G. Bellettini, Università di Roma “Tor Vergata”, Roma ... · mathematics and computer science 7 Acts as a short introduction to important and modern parts of discrete geometry

Mathematics springer.com/NEWSonline

40

M. Aigner, Freie Universität Berlin, Germany

Markov’s Theorem and 100 Years of the Uniqueness ConjectureFrom Irrational Numbers to Perfect Matchings

This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words.

Features 7 First comprehensive book on the Theorem of Markov and the Uniqueness Conjecture 7 Fresh and interdisciplinary approach presenting also the many connections to other fields 7 Leisurely but rigorous introduction to the "Markov Theme" for students and professional mathematicians

Contents Approximation of Irrational Numbers.- Markov’s Theorem and the Uniqueness Conjecture.- The Markov Tree.- The Cohn Tree.- The Modular Group SL(2,Z).- The Free Group F2.- Christof-fel Words.- Sturmian Words.- Proof of Markov’s Theorem.- The Uniqueness Conjecture.

Fields of interestNumber Theory; Group Theory and Generaliza-tions; Combinatorics

Target groupsResearch

Product categoryMonograph

Due July 2013

2013. XII, 224 p. Hardcover7 $69.99ISBN 978-3-319-00887-5

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G. Bellettini, Università di Roma “Tor Vergata”, Roma, Italy

Lecture Notes on Mean Curvature Flow: Barriers and Singular PerturbationsThe aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hyper-surfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison prin-ciple and its use in the definition of suitable weak solutions.

Features 7 Elementary introduction to mean curvature flow, including the short time existence result, using the signed distance function 7 Detailed study of minimal barriers and their regularizations for mean curvature flow 7 An example of fat-tening 7 Convergence and error estimate for the parabolic Allen-Cahn equation

Contents Signed distance from a smooth boundary.- Mean curvature vector and second fundamental form.- First variations of volume integrals and of the perimeter.- Smooth mean curvature flows.- Huis-ken’s monotonicity formula.- Inclusion principle. Local well posedness: the approach of Evans–Spruck.- Grayson’s example.- De Giorgi’s barriers.- Inner and outer regularizations.- An example of fattening.- Ilmanen’s interposition lemma.- The avoidance principle.- Comparison between barri-ers and a generalized evolution.- Barriers and level set evolution.- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.

Field of interestGeometry

Target groupsGraduate

Product categoryGraduate/Advanced undergraduate textbook

Due October 2013

2013. Approx. 350 p. (Publications of the Scuola Normale Superiore / Lecture Notes (Scuola Normale Superiore), Volume 12) Softcover7 approx. $39.99ISBN 978-88-7642-428-1

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H. Bellout, F. Bloom, Northern Illinois University, DeKalb, IL, USA

Incompressible Bipolar and Non-Newtonian Viscous Fluid FlowThe theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles.

Features 7 Exceptionally well-written and strong presenta-tion of the case for bipolar fluids 7 Provides a comprehensive and consolidated reference for the multipolar fluid model 7 Presents applications of the model to standard as well as non-standard problems

Contents Preface.- Acknowledgements.- I Incompressible Multipolar Fluid Dynamics.- II Plane Poiseuille Flow of Incompressible Bipolar Viscous Flu-ids.- III Incompressible Bipolar Fluid Dynamics: Examples of Other Flows and Geometries.- IV General Existence and Uniqueness Theorems for Incompressible Bipolar and non-Newtonian Fluid Flow.- V Attractors for Incompressible Bipolar and non-Newtonian Flows: Bounded Domains and Space Periodic Problems.- VI Inertial Manifolds, Orbit Squeezing, and Attractors for Bipolar Flow in Unbounded Channels.- A.I Notation, Defini-tions, and Results from Analysis.- A.II Estimates Involving the Rate of Deformation Tensor.- A.III The Spectral Gap Condition.- Bibliography.- In-dex.

Fields of interestMathematical Physics; Partial Differential Equa-tions; Fluid- and Aerodynamics



Due October 2013

2014. XIX, 538 p. 16 illus. (Advances in Mathematical Fluid Mechanics) Hardcover7 $149.00ISBN 978-3-319-00890-5

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www.springer.com/978-3-319-00887-5



News 7/2013 Mathematics

41

K. Bezdek, University of Calgary, AB, Canada

Lectures on Sphere Arrangements – the Discrete Geometric SideThis monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as inter-ested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.

Features 7 Contains more than 40 open research prob-lems proposed to help further research 7 Ideal for graduate students as well as researchers in mathematics and computer science 7 Acts as a short introduction to important and modern parts of discrete geometry 7 Ideal book for a one semester course at an advanced undergradu-ate or graduate level course 7 Features proofs that cover a broad range of methods of discrete geometry, often presentable in short talks

Contents 1. Unit Sphere Packings.- 2. Proofs on Unit Sphere Packings.- 3. Contractions of Sphere Arrange-ments.- 4. Proofs on Contractions of Sphere Arrangements.- 5. Ball-Polyhedra and Spindle Convex Bodies.- 6. Proofs on Ball-Polyhedra and Spindle Convex Bodies.- 7. Coverings by Cylinders.- 8. Proofs on Coverings by Cylinders.- 9. Research Problems - an Overview.- Glossary.- References.

Fields of interestConvex and Discrete Geometry; Polytopes



Due August 2013

2013. XV, 194 p. 18 illus. in color. (Fields Institute Monographs, Volume 32) Hardcover7 $109.00ISBN 978-1-4614-8117-1

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A. M. Bigatti, University of Genoa, Italy; P. Gimenez, University of Valladolid, Spain; E. Sáenz-de-Cabezón, University of La Rioja, Spain (Eds)

Monomial Ideals, Computations and ApplicationsThis work covers three important aspects of monomials ideals in the three chapters “Stanley decompositions” by Jürgen Herzog, “Edge ideals” by Adam Van Tuyl and “Local cohomology” by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that em-phasize the computational aspects of the respec-tive areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commuta-tive algebra and the main objects of combinatorial commutative algebra. Also, they are of major im-portance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combi-natorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas.

Features 7 Chapters cover leading-edge aspects of the theory of monomial ideals written by top researchers in their fields 7 Includes computer tutorials that highlight the computational aspects of the area 7 Carefully written introductions to topics of current research interest

Contents A survey on Stanley depth.- Stanley decomposi-tions using CoCoA.- A beginner’s guide to edge and cover ideals.- Edge ideals using Macaulay2.- Local cohomology modules supported on mono-mial ideals.- Local Cohomology using Macaulay2.

Field of interestAlgebra


Product categoryContributed volume

Due July 2013

2013. IX, 194 p. 42 illus. (Lecture Notes in Mathematics, Volume 2083) Softcover7 $59.99ISBN 978-3-642-38741-8

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H. Bijl, TU Delft, Netherlands; D. Lucor, Université Pierre et Marie Curie - Paris VI, Paris, France; S. Mishra, C. Schwab, ETH Zurich, Switzerland (Eds)

Uncertainty Quantification in Computational Fluid DynamicsFeatures 7 Presentation of the highly relevant issue of UQ in CFD 7 A broad spectrum of methods to ef-ficiently compute uncertainty 7 Large number of numerical examples as verification of the proposed methods and their possible comparison

Contents Timothy Barth: Non-Intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities.- Philip Beran and Bret Stanford: Uncertainty Quantification in Aeroelasticity.- Bruno Després, Gaël Poëtte and Didier Lucor: Robust uncertainty propagation in systems of conservation laws with the entropy closure method.- Richard P. Dwight, Jeroen A.S. Witteveen and Hester Bijl: Adaptive Uncertainty Quantification for Computational Fluid Dynam-ics.- Chris Lacor, Cristian Dinescu, Charles Hirsch and Sergey Smirnov: Implementation of intrusive Polynomial Chaos in CFD codes and application to 3D Navier-Stokes.- Siddhartha Mishra, Chris-toph Schwab and Jonas Šukys: Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in nonlinear systems of balance laws.- Jeroen A.S. Witteveen and Gianluca Iacca-rino: Essentially Non-Oscillatory Stencil Selection and Subcell Resolution in Uncertainty Quantifica-tion.

Fields of interestComputational Mathematics and Numerical Analysis; Computational Science and Engineering; Appl.Mathematics/Computational Methods of Engineering



Due August 2013

2013. IV, 332 p. 188 illus., 116 in color. (Lecture Notes in Computational Science and Engineering, Volume 92) Hardcover7 $129.00ISBN 978-3-319-00884-4

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42

D. Bump, Stanford University, CA, USA

Lie GroupsContents Part I: Compact Topological Groups.- 1 Haar Measure.- 2 Schur Orthogonality.- 3 Compact Operators.- 4 The Peter–Weyl Theorem.- Part II: Compact Lie Groups.- 5 Lie Subgroups of GL(n,C).- 6 Vector Fields.- 7 Left-Invariant Vec-tor Fields.- 8 The Exponential Map.- 9 Tensors and Universal Properties.- 10 The Universal Enveloping Algebra.- 11 Extension of Scalars.- 12 Representations of sl(2,C).- 13 The Universal Cover.- 14 The Local Frobenius Theorem.- 15 Tori.- 16 Geodesics and Maximal Tori.- 17 The Weyl Integration Formula.- 18 The Root System.- 19 Examples of Root Systems.- 20 Abstract Weyl Groups.- 21 Highest Weight Vectors.- 22 The Weyl Character Formula.- 23 The Fundamental Group.- Part III: Noncompact Lie Groups.- 24 Complexification.- 25 Coxeter Groups.- 26 The Borel Subgroup.- 27 The Bruhat Decomposi-tion.- 28 Symmetric Spaces.- 29 Relative Root Systems.- 30 Embeddings of Lie Groups.- 31 Spin.- Part IV: Duality and Other Topics.- 32 Mackey Theory.- 33 Characters of GL(n,C).- 34 Duality between Sk and GL(n,C).- 35 The Jacobi–Trudi Identity.- 36 Schur Polynomials and GL(n,C).- 37 Schur Polynomials and Sk. 38 The Cauchy Iden-tity.- 39 Random Matrix Theory.- 40 Symmetric Group Branching Rules and Tableaux.- 41 Unitary Branching Rules and Tableaux.- 42 Minors of Toeplitz Matrices.- 43 The Involution Model for Sk.- 44 Some Symmetric Alegras.- 45 Gelfand Pairs.- 46 Hecke Algebras.- 47 The Philosophy of Cusp Forms.- 48 Cohomology of Grassmannians.- Appendix: Sage.- References.- Index.

Field of interestTopological Groups, Lie Groups



Due August 2013

2nd ed. 2013. XV, 516 p. 63 illus. (Graduate Texts in Mathematics, Volume 225) Hardcover7 $89.99ISBN 978-1-4614-8023-5

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P. Bürgisser, Technical University of Berlin, Germany; F. Cucker, City University of Hong Kong, Hong Kong SAR

ConditionThe Geometry of Numerical Algorithms

Contents Preface.- Overture: On the Condition of Nu-merical Problems and the Numbers that Measure It.- I Condition in Linear Algebra (Adagio): 1 Normwise Condition of Linear Equation Solv-ing.- 2 Probabilistic Analysis.- 3 Error Analysis of Triangular Linear Systems.- 4 Probabilistic Analysis of Rectangular Matrices.- 5 Condition Numbers and Iterative Algorithms.- Intermezzo I: Condition of Structured Data.- II Condition in Linear Optimization (Andante): 6 A Condition Number for Polyhedral Conic Systems.- 7 The Ellipsoid Method.- 8 Linear Programs and their Solution Sets.- 9 Interior-point Methods.- 10 The Linear Programming Feasibility Problem.- 11 Condition and Linear Programming Optimiza-tion.- 12 Average Analysis of the RCC Condition Number.- 13 Probabilistic Analyses of the GCC Condition Number.- Intermezzo II: The Condition of the Condition.- III Condition in Polynomial Equation Solving (Allegro con brio): 14 A Geo-metric Framework for Condition Numbers.- 15 Homotopy Continuation and Newton’s Method.- 16 Homogeneous Polynomial Systems.- 17 Smale’s 17th Problem: I.- 18 Smale’s 17th Problem: II.- 19 Real Polynomial Systems.- 20 Probabilistic Analy-sis of Conic Condition Numbers: I. The Complex Case 4.- 21 Probabilistic Analysis of Conic Condi-tion Numbers: II. The Real Case.- Appendix .

Fields of interestAlgorithms; Mathematics of Computing; Prob-ability Theory and Stochastic Processes



Due August 2013

2013. XXX, 570 p. 31 illus. (Grundlehren der mathematischen Wissenschaften, Volume 349) Hardcover7 $149.00ISBN 978-3-642-38895-8

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L. Capogna, University of Arkansas, MN, USA; P. Guan, McGill University, QC, Canada; C. E. Gutiérrez, Temple University, PA, USA; A. Montanari, Universita di Bologna, Italy

Fully Nonlinear PDEs in Real and Complex Geometry and OpticsCetraro, Italy 2012, Editors: Cristian E. Gutiérrez, Ermanno Lanconelli

Scientific Editors: E. Lanconelli, Università degli Studi di Bologna, Italy; C. E. Gutiérrez, Temple University, Philadelphia, PA, USA

The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differen-tial Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasicon-formal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Mon-tanari.

Contents Introduction.- L∞ extremal mappings in AMLE and Teichmüller theory.- Curvature Measures, Iso-perimetric Type Inequalities and Fully Nonlinear Pde’s.- Refraction Problems In Geometric Optics.- On the Levi Monge-Ampère equation.

Fields of interestPartial Differential Equations; Optics and Electro-dynamics



Due August 2013

2013. X, 210 p. 8 illus., 4 in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2087) Softcover7 $49.99ISBN 978-3-319-00941-4

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43

V. Chulaevsky, Université de Reims Champagne-Ardenne, Reims, France; Y. Suhov, University of Cambridge, Cambridge, UK

Multi-Scale Analysis for Random Quantum Systems with InteractionThe study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-Scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area.

Features 7 Introduces the reader to a recent progress in this field 7 Attract attention to possible directions for future research 7 Presents new and exciting research the first time in the literature and includes all necessary background materi-al 7 Presents new and exciting research the first time in the literature and includes all necessary background material

Contents Preface.- Part I Single-particle Localisation.- A Brief History of Anderson Localization.- Single-Particle MSA Techniques.- Part II Multi-particle Localization.- Multi-particle Eigenvalue Concen-tration Bounds.- Multi-particle MSA Techniques.- References.- Index.

Fields of interestFunctional Analysis; Mathematical Methods in Physics; Probability Theory and Stochastic Processes



Due October 2013

2014. XVI, 222 p. 5 illus. (Progress in Mathematical Physics, Volume 65) Hardcover7 approx. $69.95ISBN 978-1-4614-8225-3

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Ł. Delong, Warsaw School of Economics, Poland

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial ApplicationsBSDEs with Jumps

Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those gen-erated by step processes and Lévy processes.

Features 7 Contains the most recent advances in BS-DEs 7 Applies BSDEs with jumps to insurance and finance 7 Full notation and results are given, followed by applications

Contents Introduction.- Stochastic Calculus.- Backward Stochastic Differential Equations – the General Case.- Forward-Backward Stochastic Differential Equations.- Numerical Methods for FBSDEs.- Nonlinear Expectations and g-Expectations.- Combined Financial and Insurance Model.- Lin-ear BSDEs and Predictable Representations of Insurance Payment Processes.- Arbitrage-Free Pricing, Perfect Hedging and Superhedging.- Qua-dratic Pricing and Hedging.- Utility Maximization and Indifference Pricing and Hedging.- Pricing and Hedging under a Least Favorable Measure.- Dynamic Risk Measures.- Other Classes of BSDEs.

Fields of interestQuantitative Finance; Actuarial Sciences; Con-tinuous Optimization



Due June 2013

2013. X, 288 p. (EAA Series) Softcover7 $69.99ISBN 978-1-4471-5330-6

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T. Diagana, Howard University, Washington, DC, USA

Almost Automorphic Type and Almost Periodic Type Functions in Abstract SpacesThis book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their re-cent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature.

Features 7 Introduces several new classes of functions as well as their applications to first, second, third, and higher-order differential equations 7 Contains material which has never before been presented in a book format 7 Can be used for beginning graduate and advanced undergraduate courses

Contents 1. Metric, Banach, and Hilbert Spaces.- 2. Linear Operators on Banach Spaces.- 3. Almost Periodic Functions.- 4. Almost Automorphic Functions.- 5. Pseudo-Almost Periodic Functions.- 6. Pseudo-Almost Automorphic Functions.- 7. Existence Results for Some Second-Order Differential Equations.- 8. Existence Results to Some Integro-differential Equations.- 9. Existence of C(m)-Pseudo-Almost Automorphic Solutions.- 10. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations.- 11. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations.- 12. Stability Results for Some Higher-Order Difference Equations.- 13. Appendix A.- References.- Index.

Fields of interestOrdinary Differential Equations; Partial Differen-tial Equations; Operator Theory



Due August 2013

2013. XV, 295 p. Hardcover7 $109.00ISBN 978-3-319-00848-6

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44

P. Duren, University of Michigan, Ann Arbor, MI, USA; L. Zalcman, Bar-Ilan University, Ramat Gan, Israel (Eds)

Menahem Max Schiffer: Selected Papers Volume 1Contents Part 1. Publications of M. M. Schiffer.- Doctoral Students of M. M. Schiffer.- Chronology of M. M. Schiffer.- Part 2. Personal Reminiscences.- Paul R. Garabedian, “Recollections of Menahem Max Schiffer”.- Robert Finn, “Memories of Menahem Schiffer”.- Peter Duren, “Working with Max Schiffer”.- Lawrence Zalcman, “Memories of Max Schiffer”.- Dennis Hejhal, “Some Reminiscences of My Thesis Advisor, Max Schiffer”.- Dov Aha-ronov, “Max Schiffer at the Technion”.- Steven R. Bell, “M. M. Schiffer, Explorer”.- Part 3. Selected Papers.- Ein neuer Beweis des Endlichkeitssatzes für Orthogonalinvarianten.- Commentary by Lawrence Zalcman.- Sur un principe nouveau pour l’évaluation des fonctions holomorphes.- Commentary by Peter Duren.- Sur un problème d’extrémum de la représentation conforme.- A method of variation within the family of simple functions.- On the coefficients of simple func-tions.- Sur un théorème de la représentation conforme.- Commentary by Peter Duren.- Sur la variation de la fonction de Green de domaines plans quelconques.- Sur la variation du diamètre transfini.- Variation of the Green function and theory of the p-valued functions.- Commentary by Peter Duren.- The span of multiply connected domains.- Commentary by Brad Osgood.- Sur l’équation différentielle de M. Löwner.- Com-mentary by Peter Duren.- Hadamard’s formula and variation of domain-functions.- Commen-tary by Peter Duren.- The kernel function of an orthonormal system.- Commentary by Dmitry Khavinson.- (with S. [...]

Fields of interestHistory of Mathematical Sciences; Calculus of Variations and Optimal Control; Optimization


Product categoryCollected works

Due August 2013

2013. XVI, 584 p. (Contemporary Mathematicians) Hardcover7 $149.00ISBN 978-0-8176-3652-4

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B. Goldengorin, University of Florida, Gainesville, FL, USA; D. Krushinsky, University of Groningen, The Netherlands; P. M. Pardalos, University of Florida, Gainesville, FL, USA

Cell Formation in Industrial EngineeringTheory, Algorithms and Experiments

This book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by man-agers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system.

Features 7 First book to address the cell formation theory and its applications from the perspective of a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology 7 Addresses new methodologies to solve cell formation problems 7 Can be used as supplementary text at the graduate and post-grad-uate levels in all fields of engineering

Contents 1. The problem of cell formation.- 2. The p-Median problem.- 3. Application of the PMP to cell formation in group technology.- 4. The minimum multicut problem and an exact model for cell formation.- 5. Multiobjective nature of cell formation.- 6. Pattern-based heuristic for the cell formation problem in group technology.- 7. Branch-and-bound algorithm for bi-criterion cell formation problems.- 8. Summary and conclu-sions.- A. Solutions to the 35 CF instances from [71].- Index.- References.

Fields of interestComputational Science and Engineering; Opera-tions Research, Management Science; Mathemati-cal Modeling and Industrial Mathematics



Due August 2013

2013. XVII, 218 p. 52 illus., 39 in color. (Springer Optimization and Its Applications, Volume 79) Hardcover7 $109.00ISBN 978-1-4614-8001-3

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D. Gonzalez–Sanchez, Intituto Tecnologico Autonomo de Mexico, Mexico City, Mexico; O. Hernandez–Lerma, CINVESTAV-IPN, Mexico City, Mexico

Discrete–Time Stochastic Control and Dynamic Potential GamesThe Euler–Equation Approach

There are several techniques to study noncoopera-tive dynamic games, such as dynamic program-ming and the maximum principle (also called the Lagrange method). It turns out, however, that one way to characterize dynamic potential games requires to analyze inverse optimal control problems, and it is here where the Euler equa-tion approach comes in because it is particularly well–suited to solve inverse problems. Despite the importance of dynamic potential games, there is no systematic study about them. This monograph is the first attempt to provide a systematic, self–contained presentation of stochastic dynamic po-tential games.

Features 7 Presents a systematic, comprehensive, self-con-tained analysis of dynamic potential games, which appears for the first time in book form 7 Reader-friendly, at a graduate student level 7 Substantial number of examples and applications, mainly from mathematical economics

Contents Introduction and summary.- Direct problem: the Euler equation approach.- The inverse optimal control problem.- Dynamic games .- Conclusion.- References.- Index

Fields of interestSystems Theory, Control; Probability Theory and Stochastic Processes; Control


Product categoryBrief

Due July 2013

2013. XVIII, 40 p. (SpringerBriefs in Mathematics) Softcover7 $49.99ISBN 978-3-319-01058-8

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45

J. Haigh, University of Sussex, Brighton, UK

Probability ModelsThe purpose of this book is to provide a sound in-troduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This popular second edition textbook contains many worked examples and several chapters have been updated and expanded. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logi-cal development of an argument.

Features 7 Very suitable for self-study 7 Provides many worked examples and exercises 7 Suitable for beginners; no prior knowledge of probability is needed

Contents Probability Spaces.- Conditional Probability and Independence.- Common Probability Distribu-tions.- Random Variables.- Sums of Random Variables.- Convergence and Limit Theorems.- Stochastic Processes in Discrete Time.- Stochastic Processes in Continuous Time.- Appendix: Com-mon Distributions and Mathematical Facts.

Fields of interestProbability Theory and Stochastic Processes; Simulation and Modeling; Probability and Statis-tics in Computer Science

Target groupsLower undergraduate

Product categoryUndergraduate textbook

Due August 2013

2nd ed. 2013. X, 274 p. 5 illus. (Springer Undergraduate Mathematics Series) Softcover7 $49.99ISBN 978-1-4471-5342-9

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A. Khovanskii, University of Toronto Dept. Mathematics, Toronto, ON, Canada

Galois Theory, Coverings, and Riemann SurfacesTransl. Russian: V. Kiritchenko, National Research University Higher School of Economics, Msocow, Russia; Transl. Russian: V. Timorin, State University Higher School of Economics, Moskva, Russia

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to the questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy be-tween the fundamental theorem of Galois theory and classification of coverings over a topological space. The third part contains a geometric descrip-tion of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to topological Galois theory developed by the author. All results are presented in the same elementary and self-con-tained manner as classical Galois theory. Due to this feature, the book will be useful and interest-ing to readers with very different background in mathematics, from undergraduate students to researchers.

Features 7 Classical Galois theory and classification of coverings are explained from scratch 7 Gentle introduction to the cutting edge of re-search 7 Written by one of the founders of topological Galois theory

Contents Introduction.- Galois Theory.- Coverings.- Rami-fied Coverings and Galois Theory.- Index

Fields of interestField Theory and Polynomials; Group Theory and Generalizations; Topology



Due October 2013

2014. 90 p. Hardcover7 approx. $59.99ISBN 978-3-642-38840-8

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A. Klenke, Johannes Gutenberg-Universität Mainz, Germany

Probability TheoryA Comprehensive Course

This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathemat-ics, physics, biology, financial engineering and computer science.

Features 7 Presents an updated, comprehensive and mod-ern introduction to the most important fields of probability theory 7 Contains many new figures and examples 7 Studies a wide variety of topics on probability theory, many of which are not found in introductory textbooks

Contents Basic Measure Theory.- Independence.- Generat-ing Functions.- The Integral.- Moments and Laws of Large Numbers.- Convergence Theorems.- Lp-Spaces and the Radon–Nikodym Theorem.- Con-ditional Expectations.- Martingales.- Optional Sampling Theorems.- Martingale Convergence Theorems and Their Applications.- Backwards Martingales and Exchangeability.- Convergence of Measures.- Probability Measures on Product Spaces.- Characteristic Functions and the Central Limit Theorem.- Infinitely Divisible Distribu-tions.- Markov Chains.- Convergence of Markov Chains.- Markov Chains and Electrical Networks.- Ergodic Theory.- Brownian Motion.- Law of the Iterated Logarithm.- Large Deviations.- The Pois-son Point Process.- The Itô Integral.- Stochastic Differential Equations.

Fields of interestProbability Theory and Stochastic Processes; Measure and Integration; Dynamical Systems and Ergodic Theory



Due August 2013

2nd ed. 2013. XII, 648 p. 44 illus., 20 in color. (Universitext) Softcover7 $89.99ISBN 978-1-4471-5360-3

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46

D. Mitrea, University of Missouri, Columbia, MO, USA

Distributions, Partial Differential Equations, and Harmonic Analysis The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differen-tial operators: the Laplace, heat, wave, Lam\’e and Schrodinger operators.

Features 7 Largely self-contained, rapid introduction to the theory of distributions and its applications to partial differential equations 7 Contains the computation of fundamental solutions for the La-placian, heat, wave, Lam\'e, Schrodinger, and Cau-chy operators 7 Each chapter contains exercises and many have solutions at the end of the book

Contents Introduction.- Summary of Topological and Func-tional Analysis Results.- Weak Derivatives.- The Space D0() of Distributions.- The Fourier Trans-form.- The Space of Tempered Distributions.- Fundamental Solution.- The Laplace Operator.- The Heat Operator.- The Wave Operator.- The Lame Operator.- Fundamental Solutions for Other Operators.- Hypoelliptic operators.- Sobolev spaces.- Appendix.- References.

Fields of interestPartial Differential Equations; Functional Analy-sis; Fourier Analysis



Due August 2013

2013. X, 498 p. (Universitext) Softcover7 $89.99ISBN 978-1-4614-8207-9

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A. Némethi, A. Szilárd, Alfréd Renyi Institute of Mathematics, Budapest, Hungary (Eds)

Deformations of Surface SingularitiesThe present publication contains a special collec-tion of research and review articles on deforma-tions of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples. The aim is to collect material that will help mathematicians already working or wish-ing to work in this area to deepen their insight and eliminate the technical barriers in this learning process.

Features 7 Special collection of research and review articles on deformations of surface singulari-ties 7 Introduces material on the newly found relationship with the theory of Stein fillings and symplectic geometry 7 Linking two main theo-ries of mathematics: low dimensional topology and algebraic geometry

Contents Altmann, K. and Kastner, L.: Negative Deforma-tions of Toric Singularities that are Smooth in Codimension Two.- Bhupal, M. and Stipsicz, A.I.: Smoothing of Singularities and Symplectic Topol-ogy.- Ilten, N.O.: Calculating Milnor Numbers and Versal Component Dimensions from P-Resolution Fans.- Némethi, A: Some Meeting Points of Singularity Theory and Low Dimensional Topol-ogy.- Stevens, J.: The Versal Deformation of Cyclic Quotient Singularities.- Stevens, J.: Computing Versal Deformations of Singularities with Hauser’s Algorithm.- Van Straten, D.: Tree Singularities: Limits, Series and Stability.

Fields of interestAlgebraic Topology; Algebraic Geometry



Due July 2013

2013. Approx. 280 p. (Bolyai Society Mathematical Studies, Volume 23) Hardcover7 $109.00ISBN 978-3-642-39130-9

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A. Osipov, V. Rokhlin, Yale University, CT, USA; H. Xiao, University of California, CA, USA

Prolate Spheroidal Wave Functions of Order ZeroMathematical Tools for Bandlimited Approximation

Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an impor-tant role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool. The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathemati-cians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.

Features 7 Aimed at a broad spectrum of scientists and engineers 7 Contains detailed description of practical numerical algorithms 7 Written by top international researchers in field

Contents Introduction.- Mathematical and Numerical Pre-liminaries.- Overview.- Analysis of the Differential Operator.- Analysis of the Integral Operator.- Ra-tional Approximations of PSWFs.-Miscellaneous Properties of PSWFs.- Asymptotic Analysis of PSWFs.- Quadrature Rules and Interpolation via PSWFs.- Numerical Algorithms .-

Fields of interestNumerical Analysis; Signal,Image and Speech Processing; Appl.Mathematics/Computational Methods of Engineering



Due September 2013

2013. X, 361 p. (Applied Mathematical Sciences, Volume 187) Hardcover7 $129.00ISBN 978-1-4614-8258-1

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47

P. Paule, Research Institute for Symbolic Computation (RISC), Linz, Austria (Ed)

Mathematics, Computer Science and Logic - A Never Ending StoryThe Bruno Buchberger Festschrift

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday.

Features 7 Gathers inspiring essays, written by interna-tional experts 7 Explores the foundations of mathematics: the state of the art, new ideas and di-rections 7 Reviews new aspects of the interplay among mathematics, logic and computer science

Contents Preface.- Henk Barendregt: Foundations of Mathematics from the Perspective of Computer Verification.- Manfred Broy: On the Role of Logic and Algebra in Software Engineering.- Stephen Wolfram: New Directions in the Foundations of Mathematics (2002).- Doron Zeilberger: Towards a Symbolic Computational Philosophy (and Meth-odology!) for Mathematics.

Fields of interestAlgorithms; Mathematical Logic and Foundations; Mathematical Software



Due August 2013

2013. X, 115 p. 35 illus. Hardcover7 $109.00ISBN 978-3-319-00965-0

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P. Pucci, Università Perugia Dipto. Matematica, Perugia, Italy; V. D. Radulescu, University of Craiova Fac. Mathematics & Computer Science, Craiova, Romania; H. Weinberger, University of Minnesota, Minneapolis, USA (Eds)

Selected Papers of James SerrinVolume 1

These two volumes present the collected works of James Serrin. He has done seminal work on a number of the basic tools needed for the study of solutions of partial differential equations. Many of them have been and are being applied to solving problems in science and engineering. Among the areas which he studied are maximum principle methods and related phenomena such as Har-nack’s inequality, the compact support principle, dead cores and bursts, free boundary problems, phase transitions, the symmetry of solutions, boundary layer theory, singularities, and fine regu-larity properties. The volumes include commen-taries by leading mathematicians to indicate the significance of the articles, and to discuss further developments along the lines of these articles.

Features 7 The two books contain a collection of challeng-ing papers in nonlinear partial differential equa-tions 7 They develop the skills for doing research in nonlinear analysis and applied functional analy-sis 7 They include incisive explanations of many important ideas in the development of some major research areas in the last few decades 7 They include an interesting and valuable historical ac-count of important ideas and techniques

Contents Photos Part 1.- Preface (Introduction).- Biography of James Serrin.- Papers and commentaries.- List of publications.

Field of interestHistory of Mathematical Sciences



Due October 2013

Only available in print

2013. IV, 796 p. (Contemporary Mathematicians) Hardcover7 approx. $189.00ISBN 978-3-0348-0684-8

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Selected Papers of James SerrinVolume 2

These two volumes present the collected works of James Serrin. He has done seminal work on a number of the basic tools needed for the study of solutions of partial differential equations. Many of them have been and are being applied to solving problems in science and engineering. Among the areas which he studied are maximum principle methods and related phenomena such as Har-nack’s inequality, the compact support principle, dead cores and bursts, free boundary problems, phase transitions, the symmetry of solutions, boundary layer theory, singularities, and fine regu-larity properties. The volumes include commen-taries by leading mathematicians to indicate the significance of the articles, and to discuss further developments along the lines of these articles.

Features 7 The two books contain a collection of chal-lenging papers in nonlinear partial differential equations 7 These papers develop the skills for doing research in nonlinear analysis and applied functional analysis 7 They include incisive explanations of many important ideas in the de-velopment of some major research areas in the last few decades 7 The work provides an interesting and valuable historical account of important ideas and techniques

Contents Photos Part 2.- Preface 2 (Introduction).- Papers 2.- List of publications.




Due October 2013


2013. IV, 796 p. (Contemporary Mathematicians) Hardcover7 approx. $189.00ISBN 978-3-0348-0686-2

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48


Selected Papers of James SerrinThese two volumes present the collected works of James Serrin. He has done seminal work on a number of the basic tools needed for the study of solutions of partial differential equations. Many of them have been and are being applied to solving problems in science and engineering. Among the areas which he studied are maximum principle methods and related phenomena such as Har-nack’s inequality, the compact support principle, dead cores and bursts, free boundary problems, phase transitions, the symmetry of solutions, boundary layer theory, singularities, and fine regu-larity properties. The volumes include commen-taries by leading mathematicians to indicate the significance of the articles, and to discuss further developments along the lines of these articles.

Features 7 The two books contain a collection of chal-lenging papers in nonlinear partial differential equations 7 These papers develop the skills for doing research in nonlinear analysis and applied functional analysis 7 They include incisive explanations of many important ideas in the de-velopment of some major research areas in the last few decades 7 The work provides an interesting and valuable historical account of important ideas and techniques




Due October 2013


2013. 1600 p. (Contemporary Mathematicians) (2-volume-set)7 approx. $319.00ISBN 978-3-0348-0685-5

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Y. Qin, Donghua University, Shanghai, China, People’s Republic

Analytic Inequalities and Their Applications in PDEsThis book is aimed at presenting some analytic in-equalities and their applications in partial differen-tial equations. These inequalities include integral inequalities, differential inequalities and difference inequalities which play a crucial role in establish-ing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equa-tions. The material summarizes a vast literature such as published papers, preprints and books in which inequalities are categorized in terms of dif-ferent properties which are consequences of those inequalities such as (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions for some partial differential equations.

Features 7 Useful basic analytic inequalities 7 Results and techniques in differential equations 7 First book to describe analytic inequalities categorized with different aims, such as uniform bounds, and to emphasize applications in partial differen-tial equations

Contents Preface.- 1 Integral Inequalities.- 2 Differential and Difference Inequalities.- 3 Global Attractors for Evolutionary Differential Equations.- 4 Global Existence and Uniqueness for Evolutionary PDEs.- 5 Asymptotic Behavior for Evolutionary PDEs.-6 Blow-up of Solutions to Evolutionary PDEs.- 7 Appendix: Basic Inequalities.

Fields of interestPartial Differential Equations; Mechanics; Opera-tor Theory



Due October 2013

2014. Approx. 670 p. (Operator Theory: Advances and Applications / Advances in Partial Differential Equations, Volume 239) Hardcover7 approx. $149.00ISBN 978-3-319-00830-1

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Y. D. Sergeyev, Università della Calabria, Rende, Italy; R. G. Strongin, N.I. Lobachevsky University of Nizhni Novgorod, Russia; D. Lera, University of Cagliari, Italy

Introduction to Global Optimization Exploiting Space-Filling CurvesIntroduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numeri-cal algorithms applying space-filling curves to re-duce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illus-trated through numerical examples.

Features 7 Presents new efficient methods for solving an important practical problem in the field of space-filling curves 7 Starting point for developing new methods 7 Contains a code for implement-ing space-filling curves that can be used in global optimization algorithms 7 Describes both stochastic and deterministic methods

Contents 1. Introduction.- 2. Approximations to Peano curves.- 3. Global optimization algorithms using curves to reduce dimensionality of the problem.- 4. Ideas for acceleration.- 5. A brief conclusion.- References.

Fields of interestManifolds and Cell Complexes (incl. Diff.Topol-ogy); Operations Research, Management Science; Mathematical Software


Product categoryBrief

Due July 2013

2013. XV, 135 p. 32 illus., 30 in color. (SpringerBriefs in Optimization) Softcover7 $49.99ISBN 978-1-4614-8041-9

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49

C. A. Tudor, Université de Lille 1,Villeneuve d’Ascq, France

Analysis of Variations for Self-similar ProcessesA Stochastic Calculus Approach

Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analy-sis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature.

Features 7 Introduces new concepts 7 Surveys modern techniques and new results on limit theorems and stochastic calculus 7 Useful to probabilists and statisticians

Contents Preface.- Introduction.- Part I Examples of Self-Similar Processes.- 1.Fractional Brownian Motion and Related Processes.- 2.Solutions to the Linear Stochastic Heat and Wave Equation.- 3.Non Gaussian Self-Similar Processes.- 4.Multiparam-eter Gaussian Processes.- Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems.- 5.First and Second Order Quadratic Variations. Wavelet-Type Variations.- 6.Hermite Variations for Self-Similar Processes.- Appendices: A.Self-Similar Processes with Stationary Incre-ments: Basic Properties.- B.Kolmogorov Continu-ity Theorem.- C.Multiple Wiener Integrals and Malliavin Derivatives.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes; Statistics, general



Due August 2013

2013. XII, 240 p. (Probability and Its Applications) Hardcover7 $109.00ISBN 978-3-319-00935-3

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G. Bellettini, Università di Roma “Tor Vergata”, Roma ... · mathematics and computer science 7 Acts as a short introduction to important and modern parts of discrete geometry