1: 51E05 General block designs [See also]05B0505B10: 1: 11B13 Additive bases, including sumsets [See also]05B1005B25: 1: 51D20 Combinatorial geometries [See also]05B25, 05B3505B30: 1: 05C51 Graph designs and isomomorphic decomposition [See also]05B3005B30: 2: 51E30 Other finite incidence structures [See also]05B3005B35: 1: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxx05B35: 1: 51D25 Lattices of subspaces [See also]05B35
445 Run: December 14, 2009
Mathematics Subject Classification 2010
05B40: 1: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C1705B40: 2: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H3105B40: 3: 52C17 Packing and covering in n dimensions [See also]05B40, 11H3105B45: 1: 52C20 Tilings in 2 dimensions [See also]05B45, 51M2005B45: 2: 52C22 Tilings in n dimensions [See also]05B45, 51M2005Bxx: 1: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX05Bxx: 1: 20N05 Loops, quasigroups [See also]05Bxx05Bxx: 2: 51E20 Combinatorial structures in finite projective spaces [See also]05Bxx05Bxx: 3: 62Kxx Design of experiments [See also]05Bxx05Bxx: 4: 94C30 Applications of design theory [See also]05Bxx05C12: 1: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxx05C25: 1: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxx05C55: 1: 05D10 Ramsey theory [See also]05C5505C57: 1: 91A43 Games involving graphs [See also]05C5705Cxx: 1: 68R10 Graph theory (including graph drawing) [See also]05Cxx, 90B10, 90B35, 90C3505Cxx: 2: 94C15 Applications of graph theory [See also]05Cxx, 68R1005Cxx: 1: 52B05 Combinatorial properties (number of faces, shortest paths, etc.) [See also]05Cxx05Cxx: 2: 57M15 Relations with graph theory [See also]05Cxx05D10: 1: 05C55 Generalized Ramsey theory [See also]05D1005E30: 1: 05C07 Vertex degrees [See also]05E3006-XX: 1: 18B35 Preorders, orders and lattices (viewed as categories) [See also]06-XX06A11: 1: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxx06B25: 1: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R1506B30: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5506B30: 2: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H1206B30: 3: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F3006B30: 4: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F3006B30: 5: 54H12 Topological lattices, etc. [See also]06B30, 06F3006Bxx: 1: 03G10 Lattices and related structures [See also]06Bxx06C15: 1: 03G12 Quantum logic [See also]06C15, 81P1006Cxx: 1: 51D30 Continuous geometries and related topics [See also]06Cxx06D25: 1: 03G20 Lukasiewicz and Post algebras [See also]06D25, 06D3006E15: 1: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A3006E30: 1: 94C10 Switching theory, application of Boolean algebra; Boolean functions [See also]06E3006Exx: 1: 03G05 Boolean algebras [See also]06Exx06F20: 1: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B4206F25: 1: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxx06F25: 1: 13J25 Ordered rings [See also]06F2506F30: 1: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H1208Axx: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C0508C10: 1: 03C60 Model-theoretic algebra [See also]08C10, 12Lxx, 13L0511-04: 1: 11Yxx Computational number theory [See also]11-04
11A55: 1: 11J70 Continued fractions and generalizations [See also]11A55, 11K5011A55: 2: 11K50 Metric theory of continued fractions [See also]11A55, 11J7011A55: 3: 30B70 Continued fractions [See also]11A55, 40A1511A63: 1: 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points,
etc. [See also]11A6311B13: 1: 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also]11B1311B25: 1: 11N13 Primes in progressions [See also]11B2511B65: 1: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxx11C08: 1: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M1011C08: 2: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B25
446 Run: December 14, 2009
Mathematics Subject Classification 2010
11C20: 1: 15B36 Matrices of integers [See also]11C2011D75: 1: 11J25 Diophantine inequalities [See also]11D7511D85: 1: 11P55 Applications of the Hardy-Littlewood method [See also]11D8511Dxx: 1: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxx11Dxx: 2: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxx11Dxx: 3: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxx11Dxx: 4: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxx11Dxx: 5: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxx11E81: 1: 19G12 Witt groups of rings [See also]11E8111E81: 2: 19G24 L-theory of group rings [See also]11E8111Exx: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6711Exx: 1: 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
[See also]11Exx11Exx: 2: 19Gxx K-theory of forms [See also]11Exx11F06: 1: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F2011F06: 2: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxx11F41: 1: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G1811Fxx: 1: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E5511Fxx: 2: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E5011Fxx: 3: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxx11Fxx: 4: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F3511Fxx: 1: 11N75 Applications of automorphic functions and forms to multiplicative problems
[See also]11Fxx11G05: 1: 14H52 Elliptic curves [See also]11G05, 11G07, 14Kxx11G15: 1: 14K10 Algebraic moduli, classification [See also]11G1511G15: 2: 14K22 Complex multiplication [See also]11G1511G40: 1: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G1011G40: 1: 14G10 Zeta-functions and related questions [See also]11G40 (Birch-Swinnerton-Dyer
conjecture)11G42: 1: 14J33 Mirror symmetry [See also]11G42, 53D3711G45: 1: 19F05 Generalized class field theory [See also]11G4511G50: 1: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P3011G50: 2: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G4011Gxx: 1: 11Dxx Diophantine equations [See also]11Gxx, 14Gxx11H06: 1: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P2111H06: 2: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P2111H31: 1: 05B40 Packing and covering [See also]11H31, 52C15, 52C1711H31: 2: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
[See also]11H31, 11H7111Hxx: 1: 52C10 Erdos problems and related topics of discrete geometry [See also]11Hxx11J25: 1: 11D75 Diophantine inequalities [See also]11J2511J71: 1: 11K06 General theory of distribution modulo 1 [See also]11J7111Jxx: 1: 11K60 Diophantine approximation [See also]11Jxx11K06: 1: 11J71 Distribution modulo one [See also]11K0611K50: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A1511K50: 2: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1011K60: 1: 11Jxx Diophantine approximation, transcendental number theory [See also]11K6011Kxx: 1: 37A45 Relations with number theory and harmonic analysis [See also]11Kxx11M41: 1: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F2711M41: 2: 11S40 Zeta functions and L-functions [See also]11M41, 19F2711M41: 3: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XX11N05: 1: 11R44 Distribution of prime ideals [See also]11N05
447 Run: December 14, 2009
Mathematics Subject Classification 2010
11N13: 1: 11B25 Arithmetic progressions [See also]11N1311N99: 1: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
[See also]11N99, 28Dxx11Nxx: 1: 11K38 Irregularities of distribution, discrepancy [See also]11Nxx11Nxx: 2: 11K65 Arithmetic functions [See also]11Nxx11Nxx: 3: 11R47 Other analytic theory [See also]11Nxx11P21: 1: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C0711P55: 1: 11D72 Equations in many variables [See also]11P5511P55: 2: 11D85 Representation problems [See also]11P5511P81: 1: 05A17 Partitions of integers [See also]11P81, 11P82, 11P8311R27: 1: 11G16 Elliptic and modular units [See also]11R2711R29: 1: 13C20 Class groups [See also]11R2911R37: 1: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F0511R37: 1: 19F15 Symbols and arithmetic [See also]11R3711R39: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4511R52: 1: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxx11R52: 2: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxx11R56: 1: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B0511R58: 1: 14H05 Algebraic functions; function fields [See also]11R5811R70: 1: 19Fxx K-theory in number theory [See also]11R70, 11S7011S15: 1: 14E22 Ramification problems [See also]11S1511S45: 1: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxx11S80: 1: 12H25 p-adic differential equations [See also]11S80, 14G2011S82: 1: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A4511T71: 1: 94A60 Cryptography [See also]11T71, 14G50, 68P25, 81P9411T71: 2: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G5011T71: 3: 94B40 Arithmetic codes [See also]11T71, 14G5011U05: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F1011U10: 1: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L0511Yxx: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1012D10: 1: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H0512D15: 1: 13J30 Real algebra [See also]12D15, 14Pxx12D15: 2: 14P05 Real algebraic sets [See also]12D15, 13J3012Dxx: 1: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exx12E15: 1: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A3012F10: 1: 20B27 Infinite automorphism groups [See also]12F1012G05: 1: 14F22 Brauer groups of schemes [See also]12G05, 16K5012G05: 2: 16K50 Brauer groups [See also]12G05, 14F2212Gxx: 1: 11R34 Galois cohomology [See also]12Gxx, 19A3112Gxx: 2: 11S25 Galois cohomology [See also]12Gxx, 16H0512H05: 1: 13Nxx Differential algebra [See also]12H05, 14F1012J15: 1: 11R80 Totally real fields [See also]12J1512J20: 1: 13A18 Valuations and their generalizations [See also]12J2012J25: 1: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P0512J25: 1: 26E30 Non-Archimedean analysis [See also]12J2512J25: 2: 30G06 Non-Archimedean function theory [See also]12J25; nonstandard function theory
[See also]03H0512Jxx: 1: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W8012K05: 1: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y3012K05: 1: 16Y30 Near-rings [See also]12K0512K10: 1: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B2012K10: 2: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B20
448 Run: December 14, 2009
Mathematics Subject Classification 2010
12K10: 1: 16Y60 Semirings [See also]12K1012Kxx: 1: 51A25 Algebraization [See also]12Kxx, 20N0512Y05: 1: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W3012Y05: 1: 13P05 Polynomials, factorization [See also]12Y0513-XX: 1: 32Bxx Local analytic geometry [See also]13-XX and 14-XX13-XX: 1: 14A05 Relevant commutative algebra [See also]13-XX13A05: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
[See also]13A05, 14M0513A18: 1: 12J20 General valuation theory [See also]13A1813A18: 2: 13F30 Valuation rings [See also]13A1813A35: 1: 13B22 Integral closure of rings and ideals [See also]13A35; integrally closed rings, related rings
(Japanese, etc.)13A50: 1: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M1713A50: 2: 14R20 Group actions on affine varieties [See also]13A50, 14L3013A50: 3: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L2413A50: 1: 14L24 Geometric invariant theory [See also]13A5013B22: 1: 13A35 Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p;
tight closure [See also]13B2213B30: 1: 16S85 Rings of fractions and localizations [See also]13B3013B35: 1: 13J10 Complete rings, completion [See also]13B3513B40: 1: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D1013B40: 1: 13J15 Henselian rings [See also]13B4013B40: 2: 14B25 Local structure of morphisms: etale, flat, etc. [See also]13B4013C10: 1: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D5013C10: 1: 19A13 Stability for projective modules [See also]13C1013C12: 1: 13D30 Torsion theory [See also]13C12, 18E4013C40: 1: 14M06 Linkage [See also]13C4013C40: 2: 14M10 Complete intersections [See also]13C4013C40: 3: 14M12 Determinantal varieties [See also]13C4013D02: 1: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E2513D05: 1: 18G20 Homological dimension [See also]13D05, 16E1013D10: 1: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxx13D10: 2: 16S80 Deformations of rings [See also]13D10, 14D1513D10: 3: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H1513D10: 1: 14B10 Infinitesimal methods [See also]13D1013D15: 1: 18F30 Grothendieck groups [See also]13D15, 16E20, 19Axx13D15: 2: 19Axx Grothendieck groups and K0 [See also]13D15, 18F3013D15: 3: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E2013D30: 1: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxx13D30: 2: 18E40 Torsion theories, radicals [See also]13D30, 16S9013D45: 1: 14B15 Local cohomology [See also]13D45, 32C3613Dxx: 1: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx13Dxx: 1: 13P20 Computational homological algebra [See also]13Dxx13Dxx: 2: 14Fxx (Co)homology theory [See also]13Dxx13F15: 1: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H1013F15: 1: 13A05 Divisibility; factorizations [See also]13F1513F20: 1: 11C08 Polynomials [See also]13F2013F20: 2: 14R15 Jacobian problem [See also]13F2013F25: 1: 13J05 Power series rings [See also]13F2513H10: 1: 13C14 Cohen-Macaulay modules [See also]13H1013H15: 1: 14C17 Intersection theory, characteristic classes, intersection multiplicities [See also]13H1513Hxx: 1: 14H20 Singularities, local rings [See also]13Hxx, 14B0513J05: 1: 13F25 Formal power series rings [See also]13J0513J10: 1: 13B35 Completion [See also]13J1013J15: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
449 Run: December 14, 2009
Mathematics Subject Classification 2010
14B2513Jxx: 1: 16W60 Valuations, completions, formal power series and related constructions [See also]13Jxx13N10: 1: 16S32 Rings of differential operators [See also]13N10, 32C3813Nxx: 1: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C3813Nxx: 1: 12H05 Differential algebra [See also]13Nxx14-XX: 1: 11R58 Arithmetic theory of algebraic function fields [See also]14-XX14-XX: 2: 51H30 Geometries with algebraic manifold structure [See also]14-XX14A22: 1: 32C11 Complex supergeometry [See also]14A22, 14M30, 58A5014A22: 2: 58A50 Supermanifolds and graded manifolds [See also]14A22, 32C1114A22: 1: 16S38 Rings arising from non-commutative algebraic geometry [See also]14A2214B05: 1: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S4514B05: 2: 14J17 Singularities [See also]14B05, 14E1514B07: 1: 32S30 Deformations of singularities; vanishing cycles [See also]14B0714B10: 1: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxx14B15: 1: 13D45 Local cohomology [See also]14B1514C17: 1: 13H15 Multiplicity theory and related topics [See also]14C1714C21: 1: 53A60 Geometry of webs [See also]14C21, 20N0514C25: 1: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F4214C30: 1: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L1014C30: 2: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D0714C30: 3: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S3514C30: 1: 32J25 Transcendental methods of algebraic geometry [See also]14C3014C35: 1: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D5014C35: 1: 19E08 K-theory of schemes [See also]14C3514D05: 1: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K3014D05: 2: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S4014D06: 1: 14R25 Affine fibrations [See also]14D0614D07: 1: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecture14D15: 1: 14B07 Deformations of singularities [See also]14D15, 32S3014D20: 1: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F0514D20: 2: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxx14D24: 1: 22E57 Geometric Langlands program: representation-theoretic aspects [See also]14D2414E08: 1: 14M20 Rational and unirational varieties [See also]14E0814E15: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxx14E15: 1: 32S15 Equisingularity (topological and analytic) [See also]14E1514E15: 2: 32S20 Global theory of singularities; cohomological properties [See also]14E1514E15: 3: 32S45 Modifications; resolution of singularities [See also]14E1514E20: 1: 14H30 Coverings, fundamental group [See also]14E20, 14F3514F05: 1: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N3014F05: 2: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N3014F05: 3: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx14F10: 1: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J1514F20: 1: 18F10 Grothendieck topologies [See also]14F2014F22: 1: 12G05 Galois cohomology [See also]14F22, 16Hxx, 16K5014Fxx: 1: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N3014Fxx: 1: 19E20 Relations with cohomology theories [See also]14Fxx14Fxx: 2: 58A12 de Rham theory [See also]14Fxx14G10: 1: 11G40 L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
[See also]14G10
450 Run: December 14, 2009
Mathematics Subject Classification 2010
14G15: 1: 11G25 Varieties over finite and local fields [See also]14G15, 14G2014G20: 1: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E5014G20: 2: 11F85 p-adic theory, local fields [See also]14G20, 22E5014G20: 3: 11G07 Elliptic curves over local fields [See also]14G20, 14H5214G25: 1: 11G35 Varieties over global fields [See also]14G2514G35: 1: 11G18 Arithmetic aspects of modular and Shimura varieties [See also]14G3514G40: 1: 11G50 Heights [See also]14G40, 37P3014H15: 1: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G1514H15: 2: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J1514H15: 3: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxx14H25: 1: 11G20 Curves over finite and local fields [See also]14H2514H25: 2: 11G30 Curves of arbitrary genus or genus 6= 1 over global fields [See also]14H2514H30: 1: 14E20 Coverings [See also]14H3014H30: 2: 14F35 Homotopy theory; fundamental groups [See also]14H3014H40: 1: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G2014H42: 1: 14K25 Theta functions [See also]14H4214H52: 1: 11G05 Elliptic curves over global fields [See also]14H5214H60: 1: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M2014H70: 1: 37K20 Relations with algebraic geometry, complex analysis, special functions [See also]14H7014J17: 1: 32S05 Local singularities [See also]14J1714J17: 2: 32S25 Surface and hypersurface singularities [See also]14J1714J20: 1: 11F41 Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their
modular and automorphic forms; Hilbert modular surfaces [See also]14J2014J30: 1: 32Q25 Calabi-Yau theory [See also]14J3014J33: 1: 11G42 Arithmetic mirror symmetry [See also]14J3314J33: 2: 53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category
[See also]14J3314Jxx: 1: 57N13 Topology of E4, 4-manifolds [See also]14Jxx, 32Jxx14K22: 1: 11G15 Complex multiplication and moduli of abelian varieties [See also]14K2214K25: 1: 14H42 Theta functions; Schottky problem [See also]14K25, 32G2014Kxx: 1: 11G10 Abelian varieties of dimension > 1 [See also]14Kxx14L05: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9014L05: 1: 11G09 Drinfel′d modules; higher-dimensional motives, etc. [See also]14L0514L05: 2: 11S31 Class field theory; p-adic formal groups [See also]14L0514L24: 1: 13A50 Actions of groups on commutative rings; invariant theory [See also]14L2414Lxx: 1: 11E57 Classical groups [See also]14Lxx, 20Gxx14Lxx: 2: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxx
14M05: 1: 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also]14M0514M06: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,
14M1214M15: 1: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T1514M15: 1: 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians,
Veronesians and their generalizations) [See also]14M1514M17: 1: 32M10 Homogeneous complex manifolds [See also]14M17, 57T1514M17: 1: 32M12 Almost homogeneous manifolds and spaces [See also]14M1714M20: 1: 14E08 Rationality questions [See also]14M2014N35: 1: 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also]14N3514Nxx: 1: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C8014Nxx: 1: 51N35 Questions of classical algebraic geometry [See also]14Nxx14P15: 1: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P2014P15: 1: 32B20 Semi-analytic sets and subanalytic sets [See also]14P1514P20: 1: 58A07 Real-analytic and Nash manifolds [See also]14P20, 32C0714Pxx: 1: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A0714Pxx: 1: 26C15 Rational functions [See also]14Pxx
451 Run: December 14, 2009
Mathematics Subject Classification 2010
14Qxx: 1: 13Pxx Computational aspects and applications [See also]14Qxx, 68W3015-XX: 1: 16S50 Endomorphism rings; matrix rings [See also]15-XX15A12: 1: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A6015A30: 1: 20Hxx Other groups of matrices [See also]15A3015A63: 1: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A6615B36: 1: 11C20 Matrices, determinants [See also]15B3615B52: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx16D50: 1: 16L60 Quasi-Frobenius rings [See also]16D5016D60: 1: 16N60 Prime and semiprime rings [See also]16D60, 16U1016E20: 1: 19-XX K-theory [See also]16E20, 18F2516E50: 1: 06E20 Ring-theoretic properties [See also]16E50, 16G3016G50: 1: 16D80 Other classes of modules and ideals [See also]16G5016Gxx: 1: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and duality16Hxx: 1: 16G30 Representations of orders, lattices, algebras over commutative rings [See also]16Hxx16L60: 1: 16D50 Injective modules, self-injective rings [See also]16L6016S30: 1: 17B35 Universal enveloping (super)algebras [See also]16S3016S32: 1: 13N10 Rings of differential operators and their modules [See also]16S32, 32C3816S34: 1: 20C05 Group rings of finite groups and their modules [See also]16S3416S34: 2: 20C07 Group rings of infinite groups and their modules [See also]16S3416S36: 1: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y6016S38: 1: 14A22 Noncommutative algebraic geometry [See also]16S3816S40: 1: 16T05 Hopf algebras and their applications [See also]16S40, 57T0516S50: 1: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxx16S85: 1: 13B30 Rings of fractions and localization [See also]16S8516T05: 1: 16S40 Smash products of general Hopf actions [See also]16T0516T05: 2: 57T05 Hopf algebras [See also]16T0516T20: 1: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B2316T20: 2: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R5016T20: 3: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B3716U20: 1: 16P50 Localization and Noetherian rings [See also]16U2016U20: 2: 16P60 Chain conditions on annihilators and summands: Goldie-type conditions
[See also]16U20, Krull dimension16W10: 1: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C5016W10: 1: 17C50 Jordan structures associated with other structures [See also]16W1016W10: 2: 46Kxx Topological (rings and) algebras with an involution [See also]16W1016W50: 1: 13A02 Graded rings [See also]16W5016W60: 1: 13Jxx Topological rings and modules [See also]16W60, 16W8016Y30: 1: 12K05 Near-fields [See also]16Y3016Y60: 1: 12K10 Semifields [See also]16Y6017A70: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A6617B10: 1: 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules,
etc.) [See also]17B1017B37: 1: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R5017B45: 1: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D3517B60: 1: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxx17B65: 1: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H0517B65: 2: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H2017B65: 3: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,
452 Run: December 14, 2009
Mathematics Subject Classification 2010
22E7017Bxx: 1: 81R12 Relations with integrable systems [See also]17Bxx, 37J3518-XX: 1: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XX18-XX: 2: 46Mxx Methods of category theory in functional analysis [See also]18-XX18A30: 1: 08B25 Products, amalgamated products, and other kinds of limits and colimits [See also]18A3018B15: 1: 18E20 Embedding theorems [See also]18B1518B20: 1: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M3518B25: 1: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C1018B30: 1: 54B30 Categorical methods [See also]18B3018B35: 1: 06-XX Order, lattices, ordered algebraic structures [See also]18B3518C05: 1: 08C05 Categories of algebras [See also]18C0518C50: 1: 68Q65 Abstract data types; algebraic specification [See also]18C5018D10: 1: 19D23 Symmetric monoidal categories [See also]18D1018D50: 1: 55P48 Loop space machines, operads [See also]18D5018E20: 1: 18B15 Embedding theorems, universal categories [See also]18E2018E30: 1: 18G35 Chain complexes [See also]18E30, 55U1518F15: 1: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2518F15: 1: 57Pxx Generalized manifolds [See also]18F1518F20: 1: 55N30 Sheaf cohomology [See also]18F20, 32C35, 32L1018F20: 1: 54B40 Presheaves and sheaves [See also]18F2018F25: 1: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J2218F30: 1: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D5018G40: 1: 55Txx Spectral sequences [See also]18G40, 55R2018G55: 1: 57T30 Bar and cobar constructions [See also]18G55, 55Uxx18G60: 1: 19D55 K-theory and homology; cyclic homology and cohomology [See also]18G6018Gxx: 1: 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and
derived functors for triples [See also]18Gxx18Gxx: 2: 55Uxx Applied homological algebra and category theory [See also]18Gxx19A13: 1: 13C10 Projective and free modules and ideals [See also]19A1319A13: 2: 16D40 Free, projective, and flat modules and ideals [See also]19A1319A22: 1: 20Cxx Representation theory of groups [See also]19A22 (for representation rings and Burnside
rings)19B10: 1: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B1419B28: 1: 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
[See also]19B2819D23: 1: 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories,
braided categories [See also]19D2319D55: 1: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J2219D55: 2: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxx19E15: 1: 14F42 Motivic cohomology; motivic homotopy theory [See also]19E1519E20: 1: 14C40 Riemann-Roch theorems [See also]19E20, 19L1019Exx: 1: 14C35 Applications of methods of algebraic K-theory [See also]19Exx19Fxx: 1: 11R70 K-theory of global fields [See also]19Fxx19Fxx: 2: 11S70 K-theory of local fields [See also]19Fxx19G12: 1: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G2419Gxx: 1: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A6319J25: 1: 57R67 Surgery obstructions, Wall groups [See also]19J2519K56: 1: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L8019K56: 2: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M2019L20: 1: 55Q50 J-morphism [See also]19L2019L47: 1: 55N91 Equivariant homology and cohomology [See also]19L4719L47: 2: 55P91 Equivariant homotopy theory [See also]19L4719L47: 3: 55Q91 Equivariant homotopy groups [See also]19L4719L47: 4: 55R91 Equivariant fiber spaces and bundles [See also]19L4719L47: 5: 55S91 Equivariant operations and obstructions [See also]19L47
453 Run: December 14, 2009
Mathematics Subject Classification 2010
20Axx: 1: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,20L05, 20Mxx
20C05: 1: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial rings20C10: 1: 11R33 Integral representations related to algebraic numbers; Galois module structure of rings
of integers [See also]20C1020C30: 1: 05E10 Combinatorial aspects of representation theory [See also]20C3020C35: 1: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
[See also]20C35, 22E7020D05: 1: 20E32 Simple groups [See also]20D0520D10: 1: 20F16 Solvable groups, supersolvable groups [See also]20D1020D10: 2: 20F17 Formations of groups, Fitting classes [See also]20D1020D15: 1: 20F18 Nilpotent groups [See also]20D1520E36: 1: 20F28 Automorphism groups of groups [See also]20E3620F17: 1: 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks
[See also]20F1720F22: 1: 20E15 Chains and lattices of subgroups, subnormal subgroups [See also]20F2220F34: 1: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D0520F60: 1: 06F15 Ordered groups [See also]20F6020F65: 1: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) [See also]20F6520F65: 2: 20E08 Groups acting on trees [See also]20F6520G05: 1: 22E50 Representations of Lie and linear algebraic groups over local fields [See also]20G0520G05: 2: 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings
[See also]20G0520G10: 1: 11E72 Galois cohomology of linear algebraic groups [See also]20G1020Gxx: 1: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N3020Gxx: 2: 51N30 Geometry of classical groups [See also]20Gxx, 14L3520Gxx: 1: 20D06 Simple groups: alternating groups and groups of Lie type [See also]20Gxx20H05: 1: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E4020H05: 1: 19B37 Congruence subgroup problems [See also]20H0520H05: 2: 51F20 Congruence and orthogonality [See also]20H0520H05: 3: 51F25 Orthogonal and unitary groups [See also]20H0520H10: 1: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F5520H10: 1: 30F40 Kleinian groups [See also]20H1020Hxx: 1: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxx20J05: 1: 20E22 Extensions, wreath products, and other compositions [See also]20J05
20M10: 1: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A2620M20: 1: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxx20M25: 1: 16S36 Ordinary and skew polynomial rings and semigroup rings [See also]20M2520M35: 1: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q4520Mxx: 1: 06F05 Ordered semigroups and monoids [See also]20Mxx22-XX: 1: 54H10 Topological representations of algebraic systems [See also]22-XX22A05: 1: 20K45 Topological methods [See also]22A05, 22B0522A05: 1: 54H11 Topological groups [See also]22A0522A10: 1: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E4522A22: 1: 58H05 Pseudogroups and differentiable groupoids [See also]22A22, 22E6522Axx: 1: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A0522D25: 1: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)
[See also]22D25, 47Lxx22D40: 1: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axx22E10: 1: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T1522E10: 1: 32M05 Complex Lie groups, automorphism groups acting on complex spaces [See also]22E1022E40: 1: 20F55 Reflection and Coxeter groups [See also]22E40, 51F1522E45: 1: 43A90 Spherical functions [See also]22E45, 22E46, 33C55
454 Run: December 14, 2009
Mathematics Subject Classification 2010
22E45: 1: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V8022E57: 1: 14D24 Geometric Langlands program: algebro-geometric aspects [See also]22E5722E65: 1: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D0522E65: 2: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S0522E65: 1: 17B65 Infinite-dimensional Lie (super)algebras [See also]22E6522Exx: 1: 43A80 Analysis on other specific Lie groups [See also]22Exx22Fxx: 1: 37A17 Homogeneous flows [See also]22Fxx26-XX: 1: 54C30 Real-valued functions [See also]26-XX26A03: 1: 54F50 Spaces of dimension ≤ 1; curves, dendrites [See also]26A0326A18: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX26A18: 2: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XX26A21: 1: 54C50 Special sets defined by functions [See also]26A2126A24: 1: 28A15 Abstract differentiation theory, differentiation of set functions [See also]26A2426A48: 1: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also]26A4826A51: 1: 39B22 Equations for real functions [See also]26A51, 26B2526A51: 2: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxx26B15: 1: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q1526B15: 2: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q2026B15: 1: 51M25 Length, area and volume [See also]26B1526B25: 1: 52A41 Convex functions and convex programs [See also]26B25, 90C2526D20: 1: 34A40 Differential inequalities [See also]26D2026E25: 1: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B1426E25: 2: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C0626E35: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0526Exx: 1: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G0528-XX: 1: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txx28-XX: 1: 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also]28-XX28A05: 1: 03E15 Descriptive set theory [See also]28A05, 54H0528A15: 1: 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-
value theorems [See also]28A1528A33: 1: 46E27 Spaces of measures [See also]28A33, 46Gxx28A51: 1: 46G15 Functional analytic lifting theory [See also]28A5128A75: 1: 26B15 Integration: length, area, volume [See also]28A75, 51M2528A75: 2: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C3528B20: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxx28B20: 2: 47H04 Set-valued operators [See also]28B20, 54C60, 58C0628B20: 3: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C0628B20: 1: 54C65 Selections [See also]28B2028Bxx: 1: 46G10 Vector-valued measures and integration [See also]28Bxx, 46B2228C20: 1: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T1228C20: 1: 60B11 Probability theory on linear topological spaces [See also]28C2028Cxx: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XX28Cxx: 2: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T1228Cxx: 1: 58C35 Integration on manifolds; measures on manifolds [See also]28Cxx28Dxx: 1: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H2028Dxx: 2: 47A35 Ergodic theory [See also]28Dxx, 37Axx28Dxx: 3: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A3528Dxx: 4: 54H20 Topological dynamics [See also]28Dxx, 37Bxx
455 Run: December 14, 2009
Mathematics Subject Classification 2010
28Dxx: 5: 60Fxx Limit theorems [See also]28Dxx, 60B1228Dxx: 1: 22D40 Ergodic theory on groups [See also]28Dxx28Dxx: 2: 37Axx Ergodic theory [See also]28Dxx30B70: 1: 40A15 Convergence and divergence of continued fractions [See also]30B7030Bxx: 1: 11N30 Turan theory [See also]30Bxx30C85: 1: 31A15 Potentials and capacity, harmonic measure, extremal length [See also]30C8530D05: 1: 37Fxx Complex dynamical systems [See also]30D05, 32H5030D05: 1: 39Bxx Functional equations and inequalities [See also]30D0530D05: 2: 39B32 Equations for complex functions [See also]30D0530D40: 1: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A4030Dxx: 1: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G3430E05: 1: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A6030E15: 1: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
[See also]30E1530E20: 1: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A3530E25: 1: 35Q15 Riemann-Hilbert problems [See also]30E25, 31A25, 31B2030F10: 1: 14H15 Families, moduli (analytic) [See also]30F10, 32G1530Fxx: 1: 14H55 Riemann surfaces; Weierstrass points; gap sequences [See also]30Fxx30G06: 1: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S1030H05: 1: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J1530H05: 2: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J1030H10: 1: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B3031-XX: 1: 47G40 Potential operators [See also]31-XX31A15: 1: 30C85 Capacity and harmonic measure in the complex plane [See also]31A1531A30: 1: 35J30 Higher-order elliptic equations [See also]31A30, 31B3031Axx: 1: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
[See also]31Axx, 31Bxx31C10: 1: 32U05 Plurisubharmonic functions and generalizations [See also]31C1031C12: 1: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B2031Cxx: 1: 60J45 Probabilistic potential theory [See also]31Cxx, 31D0532-XX: 1: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C1032-XX: 2: 58B12 Questions of holomorphy [See also]32-XX, 46G2032-XX: 1: 58C10 Holomorphic maps [See also]32-XX32A10: 1: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H0432A25: 1: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J1532B05: 1: 26E05 Real-analytic functions [See also]32B05, 32C0532B05: 1: 13J07 Analytical algebras and rings [See also]32B0532B20: 1: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C0532C07: 1: 14P20 Nash functions and manifolds [See also]32C07, 58A0732C11: 1: 14M30 Supervarieties [See also]32C11, 58A5032C30: 1: 58A25 Currents [See also]32C30, 53C6532C30: 1: 32A27 Local theory of residues [See also]32C3032C38: 1: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J1532C38: 2: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J1532Cxx: 1: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1532Cxx: 1: 53B35 Hermitian and Kahlerian structures [See also]32Cxx32Cxx: 2: 53C55 Hermitian and Kahlerian manifolds [See also]32Cxx32Cxx: 3: 53C56 Other complex differential geometry [See also]32Cxx32Cxx: 4: 58Axx General theory of differentiable manifolds [See also]32Cxx
456 Run: December 14, 2009
Mathematics Subject Classification 2010
32F10: 1: 32L15 Bundle convexity [See also]32F1032G13: 1: 14J15 Moduli, classification: analytic theory; relations with modular forms [See also]32G1332G15: 1: 30F60 Teichmuller theory [See also]32G1532G20: 1: 14C34 Torelli problem [See also]32G2032G20: 2: 14D07 Variation of Hodge structures [See also]32G2032G20: 3: 14H40 Jacobians, Prym varieties [See also]32G2032Gxx: 1: 58H15 Deformations of structures [See also]32Gxx, 58J1032L20: 1: 14F17 Vanishing theorems [See also]32L2032L25: 1: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txx32L25: 1: 53C28 Twistor methods [See also]32L2532L25: 2: 81R25 Spinor and twistor methods [See also]32L25
32M05: 1: 22E10 General properties and structure of complex Lie groups [See also]32M0532M10: 1: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M3532M10: 2: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T1532M15: 1: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J1532M15: 2: 53C35 Symmetric spaces [See also]32M15, 57T1532M25: 1: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxx32Q20: 1: 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
[See also]32Q2032Q25: 1: 14J30 3-folds [See also]32Q2532S22: 1: 52C35 Arrangements of points, flats, hyperplanes [See also]32S2232S60: 1: 58A35 Stratified sets [See also]32S6032Sxx: 1: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XX32U05: 1: 31C10 Pluriharmonic and plurisubharmonic functions [See also]32U0532W05: 1: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J1032Wxx: 1: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxx32Wxx: 2: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxx33C45: 1: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D4533C80: 1: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XX33Cxx: 1: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxx33Dxx: 1: 05A30 q-calculus and related topics [See also]33Dxx33Dxx: 2: 39A13 Difference equations, scaling (q-differences) [See also]33Dxx33F05: 1: 65D20 Computation of special functions, construction of tables [See also]33F0534-XX: 1: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H0534A12: 1: 45Dxx Volterra integral equations [See also]34A1234A12: 2: 45D05 Volterra integral equations [See also]34A1234A55: 1: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A4034A60: 1: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K2134Bxx: 1: 47Exx Ordinary differential operators [See also]34Bxx, 34Lxx34Bxx: 2: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)34C23: 1: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K1834C23: 2: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E0934C55: 1: 47J40 Equations with hysteresis operators [See also]34C55, 74N3034Cxx: 1: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxx34Cxx: 2: 70Kxx Nonlinear dynamics [See also]34Cxx, 37-XX34D08: 1: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxx34E20: 1: 78A45 Diffraction, scattering [See also]34E20 for WKB methods34E20: 2: 81U05 2-body potential scattering theory [See also]34E20 for WKB methods34E20: 1: 34M60 Singular perturbation problems in the complex domain (complex WKB, turning points,
steepest descent) [See also]34E2034F05: 1: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H15
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Mathematics Subject Classification 2010
34F05: 1: 60H10 Stochastic ordinary differential equations [See also]34F0534G10: 1: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K3034G10: 1: 47D09 Operator sine and cosine functions and higher-order Cauchy problems [See also]34G1034G20: 1: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2534Gxx: 1: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxx34Gxx: 2: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx34Gxx: 3: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxx34H05: 1: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XX34H05: 1: 93C15 Systems governed by ordinary differential equations [See also]34H0534K05: 1: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G2034K05: 2: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G2034K30: 1: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2034K30: 2: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2034K30: 3: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx34K35: 1: 93C23 Systems governed by functional-differential equations [See also]34K3534K50: 1: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E0334K50: 2: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E0334L25: 1: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxx34Lxx: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D2534Lxx: 2: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7534Lxx: 3: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7534Lxx: 1: 34B24 Sturm-Liouville theory [See also]34Lxx
34Mxx: 1: 30D05 Functional equations in the complex domain, iteration and composition of analyticfunctions [See also]34Mxx, 37Fxx, 39-XX
34Mxx: 1: 12H20 Abstract differential equations [See also]34Mxx34Mxx: 2: 32G34 Moduli and deformations for ordinary differential equations (e.g. Knizhnik-
Zamolodchikov equation) [See also]34Mxx35-XX: 1: 42B37 Harmonic analysis and PDE [See also]35-XX35-XX: 2: 58J05 Elliptic equations on manifolds, general theory [See also]35-XX35A22: 1: 58J72 Correspondences and other transformation methods (e.g. Lie-Backlund) [See also]35A2235A30: 1: 58J70 Invariance and symmetry properties [See also]35A3035Axx: 1: 37Kxx Infinite-dimensional Hamiltonian systems [See also]35Axx, 35Qxx35B32: 1: 58J55 Bifurcation [See also]35B3235Bxx: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J3535Bxx: 2: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxx35C11: 1: 76B25 Solitary waves [See also]35C1135J05: 1: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L0535J15: 1: 45E05 Integral equations with kernels of Cauchy type [See also]35J1535L60: 1: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q3035L67: 1: 76Lxx Shock waves and blast waves [See also]35L6735L67: 2: 76L05 Shock waves and blast waves [See also]35L6735Lxx: 1: 58J45 Hyperbolic equations [See also]35Lxx35N05: 1: 35Exx Equations and systems with constant coefficients [See also]35N0535Nxx: 1: 58J10 Differential complexes [See also]35Nxx; elliptic complexes35Pxx: 1: 47Fxx Partial differential operators [See also]35Pxx, 58Jxx35Pxx: 2: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)35Pxx: 1: 35J10 Schrodinger operator [See also]35Pxx35Pxx: 2: 58J50 Spectral problems; spectral geometry; scattering theory [See also]35Pxx35Q30: 1: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
[See also]35Q30
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Mathematics Subject Classification 2010
35Q30: 2: 76D03 Existence, uniqueness, and regularity theory [See also]35Q3035Q30: 3: 76D05 Navier-Stokes equations [See also]35Q3035Q35: 1: 76B03 Existence, uniqueness, and regularity theory [See also]35Q3535R25: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R3035R25: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R3035R30: 1: 86A22 Inverse problems [See also]35R3035R35: 1: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J4035R35: 2: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J4035R35: 3: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J4035R35: 4: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J4035R35: 5: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J4035R35: 6: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J4035R35: 7: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J4035R35: 8: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J4035R35: 9: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J4035R35: 10: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J4035R35: 11: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J4035R35: 12: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J4035R60: 1: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H1535R60: 2: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J6035R60: 1: 60H15 Stochastic partial differential equations [See also]35R6035Sxx: 1: 47G30 Pseudodifferential operators [See also]35Sxx, 58Jxx35Sxx: 1: 58J40 Pseudodifferential and Fourier integral operators on manifolds [See also]35Sxx37-XX: 1: 76Fxx Turbulence [See also]37-XX, 60Gxx, 60Jxx37-XX: 1: 34Cxx Qualitative theory [See also]37-XX37-XX: 2: 34Kxx Functional-differential and differential-difference equations [See also]37-XX37-XX: 3: 70Gxx General models, approaches, and methods [See also]37-XX37-XX: 4: 76F20 Dynamical systems approach to turbulence [See also]37-XX37Axx: 1: 37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also]37Axx37B15: 1: 68Q80 Cellular automata [See also]37B1537B55: 1: 37C60 Nonautonomous smooth dynamical systems [See also]37B5537Bxx: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2537C20: 1: 34D30 Structural stability and analogous concepts [See also]37C2037C25: 1: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C3037C70: 1: 34D45 Attractors [See also]37C70, 37D4537C75: 1: 34Dxx Stability theory [See also]37C75, 93Dxx37Cxx: 1: 37B10 Symbolic dynamics [See also]37Cxx, 37Dxx37Cxx: 1: 35B30 Dependence of solutions on initial and boundary data, parameters [See also]37Cxx37D45: 1: 70K55 Transition to stochasticity (chaotic behavior) [See also]37D4537Dxx: 1: 34C28 Complex behavior, chaotic systems [See also]37Dxx37Dxx: 2: 37C40 Smooth ergodic theory, invariant measures [See also]37Dxx37Dxx: 3: 81Q50 Quantum chaos [See also]37Dxx37F25: 1: 37E20 Universality, renormalization [See also]37F2537Fxx: 1: 28A80 Fractals [See also]37Fxx37Gxx: 1: 35B32 Bifurcation [See also]37Gxx, 37K50
459 Run: December 14, 2009
Mathematics Subject Classification 2010
37Gxx: 1: 34C23 Bifurcation [See also]37Gxx37Gxx: 2: 37H20 Bifurcation theory [See also]37Gxx37Jxx: 1: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxx37Jxx: 1: 70Hxx Hamiltonian and Lagrangian mechanics [See also]37Jxx37K10: 1: 35Q53 KdV-like equations (Korteweg-de Vries) [See also]37K1037K10: 2: 35Q55 NLS-like equations (nonlinear Schrodinger) [See also]37K1037K40: 1: 35Q51 Soliton-like equations [See also]37K4037K60: 1: 37L60 Lattice dynamics [See also]37K6037K60: 2: 82C23 Exactly solvable dynamic models [See also]37K6037Kxx: 1: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX37L05: 1: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D0737L60: 1: 37K60 Lattice dynamics [See also]37L60
37Mxx: 1: 65Pxx Numerical problems in dynamical systems [See also]37Mxx39A70: 1: 47B39 Difference operators [See also]39A7039Axx: 1: 12H10 Difference algebra [See also]39Axx40A35: 1: 40G15 Summability methods using statistical convergence [See also]40A3540E05: 1: 11M45 Tauberian theorems [See also]40E0540G15: 1: 40A35 Ideal and statistical convergence [See also]40G1540J05: 1: 43A55 Summability methods on groups, semigroups, etc. [See also]40J05
42-XX: 1: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XX42A15: 1: 41A05 Interpolation [See also]42A15 and 65D0542A38: 1: 44A05 General transforms [See also]42A3842C05: 1: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre,
Hermite, Askey scheme, etc.) [See also]42C05 for general orthogonal polynomials and functions43A55: 1: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B1543A55: 2: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)43A60: 1: 42A75 Classical almost periodic functions, mean periodic functions [See also]43A6044-XX: 1: 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.
[See also]44-XX44A12: 1: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A1244A15: 1: 45Hxx Miscellaneous special kernels [See also]44A1544A15: 2: 45H05 Miscellaneous special kernels [See also]44A1545Exx: 1: 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions
[See also]45Exx45Exx: 2: 30E25 Boundary value problems [See also]45Exx45Gxx: 1: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P0545Kxx: 1: 35R09 Integro-partial differential equations [See also]45Kxx45P05: 1: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M1545P05: 1: 47G10 Integral operators [See also]45P0546A13: 1: 46M40 Inductive and projective limits [See also]46A1346A22: 1: 39B82 Stability, separation, extension, and related topics [See also]46A2246A22: 2: 46M10 Projective and injective objects [See also]46A2246A25: 1: 46B10 Duality and reflexivity [See also]46A2546A32: 1: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L2046A32: 2: 46M05 Tensor products [See also]46A32, 46B28, 47A8046A32: 3: 47L05 Linear spaces of operators [See also]46A32 and 46B2846A35: 1: 46B15 Summability and bases [See also]46A3546A40: 1: 46B40 Ordered normed spaces [See also]46A40, 46B4246A40: 2: 46B42 Banach lattices [See also]46A40, 46B4046A40: 1: 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces [See also]46A4046A45: 1: 46B45 Banach sequence spaces [See also]46A4546A55: 1: 47L07 Convex sets and cones of operators [See also]46A5546A55: 2: 52A07 Convex sets in topological vector spaces [See also]46A55
460 Run: December 14, 2009
Mathematics Subject Classification 2010
46B06: 1: 52A23 Asymptotic theory of convex bodies [See also]46B0646B08: 1: 46M07 Ultraproducts [See also]46B08, 46S2046B10: 1: 46A25 Reflexivity and semi-reflexivity [See also]46B1046B15: 1: 46A35 Summability and bases [See also]46B1546B28: 1: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L2046B45: 1: 46A45 Sequence spaces (including Kothe sequence spaces) [See also]46B4546B70: 1: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M3546B70: 1: 46M35 Abstract interpolation of topological vector spaces [See also]46B7046Bxx: 1: 52A21 Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
[See also]46Bxx46C50: 1: 47B50 Operators on spaces with an indefinite metric [See also]46C5046E10: 1: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E3546E22: 1: 47B32 Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-
Rovnyak, and other structured spaces) [See also]46E2246E25: 1: 46Jxx Commutative Banach algebras and commutative topological algebras [See also]46E2546E25: 2: 46J10 Banach algebras of continuous functions, function algebras [See also]46E2546E27: 1: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxx46E40: 1: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxx46E50: 1: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H6046Exx: 1: 54C35 Function spaces [See also]46Exx, 58D1546Exx: 1: 32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA),
vanishing mean oscillation (VMOA)) [See also]46Exx46F15: 1: 32A45 Hyperfunctions [See also]46F1546Fxx: 1: 46T30 Distributions and generalized functions on nonlinear spaces [See also]46Fxx46G05: 1: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxx46G05: 2: 49J50 Frechet and Gateaux differentiability [See also]46G05, 58C2046G05: 3: 49J52 Nonsmooth analysis [See also]46G05, 58C50, 90C5646G05: 1: 46T20 Continuous and differentiable maps [See also]46G0546G10: 1: 28B05 Vector-valued set functions, measures and integrals [See also]46G1046G10: 2: 46B22 Radon-Nikodym, Kreın-Milman and related properties [See also]46G1046G12: 1: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D2046G12: 2: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B1146G15: 1: 28A51 Lifting theory [See also]46G1546G20: 1: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H6046G20: 1: 46T25 Holomorphic maps [See also]46G2046G25: 1: 47H60 Multilinear and polynomial operators [See also]46G2546Gxx: 1: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D2546H70: 1: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L7046H70: 2: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L7046H70: 3: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K7046J10: 1: 54C40 Algebraic properties of function spaces [See also]46J1046K70: 1: 46H70 Nonassociative topological algebras [See also]46K70, 46L7046L07: 1: 47L25 Operator spaces (= matricially normed spaces) [See also]46L0746L85: 1: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B3446Lxx: 1: 81R15 Operator algebra methods [See also]46Lxx, 81T0546Lxx: 1: 22D25 C∗-algebras and W ∗-algebras in relation to group representations [See also]46Lxx46Lxx: 2: 47Lxx Linear spaces and algebras of operators [See also]46Lxx
46M05: 1: 47A80 Tensor products of operators [See also]46M0546M07: 1: 46B08 Ultraproduct techniques in Banach space theory [See also]46M07
461 Run: December 14, 2009
Mathematics Subject Classification 2010
46M10: 1: 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators[See also]46M10
46M35: 1: 46B70 Interpolation between normed linear spaces [See also]46M3546M40: 1: 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) [See also]46M4046Mxx: 1: 43A95 Categorical methods [See also]46Mxx46N50: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1046Nxx: 1: 47Nxx Miscellaneous applications of operator theory [See also]46Nxx46Sxx: 1: 47Sxx Other (nonclassical) types of operator theory [See also]46Sxx46T10: 1: 58D15 Manifolds of mappings [See also]46T10, 54C3546T20: 1: 46G05 Derivatives [See also]46T20, 58C20, 58C2546T20: 2: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C1546T30: 1: 46Fxx Distributions, generalized functions, distribution spaces [See also]46T3046Txx: 1: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxx46Txx: 2: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxx46Txx: 1: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XX47A40: 1: 35P25 Scattering theory [See also]47A4047A46: 1: 47A15 Invariant subspaces [See also]47A4647A48: 1: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N7047A53: 1: 58B15 Fredholm structures [See also]47A5347A55: 1: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q1547A56: 1: 15A22 Matrix pencils [See also]47A5647A60: 1: 46H30 Functional calculus in topological algebras [See also]47A6047A64: 1: 26E60 Means [See also]47A6447A75: 1: 49Rxx Variational methods for eigenvalues of operators [See also]47A7547A75: 2: 49R05 Variational methods for eigenvalues of operators [See also]47A75 (should also be
assigned at least one other classification number in Section 49)47Axx: 1: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F0547B10: 1: 47L20 Operator ideals [See also]47B1047B32: 1: 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including
de Branges-Rovnyak and other structured spaces) [See also]47B3247B35: 1: 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf
type) [See also]47B3547B38: 1: 45Pxx Integral operators [See also]47B38, 47G1047B38: 2: 45P05 Integral operators [See also]47B38, 47G1047B39: 1: 39A70 Difference operators [See also]47B3947B50: 1: 46C20 Spaces with indefinite inner product (Kreın spaces, Pontryagin spaces, etc.)
[See also]47B5047B80: 1: 47H40 Random operators [See also]47B80, 60H2547B80: 1: 60H25 Random operators and equations [See also]47B8047D03: 1: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H1547D03: 2: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D0747D06: 1: 34G10 Linear equations [See also]47D06, 47D0947E05: 1: 34Lxx Ordinary differential operators [See also]47E0547G30: 1: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J4047H04: 1: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C6047H10: 1: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J2547H10: 2: 54H25 Fixed-point and coincidence theorems [See also]47H10, 55M2047H10: 1: 58C30 Fixed point theorems on manifolds [See also]47H1047H14: 1: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q1547H30: 1: 45Gxx Nonlinear integral equations [See also]47H30, 47Jxx47H40: 1: 47B80 Random operators [See also]47H40, 60H2547Hxx: 1: 34G20 Nonlinear equations [See also]47Hxx, 47Jxx47Hxx: 2: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxx
462 Run: December 14, 2009
Mathematics Subject Classification 2010
47Hxx: 3: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C3047J10: 1: 47A75 Eigenvalue problems [See also]47J10, 49R0547J10: 2: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E0747J20: 1: 49J40 Variational methods including variational inequalities [See also]47J2047Jxx: 1: 39B42 Matrix and operator equations [See also]47Jxx47L20: 1: 47B10 Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von
Neumann classes, etc.) [See also]47L2047L25: 1: 46L07 Operator spaces and completely bounded maps [See also]47L2547Nxx: 1: 46Nxx Miscellaneous applications of functional analysis [See also]47Nxx47Sxx: 1: 46Sxx Other (nonclassical) types of functional analysis [See also]47Sxx49-XX: 1: 58E25 Applications to control theory [See also]49-XX, 93-XX49J15: 1: 34Hxx Control problems [See also]49J15, 49K15, 93C1549J15: 2: 34H05 Control problems [See also]49J15, 49K15, 93C1549J21: 1: 34A60 Differential inclusions [See also]49J21, 49K2149J21: 2: 34K35 Control problems [See also]49J21, 49K21, 93C2349J40: 1: 47J20 Variational and other types of inequalities involving nonlinear operators (general)
[See also]49J4049J52: 1: 90C56 Derivative-free methods and methods using generalized derivatives [See also]49J5249K35: 1: 90C47 Minimax problems [See also]49K3549L20: 1: 90C39 Dynamic programming [See also]49L20
49Mxx: 1: 65K10 Optimization and variational techniques [See also]49Mxx, 93B4049Mxx: 2: 90Cxx Mathematical programming [See also]49Mxx, 65Kxx49N15: 1: 90C46 Optimality conditions, duality [See also]49N1549N70: 1: 91A23 Differential games [See also]49N7049N75: 1: 91A24 Positional games (pursuit and evasion, etc.) [See also]49N7549Q05: 1: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C4249Q05: 2: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R4249Q05: 1: 58E12 Applications to minimal surfaces (problems in two independent variables)
[See also]49Q0549Q10: 1: 76B75 Flow control and optimization [See also]49Q10, 93C20, 93C9549Q10: 2: 76D55 Flow control and optimization [See also]49Q10, 93C20, 93C9549Qxx: 1: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B0549Qxx: 1: 74Pxx Optimization [See also]49Qxx49R05: 1: 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems [See also]49R0551-XX: 1: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D2551-XX: 1: 14Nxx Projective and enumerative geometry [See also]51-XX51D20: 1: 05B25 Finite geometries [See also]51D20, 51Exx51E05: 1: 05B05 Block designs [See also]51E05, 62K1051E24: 1: 20E42 Groups with a BN -pair; buildings [See also]51E2451E30: 1: 05B30 Other designs, configurations [See also]51E3051F15: 1: 51M20 Polyhedra and polytopes; regular figures, division of spaces [See also]51F1551H25: 1: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxx51Lxx: 1: 53C75 Geometric orders, order geometry [See also]51Lxx51N05: 1: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U0551N35: 1: 14N05 Projective techniques [See also]51N3552A07: 1: 46A55 Convex sets in topological linear spaces; Choquet theory [See also]52A0752A22: 1: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axx52A22: 2: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C6552A22: 3: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C6552A23: 1: 46B06 Asymptotic theory of Banach spaces [See also]52A23
463 Run: December 14, 2009
Mathematics Subject Classification 2010
52B20: 1: 14M25 Toric varieties, Newton polyhedra [See also]52B2052B40: 1: 05B35 Matroids, geometric lattices [See also]52B40, 90C2752C20: 1: 05B45 Tessellation and tiling problems [See also]52C20, 52C2252C35: 1: 32S22 Relations with arrangements of hyperplanes [See also]52C3553A04: 1: 52A10 Convex sets in 2 dimensions (including convex curves) [See also]53A0453A05: 1: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C4553A07: 1: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C4553A10: 1: 49Q05 Minimal surfaces [See also]53A10, 58E1253A17: 1: 70Bxx Kinematics [See also]53A1753A25: 1: 51M30 Line geometries and their generalizations [See also]53A2553A60: 1: 14C21 Pencils, nets, webs [See also]53A6053Axx: 1: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxx53B25: 1: 53C40 Global submanifolds [See also]53B2553C07: 1: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E1553C20: 1: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A1453C20: 2: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C6053C28: 1: 32L25 Twistor theory, double fibrations [See also]53C2853C40: 1: 53B25 Local submanifolds [See also]53C4053C43: 1: 58E20 Harmonic maps [See also]53C43, etc.53C65: 1: 52A22 Random convex sets and integral geometry [See also]53C65, 60D0553C75: 1: 51Lxx Geometric order structures [See also]53C7553Cxx: 1: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C7053Cxx: 2: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx53Cxx: 1: 32Q20 Kahler-Einstein manifolds [See also]53Cxx53D10: 1: 37J55 Contact systems [See also]53D1053D20: 1: 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction
[See also]53D2053D45: 1: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants,
Donaldson-Thomas invariants [See also]53D4553D50: 1: 81S10 Geometry and quantization, symplectic methods [See also]53D5053Dxx: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxx54-XX: 1: 18B30 Categories of topological spaces and continuous mappings [See also]54-XX54C30: 1: 26-XX Real functions [See also]54C3054C55: 1: 55M15 Absolute neighborhood retracts [See also]54C5554C56: 1: 55P55 Shape theory [See also]54C56, 55Q0754C56: 2: 57N25 Shapes [See also]54C56, 55P55, 55Q0754E70: 1: 47S50 Operator theory in probabilistic metric linear spaces [See also]54E7054F45: 1: 55M10 Dimension theory [See also]54F4554H10: 1: 28A60 Measures on Boolean rings, measure algebras [See also]54H1054H20: 1: 37Bxx Topological dynamics [See also]54H2054H25: 1: 55M20 Fixed points and coincidences [See also]54H2555M10: 1: 54F45 Dimension theory [See also]55M1055M15: 1: 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract
(ANR), absolute retract spaces (general properties) [See also]55M1555M25: 1: 47H11 Degree theory [See also]55M25, 58C3055Mxx: 1: 54F35 Higher-dimensional local connectedness [See also]55Mxx, 55Nxx55N05: 1: 55Q70 Homotopy groups of special types [See also]55N05, 55N0755N15: 1: 19Lxx Topological K-theory [See also]55N15, 55R50, 55S2555N22: 1: 14L05 Formal groups, p-divisible groups [See also]55N2255N22: 2: 19K33 EXT and K-homology [See also]55N2255N22: 3: 19L41 Connective K-theory, cobordism [See also]55N2255N22: 4: 57R77 Complex cobordism (U- and SU-cobordism) [See also]55N2255N22: 5: 57R90 Other types of cobordism [See also]55N2255N91: 1: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S9155P48: 1: 18D50 Operads [See also]55P48
464 Run: December 14, 2009
Mathematics Subject Classification 2010
55P55: 1: 54C56 Shape theory [See also]55P55, 57N2555Q50: 1: 19L20 J-homomorphism, Adams operations [See also]55Q5055R20: 1: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T2055R60: 1: 57N55 Microbundles and block bundles [See also]55R60, 57Q5055R60: 2: 57Q50 Microbundles and block bundles [See also]55R60, 57N5555Rxx: 1: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxx55Rxx: 1: 32Lxx Holomorphic fiber spaces [See also]55Rxx55Rxx: 2: 57R22 Topology of vector bundles and fiber bundles [See also]55Rxx55Txx: 1: 18G40 Spectral sequences, hypercohomology [See also]55Txx55Txx: 2: 55R20 Spectral sequences and homology of fiber spaces [See also]55Txx55U10: 1: 13F55 Stanley-Reisner face rings; simplicial complexes [See also]55U1055U10: 2: 18G30 Simplicial sets, simplicial objects (in a category) [See also]55U1055U25: 1: 18G15 Ext and Tor, generalizations, Kunneth formula [See also]55U2557-XX: 1: 51H20 Topological geometries on manifolds [See also]57-XX57M05: 1: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxx57M05: 1: 20F06 Cancellation theory; application of van Kampen diagrams [See also]57M0557M15: 1: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
57M2557M25: 1: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q4557M40: 1: 57N12 Topology of E3 and S3 [See also]57M4057M50: 1: 57N16 Geometric structures on manifolds [See also]57M5057Mxx: 1: 57N10 Topology of general 3-manifolds [See also]57Mxx57N12: 1: 57M40 Characterizations of E3 and S3 (Poincare conjecture) [See also]57N1257N55: 1: 55R60 Microbundles and block bundles [See also]57N55, 57Q5057Q10: 1: 19B28 K1 of group rings and orders [See also]57Q1057R30: 1: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R3257R32: 1: 22E41 Continuous cohomology [See also]57R32, 57Txx, 58H1057R32: 1: 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks,
etc.) [See also]57R3257R56: 1: 81T45 Topological field theories [See also]57R56, 58Dxx57R67: 1: 19J25 Surgery obstructions [See also]57R6757Rxx: 1: 53D35 Global theory of symplectic and contact manifolds [See also]57Rxx57S17: 1: 55M35 Finite groups of transformations (including Smith theory) [See also]57S1757T35: 1: 55T20 Eilenberg-Moore spectral sequences [See also]57T3557Txx: 1: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R2057Txx: 1: 55Nxx Homology and cohomology theories [See also]57Txx58-XX: 1: 57R57 Applications of global analysis to structures on manifolds, Donaldson and Seiberg-
Witten invariants [See also]58-XX58A15: 1: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxx58A50: 1: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C5058B15: 1: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J2058B20: 1: 53C60 Finsler spaces and generalizations (areal metrics) [See also]58B2058B32: 1: 46L85 Noncommutative topology [See also]58B32, 58B34, 58J2258B32: 2: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J2258B32: 3: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J2258B34: 1: 83C65 Methods of noncommutative geometry [See also]58B3458Bxx: 1: 32K05 Banach analytic spaces [See also]58Bxx58Bxx: 2: 57N20 Topology of infinite-dimensional manifolds [See also]58Bxx58C25: 1: 26E10 C∞-functions, quasi-analytic functions [See also]58C2558C25: 2: 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also]58C2558C30: 1: 65H20 Global methods, including homotopy approaches [See also]58C30, 90C3058C35: 1: 46F25 Distributions on infinite-dimensional spaces [See also]58C3558C50: 1: 32K07 Formal and graded complex spaces [See also]58C5058Cxx: 1: 26Exx Miscellaneous topics [See also]58Cxx58D05: 1: 22E67 Loop groups and related constructions, group-theoretic treatment [See also]58D05
465 Run: December 14, 2009
Mathematics Subject Classification 2010
58D29: 1: 81T70 Quantization in field theory; cohomological methods [See also]58D2958D30: 1: 81S40 Path integrals [See also]58D3058E10: 1: 53C22 Geodesics [See also]58E1058E20: 1: 53C43 Differential geometric aspects of harmonic maps [See also]58E2058Exx: 1: 47J30 Variational methods [See also]58Exx58Exx: 2: 49Qxx Manifolds [See also]58Exx58H05: 1: 22A22 Topological groupoids (including differentiable and Lie groupoids) [See also]58H0558H10: 1: 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology [See also]58H1058Hxx: 1: 35Nxx Overdetermined systems [See also]58Hxx, 58J10, 58J1558J10: 1: 35Jxx Elliptic equations and systems [See also]58J10, 58J2058J20: 1: 19K56 Index theory [See also]58J20, 58J2258J22: 1: 19K35 Kasparov theory (KK-theory) [See also]58J2258J45: 1: 35Lxx Hyperbolic equations and systems [See also]58J4558J60: 1: 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
[See also]58J6058J65: 1: 60Hxx Stochastic analysis [See also]58J6558J65: 2: 60J60 Diffusion processes [See also]58J6558J65: 3: 60J65 Brownian motion [See also]58J6558J70: 1: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J7258Jxx: 1: 47Gxx Integral, integro-differential, and pseudodifferential operators [See also]58Jxx58Kxx: 1: 35L67 Shocks and singularities [See also]58Kxx, 76L0558Kxx: 1: 32Sxx Singularities [See also]58Kxx58Kxx: 2: 32S60 Stratifications; constructible sheaves; intersection cohomology [See also]58Kxx60A05: 1: 03B48 Probability and inductive logic [See also]60A0560B20: 1: 05C80 Random graphs [See also]60B2060Bxx: 1: 20Pxx Probabilistic methods in group theory [See also]60Bxx60Bxx: 2: 20P05 Probabilistic methods in group theory [See also]60Bxx60Bxx: 3: 46B09 Probabilistic methods in Banach space theory [See also]60Bxx60Exx: 1: 62Exx Distribution theory [See also]60Exx60Exx: 2: 62Hxx Multivariate analysis [See also]60Exx60Fxx: 1: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G1060G25: 1: 62M20 Prediction [See also]60G25; filtering [See also]60G35, 93E10, 93E1160G35: 1: 62M20 Prediction [See also]60G25; filtering [See also]60G35, 93E10, 93E1160G35: 2: 94A05 Communication theory [See also]60G35, 90B1860G35: 1: 93E10 Estimation and detection [See also]60G3560G35: 2: 93E11 Filtering [See also]60G3560G40: 1: 62L15 Optimal stopping [See also]60G40, 91A6060G40: 1: 91A60 Probabilistic games; gambling [See also]60G4060G50: 1: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C4160G50: 1: 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. [See also]60G5060Gxx: 1: 70Qxx Control of mechanical systems [See also]60Gxx, 60Jxx60H10: 1: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also]60H1060H15: 1: 35R60 Partial differential equations with randomness, stochastic partial differential equations
[See also]60H1560H20: 1: 45Rxx Random integral equations [See also]60H2060H20: 2: 45R05 Random integral equations [See also]60H2060H30: 1: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M3560Hxx: 1: 34K50 Stochastic functional-differential equations [See also]60Hxx60J50: 1: 31C35 Martin boundary theory [See also]60J5060J60: 1: 76R50 Diffusion [See also]60J6060K10: 1: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N0560K25: 1: 68M20 Performance evaluation; queueing; scheduling [See also]60K25, 90Bxx60K25: 2: 90B22 Queues and service [See also]60K25, 68M2060K35: 1: 82B43 Percolation [See also]60K3560K35: 2: 82C22 Interacting particle systems [See also]60K3560K35: 3: 82C43 Time-dependent percolation [See also]60K3562B10: 1: 94A15 Information theory, general [See also]62B10, 81P45
466 Run: December 14, 2009
Mathematics Subject Classification 2010
62Cxx: 1: 91A35 Decision theory for games [See also]62Cxx, 91B06, 90B5062Cxx: 2: 91B06 Decision theory [See also]62Cxx, 90B50, 91A3562Exx: 1: 60Exx Distribution theory [See also]62Exx, 62Hxx62H30: 1: 91C20 Clustering [See also]62H3062L15: 1: 60G40 Stopping times; optimal stopping problems; gambling theory [See also]62L15, 91A60
62M10: 1: 91B84 Economic time series analysis [See also]62M1062M20: 1: 60G35 Signal detection and filtering [See also]62M20, 93E10, 93E11, 94Axx62M20: 1: 60G25 Prediction theory [See also]62M2062P10: 1: 92B15 General biostatistics [See also]62P1065-XX: 1: 74Sxx Numerical methods [See also]65-XX, 74G15, 74H1565-XX: 2: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T8065-XX: 1: 76Mxx Basic methods in fluid mechanics [See also]65-XX65C30: 1: 60H35 Computational methods for stochastic equations [See also]65C3065C40: 1: 60J22 Computational methods in Markov chains [See also]65C4065Cxx: 1: 68U20 Simulation [See also]65Cxx65D17: 1: 51N05 Descriptive geometry [See also]65D17, 68U0765D17: 1: 68U07 Computer-aided design [See also]65D1765D18: 1: 68U05 Computer graphics; computational geometry [See also]65D1865D20: 1: 33F05 Numerical approximation and evaluation [See also]65D2065E05: 1: 30C30 Numerical methods in conformal mapping theory [See also]65E0565F35: 1: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J0565F35: 1: 15A12 Conditioning of matrices [See also]65F3565Fxx: 1: 65M22 Solution of discretized equations [See also]65Fxx, 65Hxx65Fxx: 2: 65N22 Solution of discretized equations [See also]65Fxx, 65Hxx65J15: 1: 47J25 Iterative procedures [See also]65J1565Jxx: 1: 46N40 Applications in numerical analysis [See also]65Jxx65Jxx: 2: 47N40 Applications in numerical analysis [See also]65Jxx65L80: 1: 34A09 Implicit equations, differential-algebraic equations [See also]65L8065N22: 1: 65F10 Iterative methods for linear systems [See also]65N2265Pxx: 1: 37Mxx Approximation methods and numerical treatment of dynamical systems [See also]65Pxx68-XX: 1: 03B70 Logic in computer science [See also]68-XX68M07: 1: 65Y04 Algorithms for computer arithmetic, etc. [See also]68M0768M10: 1: 90B18 Communication networks [See also]68M10, 94A0568M11: 1: 68U35 Information systems (hypertext navigation, interfaces, decision support, etc.)
[See also]68M1168M20: 1: 60K25 Queueing theory [See also]68M20, 90B2268M20: 1: 90B35 Scheduling theory, deterministic [See also]68M2068M20: 2: 90B36 Scheduling theory, stochastic [See also]68M2068N18: 1: 03B40 Combinatory logic and lambda-calculus [See also]68N1868P30: 1: 94A29 Source coding [See also]68P3068Q05: 1: 68Q12 Quantum algorithms and complexity [See also]68Q05, 81P6868Q05: 2: 81P68 Quantum computation [See also]68Q05, 68Q1268Q05: 1: 03D10 Turing machines and related notions [See also]68Q0568Q15: 1: 03C13 Finite structures [See also]68Q15, 68Q1968Q15: 2: 03D15 Complexity of computation (including implicit computational complexity)
[See also]68Q15, 68Q1768Q15: 1: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of
approximation, etc.) [See also]68Q1568Q25: 1: 11Y16 Algorithms; complexity [See also]68Q2568Q25: 2: 65Y20 Complexity and performance of numerical algorithms [See also]68Q2568Q25: 3: 68W40 Analysis of algorithms [See also]68Q2568Q25: 4: 90C60 Abstract computational complexity for mathematical programming problems
[See also]68Q2568Q30: 1: 03D32 Algorithmic randomness and dimension [See also]68Q3068Q32: 1: 68T05 Learning and adaptive systems [See also]68Q32, 91E4068Q45: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
467 Run: December 14, 2009
Mathematics Subject Classification 2010
68Q70, 68R1568Q55: 1: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q6568Q80: 1: 37B15 Cellular automata [See also]68Q8068Q85: 1: 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
[See also]68Q8568R10: 1: 05C85 Graph algorithms [See also]68R10, 68W0568R10: 2: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C1568R10: 3: 68M10 Network design and communication [See also]68R10, 90B1868T05: 1: 82C32 Neural nets [See also]68T05, 91E40, 92B2068T05: 2: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxx68T05: 1: 68Q32 Computational learning theory [See also]68T0568T05: 2: 91E40 Memory and learning [See also]68T0568T10: 1: 62H30 Classification and discrimination; cluster analysis [See also]68T10, 91C2068T15: 1: 03B35 Mechanization of proofs and logical operations [See also]68T1568T27: 1: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D0568T40: 1: 70B15 Mechanisms, robots [See also]68T40, 70Q05, 93C8568T40: 2: 70E60 Robot dynamics and control [See also]68T40, 70Q05, 93C8568T40: 3: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q0568T50: 1: 03B65 Logic of natural languages [See also]68T50, 91F2068U05: 1: 52C45 Combinatorial complexity of geometric structures [See also]68U0568U07: 1: 65D17 Computer aided design (modeling of curves and surfaces) [See also]68U0768U10: 1: 94A08 Image processing (compression, reconstruction, etc.) [See also]68U1068U20: 1: 65C20 Models, numerical methods [See also]68U2068U35: 1: 68M11 Internet topics [See also]68U3568Uxx: 1: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxx68W20: 1: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W4068W30: 1: 16Z05 Computational aspects of associative rings [See also]68W3068W30: 2: 33F10 Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also]68W3068W40: 1: 68Q25 Analysis of algorithms and problem complexity [See also]68W4070B15: 1: 52C25 Rigidity and flexibility of structures [See also]70B1570F20: 1: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxx70F25: 1: 37J60 Nonholonomic dynamical systems [See also]70F2570F25: 2: 70E18 Motion of a rigid body in contact with a solid surface [See also]70F25
70M20: 1: 70E15 Free motion of a rigid body [See also]70M2070Sxx: 1: 81Txx Quantum field theory; related classical field theories [See also]70Sxx74A15: 1: 80A17 Thermodynamics of continua [See also]74A1574A50: 1: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C2674C99: 1: 76T25 Granular flows [See also]74C99, 74E2074F10: 1: 76Zxx Biological fluid mechanics [See also]74F10, 74L15, 92Cxx74H50: 1: 70Lxx Random vibrations [See also]74H5074H50: 2: 70L05 Random vibrations [See also]74H5074L15: 1: 92C10 Biomechanics [See also]74L1574Nxx: 1: 80A22 Stefan problems, phase changes, etc. [See also]74Nxx74Qxx: 1: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M5076B45: 1: 76D45 Capillarity (surface tension) [See also]76B4576Bxx: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U0576Bxx: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576D05: 1: 35Q30 Navier-Stokes equations [See also]76D05, 76D07, 76N1076D05: 2: 35Q31 Euler equations [See also]76D05, 76D07, 76N1076D45: 1: 76B45 Capillarity (surface tension) [See also]76D4576E15: 1: 76F35 Convective turbulence [See also]76E15, 76Rxx
76M35: 1: 76F55 Statistical turbulence modeling [See also]76M3576U05: 1: 86-XX Geophysics [See also]76U05, 76V0576U05: 2: 86Axx Geophysics [See also]76U05, 76V05
468 Run: December 14, 2009
Mathematics Subject Classification 2010
76V05: 1: 80A30 Chemical kinetics [See also]76V05, 92C45, 92E2076W05: 1: 86A25 Geo-electricity and geomagnetism [See also]76W05, 78A2576Y05: 1: 85A30 Hydrodynamic and hydromagnetic problems [See also]76Y0576Z05: 1: 92C35 Physiological flow [See also]76Z0578A50: 1: 82D77 Quantum wave guides, quantum wires [See also]78A5080-XX: 1: 82B30 Statistical thermodynamics [See also]80-XX80A30: 1: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A3280A30: 1: 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
[See also]80A3080A32: 1: 76Vxx Reaction effects in flows [See also]80A3280A32: 2: 76V05 Reaction effects in flows [See also]80A3281P94: 1: 94A62 Authentication and secret sharing [See also]81P9481R05: 1: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R1081T13: 1: 58E15 Application to extremal problems in several variables; Yang-Mills functionals
[See also]81T13, etc.81T17: 1: 82B28 Renormalization group methods [See also]81T1781T17: 2: 82C28 Dynamic renormalization group methods [See also]81T1781T20: 1: 83C47 Methods of quantum field theory [See also]81T2081T30: 1: 83E30 String and superstring theories [See also]81T3081T99: 1: 76F30 Renormalization and other field-theoretical methods [See also]81T9981V80: 1: 78A60 Lasers, masers, optical bistability, nonlinear optics [See also]81V8081V80: 2: 81R30 Coherent states [See also]22E45; squeezed states [See also]81V8082B30: 1: 81T28 Thermal quantum field theory [See also]82B3082B40: 1: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582B40: 2: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582B43: 1: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C4382C31: 1: 81S22 Open systems, reduced dynamics, master equations, decoherence [See also]82C3182C80: 1: 65C35 Stochastic particle methods [See also]82C8082Cxx: 1: 37A60 Dynamical systems in statistical mechanics [See also]82Cxx82D10: 1: 76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D1082D10: 2: 76X05 Ionized gas flow in electromagnetic fields; plasmic flow [See also]82D1082D20: 1: 81V65 Quantum dots [See also]82D2082D30: 1: 76A15 Liquid crystals [See also]82D3082D50: 1: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3082D50: 2: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3083Cxx: 1: 81V17 Gravitational interaction [See also]83Cxx and 83Exx83E30: 1: 81T30 String and superstring theories; other extended objects (e.g., branes) [See also]83E3086-XX: 1: 74L05 Geophysical solid mechanics [See also]86-XX86A05: 1: 76B65 Rossby waves [See also]86A05, 86A1086A10: 1: 76B60 Atmospheric waves [See also]86A1090-XX: 1: 62Pxx Applications [See also]90-XX, 91-XX, 92-XX90B10: 1: 05C38 Paths and cycles [See also]90B1090B25: 1: 62N05 Reliability and life testing [See also]90B2590B30: 1: 60J20 Applications of Markov chains and discrete-time Markov processes on general state
spaces (social mobility, learning theory, industrial processes, etc.) [See also]90B30, 91D10, 91D35, 91E4090B50: 1: 62Cxx Decision theory [See also]90B50, 91B06; for game theory, see 91A3590Bxx: 1: 05C82 Small world graphs, complex networks [See also]90Bxx, 91D3090Bxx: 1: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
[See also]90Bxx90Bxx: 2: 60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also]90Bxx90C10: 1: 90B80 Discrete location and assignment [See also]90C1090C27: 1: 90C35 Programming involving graphs or networks [See also]90C2790C29: 1: 90B50 Management decision making, including multiple objectives [See also]90C29, 90C31,
91A35, 91B0690C29: 1: 58E17 Pareto optimality, etc., applications to economics [See also]90C2990C30: 1: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxx
469 Run: December 14, 2009
Mathematics Subject Classification 2010
90C31: 1: 49K40 Sensitivity, stability, well-posedness [See also]90C3190C35: 1: 05C35 Extremal problems [See also]90C3590C48: 1: 49J27 Problems in abstract spaces [See also]90C48, 93C2590C48: 2: 49K27 Problems in abstract spaces [See also]90C48, 93C2590C90: 1: 49N90 Applications of optimal control and differential games [See also]90C90, 93C9590C90: 1: 49Q10 Optimization of shapes other than minimal surfaces [See also]90C9090Cxx: 1: 49Mxx Numerical methods [See also]90Cxx, 65Kxx90Cxx: 1: 65K05 Mathematical programming methods [See also]90Cxx91A43: 1: 05C57 Games on graphs [See also]91A43, 91A4691B16: 1: 91A30 Utility theory for games [See also]91B1691B40: 1: 91D35 Manpower systems [See also]91B40, 90B7091B60: 1: 90B60 Marketing, advertising [See also]91B6091B72: 1: 91D25 Spatial models [See also]91B7291B84: 1: 62M10 Time series, auto-correlation, regression, etc. [See also]91B8491Bxx: 1: 62P20 Applications to economics [See also]91Bxx91D30: 1: 78A70 Biological applications [See also]91D30, 92C3091D35: 1: 90B70 Theory of organizations, manpower planning [See also]91D3592C10: 1: 74L15 Biomechanical solid mechanics [See also]92C1092C35: 1: 76Z05 Physiological flows [See also]92C3592C45: 1: 80A32 Chemically reacting flows [See also]92C45, 92E2092C55: 1: 44A12 Radon transform [See also]92C5592Dxx: 1: 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption
problems, etc.) [See also]92Dxx92Dxx: 2: 60J85 Applications of branching processes [See also]92Dxx92E10: 1: 81V55 Molecular physics [See also]92E1092E20: 1: 82B35 Irreversible thermodynamics, including Onsager-Machlup theory [See also]92E2093B52: 1: 49N35 Optimal feedback synthesis [See also]93B5293C05: 1: 49N05 Linear optimal control problems [See also]93C0593C41: 1: 49N30 Problems with incomplete information [See also]93C4193C85: 1: 68T40 Robotics [See also]93C8593Cxx: 1: 74M05 Control, switches and devices (“smart materials”) [See also]93Cxx93E20: 1: 49J55 Problems involving randomness [See also]93E2093E20: 2: 49K45 Problems involving randomness [See also]93E2094A15: 1: 81P45 Quantum information, communication, networks [See also]94A15, 94A1794A17: 1: 62B10 Information-theoretic topics [See also]94A1794A60: 1: 14G50 Applications to coding theory and cryptography [See also]94A60, 94B27, 94B4094A60: 2: 68P25 Data encryption [See also]94A60, 81P9494A60: 1: 81P94 Quantum cryptography [See also]94A6094Axx: 1: 68P30 Coding and information theory (compaction, compression, models of communication,
encoding schemes, etc.) [See also]94Axx94B05: 1: 51E22 Linear codes and caps in Galois spaces [See also]94B0594C10: 1: 06E30 Boolean functions [See also]94C1094C12: 1: 68M15 Reliability, testing and fault tolerance [See also]94C1297A20: 1: 00A08 Recreational mathematics [See also]97A2097Cxx: 1: 00A35 Methodology of mathematics, didactics [See also]97Cxx, 97Dxx06F15: 1: 20F60 Ordered groups [See mainly]06F1511Exx: 1: 15A63 Quadratic and bilinear forms, inner products [See mainly]11Exx17B35: 1: 16S30 Universal enveloping algebras of Lie algebras [See mainly]17B3522Fxx: 1: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxx22Fxx: 1: 37A15 General groups of measure-preserving transformations [See mainly]22Fxx32P05: 1: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S1037Pxx: 1: 11S82 Non-Archimedean dynamical systems [See mainly]37Pxx43-XX: 1: 32A50 Harmonic analysis of several complex variables [See mainly]43-XX46Exx: 1: 32A70 Functional analysis techniques [See mainly]46Exx46Jxx: 1: 32A65 Banach algebra techniques [See mainly]46Jxx46L55: 1: 37A55 Relations with the theory of C∗-algebras [See mainly]46L55
470 Run: December 14, 2009
Mathematics Subject Classification 2010
46L80: 1: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M2047Lxx: 1: 46H35 Topological algebras of operators [See mainly]47Lxx58Axx: 1: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axx70Fxx: 1: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxx74Hxx: 1: 37N15 Dynamical systems in solid mechanics [See mainly]74Hxx76-XX: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A1092-XX: 1: 37N25 Dynamical systems in biology [See mainly]92-XX, but also 91-XX92Exx: 1: 80A50 Chemistry (general) [See mainly]92Exx00A30: 1: 03A05 Philosophical and critical For philosophy of mathematics, see also 00A3000A79: 1: 00A69 General applied mathematics For physics, see 00A79 and Sections 70 through 8603B42: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F4503B44: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F4503B44: 2: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B4803B45: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B4803B48: 1: 03C80 Logic with extra quantifiers and operators [See also]03B42, 03B44, 03B45, 03B4803C60: 1: 08C10 Axiomatic model classes [See also]03Cxx, in particular 03C6003C60: 2: 20F11 Groups of finite Morley rank [See also]03C45, 03C6003D05: 1: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7003D40: 1: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7003D45: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S3003D78: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S3003E72: 1: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1003E72: 2: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1003F45: 1: 03B45 Modal logic (including the logic of norms) For knowledge and belief, see 03B42; for
temporal logic, see 03B44; for provability logic, see also 03F4503F45: 2: 06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
[See also]03G25, 03F4503F52: 1: 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus,
BCK and BCI logics) For proof-theoretic aspects see 03F5203F55: 1: 03D45 Theory of numerations, effectively presented structures [See also]03C57; for intuitionistic
and similar approaches see 03F5503F60: 1: 03D78 Computation over the reals For constructive aspects, see 03F6003G25: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E2503Hxx: 1: 13Lxx Applications of logic to commutative algebra [See also]03Cxx, 03Hxx03Hxx: 2: 13L05 Applications of logic to commutative algebra [See also]03Cxx, 03Hxx05A30: 1: 11B65 Binomial coefficients; factorials; q-identities [See also]05A10, 05A3005Axx: 1: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
05B35: 1: 51D20 Combinatorial geometries [See also]05B25, 05B3505C30: 1: 05Axx Enumerative combinatorics For enumeration in graph theory, see 05C3005C85: 1: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxx06B25: 1: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R1506B25: 2: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7006B35: 1: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F30
471 Run: December 14, 2009
Mathematics Subject Classification 2010
06B35: 2: 68Q55 Semantics [See also]03B70, 06B35, 18C5006C15: 1: 81P10 Logical foundations of quantum mechanics; quantum logic [See also]03G12, 06C1506D10: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5506D20: 1: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F3506D30: 1: 03G20 Lukasiewicz and Post algebras [See also]06D25, 06D3006E25: 1: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F3506E25: 1: 03F45 Provability logics and related algebras (e.g., diagonalizable algebras) [See also]03B45,
03G25, 06E2506F30: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5506F30: 1: 22A26 Topological semilattices, lattices and applications [See also]06B30, 06B35, 06F3006F30: 2: 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered
spaces [See also]06B30, 06F3006F30: 3: 54H12 Topological lattices, etc. [See also]06B30, 06F3006F35: 1: 03G25 Other algebras related to logic [See also]03F45, 06D20, 06E25, 06F3508A50: 1: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R1508A50: 2: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F1008A50: 3: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7008A50: 4: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F1008Bxx: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C0508C05: 1: 18C05 Equational categories [See also]03C05, 08C0511-XX: 1: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
11B13: 1: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]11E45: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211E45: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4511E57: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
11E88: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,see 15A75; for Clifford algebras, see 11E88, 15A66
11F30: 1: 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourierseries For automorphic theory, see mainly 11F30
11F30: 2: 42Bxx Harmonic analysis in several variables For automorphic theory, see mainly 11F3011F46: 1: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G1811F66: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211F70: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211F72: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211Fxx: 1: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxx11G05: 1: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxx11G07: 1: 14H52 Elliptic curves [See also]11G05, 11G07, 14Kxx11G10: 1: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxx11G15: 1: 11Rxx Algebraic number theory: global fields For complex multiplication, see 11G1511G18: 1: 14G35 Modular and Shimura varieties [See also]11F41, 11F46, 11G1811G25: 1: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxx11G32: 1: 14H57 Dessins d’enfants theory For arithmetic aspects, see 11G3211G35: 1: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxx11Gxx: 1: 14Gxx Arithmetic problems. Diophantine geometry [See also]11Dxx, 11Gxx
472 Run: December 14, 2009
Mathematics Subject Classification 2010
11H31: 1: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P2111H31: 2: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P2111H31: 1: 52C15 Packing and covering in 2 dimensions [See also]05B40, 11H3111H31: 2: 52C17 Packing and covering in n dimensions [See also]05B40, 11H3111H56: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
11H71: 1: 94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)[See also]11H31, 11H71
11J70: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,40A15
11J70: 2: 11K50 Metric theory of continued fractions [See also]11A55, 11J7011K16: 1: 11A63 Radix representation; digital problems For metric results, see 11K1611K50: 1: 11J70 Continued fractions and generalizations [See also]11A55, 11K5011K55: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1011Kxx: 1: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX11P21: 1: 52C05 Lattices and convex bodies in 2 dimensions [See also]11H06, 11H31, 11P2111P21: 2: 52C07 Lattices and convex bodies in n dimensions [See also]11H06, 11H31, 11P2111P70: 1: 20K01 Finite abelian groups [For sumsets, see 11B13 and 11P70]11P82: 1: 05A17 Partitions of integers [See also]11P81, 11P82, 11P8311P83: 1: 05A17 Partitions of integers [See also]11P81, 11P82, 11P8311R04: 1: 11Axx Elementary number theory For analogues in number fields, see 11R0411R42: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211R42: 2: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G1011R52: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211R52: 2: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G3011R54: 1: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxx11R54: 2: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxx11R54: 3: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G3011R70: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6711S37: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4511S40: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211S40: 2: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G1011S45: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7211S45: 2: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxx11S45: 3: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G3011S70: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6711S70: 1: 19Fxx K-theory in number theory [See also]11R70, 11S7011T06: 1: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M1011Txx: 1: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxx11Txx: 1: 05-XX Combinatorics For finite fields, see 11Txx11Txx: 2: 11Lxx Exponential sums and character sums For finite fields, see 11Txx
473 Run: December 14, 2009
Mathematics Subject Classification 2010
11Txx: 3: 13Mxx Finite commutative rings For number-theoretic aspects, see 11Txx12-XX: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6712D10: 1: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C1012Exx: 1: 26C05 Polynomials: analytic properties, etc. [See also]12Dxx, 12Exx12F10: 1: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX12J15: 1: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W8012Jxx: 1: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W8012L05: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F1012L15: 1: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L0512Lxx: 1: 03C60 Model-theoretic algebra [See also]08C10, 12Lxx, 13L0512Y05: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1013-XX: 1: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)13-XX: 1: 16-XX Associative rings and algebras For the commutative case, see 13-XX13B25: 1: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials [See also]11C08, 13B2513C11: 1: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D5013D10: 1: 14B12 Local deformation theory, Artin approximation, etc. [See also]13B40, 13D1013D15: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6713Dxx: 1: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxx13Dxx: 2: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
13F20: 1: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M1013F20: 2: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxx13F45: 1: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H1013H10: 1: 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
[See also]13F15, 13F45, 13H1013Hxx: 1: 52B20 Lattice polytopes (including relations with commutative algebra and algebraic
geometry) [See also]06A11, 13F20, 13Hxx13J25: 1: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W8013J30: 1: 14P05 Real algebraic sets [See also]12D15, 13J3013Jxx: 1: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W8013Jxx: 2: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W8013Jxx: 1: 16W80 Topological and ordered rings and modules [See also]06F25, 13Jxx13L05: 1: 03C60 Model-theoretic algebra [See also]08C10, 12Lxx, 13L0513L05: 2: 03H15 Nonstandard models of arithmetic [See also]11U10, 12L15, 13L05
13M10: 1: 13B25 Polynomials over commutative rings [See also]11C08, 11T06, 13F20, 13M1013Mxx: 1: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxx13Pxx: 1: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W3013Pxx: 2: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1014-XX: 1: 32Bxx Local analytic geometry [See also]13-XX and 14-XX14-XX: 2: 51-XX Geometry For algebraic geometry, see 14-XX14B05: 1: 14H20 Singularities, local rings [See also]13Hxx, 14B0514B07: 1: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxx14B12: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
474 Run: December 14, 2009
Mathematics Subject Classification 2010
14B2514B12: 2: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxx14B25: 1: 13B40 Etale and flat extensions; Henselization; Artin approximation [See also]13J15, 14B12,
14B2514C35: 1: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F0514C35: 2: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F4214Cxx: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6714D07: 1: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K3014D07: 1: 32S35 Mixed Hodge theory of singular varieties [See also]14C30, 14D0714D15: 1: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxx14D15: 1: 16S80 Deformations of rings [See also]13D10, 14D1514D20: 1: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J1514D22: 1: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J1514E15: 1: 14J17 Singularities [See also]14B05, 14E1514F05: 1: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxx14F05: 1: 14H60 Vector bundles on curves and their moduli [See also]14D20, 14F0514F10: 1: 13Nxx Differential algebra [See also]12H05, 14F1014F20: 1: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G1014F22: 1: 16K50 Brauer groups [See also]12G05, 14F2214F35: 1: 14H30 Coverings, fundamental group [See also]14E20, 14F3514F42: 1: 19E15 Algebraic cycles and motivic cohomology [See also]14C25, 14C35, 14F4214Fxx: 1: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S3514G10: 1: 11M41 Other Dirichlet series and zeta functions For local and global ground fields, see 11R42,
11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F7214G10: 1: 19F27 Etale cohomology, higher regulators, zeta and L-functions [See also]11G40, 11R42,
11S40, 14F20, 14G1014G20: 1: 11G25 Varieties over finite and local fields [See also]14G15, 14G2014G20: 2: 12H25 p-adic differential equations [See also]11S80, 14G2014G35: 1: 14J25 Special surfaces For Hilbert modular surfaces, see 14G3514G40: 1: 37P30 Height functions; Green functions; invariant measures [See also]11G50, 14G4014G50: 1: 94A60 Cryptography [See also]11T71, 14G50, 68P25, 81P9414G50: 1: 94B27 Geometric methods (including applications of algebraic geometry) [See also]11T71,
14G5014G50: 2: 94B40 Arithmetic codes [See also]11T71, 14G5014Gxx: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4514Gxx: 2: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxx14Gxx: 1: 11Dxx Diophantine equations [See also]11Gxx, 14Gxx14Gxx: 2: 14H25 Arithmetic ground fields [See also]11Dxx, 11G05, 14Gxx14Gxx: 3: 14J20 Arithmetic ground fields [See also]11Dxx, 11G25, 11G35, 14Gxx14Gxx: 4: 14K15 Arithmetic ground fields [See also]11Dxx, 11Fxx, 11G10, 14Gxx14H10: 1: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J1514H20: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxx14H52: 1: 11G07 Elliptic curves over local fields [See also]14G20, 14H5214Hxx: 1: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxx14J10: 1: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J1514J15: 1: 32G13 Analytic moduli problems For algebraic moduli problems, see 14D20, 14D22, 14H10,
14J10 [See also]14H15, 14J15
475 Run: December 14, 2009
Mathematics Subject Classification 2010
14J17: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxx14J60: 1: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M2014Jxx: 1: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxx14K30: 1: 32G20 Period matrices, variation of Hodge structure; degenerations [See also]14D05, 14D07,
14K3014Kxx: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4514Kxx: 1: 11Gxx Arithmetic algebraic geometry (Diophantine geometry) [See also]11Dxx, 14Gxx, 14Kxx14Kxx: 2: 14H52 Elliptic curves [See also]11G05, 11G07, 14Kxx14L24: 1: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M1714L24: 1: 15A72 Vector and tensor algebra, theory of invariants [See also]13A50, 14L2414L30: 1: 14R20 Group actions on affine varieties [See also]13A50, 14L3014L35: 1: 51N30 Geometry of classical groups [See also]20Gxx, 14L3514Lxx: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
14M05: 1: 13F15 Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)[See also]13A05, 14M05
14M10: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,14M12
14M12: 1: 13C40 Linkage, complete intersections and determinantal ideals [See also]14M06, 14M10,14M12
14M17: 1: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T1514M17: 1: 14L30 Group actions on varieties or schemes (quotients) [See also]13A50, 14L24, 14M1714M25: 1: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B2014M25: 2: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B2014M30: 1: 32C11 Complex supergeometry [See also]14A22, 14M30, 58A5014N10: 1: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B2014N10: 2: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B2014P20: 1: 32C07 Real-analytic sets, complex Nash functions [See also]14P15, 14P2014Pxx: 1: 13J30 Real algebra [See also]12D15, 14Pxx14Qxx: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1015A30: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
15A30: 1: 16Kxx Division rings and semisimple Artin rings [See also]12E15, 15A3015A60: 1: 65F35 Matrix norms, conditioning, scaling [See also]15A12, 15A6015A63: 1: 11Exx Forms and linear algebraic groups [See also]19Gxx For quadratic forms in linear
algebra, see 15A6315A66: 1: 11E88 Quadratic spaces; Clifford algebras [See also]15A63, 15A6615A66: 2: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A6615A75: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A6615B52: 1: 60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52)16-XX: 1: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or
16-XX)16D40: 1: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D5016D50: 1: 18G05 Projectives and injectives [See also]13C10, 13C11, 16D40, 16D5016D90: 1: 16B50 Category-theoretic methods and results (except as in 16D90) [See also]18-XX16E05: 1: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E2516E10: 1: 18G20 Homological dimension [See also]13D05, 16E1016E20: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R67
476 Run: December 14, 2009
Mathematics Subject Classification 2010
16E20: 2: 18F30 Grothendieck groups [See also]13D15, 16E20, 19Axx16E20: 1: 19D50 Computations of higher K-theory of rings [See also]13D15, 16E2016Exx: 1: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxx16Exx: 2: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
16Exx: 3: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx16G30: 1: 06E20 Ring-theoretic properties [See also]16E50, 16G3016G30: 2: 16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representa-
tion theory, see 16G3016Gxx: 1: 16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancella-
tion16H05: 1: 11S25 Galois cohomology [See also]12Gxx, 16H0516Hxx: 1: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxx16Hxx: 2: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxx16Hxx: 3: 12G05 Galois cohomology [See also]14F22, 16Hxx, 16K5016K20: 1: 16P10 Finite rings and finite-dimensional algebras For semisimple, see 16K20; for commuta-
tive, see 11Txx, 13Mxx16K50: 1: 12G05 Galois cohomology [See also]14F22, 16Hxx, 16K5016K50: 2: 14F22 Brauer groups of schemes [See also]12G05, 16K5016Kxx: 1: 16D30 Infinite-dimensional simple rings (except as in 16Kxx)16Kxx: 1: 11R54 Other algebras and orders, and their zeta and L-functions [See also]11S45, 16Hxx,
16Kxx16Kxx: 2: 11S45 Algebras and orders, and their zeta functions [See also]11R52, 11R54, 16Hxx, 16Kxx16Kxx: 3: 12E15 Skew fields, division rings [See also]11R52, 11R54, 11S45, 16Kxx16Nxx: 1: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxx16S32: 1: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J1516S35: 1: 16K20 Finite-dimensional For crossed products, see 16S3516S80: 1: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H1516S90: 1: 16D90 Module categories [See also]16Gxx, 16S90; module theory in a category-theoretic
context; Morita equivalence and duality16S90: 2: 16N80 General radicals and rings For radicals in module categories, see 16S9016S90: 3: 18E40 Torsion theories, radicals [See also]13D30, 16S9016U10: 1: 16N60 Prime and semiprime rings [See also]16D60, 16U1016W80: 1: 06F25 Ordered rings, algebras, modules For ordered fields, see 12J15; see also 13J25, 16W8016W80: 2: 13Jxx Topological rings and modules [See also]16W60, 16W8016W80: 3: 22Axx Topological and differentiable algebraic systems For topological rings and fields, see
12Jxx, 13Jxx, 16W8016W80: 4: 54H13 Topological fields, rings, etc. [See also]12Jxx For algebraic aspects, see 13Jxx, 16W8016Y30: 1: 51J20 Representation by near-fields and near-algebras [See also]12K05, 16Y3016Y60: 1: 20M25 Semigroup rings, multiplicative semigroups of rings [See also]16S36, 16Y6016Z05: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1017-08: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1017-XX: 1: 16Yxx Generalizations For nonassociative rings, see 17-XX17B37: 1: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R5017B37: 1: 81R50 Quantum groups and related algebraic methods [See also]16T20, 17B3717B45: 1: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B4517B67: 1: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
477 Run: December 14, 2009
Mathematics Subject Classification 2010
17Bxx: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,see 15A75; for Clifford algebras, see 11E88, 15A66
17Bxx: 1: 22E60 Lie algebras of Lie groups For the algebraic theory of Lie algebras, see 17Bxx17C40: 1: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C5017C50: 1: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxx17C50: 1: 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[See also]16W10, 17C40, 17C5017C70: 1: 16W55 “Super” (or “skew”) structure [See also]17A70, 17Bxx, 17C70 For exterior algebras,
see 15A75; for Clifford algebras, see 11E88, 15A6617D92: 1: 92D10 Genetics For genetic algebras, see 17D9218A40: 1: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A3018B35: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5518C05: 1: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C1018C05: 1: 03C05 Equational classes, universal algebra [See also]08Axx, 08Bxx, 18C0518C10: 1: 03G30 Categorical logic, topoi [See also]18B25, 18C05, 18C1018C50: 1: 68Q55 Semantics [See also]03B70, 06B35, 18C5018D35: 1: 14L17 Affine algebraic groups, hyperalgebra constructions [See also]17B45, 18D3518E25: 1: 18G10 Resolutions; derived functors [See also]13D02, 16E05, 18E2518E40: 1: 13D30 Torsion theory [See also]13C12, 18E4018E40: 2: 16S90 Torsion theories; radicals on module categories [See also]13D30, 18E40 For radicals of
rings, see 16Nxx18F20: 1: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M2018F20: 2: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N3018F20: 3: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N3018F25: 1: 55N15 K-theory [See also]19Lxx For algebraic K-theory, see 18F25, 19-XX18F25: 2: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XX18F25: 1: 19-XX K-theory [See also]16E20, 18F2518F30: 1: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D5018F30: 1: 19Axx Grothendieck groups and K0 [See also]13D15, 18F3018Fxx: 1: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx18Gxx: 1: 13Dxx Homological methods For noncommutative rings, see 16Exx; for general categories,
see 18Gxx18Gxx: 2: 16Exx Homological methods For commutative rings, see 13Dxx; for general categories, see
18Gxx19-XX: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6719-XX: 1: 55N15 K-theory [See also]19Lxx For algebraic K-theory, see 18F25, 19-XX19-XX: 2: 55R50 Stable classes of vector space bundles, K-theory [See also]19Lxx For algebraic K-
theory, see 18F25, 19-XX19A31: 1: 11R34 Galois cohomology [See also]12Gxx, 19A3119Axx: 1: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D5019Axx: 2: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D5019Axx: 1: 18F30 Grothendieck groups [See also]13D15, 16E20, 19Axx19B14: 1: 15A15 Determinants, permanents, other special matrix functions [See also]19B10, 19B1419B37: 1: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F2019D50: 1: 13D15 Grothendieck groups, K-theory [See also]14C35, 18F30, 19Axx, 19D5019D50: 2: 16E20 Grothendieck groups, K-theory, etc. [See also]18F30, 19Axx, 19D5019F05: 1: 11G45 Geometric class field theory [See also]11R37, 14C35, 19F0519F27: 1: 11R42 Zeta functions and L-functions of number fields [See also]11M41, 19F2719F27: 2: 11S40 Zeta functions and L-functions [See also]11M41, 19F27
478 Run: December 14, 2009
Mathematics Subject Classification 2010
19G24: 1: 11E81 Algebraic theory of quadratic forms; Witt groups and rings [See also]19G12, 19G2419K33: 1: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M2019Kxx: 1: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J2219Kxx: 2: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx19L10: 1: 14C40 Riemann-Roch theorems [See also]19E20, 19L1019L41: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9019Lxx: 1: 55S25 K-theory operations and generalized cohomology operations [See also]19D55, 19Lxx20C07: 1: 16S34 Group rings [See also]20C05, 20C07, Laurent polynomial rings20D45: 1: 20E36 Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]20E08: 1: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxx20F10: 1: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R1520F10: 2: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R1520F10: 1: 03B25 Decidability of theories and sets of sentences [See also]11U05, 12L05, 20F1020F10: 2: 06B25 Free lattices, projective lattices, word problems [See also]03D40, 08A50, 20F1020F10: 3: 20A10 Metamathematical considerations For word problems, see 20F1020F10: 4: 20M05 Free semigroups, generators and relations, word problems [See also]03D40, 08A50,
20F1020F55: 1: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F5520G05: 1: 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
For the purely algebraic theory, see 20G0520G40: 1: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX20G42: 1: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R5020G42: 2: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B2320Gxx: 1: 14Lxx Algebraic groups For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B4520Gxx: 2: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxx20Gxx: 1: 11E57 Classical groups [See also]14Lxx, 20Gxx20Gxx: 2: 17B45 Lie algebras of linear algebraic groups [See also]14Lxx and 20Gxx20H10: 1: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E4020H10: 2: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxx20H10: 3: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F3520H15: 1: 51F15 Reflection groups, reflection geometries [See also]20H10, 20H15; for Coxeter groups, see
20F5520H15: 1: 82D25 Crystals For crystallographic group theory, see 20H1520H30: 1: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX20Hxx: 1: 15A30 Algebraic systems of matrices [See also]16S50, 20Gxx, 20Hxx20Jxx: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
20Jxx: 2: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx20L05: 1: 18A10 Graphs, diagram schemes, precategories [See especially 20L05]20L05: 2: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
20L05, 20Mxx20M05: 1: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7020M20: 1: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M2020M35: 1: 68Q70 Algebraic theory of languages and automata [See also]18B20, 20M3520Mxx: 1: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also]20Axx,
479 Run: December 14, 2009
Mathematics Subject Classification 2010
20L05, 20Mxx20N02: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0520N02: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0520N05: 1: 51A25 Algebraization [See also]12Kxx, 20N0520N05: 2: 53A60 Geometry of webs [See also]14C21, 20N0522-XX: 1: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxx22-XX: 2: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D0522A20: 1: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E4522A22: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0522A22: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0522A26: 1: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H1222A26: 2: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5522A26: 3: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H1222A26: 1: 06A12 Semilattices [See also]20M10; for topological semilattices see 22A2622A30: 1: 08C20 Natural dualities for classes of algebras [See also]06E15, 18A40, 22A3022B05: 1: 20K45 Topological methods [See also]22A05, 22B0522B05: 2: 43A70 Analysis on specific locally compact and other abelian groups [See also]11R56, 22B0522D40: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1022Dxx: 1: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E4522E40: 1: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F2022E40: 2: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxx22E40: 3: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxx22E40: 4: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T1522E40: 5: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F3522E40: 1: 11F06 Structure of modular groups and generalizations; arithmetic groups [See also]20H05,
20H10, 22E4022E40: 2: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E4022E45: 1: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C8022E45: 2: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22E45: 1: 43A65 Representations of groups, semigroups, etc. [See also]22A10, 22A20, 22Dxx, 22E4522E46: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22E46: 2: 43A90 Spherical functions [See also]22E45, 22E46, 33C5522E47: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22E50: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E45
22E50: 2: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22E50: 1: 11F33 Congruences for modular and p-adic modular forms [See also]14G20, 22E5022E50: 2: 11F85 p-adic theory, local fields [See also]14G20, 22E5022E50: 3: 11S37 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E5022E55: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
480 Run: December 14, 2009
Mathematics Subject Classification 2010
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4522E55: 1: 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also]11Fxx, 22E5522E55: 2: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;
for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22E65: 1: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
22E65: 1: 58H05 Pseudogroups and differentiable groupoids [See also]22A22, 22E6522E67: 1: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-
Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
22E70: 1: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations[See also]20C35, 22E70
22E70: 2: 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W -algebras and other current algebras and their representations [See also]17B65, 17B67, 22E65, 22E67,22E70
22Exx: 1: 20Gxx Linear algebraic groups and related topics For arithmetic theory, see 11E57, 11H56;for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47,22E50, 22E55
22Exx: 1: 17Bxx Lie algebras and Lie superalgebras For Lie groups, see 22Exx22Exx: 2: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
22Exx: 3: 43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exx
22Exx: 4: 43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see22Exx
26A21: 1: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets[See also]03E15, 26A21, 54H05
26A21: 2: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)[See also]03E15, 26A21, 28A05
26A33: 1: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
26A33: 2: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
26B25: 1: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,26Dxx
26B25: 1: 39B22 Equations for real functions [See also]26A51, 26B2526C10: 1: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C1526C10: 1: 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of
functions with bounded Dirichlet integral) For algebraic theory, see 12D10; for real methods, see 26C1026Dxx: 1: 39B62 Functional inequalities, including subadditivity, convexity, etc. [See also]26A51, 26B25,
26Dxx26E35: 1: 28E05 Nonstandard measure theory [See also]03H05, 26E3526E40: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S3026E50: 1: 28E10 Fuzzy measure theory [See also]03E72, 26E50, 94D0526E70: 1: 34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales
see 26E7026E70: 2: 34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or
measure chains, see 26E7028A05: 1: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H0528A05: 1: 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
481 Run: December 14, 2009
Mathematics Subject Classification 2010
[See also]03E15, 26A21, 28A0528A75: 1: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q2028B20: 1: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C0628Dxx: 1: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axx28Dxx: 2: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX28Dxx: 3: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxx28Dxx: 1: 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
[See also]11N99, 28Dxx28E05: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0528E05: 2: 26E35 Nonstandard analysis [See also]03H05, 28E05, 54J0528E10: 1: 26E50 Fuzzy real analysis [See also]03E72, 28E1028E10: 2: 94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1028E10: 3: 94D05 Fuzzy sets and logic (in connection with questions of Section 94) [See also]03B52, 03E72,
28E1030B70: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A1530C15: 1: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H0530C15: 1: 12D10 Polynomials: location of zeros (algebraic theorems) For the analytic theory, see 26C10,
30C1530C30: 1: 65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C3030C30: 2: 65E05 Numerical methods in complex analysis (potential theory, etc.) For numerical
methods in conformal mapping, see also 30C3030D05: 1: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XX30E05: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
30E05: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
30E10: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
30E10: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
30E25: 1: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A3530E25: 2: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A4030F35: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4530F35: 2: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxx30F35: 1: 32Nxx Automorphic functions [See also]11Fxx, 20H10, 22E40, 30F3530Fxx: 1: 32Jxx Compact analytic spaces For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic
theory, see 14Jxx30Fxx: 1: 32G15 Moduli of Riemann surfaces, Teichmuller theory [See also]14H15, 30Fxx30G06: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0530G35: 1: 32A30 Other generalizations of function theory of one complex variable (should also be assigned
at least one classification number from Section 30) For functions of several hypercomplex variables, see 30G3531A25: 1: 35Q15 Riemann-Hilbert problems [See also]30E25, 31A25, 31B2031B20: 1: 35Q15 Riemann-Hilbert problems [See also]30E25, 31A25, 31B2031B30: 1: 35J30 Higher-order elliptic equations [See also]31A30, 31B3031Bxx: 1: 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
482 Run: December 14, 2009
Mathematics Subject Classification 2010
[See also]31Axx, 31Bxx31D05: 1: 60J45 Probabilistic potential theory [See also]31Cxx, 31D0532A20: 1: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H0432A22: 1: 32H25 Picard-type theorems and generalizations For function-theoretic properties, see 32A2232A22: 2: 32H30 Value distribution theory in higher dimensions For function-theoretic properties, see
32A2232A25: 1: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A2732A25: 2: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M1532A27: 1: 32C30 Integration on analytic sets and spaces, currents For local theory, see 32A25 or 32A2732A35: 1: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B3032A37: 1: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B3032A38: 1: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J1032A38: 2: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B3032A40: 1: 46F20 Distributions and ultradistributions as boundary values of analytic functions
[See also]30D40, 30E25, 32A4032A45: 1: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J1532C05: 1: 14P15 Real analytic and semianalytic sets [See also]32B20, 32C0532C05: 2: 26E05 Real-analytic functions [See also]32B05, 32C0532C07: 1: 58A07 Real-analytic and Nash manifolds [See also]14P20, 32C0732C11: 1: 58A50 Supermanifolds and graded manifolds [See also]14A22, 32C1132C30: 1: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C3532C35: 1: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L1032C35: 2: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N3032C35: 3: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J1532C35: 4: 55N30 Sheaf cohomology [See also]18F20, 32C35, 32L1032C36: 1: 14B15 Local cohomology [See also]13D45, 32C3632C38: 1: 13N10 Rings of differential operators and their modules [See also]16S32, 32C3832C38: 2: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomi-
als [See also]13Nxx, 32C3832C38: 3: 16S32 Rings of differential operators [See also]13N10, 32C3832Cxx: 1: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx32Fxx: 1: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1532G13: 1: 14D20 Algebraic moduli problems, moduli of vector bundles For analytic moduli problems,
see 32G1332G15: 1: 14H15 Families, moduli (analytic) [See also]30F10, 32G1532G15: 2: 30F10 Compact Riemann surfaces and uniformization [See also]14H15, 32G1532G20: 1: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecture32G20: 1: 14H42 Theta functions; Schottky problem [See also]14K25, 32G2032G20: 2: 14K30 Picard schemes, higher Jacobians [See also]14H40, 32G2032G34: 1: 34Mxx Differential equations in the complex domain [See also]30Dxx, 32G3432Gxx: 1: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxx32Gxx: 1: 13D10 Deformations and infinitesimal methods [See also]14B10, 14B12, 14D15, 32Gxx32Gxx: 2: 14D15 Formal methods; deformations [See also]13D10, 14B07, 32Gxx32H02: 1: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
32H02, 32H0432H04: 1: 37F10 Polynomials; rational maps; entire and meromorphic functions [See also]32A10, 32A20,
483 Run: December 14, 2009
Mathematics Subject Classification 2010
32H02, 32H0432H25: 1: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H3032H30: 1: 32A22 Nevanlinna theory (local); growth estimates; other inequalities For geometric theory,
see 32H25, 32H3032H50: 1: 37Fxx Complex dynamical systems [See also]30D05, 32H5032J25: 1: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecture32J25: 2: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S3532Jxx: 1: 14Jxx Surfaces and higher-dimensional varieties For analytic theory, see 32Jxx32Jxx: 2: 57N13 Topology of E4, 4-manifolds [See also]14Jxx, 32Jxx32L10: 1: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N3032L10: 1: 14F40 de Rham cohomology [See also]14C30, 32C35, 32L1032L10: 2: 55N30 Sheaf cohomology [See also]18F20, 32C35, 32L1032Lxx: 1: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M2032Lxx: 2: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx32Lxx: 3: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2532Lxx: 1: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
[See also]14D20, 14F05, 32Lxx32M10: 1: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T1532M15: 1: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M1532Nxx: 1: 11Fxx Discontinuous groups and automorphic forms [See also]11R39, 11S37, 14Gxx, 14Kxx,
22E50, 22E55, 30F35, 32Nxx For relations with quadratic forms, see 11E4532Nxx: 2: 20H10 Fuchsian groups and their generalizations [See also]11F06, 22E40, 30F35, 32Nxx32Nxx: 3: 22E40 Discrete subgroups of Lie groups [See also]20Hxx, 32Nxx32Nxx: 4: 30F35 Fuchsian groups and automorphic functions [See also]11Fxx, 20H10, 22E40, 32Gxx,
32Nxx32P05: 1: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S1032P05: 1: 46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean
functional analysis [See also]12J25, 32P0532Qxx: 1: 57-XX Manifolds and cell complexes For complex manifolds, see 32Qxx32S20: 1: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S4532S30: 1: 14B07 Deformations of singularities [See also]14D15, 32S3032S35: 1: 14C30 Transcendental methods, Hodge theory [See also]14D07, 32G20, 32J25, 32S35, Hodge
conjecture32S35: 2: 58A14 Hodge theory [See also]14C30, 14Fxx, 32J25, 32S3532S40: 1: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J1532S40: 1: 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic
geometry [See also]14D05, 32S4032S45: 1: 14E15 Global theory and resolution of singularities [See also]14B05, 32S20, 32S4532S60: 1: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J1532S65: 1: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxx32Sxx: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxx
32W10: 1: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,58J10
32Wxx: 1: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,53Cxx For geometric integration theory, see 49Q15
33-XX: 1: 33-XX Special functions (33-XX deals with the properties of functions as functions) Fororthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
33-XX: 1: 11B37 Recurrences For applications to special functions, see 33-XX33C50: 1: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D45
484 Run: December 14, 2009
Mathematics Subject Classification 2010
33C55: 1: 43A90 Spherical functions [See also]22E45, 22E46, 33C5533C80: 1: 05E15 Combinatorial aspects of groups and algebras [See also]14Nxx, 22E45, 33C8033Cxx: 1: 05A10 Factorials, binomial coefficients, combinatorial functions [See also]11B65, 33Cxx33D45: 1: 42C05 Orthogonal functions and polynomials, general theory [See also]33C45, 33C50, 33D4533Dxx: 1: 05A15 Exact enumeration problems, generating functions [See also]33Cxx, 33Dxx33F10: 1: 68W30 Symbolic computation and algebraic computation [See also]11Yxx, 12Y05, 13Pxx,
14Qxx, 16Z05, 17-08, 33F1034Cxx: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX34D08: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx34Dxx: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX34Dxx: 1: 37Cxx Smooth dynamical systems: general theory [See also]34Cxx, 34Dxx34F05: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx34K18: 1: 37Gxx Local and nonlocal bifurcation theory [See also]34C23, 34K1834K30: 1: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G2034K30: 2: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G2034K30: 1: 47D06 One-parameter semigroups and linear evolution equations [See also]34G10, 34K3034K35: 1: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XX34K50: 1: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H1534L25: 1: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A4034L40: 1: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A4034Lxx: 1: 34Bxx Boundary value problems For ordinary differential operators, see 34Lxx34Lxx: 2: 47Exx Ordinary differential operators [See also]34Bxx, 34Lxx34Lxx: 3: 47E05 Ordinary differential operators [See also]34Bxx, 34Lxx (should also be assigned at least
one other classification number in section 47)34Mxx: 1: 37F75 Holomorphic foliations and vector fields [See also]32M25, 32S65, 34Mxx34N05: 1: 26E70 Real analysis on time scales or measure chains For dynamic equations on time scales
or measure chains see 34N0534N05: 2: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N0535-XX: 1: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H0535-XX: 2: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxx35A27: 1: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J1535Bxx: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX35Dxx: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J3535J10: 1: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L0535K05: 1: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L0535K90: 1: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2535K90: 2: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxx35L05: 1: 35Qxx Equations of mathematical physics and other areas of application [See also]35J05, 35J10,
35K05, 35L0535L65: 1: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q3035L90: 1: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2535L90: 2: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
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35R15, 37Lxx, 47Jxx35P25: 1: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxx35P25: 2: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A4035Pxx: 1: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7535Pxx: 2: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7535Q30: 1: 76N10 Existence, uniqueness, and regularity theory [See also]35L60, 35L65, 35Q3035Qxx: 1: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2535Qxx: 1: 37Kxx Infinite-dimensional Hamiltonian systems [See also]35Axx, 35Qxx35Qxx: 2: 37Lxx Infinite-dimensional dissipative dynamical systems [See also]35Bxx, 35Qxx35R09: 1: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxx35R09: 2: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2035R09: 3: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2035R09: 4: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx35R10: 1: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxx35R10: 2: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2035R10: 3: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2035R10: 4: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx35R15: 1: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxx35R20: 1: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2535R30: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J3535R35: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J3537-XX: 1: 39Axx Difference equations For dynamical systems, see 37-XX; for dynamic equations on
time scales, see 34N0537-XX: 2: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D0537-XX: 1: 39B12 Iteration theory, iterative and composite equations [See also]26A18, 30D05, 37-XX37-XX: 2: 58Kxx Theory of singularities and catastrophe theory [See also]32Sxx, 37-XX37-XX: 3: 70Kxx Nonlinear dynamics [See also]34Cxx, 37-XX37A45: 1: 37Pxx Arithmetic and non-Archimedean dynamical systems [See also]11S82, 37A4537Axx: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1037Axx: 2: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxx37Axx: 3: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A3537Axx: 1: 22F10 Measurable group actions [See also]22D40, 28Dxx, 37Axx37Axx: 2: 47A35 Ergodic theory [See also]28Dxx, 37Axx37Bxx: 1: 54H20 Topological dynamics [See also]28Dxx, 37Bxx37C10: 1: 57R27 Controllability of vector fields on C∞ and real-analytic manifolds [See also]49Qxx,
37C10, 93B0537Cxx: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2537Cxx: 2: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxx37D45: 1: 34D45 Attractors [See also]37C70, 37D4537Dxx: 1: 37B10 Symbolic dynamics [See also]37Cxx, 37Dxx37Dxx: 2: 37H15 Multiplicative ergodic theory, Lyapunov exponents [See also]34D08, 37Axx, 37Cxx,
37Dxx37Exx: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2537Fxx: 1: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XX37Gxx: 1: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E0937J35: 1: 81R12 Relations with integrable systems [See also]17Bxx, 37J3537K15: 1: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxx37K50: 1: 35B32 Bifurcation [See also]37Gxx, 37K5037Kxx: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D25
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37Kxx: 2: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H2037Kxx: 3: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2537Lxx: 1: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H2037Lxx: 2: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2537Lxx: 3: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxx37Lxx: 4: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX37P30: 1: 11G50 Heights [See also]14G40, 37P3037P30: 2: 14G40 Arithmetic varieties and schemes; Arakelov theory; heights [See also]11G50, 37P3039-XX: 1: 30D05 Functional equations in the complex domain, iteration and composition of analytic
functions [See also]34Mxx, 37Fxx, 39-XX39B12: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2539B72: 1: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E1540A15: 1: 11A55 Continued fractions For approximation results, see 11J70 [See also]11K50, 30B70,
40A1540A15: 2: 30B70 Continued fractions [See also]11A55, 40A1541-XX: 1: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxx41A25: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,
etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
41A27: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
42-XX: 1: 30B50 Dirichlet series and other series expansions, exponential series [See also]11M41, 42-XX42A10: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
42A10: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
42A10: 1: 41A10 Approximation by polynomials For approximation by trigonometric polynomials, see42A10
42A15: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
42A15: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
42A16: 1: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities,etc.) For properties determined by Fourier coefficients, see 42A16; for those determined by approximationproperties, see 41A25, 41A27
42A38: 1: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
42A38: 2: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
42A70: 1: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,42A70, 42A82, 44A60
42A82: 1: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,42A70, 42A82, 44A60
42B10: 1: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For
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numerical methods, see 65R1042B10: 2: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
42B25: 1: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,see 39B72; for probabilistic inequalities, see 60E15
42B30: 1: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J1542B30: 1: 46J15 Banach algebras of differentiable or analytic functions, Hp-spaces [See also]30H10,
32A35, 32A37, 32A38, 42B3042Cxx: 1: 33-XX Special functions (33-XX deals with the properties of functions as functions) For
orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; forrepresentation theory see 22Exx
43-XX: 1: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.For abstract harmonic analysis, see 43-XX
43-XX: 2: 22E30 Analysis on real and complex Lie groups [See also]33C80, 43-XX43A05: 1: 28C10 Set functions and measures on topological groups or semigroups, Haar measures,
invariant measures [See also]22Axx, 43A0543A10: 1: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A2043A20: 1: 46Hxx Topological algebras, normed rings and algebras, Banach algebras For group algebras,
convolution algebras and measure algebras, see 43A10, 43A2043A80: 1: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A9043A85: 1: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A9043A85: 2: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J1543A90: 1: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A9044-XX: 1: 46F12 Integral transforms in distribution spaces [See also]42-XX, 44-XX44A15: 1: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A3544A35: 1: 45Exx Singular integral equations [See also]30E20, 30E25, 44A15, 44A3544A60: 1: 47A57 Operator methods in interpolation, moment and extension problems [See also]30E05,
42A70, 42A82, 44A6045Jxx: 1: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx45Kxx: 1: 47G20 Integro-differential operators [See also]34K30, 35R09, 35R10, 45Jxx, 45Kxx45P05: 1: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7545P05: 2: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7545P05: 1: 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiı, Uryson, etc.)
[See also]45Gxx, 45P0546-XX: 1: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1546A35: 1: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B1546A35: 2: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)46B15: 1: 40Jxx Summability in abstract structures [See also]43A55, 46A35, 46B1546B15: 2: 40J05 Summability in abstract structures [See also]43A55, 46A35, 46B15 (should also be
assigned at least one other classification number in this section)46B22: 1: 46G10 Vector-valued measures and integration [See also]28Bxx, 46B2246B28: 1: 46M05 Tensor products [See also]46A32, 46B28, 47A8046B28: 1: 47L05 Linear spaces of operators [See also]46A32 and 46B2846B40: 1: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B4246B40: 1: 46B42 Banach lattices [See also]46A40, 46B4046B42: 1: 46A40 Ordered topological linear spaces, vector lattices [See also]06F20, 46B40, 46B4246B42: 2: 46B40 Ordered normed spaces [See also]46A40, 46B4246E35: 1: 46F05 Topological linear spaces of test functions, distributions and ultradistributions
[See also]46E10, 46E3546E50: 1: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C10
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46Exx: 1: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)[See also]46Txx, 53Cxx
46Exx: 1: 46Axx Topological linear spaces and related structures For function spaces, see 46Exx46Exx: 2: 46Bxx Normed linear spaces and Banach spaces; Banach lattices For function spaces, see
46Exx46Exx: 3: 46Cxx Inner product spaces and their generalizations, Hilbert spaces For function spaces, see
46Exx46F05: 1: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J1046F12: 1: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
46F12: 2: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
46G05: 1: 58C20 Differentiation theory (Gateaux, Frechet, etc.) [See also]26Exx, 46G0546G10: 1: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxx46G12: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XX46G20: 1: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B1246G20: 2: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H6046G20: 1: 58B12 Questions of holomorphy [See also]32-XX, 46G2046G25: 1: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H6046Gxx: 1: 46E27 Spaces of measures [See also]28A33, 46Gxx46J10: 1: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J1546J10: 2: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J1546J10: 1: 46Exx Linear function spaces and their duals [See also]30H05, 32A38, 46F05 For function
algebras, see 46J1046J15: 1: 32A35 Hp-spaces, Nevanlinna spaces [See also]32M15, 42B30, 43A85, 46J1546J15: 2: 32A38 Algebras of holomorphic functions [See also]30H05, 46J10, 46J1546J15: 3: 46E25 Rings and algebras of continuous, differentiable or analytic functions For Banach
function algebras, see 46J10, 46J1546K70: 1: 46L70 Nonassociative selfadjoint operator algebras [See also]46H70, 46K7046Kxx: 1: 16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also]17B60,
17C50, 46Kxx46L05: 1: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M2046L10: 1: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M2046L70: 1: 17C65 Jordan structures on Banach spaces and algebras [See also]46H70, 46L7046L70: 2: 46H70 Nonassociative topological algebras [See also]46K70, 46L7046L70: 3: 46K70 Nonassociative topological algebras with an involution [See also]46H70, 46L7046L80: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6746L80: 2: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J2246L80: 3: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M2046L80: 4: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx46L80: 5: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M2046L80: 1: 58J20 Index theory and related fixed point theorems [See also]19K56, 46L8046L87: 1: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B3446Lxx: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX46M05: 1: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L20
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46M05: 2: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,47L05, 47L20
46M15: 1: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx
46M18: 1: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M2046M18: 2: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx46M20: 1: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J2246M20: 2: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2546M20: 1: 14F05 Sheaves, derived categories of sheaves and related constructions [See also]14H60, 14J60,
18F20, 32Lxx, 46M2046M20: 2: 19Kxx K-theory and operator algebras [See mainly]46L80, and also 46M2046M20: 3: 46M15 Categories, functors For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M2046M20: 4: 58J22 Exotic index theories [See also]19K56, 46L05, 46L10, 46L80, 46M2046M35: 1: 46C07 Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
[See also]46B70, 46M3546N55: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1046S10: 1: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S1046S10: 2: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S1046S20: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0546S20: 1: 46M07 Ultraproducts [See also]46B08, 46S2046S30: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S3046T12: 1: 46G12 Measures and integration on abstract linear spaces [See also]28C20, 46T1246T12: 2: 58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also]28Cxx, 46T1246T25: 1: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C1046Txx: 1: 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also]28-XX, 46Txx47A35: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1047A35: 1: 37A30 Ergodic theorems, spectral theory, Markov operators For operator ergodic theory, see
mainly 47A3547A35: 2: 47H25 Nonlinear ergodic theorems [See also]28Dxx, 37Axx, 47A3547A40: 1: 81Uxx Scattering theory [See also]34A55, 34L25, 34L40, 35P25, 47A4047A50: 1: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47A52: 1: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R3047A57: 1: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N7047A75: 1: 45Cxx Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7547A75: 2: 45C05 Eigenvalue problems [See also]34Lxx, 35Pxx, 45P05, 47A7547A80: 1: 46M05 Tensor products [See also]46A32, 46B28, 47A8047B35: 1: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N7047B80: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx47Bxx: 1: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F0547D03: 1: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47D06: 1: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47D07: 1: 60J35 Transition functions, generators and resolvents [See also]47D03, 47D0747D09: 1: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47D09: 1: 34G10 Linear equations [See also]47D06, 47D0947Dxx: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
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Mathematics Subject Classification 2010
58D2547F05: 1: 35Pxx Spectral theory and eigenvalue problems [See also]47Axx, 47Bxx, 47F0547G10: 1: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also]45P05, 47G10 for
other integral operators; see also 32A25, 32M1547G10: 1: 45Pxx Integral operators [See also]47B38, 47G1047G10: 2: 45P05 Integral operators [See also]47B38, 47G1047G20: 1: 45Jxx Integro-ordinary differential equations [See also]34K05, 34K30, 47G2047G20: 2: 45J05 Integro-ordinary differential equations [See also]34K05, 34K30, 47G2047G20: 3: 45Kxx Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2047G20: 4: 45K05 Integro-partial differential equations [See also]34K30, 35R09, 35R10, 47G2047H04: 1: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C0647H04: 2: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C0647H10: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2547H20: 1: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H1547H20: 2: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47H20: 3: 47D03 Groups and semigroups of linear operators For nonlinear operators, see 47H20; see
also 20M2047H20: 4: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2547H20: 1: 58D07 Groups and semigroups of nonlinear operators [See also]17B65, 47H2047H60: 1: 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also]46G20, 46G25, 47H6047H60: 2: 46G25 (Spaces of) multilinear mappings, polynomials [See also]46E50, 46G20, 47H6047Hxx: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D2547Hxx: 2: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1547Hxx: 3: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxx47J06: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R3047J25: 1: 47J05 Equations involving nonlinear operators (general) [See also]47H10, 47J2547J35: 1: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D0747Jxx: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D2547Jxx: 2: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxx47Jxx: 3: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C3047Jxx: 1: 34G20 Nonlinear equations [See also]47Hxx, 47Jxx47Jxx: 2: 34K30 Equations in abstract spaces [See also]34Gxx, 35R09, 35R10, 47Jxx47Jxx: 3: 35R20 Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for
abstract space valued functions) [See also]34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx47Jxx: 4: 45Gxx Nonlinear integral equations [See also]47H30, 47Jxx47Jxx: 5: 58Cxx Calculus on manifolds; nonlinear operators [See also]46Txx, 47Hxx, 47Jxx47Jxx: 6: 58D25 Equations in function spaces; evolution equations [See also]34Gxx, 35K90, 35L90,
35R15, 37Lxx, 47Jxx47L05: 1: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L2047L05: 2: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L2047L20: 1: 46A32 Spaces of linear operators; topological tensor products; approximation properties
[See also]46B28, 46M05, 47L05, 47L2047L20: 2: 46B28 Spaces of operators; tensor products; approximation properties [See also]46A32, 46M05,
47L05, 47L2047L90: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1047Lxx: 1: 46Lxx Selfadjoint operator algebras (C∗-algebras, von Neumann (W ∗-) algebras, etc.)
[See also]22D25, 47Lxx
491 Run: December 14, 2009
Mathematics Subject Classification 2010
47N70: 1: 93B28 Operator-theoretic methods [See also]47A48, 47A57, 47B35, 47N7047S10: 1: 12J25 Non-Archimedean valued fields [See also]30G06, 32P05, 46S10, 47S1047S10: 2: 12J27 Krasner-Tate algebras [See mainly]32P05; see also 46S10, 47S1047S20: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0547S30: 1: 03F60 Constructive and recursive analysis [See also]03B30, 03D45, 03D78, 26E40, 46S30, 47S30
49-XX: 1: 93-XX Systems theory; control For optimal control, see 49-XX49J21: 1: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K2149J40: 1: 35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities
[See also]35R35, 49J4049J40: 2: 35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities
[See also]35R35, 49J4049J40: 3: 35J88 Systems of elliptic variational inequalities [See also]35R35, 49J4049J40: 4: 35K85 Linear parabolic unilateral problems and linear parabolic variational inequalities
[See also]35R35, 49J4049J40: 5: 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities
[See also]35R35, 49J4049J40: 6: 35K87 Systems of parabolic variational inequalities [See also]35R35, 49J4049J40: 7: 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities
[See also]35R35, 49J4049J40: 8: 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational
inequalities [See also]35R35, 49J4049J40: 9: 35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also]35R35,
49J4049J40: 10: 35M85 Linear unilateral problems and variational inequalities of mixed type [See also]35R35,
49J4049J40: 11: 35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
[See also]35R35, 49J4049J40: 12: 35M87 Systems of variational inequalities of mixed type [See also]35R35, 49J4049J52: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxx49J53: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxx49J53: 2: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxx49K15: 1: 34Hxx Control problems [See also]49J15, 49K15, 93C1549K15: 2: 34H05 Control problems [See also]49J15, 49K15, 93C1549K21: 1: 34K35 Control problems [See also]49J21, 49K21, 93C2349K21: 1: 34A60 Differential inclusions [See also]49J21, 49K2149K21: 2: 47J22 Variational and other types of inclusions [See also]34A60, 49J21, 49K2149Q10: 1: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C4249Q10: 2: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R4249Q15: 1: 28A75 Length, area, volume, other geometric measure theory [See also]26B15, 49Q1549Q15: 2: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1549Q20: 1: 52A38 Length, area, volume [See also]26B15, 28A75, 49Q2049R05: 1: 47A75 Eigenvalue problems [See also]47J10, 49R0551-XX: 1: 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
[See also]05Bxx, 12F10, 20G40, 20H30, 51-XX51Exx: 1: 05B25 Finite geometries [See also]51D20, 51Exx51F15: 1: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D2551F15: 1: 20F55 Reflection and Coxeter groups [See also]22E40, 51F1551F20: 1: 20H05 Unimodular groups, congruence subgroups [See also]11F06, 19B37, 22E40, 51F20
51M20: 1: 52C20 Tilings in 2 dimensions [See also]05B45, 51M20
492 Run: December 14, 2009
Mathematics Subject Classification 2010
51M20: 2: 52C22 Tilings in n dimensions [See also]05B45, 51M2051M25: 1: 26B15 Integration: length, area, volume [See also]28A75, 51M2551M35: 1: 14M15 Grassmannians, Schubert varieties, flag manifolds [See also]32M10, 51M3551N30: 1: 14L35 Classical groups (geometric aspects) [See also]20Gxx, 51N3052A40: 1: 51M16 Inequalities and extremum problems For convex problems, see 52A4052B20: 1: 14Txx Tropical geometry [See also]12K10, 14M25, 14N10, 52B2052B20: 2: 14T05 Tropical geometry [See also]12K10, 14M25, 14N10, 52B2052C05: 1: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C0752C07: 1: 11H06 Lattices and convex bodies [See also]11P21, 52C05, 52C0752C15: 1: 05B40 Packing and covering [See also]11H31, 52C15, 52C1752C15: 2: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C1752C17: 1: 05B40 Packing and covering [See also]11H31, 52C15, 52C1752C17: 2: 11H31 Lattice packing and covering [See also]05B40, 52C15, 52C1752C22: 1: 05B45 Tessellation and tiling problems [See also]52C20, 52C2252Cxx: 1: 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial
structures, etc.) [See also]05B35, 52Cxx53A10: 1: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R4253C30: 1: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T1553C35: 1: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T1553C42: 1: 53A10 Minimal surfaces, surfaces with prescribed mean curvature [See also]49Q05, 49Q10,
53C4253C45: 1: 52A15 Convex sets in 3 dimensions (including convex surfaces) [See also]53A05, 53C4553C45: 2: 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also]53A07, 53C4553C60: 1: 58B20 Riemannian, Finsler and other geometric structures [See also]53C20, 53C6053C65: 1: 58A25 Currents [See also]32C30, 53C6553C65: 2: 60Dxx Geometric probability and stochastic geometry [See also]52A22, 53C6553C65: 3: 60D05 Geometric probability and stochastic geometry [See also]52A22, 53C6553C70: 1: 51H25 Geometries with differentiable structure [See also]53Cxx, 53C7053Cxx: 1: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxx53Cxx: 1: 58-XX Global analysis, analysis on manifolds [See also]32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx,
53Cxx For geometric integration theory, see 49Q1553Cxx: 2: 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
[See also]46Txx, 53Cxx53Cxx: 3: 58Jxx Partial differential equations on manifolds; differential operators [See also]32Wxx, 35-
XX, 53Cxx53D37: 1: 14J33 Mirror symmetry [See also]11G42, 53D3753Dxx: 1: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx54-XX: 1: 06D22 Frames, locales For topological questions see 54-XX54B40: 1: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N3054C35: 1: 58D15 Manifolds of mappings [See also]46T10, 54C3554C50: 1: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H0554C60: 1: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B1454C60: 2: 47H04 Set-valued operators [See also]28B20, 54C60, 58C0654C60: 3: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C0654C60: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxx54C60: 2: 58C06 Set valued and function-space valued mappings [See also]47H04, 54C6054C65: 1: 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable
selections [See also]26E25, 54C60, 54C65, 91B1454D80: 1: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
[See also]03Exx For ultrafilters, see 54D8054F05: 1: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H12
493 Run: December 14, 2009
Mathematics Subject Classification 2010
54F05: 2: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H1254H05: 1: 03E15 Descriptive set theory [See also]28A05, 54H0554H05: 2: 26A21 Classification of real functions; Baire classification of sets and functions [See also]03E15,
28A05, 54C50, 54H0554H05: 3: 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets
[See also]03E15, 26A21, 54H0554H12: 1: 06B30 Topological lattices, order topologies [See also]06F30, 22A26, 54F05, 54H1254H12: 2: 06F30 Topological lattices, order topologies [See also]06B30, 22A26, 54F05, 54H1254H15: 1: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XX54H15: 2: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D0754H15: 3: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D0554H15: 1: 20M20 Semigroups of transformations, etc. [See also]47D03, 47H20, 54H1554H20: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1054H20: 1: 46L55 Noncommutative dynamical systems [See also]28Dxx, 37Kxx, 37Lxx, 54H2054H25: 1: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C3054H25: 1: 26A18 Iteration [See also]37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H2554J05: 1: 03H05 Nonstandard models in mathematics [See also]26E35, 28E05, 30G06, 46S20, 47S20,
54J0554J05: 2: 26E35 Nonstandard analysis [See also]03H05, 28E05, 54J05
55M20: 1: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C3055M20: 1: 54H25 Fixed-point and coincidence theorems [See also]47H10, 55M2055N07: 1: 55Q70 Homotopy groups of special types [See also]55N05, 55N0755N30: 1: 18F20 Presheaves and sheaves [See also]14F05, 32C35, 32L10, 54B40, 55N3055N30: 2: 32C35 Analytic sheaves and cohomology groups [See also]14Fxx, 18F20, 55N3055N30: 3: 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also]14F05, 18F20, 55N3055Nxx: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
55Nxx: 2: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx55Nxx: 1: 54F35 Higher-dimensional local connectedness [See also]55Mxx, 55Nxx55P55: 1: 57N25 Shapes [See also]54C56, 55P55, 55Q0755P91: 1: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S9155Q07: 1: 55P55 Shape theory [See also]54C56, 55Q0755Q07: 2: 57N25 Shapes [See also]54C56, 55P55, 55Q0755Q91: 1: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S9155R20: 1: 55Txx Spectral sequences [See also]18G40, 55R2055R50: 1: 19Lxx Topological K-theory [See also]55N15, 55R50, 55S2555R91: 1: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S9155Rxx: 1: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J2255Rxx: 2: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxx55Rxx: 1: 46M20 Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also]14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx55S25: 1: 19Lxx Topological K-theory [See also]55N15, 55R50, 55S2555S91: 1: 19L47 Equivariant K-theory [See also]55N91, 55P91, 55Q91, 55R91, 55S9155T20: 1: 57T35 Applications of Eilenberg-Moore spectral sequences [See also]55R20, 55T2055U15: 1: 18G35 Chain complexes [See also]18E30, 55U1555Uxx: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
55Uxx: 2: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx55Uxx: 1: 57T30 Bar and cobar constructions [See also]18G55, 55Uxx57M25: 1: 05C10 Planar graphs; geometric and topological aspects of graph theory [See also]57M15,
494 Run: December 14, 2009
Mathematics Subject Classification 2010
57M2557M25: 2: 57Q45 Knots and links (in high dimensions) For the low-dimensional case, see 57M2557M60: 1: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E4057Mxx: 1: 20F65 Geometric group theory [See also]05C25, 20E08, 57Mxx57N20: 1: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxx57N25: 1: 54C56 Shape theory [See also]55P55, 57N2557N55: 1: 57Q50 Microbundles and block bundles [See also]55R60, 57N5557Nxx: 1: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxx57Nxx: 1: 54-XX General topology For the topology of manifolds of all dimensions, see 57Nxx57Nxx: 2: 55Mxx Classical topics For the topology of Euclidean spaces and manifolds, see 57Nxx57Pxx: 1: 18F15 Abstract manifolds and fiber bundles [See also]55Rxx, 57Pxx57Q10: 1: 55Pxx Homotopy theory For simple homotopy type, see 57Q1057Q45: 1: 32S55 Milnor fibration; relations with knot theory [See also]57M25, 57Q4557Q45: 2: 57M25 Knots and links in S3 For higher dimensions, see 57Q4557Q50: 1: 55R60 Microbundles and block bundles [See also]57N55, 57Q5057Q50: 2: 57N55 Microbundles and block bundles [See also]55R60, 57Q5057R20: 1: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2557R20: 1: 55R40 Homology of classifying spaces, characteristic classes [See also]57Txx, 57R2057R22: 1: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2557R25: 1: 55Rxx Fiber spaces and bundles [See also]18F15, 32Lxx, 46M20, 57R20, 57R22, 57R2557R30: 1: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxx57R32: 1: 53C12 Foliations (differential geometric aspects) [See also]57R30, 57R3257R40: 1: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R4257R42: 1: 53C42 Immersions (minimal, prescribed curvature, tight, etc.) [See also]49Q05, 49Q10, 53A10,
57R40, 57R4257R65: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6757R67: 1: 18F25 Algebraic K-theory and L-theory [See also]11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx,
16E20, 19-XX, 46L80, 57R65, 57R6757R75: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9057R77: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9057R85: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9057R90: 1: 55N22 Bordism and cobordism theories, formal group laws [See also]14L05, 19L41, 57R75,
57R77, 57R85, 57R9057Rxx: 1: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axx57Rxx: 1: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxx57S05: 1: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds [See also]22E65, 57S0557S20: 1: 22F05 General theory of group and pseudogroup actions For topological properties of spaces
with an action, see 57S2057Sxx: 1: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XX57Sxx: 2: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;
for analysis thereon, see 43A80, 43A85, 43A9057Sxx: 3: 22F30 Homogeneous spaces For general actions on manifolds or preserving geometrical
structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E4057Sxx: 1: 20F34 Fundamental groups and their automorphisms [See also]57M05, 57Sxx57Sxx: 2: 37C85 Dynamics of group actions other than Z and R, and foliations [See mainly]22Fxx, and
also 57R30, 57Sxx
495 Run: December 14, 2009
Mathematics Subject Classification 2010
57Sxx: 3: 54H15 Transformation groups and semigroups [See also]20M20, 22-XX, 57Sxx57T05: 1: 16T05 Hopf algebras and their applications [See also]16S40, 57T0557T15: 1: 14M17 Homogeneous spaces and generalizations [See also]32M10, 53C30, 57T1557T15: 2: 32M10 Homogeneous complex manifolds [See also]14M17, 57T1557T15: 3: 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
[See also]22E10, 22E40, 53C35, 57T1557T15: 4: 53C30 Homogeneous manifolds [See also]14M15, 14M17, 32M10, 57T1557T15: 5: 53C35 Symmetric spaces [See also]32M15, 57T1557Txx: 1: 18-XX Category theory; homological algebra For commutative rings see 13Dxx, for
associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and55Uxx for algebraic topology
57Txx: 2: 22Exx Lie groups For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx;for analysis thereon, see 43A80, 43A85, 43A90
57Txx: 3: 22E41 Continuous cohomology [See also]57R32, 57Txx, 58H1057Txx: 1: 18Gxx Homological algebra [See also]13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx58-XX: 1: 22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX.
For abstract harmonic analysis, see 43-XX58-XX: 2: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxx58-XX: 3: 53Cxx Global differential geometry [See also]51H25, 58-XX; for related bundle theory, see
55Rxx, 57Rxx58-XX: 1: 28-XX Measure and integration For analysis on manifolds, see 58-XX58-XX: 2: 30-XX Functions of a complex variable For analysis on manifolds, see 58-XX58-XX: 3: 47Jxx Equations and inequalities involving nonlinear operators [See also]46Txx For global
and geometric aspects, see 58-XX58A07: 1: 14P20 Nash functions and manifolds [See also]32C07, 58A0758A07: 2: 32C05 Real-analytic manifolds, real-analytic spaces [See also]14Pxx, 58A0758A14: 1: 31C12 Potential theory on Riemannian manifolds [See also]53C20; for Hodge theory, see 58A1458A17: 1: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxx58A25: 1: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C3558A50: 1: 14M30 Supervarieties [See also]32C11, 58A5058A50: 2: 32C11 Complex supergeometry [See also]14A22, 14M30, 58A5058Axx: 1: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxx58Axx: 1: 53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions
of differentiable manifolds, see 58Axx58Axx: 2: 70G45 Differential-geometric methods (tensors, connections, symplectic, Poisson, contact,
Riemannian, nonholonomic, etc.) [See also]53Cxx, 53Dxx, 58Axx58B12: 1: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C1058B12: 1: 32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy,
see 46G20, 58B1258B20: 1: 53C20 Global Riemannian geometry, including pinching [See also]31C12, 58B2058B25: 1: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
[See also]17B65, 58B25, 58H0558B34: 1: 46L85 Noncommutative topology [See also]58B32, 58B34, 58J2258B34: 2: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J2258B34: 3: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J2258B34: 1: 81T75 Noncommutative geometry methods [See also]46L85, 46L87, 58B3458Bxx: 1: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H1558Bxx: 2: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxx58Bxx: 1: 46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx,
58Bxx58Bxx: 2: 57Rxx Differential topology For foundational questions of differentiable manifolds, see
58Axx; for infinite-dimensional manifolds, see 58Bxx
496 Run: December 14, 2009
Mathematics Subject Classification 2010
58C06: 1: 47H04 Set-valued operators [See also]28B20, 54C60, 58C0658C06: 2: 49J53 Set-valued and variational analysis [See also]28B20, 47H04, 54C60, 58C0658C06: 3: 54C60 Set-valued maps [See also]26E25, 28B20, 47H04, 58C0658C10: 1: 46G20 Infinite-dimensional holomorphy [See also]32-XX, 46E50, 46T25, 58B12, 58C1058C15: 1: 47J07 Abstract inverse mapping and implicit function theorems [See also]46T20 and 58C1558C20: 1: 46G05 Derivatives [See also]46T20, 58C20, 58C2558C20: 1: 49J50 Frechet and Gateaux differentiability [See also]46G05, 58C2058C25: 1: 46G05 Derivatives [See also]46T20, 58C20, 58C2558C30: 1: 47H10 Fixed-point theorems [See also]37C25, 54H25, 55M20, 58C3058C30: 2: 47H11 Degree theory [See also]55M25, 58C3058C35: 1: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D2058C35: 2: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B1158C35: 1: 49Q15 Geometric measure and integration theory, integral and normal currents
[See also]28A75, 32C30, 58A25, 58C3558C40: 1: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C3058C50: 1: 49J52 Nonsmooth analysis [See also]46G05, 58C50, 90C5658C50: 1: 46S60 Functional analysis on superspaces (supermanifolds) or graded spaces [See also]58A50
and 58C5058Cxx: 1: 26E25 Set-valued functions [See also]28B20, 49J53, 54C60 For nonsmooth analysis, see
49J52, 58Cxx, 90Cxx58Cxx: 2: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxx58Cxx: 1: 26E15 Calculus of functions on infinite-dimensional spaces [See also]46G05, 58Cxx58Cxx: 2: 26E20 Calculus of functions taking values in infinite-dimensional spaces [See also]46E40,
46G10, 58Cxx58Cxx: 3: 47Hxx Nonlinear operators and their properties For global and geometric aspects, see 49J53,
58-XX, especially 58Cxx58D05: 1: 57Sxx Topological transformation groups [See also]20F34, 22-XX, 37-XX, 54H15, 58D0558D05: 2: 58B25 Group structures and generalizations on infinite-dimensional manifolds [See also]22E65,
58D0558D07: 1: 47H20 Semigroups of nonlinear operators [See also]37L05, 47J35, 54H15, 58D0758D15: 1: 54C35 Function spaces [See also]46Exx, 58D1558D20: 1: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B1158D20: 1: 28Cxx Set functions and measures on spaces with additional structure [See also]46G12, 58C35,
58D2058D25: 1: 34Gxx Differential equations in abstract spaces [See also]34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx,
58D2558D25: 2: 35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in
infinitely many variables) [See also]46Gxx, 58D2558D25: 3: 47J35 Nonlinear evolution equations [See also]34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx,
37Lxx, 47H20, 58D2558Dxx: 1: 46Txx Nonlinear functional analysis [See also]47Hxx, 47Jxx, 58Cxx, 58Dxx58Dxx: 2: 46T05 Infinite-dimensional manifolds [See also]53Axx, 57N20, 58Bxx, 58Dxx58Dxx: 3: 81T45 Topological field theories [See also]57R56, 58Dxx58E07: 1: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E0958E07: 2: 65H17 Eigenvalues, eigenvectors [See also]47Hxx, 47Jxx, 58C40, 58E07, 90C3058E07: 1: 58C40 Spectral theory; eigenvalue problems [See also]47J10, 58E0758E09: 1: 47J15 Abstract bifurcation theory [See also]34C23, 37Gxx, 58E07, 58E0958E12: 1: 49Q05 Minimal surfaces [See also]53A10, 58E1258E15: 1: 81T13 Yang-Mills and other gauge theories [See also]53C07, 58E1558H05: 1: 20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0558H05: 2: 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets
with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H0558H05: 3: 22E05 Local Lie groups [See also]34-XX, 35-XX, 58H05
497 Run: December 14, 2009
Mathematics Subject Classification 2010
58H05: 4: 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties[See also]17B65, 58B25, 58H05
58H10: 1: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H1558H10: 1: 22E41 Continuous cohomology [See also]57R32, 57Txx, 58H1058H15: 1: 32G05 Deformations of complex structures [See also]13D10, 16S80, 58H10, 58H1558Hxx: 1: 35B60 Continuation and prolongation of solutions [See also]58A15, 58A17, 58Hxx58J10: 1: 35Nxx Overdetermined systems [See also]58Hxx, 58J10, 58J1558J10: 1: 35N15 ∂-Neumann problem and generalizations; formal complexes [See also]32W05, 32W10,
58J1058J10: 2: 58H15 Deformations of structures [See also]32Gxx, 58J1058J15: 1: 32C38 Sheaves of differential operators and their modules, D-modules [See also]14F10, 16S32,
35A27, 58J1558J15: 2: 35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE
[See also]32C38, 58J1558J15: 3: 35Nxx Overdetermined systems [See also]58Hxx, 58J10, 58J1558J15: 4: 35S35 Topological aspects: intersection cohomology, stratified sets, etc. [See also]32C38, 32S40,
32S60, 58J1558J15: 5: 46F15 Hyperfunctions, analytic functionals [See also]32A25, 32A45, 32C35, 58J1558J20: 1: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J2258J20: 1: 35Jxx Elliptic equations and systems [See also]58J10, 58J2058J20: 2: 47A53 (Semi-) Fredholm operators; index theories [See also]58B15, 58J2058J22: 1: 18G60 Other (co)homology theories [See also]19D55, 46L80, 58J20, 58J2258J22: 2: 19K56 Index theory [See also]58J20, 58J2258J22: 3: 46L80 K-theory and operator algebras (including cyclic theory) [See also]18F25, 19Kxx,
46M20, 55Rxx, 58J2258J22: 4: 46L85 Noncommutative topology [See also]58B32, 58B34, 58J2258J22: 5: 46L87 Noncommutative differential geometry [See also]58B32, 58B34, 58J2258J22: 6: 46L89 Other “noncommutative” mathematics based on C∗-algebra theory [See also]58B32,
58B34, 58J2258J35: 1: 35Kxx Parabolic equations and systems [See also]35Bxx, 35Dxx, 35R30, 35R35, 58J3558J37: 1: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q1558J37: 2: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q1558J40: 1: 35Sxx Pseudodifferential operators and other generalizations of partial differential operators
[See also]47G30, 58J4058J50: 1: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxx58J72: 1: 35A30 Geometric theory, characteristics, transformations [See also]58J70, 58J7258Jxx: 1: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H1558Jxx: 2: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX58Jxx: 1: 35R01 Partial differential equations on manifolds [See also]32Wxx, 53Cxx, 58Jxx58Jxx: 2: 47Fxx Partial differential operators [See also]35Pxx, 58Jxx58Jxx: 3: 47F05 Partial differential operators [See also]35Pxx, 58Jxx (should also be assigned at least one
other classification number in section 47)58Jxx: 4: 47G30 Pseudodifferential operators [See also]35Sxx, 58Jxx58Kxx: 1: 14B05 Singularities [See also]14E15, 14H20, 14J17, 32Sxx, 58Kxx60-XX: 1: 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on
manifolds [See also]28Cxx, 46G12, 60-XX60B11: 1: 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener
measure, Gaussian measure, etc.) [See also]46G12, 58C35, 58D20, 60B1160B12: 1: 60Fxx Limit theorems [See also]28Dxx, 60B1260Bxx: 1: 28A33 Spaces of measures, convergence of measures [See also]46E27, 60Bxx60D05: 1: 52A22 Random convex sets and integral geometry [See also]53C65, 60D0560D05: 2: 53C65 Integral geometry [See also]52A22, 60D05; differential forms, currents, etc.
[See mainly]58Axx60E15: 1: 26Dxx Inequalities For maximal function inequalities, see 42B25; for functional inequalities,
see 39B72; for probabilistic inequalities, see 60E15
498 Run: December 14, 2009
Mathematics Subject Classification 2010
60Fxx: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,60Fxx, 60G10
60Fxx: 1: 60A10 Probabilistic measure theory For ergodic theory, see 28Dxx and 60Fxx60G10: 1: 28Dxx Measure-theoretic ergodic theory [See also]11K50, 11K55, 22D40, 37Axx, 47A35, 54H20,
60Fxx, 60G1060G10: 2: 37A50 Relations with probability theory and stochastic processes [See also]60Fxx and 60G1060Gxx: 1: 76Fxx Turbulence [See also]37-XX, 60Gxx, 60Jxx60H10: 1: 34Fxx Equations and systems with randomness [See also]34K50, 60H10, 93E0360H10: 2: 34F05 Equations and systems with randomness [See also]34K50, 60H10, 93E0360H10: 3: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H1560H10: 4: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H1560H10: 5: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J6060H15: 1: 35Rxx Miscellaneous topics For equations on manifolds, see 58Jxx; for manifolds of solutions,
see 58Bxx; for stochastic PDE, see also 60H1560H15: 2: 37H10 Generation, random and stochastic difference and differential equations [See also]34F05,
34K50, 60H10, 60H1560H15: 3: 37L55 Infinite-dimensional random dynamical systems; stochastic equations [See also]35R60,
60H10, 60H1560H25: 1: 47B80 Random operators [See also]47H40, 60H2560H25: 2: 47H40 Random operators [See also]47B80, 60H2560H35: 1: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H3560J45: 1: 31-XX Potential theory For probabilistic potential theory, see 60J4560J60: 1: 58J65 Diffusion processes and stochastic analysis on manifolds [See also]35R60, 60H10, 60J6060Jxx: 1: 47D07 Markov semigroups and applications to diffusion processes For Markov processes, see
60Jxx60Jxx: 2: 70Qxx Control of mechanical systems [See also]60Gxx, 60Jxx60Jxx: 3: 76Fxx Turbulence [See also]37-XX, 60Gxx, 60Jxx62-XX: 1: 60-XX Probability theory and stochastic processes For additional applications, see 11Kxx,
62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX62-XX: 1: 91Cxx Social and behavioral sciences: general topics For statistics, see 62-XX62H30: 1: 68T10 Pattern recognition, speech recognition For cluster analysis, see 62H3062Hxx: 1: 60Exx Distribution theory [See also]62Exx, 62Hxx62K10: 1: 05B05 Block designs [See also]51E05, 62K1062N05: 1: 90B25 Reliability, availability, maintenance, inspection [See also]60K10, 62N0562P20: 1: 91Bxx Mathematical economics For econometrics, see 62P2065-XX: 1: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxx65B15: 1: 40A25 Approximation to limiting values (summation of series, etc.) For the Euler-Maclaurin
summation formula, see 65B1565D05: 1: 41A05 Interpolation [See also]42A15 and 65D0565Dxx: 1: 41-XX Approximations and expansions For all approximation theory in the complex domain,
see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
65Dxx: 2: 41Axx Approximations and expansions For all approximation theory in the complex domain,see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numericalapproximation, see 65Dxx
65F22: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,65R30
65F22: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,65R30
65Fxx: 1: 65J10 Equations with linear operators (do not use 65Fxx)65H05: 1: 26C10 Polynomials: location of zeros [See also]12D10, 30C15, 65H0565Hxx: 1: 65J15 Equations with nonlinear operators (do not use 65Hxx)65Hxx: 1: 65M22 Solution of discretized equations [See also]65Fxx, 65Hxx
499 Run: December 14, 2009
Mathematics Subject Classification 2010
65Hxx: 2: 65N22 Solution of discretized equations [See also]65Fxx, 65Hxx65J05: 1: 15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
[See also]65F35, 65J0565J20: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R3065J20: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R3065Kxx: 1: 49-XX Calculus of variations and optimal control; optimization [See also]34H05, 34K35, 65Kxx,
90Cxx, 93-XX65Kxx: 1: 49Mxx Numerical methods [See also]90Cxx, 65Kxx65Kxx: 2: 49M37 Methods of nonlinear programming type [See also]90C30, 65Kxx65Kxx: 3: 90Cxx Mathematical programming [See also]49Mxx, 65Kxx65L08: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,
65R3065L08: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,
65R3065Lxx: 1: 34A45 Theoretical approximation of solutions For numerical analysis, see 65Lxx
65M30: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,65R30
65M30: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,65R30
65Mxx: 1: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxx65Nxx: 1: 35A35 Theoretical approximation to solutions For numerical analysis, see 65Mxx, 65Nxx65R10: 1: 92C55 Biomedical imaging and signal processing [See also]44A12, 65R10, 94A08, 94A1265R10: 1: 44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see
26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
65R10: 2: 44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. Fornumerical methods, see 65R10
65R30: 1: 47A52 Ill-posed problems, regularization [See also]35R25, 47J06, 65F22, 65J20, 65L08, 65M30,65R30
65R30: 2: 47J06 Nonlinear ill-posed problems [See also]35R25, 47A52, 65F22, 65J20, 65L08, 65M30,65R30
65Rxx: 1: 45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxx65Rxx: 2: 45L05 Theoretical approximation of solutions For numerical analysis, see 65Rxx65Yxx: 1: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxx68M20: 1: 90B22 Queues and service [See also]60K25, 68M2068P25: 1: 94A60 Cryptography [See also]11T71, 14G50, 68P25, 81P9468Q12: 1: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P6868Q12: 1: 81P68 Quantum computation [See also]68Q05, 68Q1268Q17: 1: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q1968Q17: 1: 03D15 Complexity of computation (including implicit computational complexity)
[See also]68Q15, 68Q1768Q19: 1: 03C13 Finite structures [See also]68Q15, 68Q1968Q19: 2: 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
[See also]03D15, 68Q17, 68Q1968Q25: 1: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxx68Q45: 1: 94A45 Prefix, length-variable, comma-free codes [See also]20M35, 68Q4568Q55: 1: 06B35 Continuous lattices and posets, applications [See also]06B30, 06D10, 06F30, 18B35,
22A26, 68Q5568Q65: 1: 18C50 Categorical semantics of formal languages [See also]68Q55, 68Q6568Q70: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R15
500 Run: December 14, 2009
Mathematics Subject Classification 2010
68Q70: 2: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T5068Q70: 3: 68Q45 Formal languages and automata [See also]03D05, 68Q70, 94A4568Q70: 1: 20F10 Word problems, other decision problems, connections with logic and automata
[See also]03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q7068Qxx: 1: 18B20 Categories of machines, automata, operative categories [See also]03D05, 68Qxx68R10: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C1568R10: 1: 05C62 Graph representations (geometric and intersection representations, etc.) For graph
drawing, see also 68R1068R10: 2: 94C15 Applications of graph theory [See also]05Cxx, 68R1068R15: 1: 03D05 Automata and formal grammars in connection with logical questions [See also]68Q45,
68Q70, 68R1568R15: 2: 03D40 Word problems, etc. [See also]06B25, 08A50, 20F10, 68R1568R15: 3: 08A50 Word problems [See also]03D40, 06B25, 20F10, 68R1568Rxx: 1: 46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and
computer science [See also]05C12, 68Rxx68Rxx: 2: 68Wxx Algorithms For numerical algorithms, see 65-XX; for combinatorics and graph theory,
see 05C85, 68Rxx68T37: 1: 03B52 Fuzzy logic; logic of vagueness [See also]68T27, 68T37, 94D0568T50: 1: 20M35 Semigroups in automata theory, linguistics, etc. [See also]03D05, 68Q70, 68T5068T50: 2: 91F20 Linguistics [See also]03B65, 68T5068U05: 1: 52B55 Computational aspects related to convexity For computational geometry and
algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx [See also]68Uxx68U05: 1: 65D18 Computer graphics, image analysis, and computational geometry [See also]51N05,
68U0568U07: 1: 51N05 Descriptive geometry [See also]65D17, 68U0768U20: 1: 65Cxx Probabilistic methods, simulation and stochastic differential equations For theoretical
aspects, see 68U20 and 60H3568Uxx: 1: 65Dxx Numerical approximation and computational geometry (primarily algorithms) For
theory, see 41-XX and 68Uxx68W05: 1: 05C85 Graph algorithms [See also]68R10, 68W0568W30: 1: 13Pxx Computational aspects and applications [See also]14Qxx, 68W3068W30: 2: 14Qxx Computational aspects in algebraic geometry [See also]12Y05, 13Pxx, 68W3068W40: 1: 68Q87 Probability in computer science (algorithm analysis, random structures, phase
transitions, etc.) [See also]68W20, 68W4070-XX: 1: 37-XX Dynamical systems and ergodic theory [See also]26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx,
46Lxx, 58Jxx, 70-XX70B15: 1: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q0570F15: 1: 85-XX Astronomy and astrophysics For celestial mechanics, see 70F1570F15: 2: 85Axx Astronomy and astrophysics For celestial mechanics, see 70F1570F25: 1: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxx70Fxx: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxx70Gxx: 1: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxx70Gxx: 1: 70H45 Constrained dynamics, Dirac’s theory of constraints [See also]70F20, 70F25, 70Gxx70H09: 1: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q1570H09: 2: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q1570Hxx: 1: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxx70Hxx: 1: 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[See also]53Dxx, 70Fxx, 70Hxx70Hxx: 2: 53Dxx Symplectic geometry, contact geometry [See also]37Jxx, 70Gxx, 70Hxx70K60: 1: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q1570Kxx: 1: 37N05 Dynamical systems in classical and celestial mechanics [See mainly]70Fxx, 70Hxx,
70Kxx70L05: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx
501 Run: December 14, 2009
Mathematics Subject Classification 2010
70Q05: 1: 70B15 Mechanisms, robots [See also]68T40, 70Q05, 93C8570Q05: 2: 70E60 Robot dynamics and control [See also]68T40, 70Q05, 93C8570Q05: 1: 93C85 Automated systems (robots, etc.) [See also]68T40, 70B15, 70Q0574-XX: 1: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XX74A15: 1: 80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A1574Axx: 1: 76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XX74E20: 1: 76T25 Granular flows [See also]74C99, 74E2074G15: 1: 74Sxx Numerical methods [See also]65-XX, 74G15, 74H1574H15: 1: 74Sxx Numerical methods [See also]65-XX, 74G15, 74H1574L15: 1: 76Zxx Biological fluid mechanics [See also]74F10, 74L15, 92Cxx74N30: 1: 47J40 Equations with hysteresis operators [See also]34C55, 74N3076D05: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A1076D07: 1: 35Q30 Navier-Stokes equations [See also]76D05, 76D07, 76N1076D07: 2: 35Q31 Euler equations [See also]76D05, 76D07, 76N1076E20: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U0576E20: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576F20: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A1076L05: 1: 35L67 Shocks and singularities [See also]58Kxx, 76L05
76M35: 1: 76D06 Statistical solutions of Navier-Stokes and related equations [See also]60H30, 76M3576M50: 1: 35B27 Homogenization; equations in media with periodic structure [See also]74Qxx, 76M5076N10: 1: 35Q30 Navier-Stokes equations [See also]76D05, 76D07, 76N1076N10: 2: 35Q31 Euler equations [See also]76D05, 76D07, 76N1076N15: 1: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576Q05: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U0576Q05: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576Rxx: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U0576Rxx: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576Rxx: 1: 76F35 Convective turbulence [See also]76E15, 76Rxx76U05: 1: 86A05 Hydrology, hydrography, oceanography [See also]76Bxx, 76E20, 76Q05, 76Rxx, 76U0576U05: 2: 86A10 Meteorology and atmospheric physics [See also]76Bxx, 76E20, 76N15, 76Q05, 76Rxx,
76U0576V05: 1: 86-XX Geophysics [See also]76U05, 76V0576V05: 2: 86Axx Geophysics [See also]76U05, 76V0578-XX: 1: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX78A25: 1: 86A25 Geo-electricity and geomagnetism [See also]76W05, 78A2580A32: 1: 92E20 Classical flows, reactions, etc. [See also]80A30, 80A3280Axx: 1: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C2681P10: 1: 03G12 Quantum logic [See also]06C15, 81P1081P10: 2: 06C15 Complemented lattices, orthocomplemented lattices and posets [See also]03G12, 81P1081P45: 1: 94A15 Information theory, general [See also]62B10, 81P4581P68: 1: 68Q05 Models of computation (Turing machines, etc.) [See also]03D10, 68Q12, 81P6881P68: 2: 68Q12 Quantum algorithms and complexity [See also]68Q05, 81P6881P94: 1: 68P25 Data encryption [See also]94A60, 81P9481P94: 2: 94A60 Cryptography [See also]11T71, 14G50, 68P25, 81P9481Q15: 1: 47A55 Perturbation theory [See also]47H14, 58J37, 70H09, 81Q1581Q15: 2: 47H14 Perturbations of nonlinear operators [See also]47A55, 58J37, 70H09, 70K60, 81Q1581Q30: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C1581Q30: 2: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C1581R10: 1: 22E70 Applications of Lie groups to physics; explicit representations [See also]81R05, 81R1081R50: 1: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
502 Run: December 14, 2009
Mathematics Subject Classification 2010
[See also]16T20, 20G42, 81R50, 82B2381R50: 1: 16T20 Ring-theoretic aspects of quantum groups [See also]17B37, 20G42, 81R5081R50: 2: 20G42 Quantum groups (quantized function algebras) and their representations
[See also]16T20, 17B37, 81R5081T05: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1081T05: 1: 81R15 Operator algebra methods [See also]46Lxx, 81T0581T15: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C1581T15: 2: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C1581T80: 1: 82B80 Numerical methods (Monte Carlo, series resummation, etc.) [See also]65-XX, 81T8081Txx: 1: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX81Txx: 1: 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor
theory, instantons, quantum field theory) [See also]32L25, 81Txx81Uxx: 1: 47A40 Scattering theory [See also]34L25, 35P25, 37K15, 58J50, 81Uxx81V80: 1: 78-XX Optics, electromagnetic theory For quantum optics, see 81V8082-XX: 1: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XX82B10: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1082B20: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C1582B20: 2: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C1582B23: 1: 17B37 Quantum groups (quantized enveloping algebras) and related deformations
[See also]16T20, 20G42, 81R50, 82B2382B26: 1: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C2682C05: 1: 37Hxx Random dynamical systems [See also]15B52, 34D08, 34F05, 47B80, 70L05, 82C05,
93Exx82C10: 1: 46L60 Applications of selfadjoint operator algebras to physics [See also]46N50, 46N55, 47L90,
81T05, 82B10, 82C1082C20: 1: 05Cxx Graph theory For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20,
90C35, 92E10, 94C1582C20: 2: 05C90 Applications [See also]68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C1582C26: 1: 74Nxx Phase transformations in solids [See also]74A50, 80Axx, 82B26, 82C2682C32: 1: 92B20 Neural networks, artificial life and related topics [See also]68T05, 82C32, 94Cxx82C40: 1: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582C40: 2: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582C41: 1: 82B41 Random walks, random surfaces, lattice animals, etc. [See also]60G50, 82C4182C43: 1: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
[See also]82B43, 82C4382D05: 1: 76Pxx Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582D05: 2: 76P05 Rarefied gas flows, Boltzmann equation [See also]82B40, 82C40, 82D0582D25: 1: 20H15 Other geometric groups, including crystallographic groups [See also]51-XX, especially
51F15, and 82D2583-XX: 1: 70Sxx Classical field theories [See also]37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX83A05: 1: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XX83C10: 1: 70-XX Mechanics of particles and systems For relativistic mechanics, see 83A05 and 83C10;
for statistical mechanics, see 82-XX83C55: 1: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3083C55: 2: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3083Exx: 1: 81V17 Gravitational interaction [See also]83Cxx and 83Exx83F05: 1: 85A40 Cosmology For relativistic cosmology, see 83F0585A30: 1: 76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3085A30: 2: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics [See also]82D50, 83C55, 85A3086A05: 1: 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly]76-
XX, especially 76D05, 76F20, 86A05, 86A10
503 Run: December 14, 2009