D. Angella, Università di Pisa, Pisa, Italy M. Bramanti ...folds 7 Coherent summary of existing literature Contents Preliminaries on (almost-) complex manifolds.- Cohomology of complex

News 10/2013 Mathematics

39

S. Ahmad, University of Texas San Antonio, San Antonio, TX, USA; A. Ambrosetti, SISSA, Trieste, Italy

A textbook on Ordinary Differential EquationsThe book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications.

Features 7 Application to applied sciences 7 Rich of ex-ercises with a set of selected solutions 7 Concise, rigorous, clear in analyzing the solutions

Contents 1 First order linear differential equations.- 2 Theory of first order differential equations.- 3 First order nonlinear differential equations.- 4 Existence and uniqueness for systems and higher order equations.- 5 Second Order Equations.- 6 Higher Order Linear Equations.- 7 Systems of First Order Equations.- 8 Qualitative analysis of 2×2 systems and nonlinear second order equa-tions.- 9 Sturm Liouville eigenvalue theory.- 10 Solutions by infinite series and Bessel func-tions.- 11 Laplace transform.- 12 Stability Theory.- 13 Boundary Value problems.- Appendix A. Nu-merical methods.- Answers to Selected Exercises.

Fields of interestOrdinary Differential Equations; Analysis; Nu-merical Analysis

Target groupsLower undergraduate

Discount groupProfessional Non-Medical

Due November 2013

2014. Approx. 360 p. (UNITEXT / La Matematica per il 3+2, Volume 73) Softcover7 approx. $69.99ISBN 978-3-319-02128-7

9<HTODMJ=acbcih>

D. Angella, Università di Pisa, Pisa, Italy

Cohomological Aspects in Complex Non-Kähler GeometryIn these notes, we provide a summary of recent re-sults on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit ex-amples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

Features 7 Provides detailed examples 7 Explicit com-putations of cohomologies on complex mani-folds 7 Coherent summary of existing literature

Contents Preliminaries on (almost-) complex manifolds.- Cohomology of complex manifolds.- Cohomology of nilmanifolds.- Cohomology of almost-complex manifolds.- References.

Fields of interestDifferential Geometry; Several Complex Variables and Analytic Spaces

Target groupsResearch


Due November 2013

2014. X, 186 p. 7 illus. (Lecture Notes in Mathematics, Volume 2095) Softcover7 $49.99ISBN 978-3-319-02440-0

9<HTODMJ=aceeaa>

M. Bramanti, Politecnico di Milano, Milan, Italy

An Invitation to Hypoelliptic Operators and Hörmander’s Vector Fields Hörmander’s operators are an important class of linear elliptic-parabolic degenerate partial dif-ferential operators with smooth coefficients: this text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development. These topics have been intensively studied since the late 1960s and are still an active field of research.

Features 7 Contains an overview of the recent lines of research in this area 7 Provides the relevant motivations behind the research in this area, rang-ing on several different disciplines 7 It contains also an overview of the recent lines of research in this area

Contents 1 Hörmander’s operators: what they are.- 2 Hörmander’s operators: why they are studied.- 3 A priori estimates in Sobolev spaces.- 4 Ge-ometry of Hörmander’s vector fields.- 5 Beyond Hörmander’s operators.

Fields of interestPartial Differential Equations; Analysis; Operator Theory

Target groupsGraduate


Due November 2013

2014. IX, 149 p. 3 illus. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-3-319-02086-0

9<HTODMJ=acaiga>

www.springer.com/978-3-319-02128-7



Mathematics springer.com/NEWSonline

40

M. Broué, Université Paris Diderot - Paris 7, Paris, France

Some Topics in AlgebraAn Advanced Undergraduate Course at PKU

During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be too exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It cer-tainly reflects some of the author’s own tastes, and it was influenced by the feelings and the reactions of the students. Nevertheless, the result covers some advanced undergraduate algebra (rings, ide-als, basics of fields theory, algebraic integers, mod-ules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counter-examples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains.

Features 7 Could serve as a syllabus for second, third and fourth year undergraduate students in first rate universities 7 Covers most of the material beyond usual linear algebra which is necessary for starting number theory, representation theory, algebraic geometry, and general algebra 7 Not a standard presentation, lots of examples, subliminal introduction to categorical approach 7 Offers a unique treatment of Dedekind Rings and modules over those

Contents Preface.- Rings and polynomial algebras.- Mod-ules.

Field of interestAlgebra



Due November 2013

2014. XIV, 198 p. (Mathematical Lectures from Peking University) Hardcover7 $109.00ISBN 978-3-642-41268-4

9<HTOGPC=ebcgie>

S.‑S. Chern, University of Chicago, Chicago, USA

Selected Papers IIIn recognition of professor Shiing-Shen Chern’s long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Sympo-sium was published in a series of three separate volumes, comprising approximately a third of Professor Chern’s total publications up to 1979. Later, a fourth volume was published, focusing on papers written during the Eighties. This second volume comprises selected papers written between 1932 and 1965.

Contents Curriculum Vitae.- A Summary of My Scientific Life and Works (Revised Version, 1988).- Bibli-ography of the Publications of S.S. Chern.- Pairs of Plane Curves with Points in One-to-One Cor-respondence.- Associate Quadratic Complexes of a Rectilinear Congruence.- Sur la Geometrie d’une Equation Differentielle du Troisieme Ordre.- On Projective Normal Coordinates.- On Two Affine Connections.- Sur la Geometrie d’un Systeme d’Equations DifTerentielles du Second Ordre.

Fields of interestMathematics, general; Differential Geometry



Due October 2013

Only available in print

1989. Reprint 2013 of the 1989 edition. XXX, 444 p. (Springer Collected Works in Mathematics) Softcover7 $79.99ISBN 978-1-4614-8976-4

9<HTMERB=eijhge>

S.‑s. Chern

Selected Papers IVIn recognition of professor Shiing-Shen Chern’s long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Sympo-sium was published in a series of three separate volumes, comprising approximately a third of Professor Chern’s total publications up to 1979. Later, this fourth volume was published, focusing on papers written during the Eighties.

Contents Bibliography of the Publications of S.S. Chern.- 19 original papers from 1981-1989.

Fields of interestMathematics, general; Differential Geometry; History of Mathematical Sciences



Due October 2013

Only available in print

1989. Reprint 2013 of the 1989 edition. XIV, 463 p. 1 illus. in color. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-1-4614-9085-2

9<HTMERB=ejaifc>





41

J. B. Conway, The George Washington University, Washington, DC, USA

A Course in Point Set TopologyThis textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topo-logical spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of para-compact spaces.

Features 7 Features undergraduate material in metric spaces, abstract topological spaces, and con-tinuous real-valued functions 7 Develops the material from the more particular to the general concepts 7 Contains many exercises of varying difficulty 7 Includes interesting historical notes

Contents Metric Spaces.- Topological Spaces.- Continuous Real-Valued Functions.- Appendix.- Bibliogra-phy.- Terms.- Symbols.

Field of interestTopology

Target groupsUpper undergraduate


Due November 2013

2014. XV, 128 p. (Undergraduate Texts in Mathematics) Hardcover7 $39.99ISBN 978-3-319-02367-0

9<HTODMJ=acdgha>

M. Corazza, C. Pizzi, Ca’ Foscari University of Venice, Venezia, Italy (Eds)

Mathematical and Statistical Methods for Actuarial Sciences and FinanceContents Weak form efficiency of selected European stock markets: alternative testing approaches (G. Albano, M. La Rocca, C. Perna).- An empiri-cal comparison of variable selection methods in competing risks model (A. Amendola, M. Restaino, L. Sensini).- A comparison between different numerical schemes for the valuation of unit-linked contracts embedding a surrender option (A.R. Bacinello, P. Millossovich, A. Mon-tealegre).- Dynamic tracking error with shortfall control using stochastic programming (D. Barro, E. Canestrelli).- Firm’s volatility risk under micro-structure noise (F. Barsotti, S. Sanfelici).- Socially responsible mutual funds: an efficiency compari-son among the European countries (A. Basso, S. Funari).- Fitting financial returns distributions: a mixture normality approach (R. Bramante, D. Zappa).- Single-name concentration risk measurements in credit portfolios (R. Calabrese, F. Porro).- Bifactorial pricing models: light and shadows in correlation role (R. Cocozza, A. De Simone).- Dynamic strategies for Defined Benefit pension plans risk management (I. Colivicchi, G. Piscopo, E. Vannucci).- Particle Swarm Optimiza-tion for preference disaggregation in multicriteria credit scoring problems (M. Corazza, S. Funari, R. Gusso).- Time series clustering on lower tail dependence for portfolio selection (G. De Luca, P. Zuccolotto).- Solvency Analysis of Defined Ben-efit pension schemes (P. Devolder, G. Piscopo). [...]

Fields of interestQuantitative Finance; Actuarial Sciences; Statistics for Business/Economics/Mathematical Finance/Insurance



Due December 2013

2014. Approx. 325 p. Hardcover7 approx. $129.00ISBN 978-3-319-02498-1

9<HTODMJ=acejib>

D. A. Dawson, Carleton University, School of Mathematics & Statistics, Ottawa, ON, Canada; A. Greven, Universität Erlangen-Nürnberg, Mathematisches Institut, Erlangen, Germany

Spatial Fleming-Viot Models with Selection and MutationFeatures 7 Develops a class of spatial models of a population undergoing mutation, selection and migration 7 Develops new duality methods for multitype population models 7 Develops the McKean-Vlasov limit of exchangeable popula-tion models and their entrance laws 7 Identifies mutation-selection equilibria 7 Offers valuable insights into the role of migration in the emer-gence of rare mutants in spatial Fleming-Viot models 7 Sheds new light on the role of migra-tion in sustaining biodiversity in evolution

Contents Introduction.- Emergence and fixation in the F-W model with two types.- Formulation of the multitype and multiscale model.- Formulation of the main results in the general case.- A Basic Tool: Dual Representations.- Long-time behav-iour: ergodicity and non-ergodicity.- Mean-field emergence and fixation of rare mutants (Phase 1,2).- Methods and proofs for the F-W model with two types.- Emergence, fixation with M ≥ 2 lower order types.- Emergence, fixation: The general (M, M)-type mean-field model.- Neutral evolution on E1 after fixation (Phase 3).- Re-equilibration on higher level E1 (Phase 4).- Iteration of the cycle I: Emergence and fixation on E2.- Iteration of the cycle – the general multilevel hierarchy.- Winding-up: Proofs of the Theorems 3-11.- Appendix 1 – Tightness.- Appendix 2. Nonlinear semigroup perturbations.- References.- Index of Notation and Tables of Basic Objects.- Index.

Fields of interestProbability Theory and Stochastic Processes; Evolutionary Biology



Due November 2013

2014. VIII, 770 p. 1 illus. in color. (Lecture Notes in Mathematics, Volume 2092) Softcover7 $119.00ISBN 978-3-319-02152-2

9<HTODMJ=acbfcc>





42

E. De Giorgi L. Ambrosio, Napoli, Italy; G. Dal Maso, SISSA, Trieste, Italy; M. Forti, Università di Pisa Dipto. Matematica Applicata, Pisa, Italy; M. Miranda, Centro Internationale per la Ricerca Matematica, Trento, Italy; S. Spagnolo (Eds)

Selected PapersPublished with the support of Unione Matematica Italiana and Scuola Normale Superiore

The book contains a selection of 43 scientific pa-pers by the great mathematician Ennio De Giorgi (1928-1996), which display the broad range of his achievements and his entire intellectual career as a problem solver and as a proponent of deep and ambitious mathematical theories. All papers are written in English and 17 of them appear also in their original Italian version in order to give an impression of De Giorgi’s original style.

Contents Preface.- Biography.- Prizes and academic awards.- Teaching and academic commitment.- The activities out of Pisa.- Civil, religious and po-litical commitment.- The scientific work of Ennio De Giorgi.- From the juvenile papers to Plateau’s problem and the solution of Hilbert’s19th prob-lem.- Partial differential equations and the founda-tions of G-convergence.- Asymptotic problems in the Calculus of Variations.- The most recent developments in the Calculus of Variations.- The work on Foundations of Mathematics.- De Giorgi’s contribution to the regularity theory for elliptic partial differential equations, by Luis Caffarelli.- Remarks on some of the analytical work of Ennio De Giorgi, by Louis Nirenberg.- Complete list of De Giorgi’s scientific publications.- Selected papers.

Fields of interestAnalysis; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization



Due November 2013

Published with the support of Unione Matematica Italiana, Bologna, Italy and Scuala Normale Superiore, Pisa, Italy

2006. Reprint 2013 of the 2006 edition. X, 889 p. 2 illus. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-3-642-40379-8

9<HTOGPC=eadhji>

G. Deelstra, Université Libre de Bruxelles, Brussels, Belgium; G. Plantin, Toulouse School of Economics, Toulouse, France

Risk Theory and ReinsuranceReinsurance is an important production factor of non-life insurance. The efficiency and the capacity of the reinsurance market directly regulate those of insurance markets. The purpose of this book is to provide a concise introduction to risk theory, as well as to its main application procedures to reinsurance. The first part of the book covers risk theory. It presents the most prevalent model of ruin theory, as well as a discussion on insurance premium calculation principles and the math-ematical tools that enable portfolios to be ordered according to their risk levels. The second part describes the institutional context of reinsurance. It first strives to clarify the legal nature of reinsur-ance transactions. It describes the structure of the reinsurance market and then the different legal and technical features of reinsurance contracts, known as reinsurance ‘treaties’ by practitioners. The third part creates a link between the theories presented in the first part and the practice described in the second one. Indeed, it sets out, mostly through examples, some methods for pric-ing and optimizing reinsurance.

Features 7 Provides a concise introduction to risk theory and its application procedures to reinsur-ance 7 Applies the formalism of risk theory to the institutional framework of reinsuranc-es 7 Useful for both academics and practitioners wishing to revive their knowledge of risk theory or to quickly learn about the main mechanisms of reinsurance

Contents Elements of Risk Theory.- Reinsurance Market Practices.- Optimal Reinsurance.

Field of interestActuarial Sciences



Due November 2013

2014. VIII, 88 p. 3 illus. (EAA Series) Softcover7 $49.99ISBN 978-1-4471-5567-6

9<HTMEPH=bffghg>

R. Denk, M. Kaip, Universität Konstanz, Konstanz, Germany

General Parabolic Mixed Order Systems in $L_p$ and ApplicationsIn this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces.

Features 7 General approach to non-standard parabolic equations and systems 7 Unified treatment in several types of non-integer Lp-Sobolev spac-es 7 Applicable to a large class of equations, e.g. to free boundary value problems and to equations in fluid dynamics and thermoelasticity

Contents Introduction and Outline.- 1 The joint time-space H(infinity)-calculus.- 2 The Newton polygon ap-proach for mixed-order systems.-3 Triebel-Lizor-kin spaces and the Lp-Lq setting.- 4 Application to parabolic differential equations.- List of figures.-Bibliography.- List of symbols.- Index.

Fields of interestPartial Differential Equations; Mathematical Phys-ics; Operator Theory



Due December 2013

2014. Approx. 250 p. 16 illus. (Operator Theory: Advances and Applications, Volume 239) Hardcover7 approx. $119.00ISBN 978-3-319-01999-4

9<HTODMJ=abjjje>





43

Y. Eidelman, Tel Aviv University Raymond & Beverly Sackler Faculty of Exa, Tel Aviv, Israel; I. Gohberg, Ra’anana, Israel; I. Haimovici, Tel Aviv University Raymond & Beverly Sackler Faculty of Exa, Tel Aviv, Israel

Separable Type Representations of Matrices and Fast AlgorithmsThis two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semisepa-rable, quasiseparable, band and companion form. The work examines algorithms of multiplica-tion, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representa-tions of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary condi-tions play an essential role.

Features 7 Self-contained two-volume monograph with material developed over the last 30 years 7 Sys-tematic theoretical and computational study of several types of generalizations of separable ma-trices 7 Many illustrative examples in different chapters of the book

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Numerical Analysis



Due October 2013

2013. 788 p. (Operator Theory: Advances and Applications, Volume 234/235) (2-volume-set)7 $209.00ISBN 978-3-0348-0728-9

9<HTOAOE=iahcij>

New SeriesStudies in Universal LogicSeries editors: J.‑Y. Béziau, A. Herzig, J. M. Font, A. Koslow, J.‑L. Lee, L. Maksimova, Editorial board: G. Malinowski, D. Sarenac, P. Schroeder‑Heister, V. Vasyukov

This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matri-ces, Kripke structures, combination of logics, cat-egorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discus-sions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers.

O. Gasquet, A. Herzig, B. Said, F. Schwarzentruber, Université Paul Sabatier, Toulouse, France

Kripke’s WorldsAn Introduction to Modal Logics via Tableaux

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world’s model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, tem-poral, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, condi-tional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in com-puter science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also stud-ied proof theoretically.

Features 7 Aims at filling the gap between existing intro-ductory and advanced textbooks 7 Introduces to the most important modal logics with multiple modalities from the perspective of the associ-ated reasoning tasks 7 Concentrates on the most general and powerful reasoning method for modal logics: tableaux systems

Contents Preface.- 1 Modelling things with graphs.- 2 Talking about graphs.- 3 The basics of the model construction method.- 4 Logics with simple constraints on models.- 5 Logics with transitive accessibility relations.- 6 Model Checking.- 7 Modal logics with transitive closure.- Bibliogra-phy.- Index.

Fields of interestMathematical Logic and Foundations; Mathemat-ics, general



Due November 2013

2014. XVI, 220 p. 73 illus. (Studies in Universal Logic) Softcover7 $109.00ISBN 978-3-7643-8503-3

9<HTOHRE=difadd>




44

G. Frei, Hombrechtikon, Switzerland; F. Lemmermeyer, Jagstzell, Germany; P. J. Roquette, Universität Heidelberg, Heidelberg, Germany (Eds)

Emil Artin and Helmut HasseThe Correspondence 1923‑1958

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understand-ing these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin’s reciprocity law.

Features 7 Insight into the birth of class field theory by presenting the letters between two of its main con-tributors, Emil Artin and Helmut Hasse 7 First English translation of these letters 7 Complete coverage of the letters from 1937 until 1958

Contents Part I: Introduction to the Correspondence.- 1. In-troduction.- 2. Emil Artin, his Life and his Work.- 3. Reminiscing Helmut Hasse.- 4. Reciprocity Laws for Power Residues.- 5. Class Field Theory.- 6. Time Table.- Part II: The Letters. References.- Name Index.- Subject Index.

Fields of interestNumber Theory; History of Mathematical Sci-ences



Due January 2014

2014. XVIII, 482 p. 27 illus. (Contributions in Mathematical and Computational Sciences, Volume 5) Hardcover7 approx. $129.00ISBN 978-3-0348-0714-2

9<HTOAOE=iahbec>

Y. Kabanov, Université de Besancon, Besancon, France; M. Rutkowski, University of Sydney, Sydney, NSW, Australia; T. Zariphopoulou, University of Oxford, Oxford, UK (Eds)

Inspired by FinanceThe Musiela Festschrift

Contents R. Ahlip and M. Rutkowski:Forward Start Foreign Exchange Options under Heston’s Volatility and the CIR Interest R.- A. Ben-soussan and S. R. Hoe:Real Options with Competition and Incomplete Market.- T. R. Bielecki and S. Crépey:Dynamic Hedging of Counterparty Exposure.- L. Campi:A Note on Market Completeness with American Put Options.- S. Cawston and L. Vostrikova:An f -Divergence Approach for Optimal Portfolios in Exponential Lévy Models.- B. Chouaf and S. Pergamenchtchikov:Optimal Investment with Bounded VaR for Power Utility Functions.- T. Choulli, J. Ma and M.-A. Morlais:Three Essays on Exponential Hedging with Variable Exit Times.- S. Darses and E.l Lépinette:Mean Square Error and Limit Theorem for the Modified Leland Hedg-ing Strategy with a Constant Transaction Costs Coefficient.- N. El Karoui, M. Jeanblanc, Y. Jiao, B. Zargari:Conditional Default Probability and Density.- R. Douady:Yield Curve Smoothing and Residual Variance of Fixed Income Positions.- E. Eberlein and D. B. Madan:Maximally Acceptable Portfolios.- P. V. Gapeev:Some Extensions of Nor-ros’ Lemma in Models with Several Defaults.- P. V. Gapeev and N. Rodosthenous:On the Pricing of Perpetual American Compound Options.- E. Go-bet and A. Suleiman:New Approximations in Lo-cal Volatility Models.- P. Hepperger:Low-Dimen-sional Partial Integro-Differential Equations for High-Dimensional Asian Options.- C. Kardaras:A Time BeforeWhich Insiders Would Not Undertake Risk.- P.l C. Kettler, F. Proske, M. [...]

Field of interestQuantitative Finance



Due November 2013

2014. XVIII, 536 p. 30 illus., 13 in color. Hardcover7 $149.00ISBN 978-3-319-02068-6

9<HTODMJ=acagig>

A. Karp, Columbia University, New York, NY, USA; G. Schubring, Universität Bielefeld Institut für Didaktik der Mathematik, Bielefeld, Germany (Eds)

Handbook on the History of Mathematics EducationContents Part 1.History and Methodology of the Field.- 1.On historiography of teaching and learning mathematics.- 2.The History of Mathematics Education: Developing a Research Methodol-ogy.- Part 2.Mathematics Education in Different Epochs and in Different Regions: Antiquity and the Middle Ages.- 3.Mathematics Education in Antiquity.- 4.Mathematics Education in Orien-tal Antiquity and the Middle Ages.- 5.Teaching the Mathematical Sciences in Islamic Societies, 8th-17th Centuries.- 6.Mathematics Education in the European Middle Ages.- Part 3.Mathematics Education in Different Epochs and in Different Regions: Pre-Modern Period.- 7.Mathematics Education in Europe in the Pre-Modern Period.- 8.Mathematics Education in East Asia in the Pre-modern Period.- 9.Mathematics Education in the Americas in the Pre-Modern Period.- Part 4.Mathematics Education in Different Epochs and in Different Regions: Modern Period.- 10.Second-ary School Mathematics Teaching in Italy from the Early Nineteenth Century to the Mid-Twentieth Century.- 11.Mathematics Education in France: 1800-1980.- 12.Mathematics Education in Ger-many (Modern Times).- 13.Mathematics Educa-tion in the United Kingdom.- 14.Mathematics Education in Spain and Portugal.- 15.Mathematics Education in Russia.- 16.Mathematics Education in the United States and Canada.- 17.Mathemat-ics Education in Latin America.- 18.Mathemat-ics Education in Modern Asia.- 19.Mathematics Education in Africa. [...]

Fields of interestHistory of Mathematical Sciences; Mathematics Education



Due November 2013

2014. XII, 822 p. 21 illus., 5 in color. Hardcover7 $349.00ISBN 978-1-4614-9154-5

9<HTMERB=ejbfef>





45

S. G. Krantz, Washington University in St. Louis, St. Louis, MO, USA; H. R. Parks, Oregon State University, Corvallis, OR, USA

A Mathematical OdysseyJourney from the Real to the Complex

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conver-sant with what goes on in mathematics. Just as ev-eryone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe.

Features 7 Explores several hot-button topics that are difficult to find elsewhere in popular litera-ture 7 Contains thirteen chapters intended to intrigue a broad audience of readers, on subjects such as RSA encryption, wavelets, and relativity theory 7 Makes math accessible with real-word examples, color figures, tables, graphs, and dia-gram analysis that almost any reader can appreci-ate and understand

Contents Preface.-1. The Four-Color Problem.-2. The Mathematics of Finance.-3. Ramsey Theory.-4. Dynamical Systems.-5. The Plateau Problem.-6. Euclidean and Non-Euclidean Geometries.-7. Spe-cial Relativity-8. Wavelets in Our World.-9. RSA Encryption.-10. The P/NP Problem.-11. Primality Testing.-12. The Foundations of Mathematics.-13. Fermat’s Last Theorem.

Fields of interestHistory of Mathematical Sciences; Popular Science in Mathematics/Computer Science/Natural Sci-ence/Technology; Applications of Mathematics

Target groupsPopular/general


Due January 2014

2014. XVI, 368 p. 186 illus., 62 in color. Hardcover7 approx. $39.95ISBN 978-1-4614-8938-2

9<HTMERB=eijdic>

R. Kruse, Bielefeld University, Bielefeld, Germany

Strong and Weak Approximation of Semilinear Stochastic Evolution EquationsIn this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numeri-cal schemes considered combine Galerkin finite element methods with Euler-type temporal ap-proximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book.

Features 7 Employing Galerkin finite element methods closes the gap between theoretical convergence results and standard PDE solvers in widely used software packages 7 Derives the optimal order of strong convergence through optimal regularity re-sults 7 Includes a self-contained introduction to Malliavin calculus 7 Effectively approaches weak convergence for SPDEs with stochastic coefficients by avoiding Kolmogorov’s backward equation

Contents Introduction.- Stochastic Evolution Equations in Hilbert Spaces.- Optimal Strong Error Estimates for Galerkin Finite Element Methods.- A Short Review of the Malliavin Calculus in Hilbert Spaces.- A Malliavin Calculus Approach to Weak Convergence.- Numerical Experiments.- Some Useful Variations of Gronwall’s Lemma.- Results on Semigroups and their Infinitesimal Genera-tors.- A Generalized Version of Lebesgue’s Theo-rem.- References.- Index.

Fields of interestNumerical Analysis; Probability Theory and Sto-chastic Processes; Partial Differential Equations



Due November 2013

2014. X, 168 p. 4 illus. in color. (Lecture Notes in Mathematics, Volume 2093) Softcover7 $49.99ISBN 978-3-319-02230-7

9<HTODMJ=accdah>

A. E. Kyprianou, University of Bath, Bath, UK

Gerber–Shiu Risk TheoryMotivated by the many and long-standing contri-butions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies mar-tingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by mak-ing dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter cor-responds to approximately two hours of lectures.

Features 7 Provides a self-contained and easy-to-read introduction to classical ruin theory 7 Includes recent developments in exotic ruin theo-ry 7 Makes transparent the connection with the theory of spectrally negative Lévy processes

Contents Introduction.- The Wald martingale and the maxi-mum.- The Kella-Whitt martingale and the mini-mum.- Scale functions and ruin probabilities.- The Gerber–Shiu measure.- Reflection strategies.- Perturbation-at-maximum strategies.- Refraction strategies.- Concluding discussion.- References.

Fields of interestProbability Theory and Stochastic Processes; Actu-arial Sciences



Due October 2013

2013. VIII, 95 p. 7 illus., 3 in color. (EAA Series) Softcover7 $49.99ISBN 978-3-319-02302-1

9<HTODMJ=acdacb>





46

R. Lupacchini, A. Angelini, University of Bologna, Bologna, Italy (Eds)

The Art of ScienceExploring Symmetries between the Renaissance and Quantum Physics

In addition to linear perspective, complex num-bers and probability were notable discoveries of the Renaissance.

Features 7 Extends Leonardo's vision of painting as a science to "scientific representation" 7 Restores a visual dimension to the mathematical scienc-es 7 Highlights the shared characteristics of the space opened to painting by linear perspective and that opened to science by complex numbers

Contents ‘Continuous Quantities’: the Primacy of Geom-etry in Renaissance Art from a Leonardesque Perspective.- Seeing Reality in Perspective. The ‘Art of Optics’ and the ‘Science of Painting.- Visual Differential Geometry and Beltrami’s Hyperbolic Plane.- On the Genesis of Linear Harmony in Renaissance Art.- All Done with Mirrors. Symme-tries, Quaternions, Spinors and Clifford Algebras.- The Role of Perspective in the Trasformation of European Culture.- Questioning Visual Abstract-ness. From ‘Imaginary Quantities’ to Heisenberg’s Relations and Today.- Fundamental Theorem of Algebra.- Radices sophisticae, racines imaginaires: the Origins of Complex Numbers in the Late Renaissance.- Random, Complex and Quan-tum.- Hilbert’s Vision of Geometric Intuition as a Method of Mathematical Physics.- From Perspec-tive Drawing to the Eighth Dimension.

Fields of interestMathematics in Art and Architecture; History and Philosophical Foundations of Physics; History of Mathematical Sciences



Due January 2014

2014. X, 190 p. 80 illus. Hardcover7 approx. $89.99ISBN 978-3-319-02110-2

9<HTODMJ=acbbac>

T. Ma, Sichuan University, Sichuan, China, People’s Republic; S. Wang, Indiana University, Bloomington, IN, USA

Phase Transition DynamicsThis book is an introduction to a comprehensive and unified dynamic transition theory for dis-sipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to intro-duce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields.

Features 7 Theory and methods are applicable to a wide range of scientific problems 7 Provides a thorough introduction to dynamic transition theory for nonlinear partial differential equa-tions 7 Mathematical discussion of dynamic transition theory is developed with attention to physics

Contents User’s Guide.- General Theory of Phase Transition Dynamics.- Dynamic Transition Theory.- Equilib-rium Phase Transition in Statistical Physics.- Fluid Dynamics.- Geophysical Fluid Dynamics and Climate Dynamics.- Dynamical Transitions in Chemistry and Biology.- References .

Fields of interestPartial Differential Equations; Fluid- and Aerody-namics; Complex Systems



Due October 2013

2014. XX, 558 p. 153 illus., 2 in color. Hardcover7 $149.00ISBN 978-1-4614-8962-7

9<HTMERB=eijgch>

V. Maz’ya, Sollentuna, Sweden

Differential Equations of My Young YearsTranslated by: A. Alexeev, Berkeley, CA, USA

Contents Foreword.- The beginning.- The time of peace is over.- My mother’s story.- My father’s story.- In Sverdlovsk.- Back to Leningrad.- Crime without punishment.- Even the sun has spots.- It is so diffi-cult to become an “A” student.- The importance of being an “A” student.- Slingshots.- Illnesses.- “Phy-scult” and sports.- A sharp kid.- Foreign languag-es.- My interests.- Poetry.- Fimka.- The first place in the District!.- The indecent topic.- My circle of reading.- I chose mathematics.- A circle at the Palace of Pioneers.- Two lectures for the school teachers.- The English teacher.- Arkady Alexeev.- Alexeev’s story.- Vanity of vanities, all is vanity.-You cannot live without the women. No!.- The first Mathmech year.- Student contests.- We lead our life in major key.- A mysterious ID.- Musical moments.- Valery Maisky.- The authorities did not like me.- How did I not become a dissident.- Misha Danilov.- Fractional derivatives.- Student Scientific Society (SSS) and Tseitin.- “Quasi-publi-cation” and S. M. Lozinsky.- The Mathmech choir.- My doubts and S. G. Mikhlin’s advice.- A few words about Mikhlin The virgin soil.- Bakelman’s special course.- Job placement.- Siegfried.- Steel sheets and YMS.- Possibility and reality.- Defense at the Moscow State University.- Defense at the Leningrad University.- About V.I. Smirnov.- An order: scatter the composed type.- About the “Big Seminar”.- After the defense of the Doctor’s degree dissertation.- Non-travels to foreign countries.- Counterexamples to the Hilbert problem.- Tal-ent.- Farewell, my young years!.- Under close surveillance?

Fields of interestHistory of Mathematical Sciences; Mathematics, general

Target groupsPopular/general


Due January 2014

2014. Approx. 250 p. 105 illus. Hardcover7 approx. $59.99ISBN 978-3-319-01808-9

9<HTODMJ=abiaij>





47

J. Milton, Claremont University, Claremont, CA, USA; T. Ohira, Sony Computer Science Laboratories, Inc., Tokyo, Japan

Mathematics as a Laboratory ToolDynamics, Delays and Noise

This introductory textbook is based on the premise that the foundation of good science is good data. The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.

Features 7 Uses real data 7 Uses mathematical methods that are used in the laboratory 7 Real laboratory exercises provided as supplementary material

Contents Science and the mathematics of black boxes.- The mathematics of change.- Equilibria and steady states.- Stability.- Fixed–points: Creation and destruction.- Transient dynamics.- Frequency domain I: Bode plots and transfer functions.- Fre-quency domain II: Fourier analysis and power spectra.- Feedback and control systems.- Oscil-lations.- Beyond limit cycles.- Random pertur-bations.- Noisy dynamical systems.- Random walkers.- Thermodynamic perspectives.

Fields of interestMathematical and Computational Biology; Neu-rology; Cell Physiology



Due October 2013

2013. X, 488 p. 159 illus., 4 in color. Hardcover7 $59.99ISBN 978-1-4614-9095-1

9<HTMERB=ejajfb>

J. D. Monk, University of Colorado at Boulder, Boulder, CO, USA

Cardinal Invariants on Boolean AlgebrasThis book is concerned with cardinal number val-ued functions defined for any Boolean algebra. Ex-amples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cel-lularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultra-products, and their relationships to one another.

Features 7 Covers most of what is known on cardinal in-variants in Boolean algebras 7 Includes a list of 185 interesting open problems 7 Detailed study of 21 cardinal number valued functions defined for any Boolean algebra

Contents Introduction.- 1. Special operations on Boolean algebras.- 2. Special classes of Boolean algebras.- 3. Cellularity.- 4. Depth.- 5. Topological density.- 6. Pi-weight.- 7. Length.- 8. Irredundance.- 9. Car-dinality.- 10. Independence.- 11. Pi-character.- 12. Tightness.- 13. Spread.- 14. Character.- 15. He-reditary Lindelöf degree.- 16. Hereditary density.- 17. Incomparability.- 18. Hereditary cofinality.- 19. Number of ultrafilters.- 20. Number of automor-phisms.- 21. Number of endomorphisms.- 22. Number of ideals.- 23. Number of subalgebras.- 24. Other cardinal functions.- 25. Diagrams.- 26. Examples.- Index of problems.- References.- Index of symbols.- Index of names and words.

Fields of interestMathematical Logic and Foundations; Order, Lat-tices, Ordered Algebraic Structures



Due January 2014

Originally published as volume 142 in the series: Progress in Mathematics

2nd ed. 2014. Approx. 515 p. (Progress in Mathematics, Volume 142) Hardcover7 approx. $149.00ISBN 978-3-0348-0729-6

9<HTOAOE=iahcjg>

J. J. Morales Ruiz

Differential Galois Theory and Non-Integrability of Hamiltonian SystemsThis book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system.

Features 7 Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1998 7 Well-balanced exposition addressing the relation between two different concepts of integrability 7 Proposes problems and conjectures which open new lines of research

Contents 1 Introduction.- 2 Differential Galois Theory.- 3 Hamiltonian Systems.- 4 Non-integrability Theorems.- 5 Three Models.- 6 An Application of the Lamé Equation.- 7 A Connection with Cha-otic Dynamics.- 8 Complementary Results and Conjectures.- A Meromorphic Bundles.- B Galois Groups and Finite Coverings.- C Connections with Structure Group.- Bibliography.- Index.

Fields of interestOrdinary Differential Equations; Global Analysis and Analysis on Manifolds; Field Theory and Polynomials



Due October 2013

Originally published as volume 179 in the Progress in Mathematics series

1999. Reprint 2013 of the 1999 edition. XIV, 167 p. (Modern Birkhäuser Classics) Softcover7 $69.99ISBN 978-3-0348-0720-3

9<HTOAOE=iahcad>





48

D. Motreanu, University of Perpignan, Perpignan, France; V. V. Motreanu, Ben-Gurion University of the Negev, Beer-Sheva, Israel; N. Papageorgiou, National Technical University Zografou Campus, Athens, Greece

Topological and Variational Methods with Applications to Nonlinear Boundary Value ProblemsThis book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory.

Features 7 Parallel treatment of smooth and nonsmooth problems 7 Contains proofs for many of the results stated herein 7 Presents recent research in the field for the first time in book form

Contents Preface.- Introduction.- Sobolev Spaces.- Non-linear Operators.- Nonsmooth Analysis.- Degree Theory.- Variational Principles and Critical Point Theory.- Morse Theory.- Bifurcation Theory.- Regularity Theorems and Maximum Principles.- Spectrum of Differential Operators.- Ordinary Differential Equations.- Nonlinear Elliptic Equa-tions with Dirichlet Boundary Conditions.- Non-linear Elliptic Equations with Neumann Boundary Conditions.- List of Symbols.- References.- Index .

Fields of interestPartial Differential Equations; Calculus of Varia-tions and Optimal Control; Optimization; Opera-tor Theory



Due December 2013

2014. X, 440 p. Hardcover7 $129.00ISBN 978-1-4614-9322-8

9<HTMERB=ejdcci>

P. Natarajan, Ramakrishna Mission Vivekananda College, Chennai, India

An Introduction to Ultrametric Summability TheoryUltrametric analysis has emerged as an impor-tant branch of mathematics in recent years. This book presents, for the first time, a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis.

Features 7 Studies ultrametric analysis, an emerg-ing branch of mathematics 7 Introduces the concepts of ultrametric summability theory—a fusion of summability theory and ultrametric analysis 7 Appeals to young researchers as well as mature mathematicians

Contents Preface.- Introduction and Preliminaries.- Some Arithmetic and Analysis in Qp : Derivatives in Ultrametric Analysis.- Ultrametric Functional Analysis.- Ultrametric Summability Theory.- Ref-erences.- Index.

Fields of interestSequences, Series, Summability; Analysis



Due October 2013

2013. IX, 102 p. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-81-322-1646-9

9<HTTBOC=cbgegj>

T. Nishitani, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan

Hyperbolic Systems with Analytic CoefficientsWell‑posedness of the Cauchy Problem

This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general neces-sary conditions for question (B) in terms of mi-nors of the principal symbols. With regard to suf-ficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contain strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby.

Contents Introduction.- Necessary conditions for strong hyperbolicity.- Two by two systems with two inde-pendent variables.- Systems with nondegenerate characteristics.- Index.

Fields of interestPartial Differential Equations; Mathematical Methods in Physics



Due November 2013

2014. X, 208 p. (Lecture Notes in Mathematics, Volume 2097) Softcover7 $59.99ISBN 978-3-319-02272-7

9<HTODMJ=acchch>





49

J. Noguchi, J. Winkelmann, Ruhr-Universität Bochum, Bochum, Germany

Nevanlinna Theory in Several Complex Variables and Diophantine ApproximationThe aim of this book is to provide a compre-hensive account of higher dimensional Nevan-linna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chap-ters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap.

Features 7 This is an important state-of-the-art book on Nevanlinna theory in higher dimension and the relations with Diophantine approximation theory 7 The contents include materials that cannot be easily found in other sources 7 The treatment and proofs are given in a self-contained manner except for some results over number fields in Chap. 9, suitable for graduate students and in-terested researchers, specialists and non-specialists alike

Contents Nevanlinna Theory of Meromorphic Functions.- First Main Theorem.- Differentiably Non-Degen-erate Meromorphic Maps.- Entire Curves into Al-gebraic Varieties.- Semi-Abelian Varieties.- Entire Curves into Semi-Abelian Varieties.- Kobayashi Hyperbolicity.- Nevanlinna Theory over Function Fields.- Diophantine Approximation.- Bibliogra-phy.- Index.- Symbols

Fields of interestFunctions of a Complex Variable; Several Com-plex Variables and Analytic Spaces; Algebraic Geometry



Due November 2013

2014. XII, 412 p. 6 illus. (Grundlehren der mathematischen Wissenschaften, Volume 350) Hardcover7 $129.00ISBN 978-4-431-54570-5

9<HTPEOB=fefhaf>

P. Olver, University of Minnesota, Minneapolis, MN, USA

Introduction to Partial Differential Equations This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergradu-ates and beginning graduate students in math-ematics, science and engineering. Exercises appear at the end of almost every subsection, and come in a variety of flavors. Most exercise sets start with some straightforward computational problems to develop and reinforce the principal new tech-niques and ideas.

Features 7 Many interesting examples and exercises that are connected to real world problems balanced with well explained theory 7 Provides an excel-lent reading course for undergraduate partial differential equations 7 Treats both linear and nonlinear partial differential equations

Contents What are Partial Differential Equations?.- Linear and Nonlinear Waves.- Fourier Series.- Separa-tion of Variables.- Finite Differences.- General-ized Functions and Green’s Functions.- Complex Analysis and Conformal Mapping.- Fourier Trans-forms.- Linear and Nonlinear Evolution Equa-tions.- A General Framework for Linear Partial Differential Equations .- Finite Elements and Weak Solutions.- Dynamics of Planar Media.- Partial Differential Equations in Space .-

Fields of interestPartial Differential Equations; Complex Systems; Fourier Analysis



Due November 2013

2013. X, 640 p. (Undergraduate Texts in Mathematics) Hardcover7 approx. $59.00ISBN 978-3-319-02098-3

9<HTODMJ=acajid>

M. S. Osborne, University of Washington, Seattle, WA, USA

Locally Convex SpacesFor most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focus-ing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topo-logical vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform bounded-ness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.

Features 7 Introduces functional analysis while focusing on locally convex spaces 7 Focuses on applica-tions to other topics in analysis 7 Contains over 100 exercises with varying levels of difficulty to motivate the reader

Contents 1 Topological Groups.- 2 Topological Vector Spaces.- 3 Locally Convex Spaces.- 4 The Clas-sics.- 5 Dual Spaces.- 6 Duals of Fré chet Spaces.- A Topological Oddities.- B Closed Graphs in Topological Groups.- C The Other Krein–Smulian Theorem.- D Further Hints for Selected Exercises.- Bibliography.- Index.

Fields of interestFunctional Analysis; Topological Groups, Lie Groups



Due October 2013

2014. X, 202 p. (Graduate Texts in Mathematics, Volume 269) Hardcover7 $69.99ISBN 978-3-319-02044-0

9<HTODMJ=acaeea>





50

P.‑Q. PAN, Southeast University, Nanjing, China, People’s Republic

Linear Programming Computation With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods.

Features 7 A landmark work on LP 7 Includes a wealth of rich and advanced materials 7 A must-read for all students, researchers and practitioners interested in LP and related areas

Contents Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- Variants of the Simplex Method.- Decomposition Method.- Interior Point Method.- Integer Linear Programming (ILP).- Pivot Rule.- Dual Pivot Rule.- Simplex Phase-I Method.- Dual Simplex Phase-l Method.- Reduced Simplex Method.- Im-proved Reduced Simplex Method.- D-Reduced Simplex Method.- Criss-Cross Simplex Meth-od.- Generalizing Reduced Simplex Method.- Deficient-Basis Method.- Dual Deficient-Basis Method.- Face Method.- Dual Face Method.- Piv-otal interior-point Method.- Special Topics.- Ap-pendix.- References.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Mathematics, general; Economics general



Due November 2013

2014. XX, 850 p. 14 illus. Hardcover7 $189.00ISBN 978-3-642-40753-6

9<HTOGPC=eahfdg>

E. Pappalardo, Johns Hopkins University, Baltimore, MD, USA; P. M. Pardalos, University of Florida, Gainesville, FL, USA; G. Stracquadanio, Johns Hopkins University, Baltimore, MD, USA

Optimization Approaches for Solving String Selection ProblemsOptimization Approaches for Solving String Selection Problems provides an overview of op-timization methods for a wide class of genomics-related problems in relation to the string selection problems. This class of problems addresses the recognition of similar characteristics or differences within biological sequences. Specifically, this book considers a large class of problems, ranging from the closest string and substring problems, to the farthest string and substring problems, to the far from most string problem. Each problem includes a detailed description, highlighting both biological and mathematical features, and presents state-of-the-art approaches.

Features 7 Provides both an easy and deep understanding of optimization methods for string selection prob-lems 7 Problems are presented in a theoretical and practical manner 7 Highlights the impor-tance of applying theoretical results to challenging problems occurring in genomics

Contents 1. Biological Sequences.- 2. Strings: Theory, Properties and Applications.- 3. Mathematical Optimization.- 4. String Selection Problems.

Fields of interestDiscrete Optimization; Mathematical and Computational Biology; Discrete Mathematics in Computer Science



Due October 2013

2013. VIII, 49 p. 2 illus. in color. (SpringerBriefs in Optimization) Softcover7 $54.99ISBN 978-1-4614-9052-4

9<HTMERB=ejafce>

R. Paulavičius, J. Zilnskas, Vilnius University, Vilnius, Lithuania

Simplicial Global OptimizationSimplicial Global Optimization is centered on deterministic covering methods partitioning fea-sible region by simplices. This book looks into the advantages of simplicial partitioning in global op-timization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors pro-vide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text.

Features 7 Extends class of algorithms for Lipschitz global optimization without the Lipschitz constant 7 Contains a deep investigation of particular cases of simplicial partitions 7 Pro-vides applications where simplicial partitioning is beneficial

Contents 1. Simplicial Partitions in Global Optimization.- 2. Lipschitz Optimization with Different Bounds over Simplices.- 3. Simplicial Lipschitz Optimiza-tion without Lipschitz Constant.- 4. Applications of Global Optimization Benefiting from Simpli-cial Partitions.- References.-Description of Test Problems.

Fields of interestOperations Research, Management Science; Com-binatorics; Applications of Mathematics



Due October 2013

2014. X, 144 p. 51 illus. in color. (SpringerBriefs in Optimization) Softcover7 $54.99ISBN 978-1-4614-9092-0

9<HTMERB=ejajca>





51

A. Quarteroni, Politecnico di Milano, Milano, Italy; G. Rozza, SISSA - International School for Advanced Studies, Trieste, Italy (Eds)

Reduced Order Methods for modeling and computational reductionThe monograph deals with the state of the art of current advances and developments in reduced order methods for modeling and computational reduction of complex parametrized systems, held by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques. All the contributions in the book have been peer-reviewed and contain examples of ap-plications in computational mechanics.

Features 7 A complete review on the state of the art of model order reduction advances and develop-ments 7 A gallery of application examples on reduced order modeling in computational science and engineering 7 It covers several topics and techniques by leading experts

Fields of interestComputational Mathematics and Numerical Analysis; Numeric Computing; Appl.Mathemat-ics/Computational Methods of Engineering

Target groupsProfessional/practitioner


Due November 2013

2014. Approx. 300 p. (MS&A, Volume 8) Hardcover7 approx. $119.00ISBN 978-3-319-02089-1

9<HTODMJ=acaijb>

R. Roussarie

Bifurcations of Planar Vector Fields and Hilbert’s Sixteenth ProblemIn a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymp-totic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert’s 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations.

Features 7 Presents tools for studying local bifurca-tions of limit cycles in families of planar vector fields 7 Provides systematic introduction to classical analytic geometric methods applied to regular limit periodic sets and more recent tools for singular limit sets 7 Well-balanced basis for teaching special courses

Contents Preface.- 1 Families of Two-dimensional Vector Fields.- 2 Limit Periodic Sets.- 3 The 0-Parameter Case.- 4 Bifurcations of Regular Limit Periodic Sets.- 5 Bifurcations of Elementary Graphics.- 6 Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets.- Bibliogra-phy.- Index.

Fields of interestAnalysis; Global Analysis and Analysis on Mani-folds; Partial Differential Equations



Due October 2013

Originally published as volume 164 in the Progress in Mathematics series

1998. Reprint 2013 of the 1998 edition. XVII, 204 p. (Modern Birkhäuser Classics) Softcover7 approx. $69.99ISBN 978-3-0348-0717-3

9<HTOAOE=iahbhd>

D. Simchi‑Levi, Massachusetts Institute of Technology Dept. Civil & Environmental Engineering, Cambridge, MA, USA; X. Chen, University of Illinois, Urbana-Champaign Dept. Mechanical &, Urbana, IL, USA; J. Bramel, New York, NY, USA

The Logic of LogisticsTheory, Algorithms, and Applications for Logistics Management

Features 7 Presents a survey of the modern theory and application of logistics management 7 Only book that combines theory, algorithms and best practice in logistics and supply chain manage-ment 7 Timely and authoritative survey of the field 7 Four new chapters added in addition to five new sections with a significant update of two existing sections

Contents Introduction.- Convexity and Supermodularity.- Game Theory.- Worst-Case Analysis.- Average-Case Analysis.- Mathematical Programming Based Bounds.- Economic Lot Size Models with Constant Demands.- Economic Lot Size Models with Varying Demands.- Stochastic Inventory Models.- Integration of Inventory and Pricing.- Supply Chain Competition and Collaboration Models.- Procurement Contracts.- Process Flex-ibility.- Supply Chain Planning Models.- Facility Location Models.- The Capacitated VRP with Equal Demands.- The Capacitated VRP with Unequal Demands.- The VRP with Time Window Constraints.- Solving the VRP Using a Column Generation Approach.- Network Planning.- A Case Study: School Bus Routing.

Fields of interestOperations Research, Management Science; Production/Logistics/Supply Chain Management; Industrial and Production Engineering

Target groupsProfessional/practitioner


Due November 2013

3rd ed. 2014. XXI, 444 p. 38 illus. (Springer Series in Operations Research and Financial Engineering) Hardcover7 $79.99ISBN 978-1-4614-9148-4

9<HTMERB=ejbeie>





52

G. Stefani, Università degli Studi di Firenze, Firenze, Italy; U. Boscain, Ecole Polytechnique and team INRIA GECO, Palaiseau Cedex, France; M. Sigalotti, Ecole Polytechnique, Palaiseau Cedex, France; J.‑P. Gauthier, Université de Toulon, LA GARDE CEDEX, France; A. Sarichev, Universita’ degli studi di Firenze, Firenze, Italy (Eds)

Geometric Control Theory and sub-Riemannian GeometryContents 1 A. A. Agrachev - Some open problems.- 2 D. Barilari, A. Lerario - Geometry of Maslov cycles.- 3 Y. Baryshnikov, B. Shapiro - How to Run a Centipede: a Topological Perspective.- 4 B. Bonnard, O. Cots, L. Jassionnesse - Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces.- 5 J-B. Caillau, C. Royer - On the injectivity and nonfocal domains of the ellipsoid of revolution.- 6 P. Cannarsa, R. Guglielmi - Null controllability in large time for the parabolic Grushin operator with singular potential.- 7 Y. Chitour, M. Godoy Molina, P. Kokkonen - The rolling problem: overview and challenges.- 8 A. A. Davydov, A. S. Platov - Op-timal stationary exploitation of size-structured population with intra-specific competition.- 9 B. Doubrov, I. Zelenko - On geometry of affine control systems with one input.- 10 B. Franchi, V. Penso, R. Serapioni - Remarks on Lipschitz domains in Carnot groups.- 11 R. V. Gamkrelidze - Differential-geometric and invariance properties of the equations of Maximum Principle (MP).- 12 N. Garofalo - Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spac-es.- 13 R. Ghezzi, F. Jean - Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds.- 14 V. Jurdjevic - The Delauney-Dubins Problem.- 15 M. Karmanova, S. [...]

Fields of interestCalculus of Variations and Optimal Control; Optimization; Global Analysis and Analysis on Manifolds; Differential Geometry



Due November 2013

2014. Approx. 400 p. (Springer INdAM Series, Volume 5) Hardcover7 approx. $129.00ISBN 978-3-319-02131-7

9<HTODMJ=acbdbh>

X. Tolsa, Universitat Autónoma de Barcelona ICREA, Bellaterra (Cerdanyola), Spain

Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund TheoryThis book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered.

Features 7 A large part of the material, such as the proof of the semiadditivity of analytic capacity, is acces-sible in book form for the first time 7 The book provides a unified approach to the material and simplified proofs Many results have important ap-plications to several areas in analysis 7 The book is largely self contained and accessible to graduate students 7 The author is a well known leading expert in the area

Contents Introduction.- Basic notation.- Chapter 1. Analytic capacity.- Chapter 2. Basic Calderón-Zygmund theory with non doubling measures.- Chapter 3. The Cauchy transform and Menger curvature.- Chapter 4. The capacity γ+.- Chapter 5. A Tb theorem of Nazarov, Treil and Volberg.- Chapter 6. The comparability between γ and γ +, and the semiadditivity of analytic capacity.- Chapter 7. Curvature and rectifiability.- Chapter 8. Principal values for the Cauchy transform and rectifiability.- Chapter 9. RBMO(μ) and H1 atb(μ).- Bibliogra-phy.- Index.

Fields of interestFunctions of a Complex Variable; Potential Theory; Calculus of Variations and Optimal Con-trol; Optimization



Due January 2014

2014. Approx. 390 p. (Progress in Mathematics, Volume 307) Hardcover7 approx. $129.00ISBN 978-3-319-00595-9

9<HTODMJ=aafjfj>



Documents

D. Angella, Università di Pisa, Pisa, Italy M. Bramanti ...folds 7 Coherent summary of existing literature Contents Preliminaries on (almost-) complex manifolds.- Cohomology of complex