Statistical Genetics Constant-Sign Solutions of Systems of ......tems of Higher Order Boundary Value...

News 8/2013 Mathematics

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R. P. Agarwal, Texas A&M University, Kingsville, TX, USA; D. O’Regan, National University of Ireland, Galway, Ireland; P. J. Wong, Nanyang Technological University, Singapore

Constant-Sign Solutions of Systems of Integral EquationsContents Introduction and Preliminaries.- System of Fred-holm Integral Equations: Existence of a Constant-Sign Solution.- System of Fredholm Integral Equations: Eigenvalues.- System of Fredholm Integral Equations: Triple Constant-Sign Solu-tions.- System of Fredholm Integral Equations: Existence of a Constant-Sign Lp Solution.- System of Fredholm Integral Equations: Semipositone and Singular Case.- Systems of Fredholm and Volterra Integral Equations: Integrable Singularities.- Sys-tems of Higher Order Boundary Value Problems: Integrable Singularities.- System of Volterra Integral Equations: Integrable Singularities.- Sys-tems of Fredholm and Volterra Integral Equations: the Singular Case.- System of Singular Fredholm Integral Equations.- System of Singular Integral Equations of Hammerstein Type.- System Model-ing the Spread of Interdependent Epidemics: Constant-Sign Periodic Solutions.- System of Hill’s Equations: Constant-Sign Periodic Solutions.- System of Integral Equations: Constant-Sign Pe-riodic and Almost Periodic Solutions.- System of Fredholm Integral Equations: Solutions in Orlicz Spaces.- System of Volterra Integral Equations: Constant-Sign Solutions in Orlicz Spaces.- Sys-tem of Urysohn Integral Equations: Existence of a Constant-Sign Solution.- System of Fredholm Integral Equations: Existence Results via Brezis-Browder Arguments.- System of Volterra Integral Equations: Existence Results via Brezis-Browder Arguments.- Bibliography.- Subject Index.

Fields of interestIntegral Equations; Ordinary Differential Equa-tions

Target groupsResearch

Product categoryMonograph

Due September 2013

2013. XIV, 664 p. Hardcover7 $149.00ISBN 978-3-319-01254-4

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L. Almasy, Southwest Foundation Biomedical Research, San Antonio, TX, USA (Ed)

Statistical GeneticsField of interestGenetics and Population Dynamics


Product categoryContributed volume

Due December 2013

2012. (Methods in Molecular Biology, Tentative volume 2145) Hardcover7 approx. $99.50ISBN 978-1-58829-728-0

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A. Bensoussan, University of Texas at Dallas Naveen Jindal School of Management, Richardson, TX, USA; J. Frehse, Universitat Bonn Institut für Angewandte Mathematik, Bonn, Germany; P. Yam, The Chinese University of Hong Kong, Shatin, Hong Kong SAR

Mean Field Games and Mean Field Type Control Theory Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolu-tion of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent.

Features 7 This is the first contribution of this work to present a unified approach for both problems, using either HJB and FP coupled equations or stochastic maximum principle 7 Subject matter is interesting and has received much recent atten-tion 7 Gives an overview of the mean-field game and mean-field type control problems

Contents Introduction.- General Presentation of Mean Field Control Problems.- Discussion of the Mean Field game.- Discussion of the Mean Field Type Con-trol.- Approximation of Nash Games with a large number of players.- Linear Quadratic Models.- Stationary Problems- Different Populations.- Nash differential games with Mean Field effect.

Fields of interestSystems Theory, Control; Probability Theory and Stochastic Processes; Partial Differential Equations


Product categoryBrief

Due October 2013

2013. X, 115 p. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-1-4614-8507-0

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www.springer.com/978-3-319-01254-4



Mathematics springer.com/NEWSonline

58

W.‑J. Beyn, University of Bielefeld, Germany; L. Dieci, Georgia Institute of Technology, Atlanta, GA, USA; N. Guglielmi, Università dell’Aquila, Italy; E. Hairer, Université de Genève, Switzerland; J. M. Sanz‑Serna, Universidad de Valladolid, Spain; M. Zennaro, Università di Trieste, Italy

Current Challenges in Stability Issues for Numerical Differential EquationsCetraro, Italy 2011, Editors: Luca Dieci, Nicola Guglielmi

This volume addresses some of the research areas in the general field of stability studies for differen-tial equations, with emphasis on issues of concern for numerical studies.

Features 7 Accessible presentation on cutting edge tech-niques 7 World leaders on their respective top-ics 7 Ample and exhaustive references 7 Di-dactic exposition on arguments not represented in textbooks

Contents Studies on current challenges in stability issues for numerical differential equations.- Long-Term Stability of Symmetric Partitioned Linear Multi-step Methods.- Markov Chain Monte Carlo and Numerical Differential Equations.- Stability and Computation of Dynamic Patterns in PDEs.- Con-tinuous Decompositions and Coalescing Eigen values for Matrices Depending on Parameters.- Stability of linear problems: joint spectral radius of sets of matrices.

Fields of interestComputational Mathematics and Numerical Analysis; Applications of Mathematics; Ordinary Differential Equations



Due September 2013

2013. X, 295 p. 121 illus., 105 in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2082) Softcover7 $59.99ISBN 978-3-319-01299-5

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A. B. Buan, I. Reiten, Ø. Solberg, NTNU, Trondheim, Norway (Eds)

Algebras, Quivers and RepresentationsThe Abel Symposium 2011

Contents C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions.- L. Avramov : (Contravariant) Koszul duality for DG algebras.- R. Buchweitz: The fundamental group of a morphism in a triangulated category.- K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras.- D. Happel: Algebras of finite global dimension.- K. Igusa (with G. Todorov): Continuous Frobenius categories.- D.A. Jorgensen: Triangle functors from generic hypersurfaces.- Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian.- H. Krause: Morphisms determined by objects in triangulated categories.- P. Malicki (with J. A. de la Pena and A. Skowron-ski): Cycle-finite module categories.- J.A. de la Pena, P. Malicki and A. Skowronski: Cycle-finite module categories.- C.M. Ringel: Distinguished bases of exceptional modules.- A. Skowronski (with P. Malicki and J. A. de la Pena): Cycle-finite module categories.- D. Speyer and H. Thomas: Acyclic cluster algebras revisited.- H. Thomas and D. Speyer: Acyclic cluster algebras revisited.- G. Todorov and K. Igusa: Continuous Frobenius categories.- L. Williams and Y. Kodama: Combi-natorics of KP solutions from the real Grassman-nian.- D. Zacharia and D. Happel: Algebras of finite global dimension.

Fields of interestCommutative Rings and Algebras; Algebraic Ge-ometry; Associative Rings and Algebras



Due August 2013

2013. XX, 284 p. 13 illus., 1 in color. (Abel Symposia, Volume 8) Hardcover7 $109.00ISBN 978-3-642-39484-3

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H.‑J. Bungartz, TU München Inst. Informatik, Garching, Germany; S. Zimmer, University of Stuttgart IPVS, Stuttgart, Germany; M. Buchholz, Realtime Technology AG, Munich, Germany; D. Pflüger, University of Stuttgart IPVS, Stuttgart, Germany

Modeling and SimulationAn Application‑Oriented Introduction

Translated by: S. Le Borne, R. Le Borne, Tennessee Technological University Dept of Mathematics, Cookeville, TN, USA

Features 7 Covering a wide range of modeling-driven domains: decisions, traffic, dynamical systems, physics 7 Motivated by concrete relevant sce-narios, but not application-bound 7 Looking at modeling and simulation as a general methodol-ogy for science and engineering fed by mathemat-ics and informatics

Contents 1 Introduction.- 2 The necessary instruments in brief.- Part I Playing – deciding – planning: A modeling warm-up.- 3 Game theory.- 4 Group decisions.- 5 Schedules.- 6 Wiener processes.- Part II Traffic on highways and data highways: A trip through the simulation pipeline.- 7 Macroscopic simulation of traffic.- 8 Microscopic simulation of traffic.- 9 Stochastic traffic simulations.- Part III Dynamic systems: Cause, effect and interaction.- 10 Population dynamics.- 11 Controllers.- 12 Chaos theory.- Part IV Physics on the computer: The switch to number crunchers.- 13 Molecular dynamics.- 14 Thermal conduction.- 15 Fluid mechanics.- 16 Global illumination in computer graphics.- Closing remarks.- Bibliography.- Index.

Fields of interestComputational Science and Engineering; Com-putational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathemat-ics

Target groupsUpper undergraduate

Product categoryUndergraduate textbook

Due September 2013

2013. 407 p. 154 illus., 4 in color. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover7 $59.99ISBN 978-3-642-39523-9

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59

Y. J. Cho, Gyeongsang National University, Chinju, Korea, Republic of (South Korea); T. M. Rassias, National Technical University of Athens, Athens, Greece; R. Saadati, Iran University of Science and Technology, Behshahr, Iran

Stability of Functional Equations in Random Normed SpacesThis book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for ap-proximate homomorphisms. The seminal work of Donald H.

Features 7 Presents results proved in detail with several outlines examples to make the presentation of the theory well understood by large audienc-es 7 Discusses useful research to both pure and applied mathematicians who search for both new and old results 7 Presents written results for sci-entists and engineers who are orienting their study in the language of interdisciplinary research

Contents Preface.- 1. Preliminaries.- 2. Generalized Spaces.- 3. Stability of Functional Equations in Random Normed Spaces Under Special t-norms.- 4. Stabil-ity of Functional Equations in Random Normed Spaces Under Arbitrary t-norms.- 5. Stability of Functional Equations in random Normed Spaces via Fixed Point Method.- 6. Stability of Functional Equations in Non-Archimedean Random Spaces.- 7. Random Stability of Functional Equations Re-lated to Inner Product Spaces.- 8. Random Banach Algebras and Stability Results.

Fields of interestFunctional Analysis; Optimization; Partial Dif-ferential Equations



Due August 2013

2013. XX, 248 p. (Springer Optimization and Its Applications, Volume 86) Hardcover7 $109.00ISBN 978-1-4614-8476-9

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R. Corless, University of Western Ontario Middlesex College, London, ON, Canada; N. Fillion, University of Western Ontario, London, Canada

A Graduate Introduction to Numerical Methodsand Backward Error Analysis

This book is designed to be used for a graduate-level survey of numerical methods. It gathers important material from floating-point arithmetic, numerical linear algebra, polynomials, series, interpolation, the discrete Fourier transform, nu-merical differentiation and integration, numerical solutions of ODEs, BVPs, DDEs, and PDEs, and optimization. Advanced topics such as spectral methods and high-order methods are presented in context.

Features 7 Provides consistent development of formulae using barycentric interpolation 7 Independence of chapters allowing for greater teaching flexibil-ity 7 Integration with Matlab and Maple, many algorithms presented in pseudocode

Contents Computer Arithmetic & Fundamental Concepts of Computation .- Polynomials and Series.- Func-tion Evaluation and Rootfinding.- Solving Ax = b .- Solving Ax =l x .- Sparse and Structured Linear Systems.-IterativeMethods.- Polynomial and Rational Interpolation.- The Discrete Fourier Transform.- Numerical integration.- Numeri-cal Differentiation and Finite Differences.- Nu-merical Solution of ODEs.- Old material.- Stiff ODEs.- Numerical Solutions of Boundary Value Problems.- New BVP Chapter: Solution of a Linear Two-Point BVP by Collocation.- Numerical Solution of Delay Des.

Fields of interestComputational Mathematics and Numerical Analysis; Algorithms; Numerical Analysis

Target groupsProfessional/practitioner

Product categoryReference work

Due November 2013

2014. X, 863 p. Hardcover7 approx. $89.95ISBN 978-1-4614-8452-3

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J. P. D’Angelo, University of Illinois, Urbana-Champaign, Urbana, IL, USA

Hermitian AnalysisFrom Fourier Series to Cauchy‑Riemann Geometry

Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from under-graduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several com-plex variables, and includes some of the author’s results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathemat-ics, graduate students interested in analysis, and researchers interested in some basic aspects of CR Geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.

Features 7 Many examples and hundreds of exercises are provided to promote understanding 7 Uses the concept of orthogonality to unify various math-ematical topics 7 Includes accessible content designed to lead students from undergraduate- to research-level mathematics

Contents Preface.- Introduction to Fourier series.- Hilbert spaces.- Fourier transform on R.- Geometric con-siderations.- Appendix.- References.- Index.

Fields of interestFourier Analysis; Differential Geometry; Ordinary Differential Equations


Product categoryGraduate/Advanced undergraduate textbook

Due September 2013

2013. VIII, 196 p. 27 illus., 14 in color. (Cornerstones) Hardcover7 $69.99ISBN 978-1-4614-8525-4

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60

V. Demyanov, Universitetskii prospekt, Saint Petersburg, Russia; P. M. Pardalos, University of Florida, Gainesville, FL, USA; M. Batsyn, Higher School of Economics, Nizhny Novgorod, Russia (Eds)

Constructive Nonsmooth Analysis and Related TopicsContents Constructive Noonsmooth Analysis and Related Topics (V. Demyanov, P.M. Pardalos, M. Batsyn).- Use Model Theory in Nonsmooth Analysis (S.S. Kutateladze).- Demyanov Difference in Infinite Dimensional Spaces (J. Grzybowski, D. Pallaschke, R. Urbanski).- Separable Reduction of Metric Reg-ularity Properties (A.D. Ioffe).- Construction of Pairs of Reproducing Kernel Banach Spaces (P.G. Georgiev, L. Sanchez-Gonzalez, P.M. Pardalos).- On the Regularization Method in Nondifferen-tiable Optimization Applied to Hemivariational Inequalities (N. Ovcharova, J. Gwinner).- Dynam-ics and Optimization of Multibody Systems in the Presence of Dry Friction (F.L. Chemousko).- Method of Steepest Descent for Two-Dimen-sional Problems of Calculus in Variations (M.V. Dolgopolik, G.Sh.Tamasyan).- On a Quantitative Semicontinuity Property of Variational Systems with Applications to Perturbed Quasidifferentiable Optimization (A. Uderzo).- Some Remarks on Bi-Level Vector Extremum Problems (C. Antoni, F. Giannessi).- Well-Posedness for Lexicographic Vector Equilibrium Problems (L.Q. Anh, T.Q. Duy, A.Y. Kruger, N.H. Thao).- The Best Linear Separa-tion of Two Sets (V.N. Malozemov, E.K. Cherneut-sanu).- Alternance Form of Optimality Conditions in the Finite-Dimensional Space (V.F. Demyanov, V.N. Malozemov).- Optimal Multiple Decision Statistical Procedure for Inverse Covariance Ma-trix (A.P. Koldanov, P.A. Koldanov).- Conciliating Generalized Derivatives (J.-P. Penot).[...]

Fields of interestOptimization; Algorithms; Dynamical Systems and Ergodic Theory



Due September 2013

2013. XVIII, 254 p. 10 illus., 4 in color. (Springer Optimization and Its Applications, Volume 87) Hardcover7 $109.00ISBN 978-1-4614-8614-5

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V. Dragan, T. Morozan, Institute of Mathematics “Simion Stoilow”, Bucharest, Romania; A.‑M. Stoica, University Politechnica Bucharest Fac. Aerospace Engineering, Bucharest, Romania

Mathematical Methods in Robust Control of Linear Stochastic SystemsThis second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems.

Features 7 Updates the previous edition to include recent results in robust control of linear stochastic sys-tems 7 Presents the treatment of the fundamen-tal properties of stochastic systems subjected both to multiplicative white noise and to jump Markov-ian perturbations 7 Proposes new numerical algorithms to solve coupled matrix algebraic Riccati equations

Contents Preliminaries to Probability Theory and Stochas-tic Differential Equations.- Linear Differential Equations with Positive Evolution on Ordered Banach Spaces.- Exponential Stability in Mean Square.- Structural Properties of Linear Stochastic Systems.- A Class of Nonlinear Differential Equa-tions on an Ordered Linear Space of Symmetric Matrices with Applications to Riccati Differ-ential Equations of Stochastic Control.- Linear Quadratic Optimization Problems for Linear Stochastic Systems.- Stochastic H2 Optimal Control.- Stochastic Version of the Bounded Real Lemma and Applications.- Robust Stabilization of Linear Stochastic Systems.

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



Due September 2013

2nd ed. 2013. XXII, 450 p. 10 illus., 8 in color. Hardcover7 $129.00ISBN 978-1-4614-8662-6

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S. S. Dragomir, Victoria University, Melbourne, Australia

Inequalities for the Numerical Radius of Linear Operators in Hilbert SpacesAimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequali-ties for bounded linear operators on complex Hilbert spaces for the case of one and two opera-tors. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numeri-cal radius of bounded linear operators in Hilbert spaces.

Features 7 Centered on numerical radius inequalities for bounded linear operators on complex 7 Hilbert spaces for the case of one and two operators Clas-sical inequalities due to Berger, Holbrook, Fong and Holbrook and Bouldin are given 7 Numer-ous references for the Kantorovich inequality that is extended to larger classes of operators than positive operators are provided

Contents 1. Introduction.- 2. Inequalities for One Operator.- 3. Inequalities for Two Operators .

Fields of interestOperator Theory; Ordinary Differential Equations; Analysis



Due September 2013

2013. VI, 121 p. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-3-319-01447-0

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61

M. Ehrhardt, Bergische Universität Wuppertal Lehrstuhl für Angewandte Mathematik, Wuppertal, Germany; T. Koprucki, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, Germany (Eds)

Advanced Mathematical Models and Numerical Techniques for Multi-Band Effective Mass ApproximationsThis book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects.

Features 7 First book on this subject at the interface of mathematics and physics 7 Many interdisci-plinary aspects covered ranging from the proper modelling to the accurate and stable numerical solution 7 Describes concisely in 9 chapters the state-of-the art in modelling and numerical simulations of Multiband Effective Mass Approxi-mations

Contents Introduction.- Part I: Physical Models.- Part II: Numerical Methods.- Part III: Applications.- Part IV: Advanced Mathematical Topics.

Fields of interestComputational Mathematics and Numerical Analysis; Theoretical, Mathematical and Compu-tational Physics; Mathematical Methods in Physics



Due November 2013

2014. 350 p. (Lecture Notes in Computational Science and Engineering, Volume 94) Hardcover7 $129.00ISBN 978-3-319-01426-5

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L. Elefteriadou, University of Florida, Gainesville, FL, USA

An Introduction to Traffic Flow TheoryThis text provides a comprehensive and concise treatment of the topic of traffic flow theory and includes several topics relevant to today’s highway transportation system. It provides the funda-mental principles of traffic flow theory as well as applications of those principles for evaluating specific types of facilities (freeways, intersections, etc.). Newer concepts of Intelligent transporta-tion systems (ITS) and their potential impact on traffic flow are discussed. State-of-the-art in traffic flow research and microscopic traffic analysis and traffic simulation have significantly advanced and are also discussed in this text. Real world examples and useful problem sets complement each chapter.

Features 7 First textbook to address the modern advances in traffic flow theory in 20 years 7 Contains real-world examples and a problem set in each chapter 7 Discusses topics such as microscopic traffic analysis and traffic simulation and includes research related to traffic flow

Contents Introduction.- Part 1.- 1. Modeling the Motion of a Single Vehicle.- 2. Modeling Vehicle Interactions and the Movement of Groups of Vehicles.- Part 2.- 3. The Traffic Stream: Traffic Flow Performance Characteristics.- 4. Capacity.- 5. Traffic Operation-al Performance Measures.- Part 3.- 6. Analytical Models for Bottleneck and Queuing Evaluations.- 7. Simulation Modeling.- Part 4.- 8. Freeways.- 9. Signalized Intersections and Networks.- 10. Unsig-nalized Intersections.- 11. Two-Lane Highways.- Appendix A.- Appendix B.- Index.

Fields of interestOptimization; Civil Engineering

Target groupsGraduate


Due November 2013

2014. XVI, 272 p. 100 illus., 25 in color. (Springer Optimization and Its Applications, Volume 84) Hardcover7 approx. $69.95ISBN 978-1-4614-8434-9

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S. Foucart, Drexel University, Philadelphia, PA, USA; H. Rauhut, RWTH Aachen University, Aachen, Germany

A Mathematical Introduction to Compressive SensingAt the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing.

Features 7 The first textbook completely devoted to the topic of compressive sensing 7 Comprehensive treatment of the subject, including background material from probability theory, detailed proofs of the main theorems, and an outline of possible applications 7 Numerous exercises designed to help students understand the material 7 An extensive bibliography with over 500 references that guide researchers through the literature

Contents 1 An Invitation to Compressive Sensing.- 2 Sparse Solutions of Underdetermined Systems.- 3 Basic Algorithms.- 4 Basis Pursuit.- 5 Coherence.- 6 Restricted Isometry Property.- 7 Basic Tools from Probability Theory.- 8 Advanced Tools from Prob-ability Theory.- 9 Sparse Recovery with Random Matrices.- 10 Gelfand Widths of l1-Balls.- 11 Instance Optimality and Quotient Property.- 12 Random Sampling in Bounded Orthonormal Systems.- 13 Lossless Expanders in Compres-sive Sensing.- 14 Recovery of Random Signals using Deterministic Matrices.- 15 Algorithms for l1-Minimization.- Appendix A Matrix Analy-sis.- Appendix B Convex Analysis.- Appendix C Miscellanea.- List of Symbols.- References.

Fields of interestComputational Science and Engineering; Signal,Image and Speech Processing; Math Ap-plications in Computer Science



Due July 2013

2013. XVIII, 625 p. 13 illus. (Applied and Numerical Harmonic Analysis) Hardcover7 $89.99ISBN 978-0-8176-4947-0

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62

C. Graham, Centre de Mathématiques Appliquées École Polytechnique, Palaiseau, France; D. Talay, INRIA, Sophia Antipolis, France

Stochastic Simulation and Monte Carlo MethodsMathematical Foundations of Stochastic Simulation

In various scientific and industrial fields, stochas-tic simulations are taking on a new importance.

Features 7 Combines advanced mathematical tools and theoretical analysis of stochastic numerical methods at a high level 7 Provides methods to reach optimal results on the accuracy of Monte Carlo simulations of stochastic processes 7 Con-tains exercises in the text and problem sets of increasing demand at the end of each chapter

Contents Part I:Principles of Monte Carlo Methods.- 1.In-troduction.- 2.Strong Law of Large Numbers and Monte Carlo Methods.- 3.Non Asymptotic Error Estimates for Monte Carlo Methods.- Part II:Exact and Approximate Simulation of Markov Processes.- 4.Poisson Processes.- 5.Discrete-Space Markov Processes.- 6.Continuous-Space Markov Processes with Jumps.- 7.Discretization of Sto-chastic Differential Equations.- Part III:Variance Reduction, Girsanov’s Theorem, and Stochastic Algorithms.- 8.Variance Reduction and Stochastic Differential Equations.- 9.Stochastic Algorithms.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes; Nu-merical Analysis; Quantitative Finance



Due August 2013

2013. XVI, 260 p. 4 illus. (Stochastic Modelling and Applied Probability, Volume 68) Hardcover7 $69.99ISBN 978-3-642-39362-4

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P. Griffiths, Princeton University Institute for Advanced Study, Princeton, NJ, USA; J. Morgan, Stonybrook University, Stonybrook, NY, USA

Rational Homotopy Theory and Differential FormsThis completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addi-tion, Sullivan’s results on computing the rational homotopy type from forms is presented.

Features 7 Second edition with fully updated con-tent 7 Includes a readable introduction for non-specialists 7 Provides many elementary examples and exercises

Contents 1 Introduction.- 2 Basic Concepts.- 3 CW Homol-ogy Theorem.- 4 The Whitehead Theorem and the Hurewicz Theorem.- 5 Spectral Sequence of a Fibration.- 6 Obstruction Theory.- 7 Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations.- 8 Postnikov Towers and Rational Homotopy Theory.- 9 deRham’s theorem for simplicial complexes.- 10 Differential Graded Algebras.- 11 Homotopy Theory of DGAs.- 12 DGAs and Rational Homotopy Theory.- 13 The Fundamental Group.- 14 Examples and Computa-tions.- 15 Functorality.- 16 The Hirsch Lemma.- 17 Quillen’s work on Rational Homotopy Theory.- 18 A1-structures and C1-structures.- 19 Exercises.

Fields of interestAlgebraic Topology; Category Theory, Homologi-cal Algebra; Commutative Rings and Algebras



Due September 2013

2nd ed. 2013. XV, 217 p. 143 illus. (Progress in Mathematics, Volume 16) Hardcover7 $109.00ISBN 978-1-4614-8467-7

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W. Hackbusch, MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany

The Concept of Stability in Numerical MathematicsIn this book, the author compares the meaning of stability in different subfields of numerical math-ematics. Concept of Stability in numerical math-ematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discus-sion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisa-tions of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.

Features 7 Offers a self-contained presentation of aspects of stability in numerical mathematics 7 Com-pares and characterizes stability in different subfields of numerical mathematics 7 Covers numerical treatment of ordinary differential equa-tions, discretisation of partial differential equa-tions, discretisation of integral equations and more

Fields of interestNumerical Analysis; Partial Differential Equations; Integral Equations



Due December 2013

2014. Approx. 200 p. (Springer Series in Computational Mathematics, Volume 45) Hardcover7 approx. $119.00ISBN 978-3-642-39385-3

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63

C. S. Hardin, New York, NY, USA; A. D. Taylor, Union College, Schenectady, NY, USA

The Mathematics of Coordinated InferenceA Study of Generalized Hat Problems

Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads; each hat is either red or green. The two prisoners must simultaneously submit a guess of their own hat color, and they both go free if at least one of them guesses correctly. While no communication is allowed once the hats have been placed, they will, however, be allowed to have a strategy session be-fore being brought to the room. Is there a strategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a “hat problem.

Features 7 Presents a comprehensive treatment of material previously available in journals only 7 Contains a number of new results and extensions of known results 7 States a number of open and acces-sible problems 7 Unified notation is used for a cohesive presentation

Contents 1. Introduction.- 2. The Finite Setting.- 3. The Denumerable Setting: Full Visibility.- 4. The Denumerable Setting: One-Way Visibility.- 5. Dual Hat Problems and the Uncountable.- 6. Galvin’s Setting: Neutral and Anonymous Predictors.- 7. The Topological Setting.- 8. Universality of the μ-Predictor.- 9. Generalizations and Galois-Tukey Connections.- Bibliography.- Index.

Fields of interestMathematical Logic and Foundations; Topology; Game Theory, Economics, Social and Behav. Sci-ences



Due September 2013

2013. XII, 122 p. (Developments in Mathematics, Volume 33) Hardcover7 $109.00ISBN 978-3-319-01332-9

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H. Holden, Norwegian University of Science and Technology, Trondheim, Norway; R. Piene, University of Oslo Department of Mathematics, Oslo, Norway (Eds)

The Abel Prize 2008-2012The book presents the winners of the Abel Prize in mathematics for the period 2008–2012: 2008 John G. Thompson and Jacques Tits, 2009 Misha Gro-mov, 2010 John T. Tate Jr., 2011 John W. Milnor, and 2012 Endre Szemerédi. Each laureate provides an autobiography. In addition, there is a scholarly description of their work, a curriculum vitae, and a complete bibliography. Interviews with the Lau-reates are presented on an accompanying web site. The historian K. Helsvig presents the history of the Abel Prize. A facsimile of a letter by Niels Henrik Abel to Crelle from 1828 is included together with a commentary by C. Skau.

Features 7 Details the history of the Abel Prize in math-ematics , which is the equivalent of the Nobel Prize 7 Presents the laureates of the second five year period of the Abel Prize, complete with photographs 7 Autobiographical information by each laureate, followed by a more extensive review of their work

Contents K. Helsvig: The Abel Prize – the Missing Nobel in Mathematics.- 2008 John G. Thompson and Jacques Tits.- 2009 Misha Gromov.- 2010 John T. Tate Jr.- 2011 John W. Milnor.- 2012 Endre Szemerédi.

Fields of interestHistory of Mathematical Sciences; Mathematics, general; Computer Science, general


Product categoryCommemorative publication

Due October 2013

2013. 500 p. 30 illus., 15 in color. Hardcover7 approx. $109.00ISBN 978-3-642-39448-5

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H. Hopf, Heidelberg, Germany B. Eckmann, ETH Zürich Dept. Mathematik, Zürich, Switzerland (Ed)

Collected Papers - Gesammelte AbhandlungenFrom the preface: “Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics with-out all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of topology with its influence on group theory, analysis and algebraic geometry. It is astonishing to realize that this oeuvre of a whole scientific life consists of only about 70 writings. Astonishing also the transparent and clear style, the concreteness of the problems, and how abstract and far-reaching the methods Hopf invented.”

Contents Table of Contents.- List of Publications of Heinz Hopf.- Editor’s Preface.- Papers of Heinz Hopf.- Heinz Hopf Selecta.

Fields of interestAlgebraic Topology; K-Theory; Group Theory and Generalizations


Product categoryCollected works

Due July 2013

Only available in print

2001. Reprint 2013 of the 2001 edition. XIII, 1271 p. (Springer Collected Works in Mathematics) Softcover7 approx. $79.99ISBN 978-3-642-38368-7

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64

B. S. Jovanović, University of Belgrade, , Serbia; E. Süli, University of Oxford, , UK

Analysis of Finite Difference SchemesFor Linear Partial Differential Equations with Generalized Solutions

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smooth-ness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the ap-plication of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associ-ated analytical solution are however frequently unrealistic.

Features 7 Develops a systematic and rigorous theory for the construction and analysis of finite difference methods 7 Presents the theory with minimal regularity conditions i.e. for PDEs with nons-mooth solutions and data 7 Partially accessible to advanced undergraduate and masters students interested in numerical analysis

Contents Distributions and function spaces.- Elliptic boundary-value problems.- Finite difference ap-proximation of parabolic problems.- Finite differ-ence approximation of hyperbolic problems.

Fields of interestNumerical Analysis; Partial Differential Equations



Due September 2013

2013. XIV, 402 p. (Springer Series in Computational Mathematics, Volume 46) Hardcover7 $129.00ISBN 978-1-4471-5459-4

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V. Jullien, Université de Nantes, Nantes, France (Ed)

Seventeenth-Century Indivisibles RevisitedThe tremendous success of Indivisibles methods in geometry in the seventeenth century responds to a vast project: installation of infinity in mathemat-ics.

Features 7 The first exhaustive study on the indivisi-bles 7 A mathematical, historical and philosoph-ical approach of the intrusion and use of infinity in geometry during the XVIIth century 7 Written by a team of well known scholars, after long com-mon work and discussions 7 Explains in what sense we can think about infinite, atom, continu-ity, indivisible in mathematics

Contents Introduction.- 1 From Aristotle to the Classical Age : the Debate around Indivibilism.- 2 Kepler, Cavalieri, Guldin.- 3 Cavalieri’s Indivisibles.- 4 Galileo and the indivisibles.- 5 Torricelli’s indivis-ibles.- 6 The method of indivisibles that Gregory of Saint Vincent could have used for his own quadrature of Hyperbola.- 7 Descartes and the use of indivisibles.- 8 Roberval’s indivisibles.- 9 Pas-cal’s indivisibles.- 10 Two jesuits against indivibles, Lalouvère and Tacquet.- 11 Isaac Barrow’s indivisi-bles.- 12 Pietro Mengoli and the indivisibles.- 13 Wallis’ indivisibles.- 14 Leibniz’s rigorous founda-tions of the method of indivisibles.- 15 Highlights on the historiography of indivisibles.- Annexes: 16 Archimedes.- 17 Latitudo formarum.- 18 About Halley and Bernoulli and the Iris.- 19 Newton reads Wallis and gives the indivisibles out.

Field of interestHistory of Mathematical Sciences


Product categoryCollection of essays

Due November 2013

2014. Approx. 350 p. 250 illus. (Science Networks. Historical Studies, Volume 46) Hardcover7 approx. $129.00ISBN 978-3-319-00130-2

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O. Karpenkov, The University of Liverpool, UK

Geometry of Continued FractionsContents Preface.- Introduction.- Part 1. Regular con-tinued fractions: Chapter 1. Classical notions and definitions.- Chapter 2. On integer geom-etry.- Chapter 3. Geometry of regular continued fractions.- Chapter 4. Complete invariant of integer angles.- Chapter 5. Integer trigonometry for integer angles.- Chapter 6. Integer angles of integer triangles.- Chapter 7. Continued fractions and SL(2; Z) conjugacy classes. Elements of Gauss Reduction Theory. Markoff spectrum.- Chapter 8. Lagrange theorem.- Chapter 9. Gauss-Kuzmin statistics.- Chapter 10. Geometric approximation aspects.- Chapter 11. Geometry of continued fractions with real elements and the second Kepler law.- Chapter 12. Integer angles of polygons and global relations to toric singularities.- Part 2. Klein polyhedra: Chapter 13. Basic notions and definitions of multidimensional integer geom-etry.- Chapter 14. On empty simplices, pyramids, parallelepipeds.- Chapter 15. Multidimensional continued fractions in the sense of Klein.- Chapter 16. Dirichlet groups and lattice reduction.- Chap-ter 17. Periodicity of Klein polyhedra. Generaliza-tion of Lagrange theorem.- Chapter 18. Multidi-mensional Gauss-Kuzmin statistics.- Chapter 19. On construction of multidimensional continued fractions.- Chapter 20. Gauss Reduction in higher dimensions.- Chapter 21. Decomposable forms. Relation to Littlewood and Oppenheim conjec-tures.- Chapter 22. Approximation of maximal commutative subgroups.- Chapter 23. Other gen-eralizations of continued fractions.- Bibliography .

Fields of interestAlgebra; Order, Lattices, Ordered Algebraic Struc-tures; Approximations and Expansions



Due August 2013

2013. XVIII, 404 p. 61 illus. (Algorithms and Computation in Mathematics, Volume 26) Hardcover7 $79.99ISBN 978-3-642-39367-9

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65

C. Kawan, University of Augsburg, Germany, Augsburg, Germany

Invariance Entropy for Deterministic Control SystemsAn Introduction

This monograph provides an introduction to the concept of invariance entropy, the central motiva-tion of which lies in the need to deal with commu-nication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair.

Features 7 The first book to present results on the rela-tively new notions of feedback and invariance entropy 7 Provides detailed proofs of all key results, together with a comprehensive exposition of the mathematical background material used therein 7 Will be particularly interesting for readers with a background in dynamical systems theory 7 The basic knowledge of control theory needed for its understanding is presented at great length in the first chapter

Contents Basic Properties of Control Systems.- Introduc-tion to Invariance Entropy.- Linear and Bilinear Systems.- General Estimates.- Controllability, Lyapunov Exponents, and Upper Bounds.- Escape Rates and Lower Bounds.- Examples.- Notation.- Bibliography.- Index.

Fields of interestDynamical Systems and Ergodic Theory; Systems Theory, Control



Due September 2013

2013. X, 260 p. 2 illus., 1 in color. (Lecture Notes in Mathematics, Volume 2089) Softcover7 $59.99ISBN 978-3-319-01287-2

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

Topological Galois TheoryTransl. Russian: V. Timorin, State University Higher School of Economics, Moskva, Russia; V. Kiritchenko, National Research University Higher School of Economics, Msocow, Russia

This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equa-tions in explicit form. In particular, a complete exposition of topological Galois theory is given. This theory is due to the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of the Picard-Vessiot theory, Li-ouville’s results on the class of functions represent-able by quadratures are also discussed.

Features 7 The largest collection of unsolvability re-sults 7 Classical Galois theory and Liouville's explicit integration theory are explained from scratch 7 A gentle introduction to the cutting edge of research

Contents Introduction.- Chapter 1: Liouville’s Theory.- Chapter 2: Galois Theory.- Chapter 3: Picard–Ves-siot Theory.- Chapter 4: Coverings and Galois Theory.- Chapter 5: One-Dimensional Topological Galois Theory.- Chapter 6: Solvability of Fuchsian Equations.- Chapter 7: Multidimensional Topo-logical Galois Theory.- Appendix 1: Ruler and Compass Constructions.- Appendix 2: Chebyshev Polynomials and Their Inverses.- Appendix 3: Signatures of Branched Coverings.- Appendix 4: On an Algebraic Version of Hilbert’s 13th Prob-lem.- Index.

Fields of interestField Theory and Polynomials; Functions of a Complex Variable; Group Theory and Generaliza-tions



Due February 2014

2014. Approx. 300 p. 3 illus. (Springer Monographs in Mathematics) Hardcover7 approx. $119.00ISBN 978-3-642-38870-5

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P. S. Knopov, National Academy of Sciences of Ukraine VM Glushkov Institute of Cybernetics, Kiev, Ukraine; O. N. Deriyeva, National Acadamy of Sciences of Ukraine V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine

Estimation and Control Problems for Stochastic Partial Differential EquationsFocusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered.

Features 7 Investigates important aspects of estimation and control theory for systems modeled by sto-chastic partial differential equations 7 Presents research on problems of estimation and control theory for random fields that has not been previ-ously covered by researchers 7 Includes research on control, prediction, and estimation for systems with two parameters and additive noise

Contents 1. Two Parameter Martingales and Their Proper-ties.- 2. Stochastic Differential Equations on the Plane.- 3. Filtration and Prediction Problems for Stochastic Fields.- 4. Control Problem for Diffusion-Type Random Fields.- 5. Stochastic Processes in a Hilbert Space.- References.

Fields of interestPartial Differential Equations; Calculus of Varia-tions and Optimal Control; Optimization; Systems Theory, Control



Due September 2013

2013. XVIII, 240 p. (Springer Optimization and Its Applications, Volume 83) Hardcover7 $109.00ISBN 978-1-4614-8285-7

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66

N. L. Komarova, University of California, Irvine Dept. Mathematics, Irvine, CA, USA; D. Wodarz, University of California, Irvine Department of Ecology & Evolutionary Bio, Irvine, CA, USA

Targeted Cancer Treatment in SilicoSmall Molecule Inhibitors and Oncolytic Viruses

Contents Background and Scope of the Book.- Part I Treat-ment of Cancer with Small Molecule Inhibitors.- An Introduction to Small Molecule Inhibitors and Chronic Myeloid Leukemia.- Basic Dynamics of Chronic Myeloid Leukemia During Imatinib Treatment.- Stochastic Modeling of Cellular Growth, Treatment, and Resistance Generation.- Evolutionary Dynamics of Drug Resistant Mutants in Targeted Treatment of CML.- Effect of Cellular Quiescence on the Evolution of Drug Resistance in CML.- Combination Therapies: Short term ver-sus Long term Strategies.- Cross Resistance: Treat-ment and Modeling.- Mathematical Modeling of Cyclic Cancer Treatments.- Part II Treatment of Cancer with Oncolytic Viruses.- Introduction to Oncolytic Viruses.- Basic Dynamics of Oncolytic Viruses.- Mitotic Virus Transmission and Immune Responses.- Axiomatic Approaches to Oncolytic Virus Modeling.- Spatial Oncolytic Virus Dynam-ics.- Oncolytic Viruses and the Eradication of Drug-resistant Tumor Cells.

Fields of interestPhysiological, Cellular and Medical Topics; Cancer Research; Mathematical and Computational Biol-ogy



Due September 2013

2013. XIV, 238 p. 71 illus., 26 in color. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 $69.99ISBN 978-1-4614-8300-7

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T. Koshy, Framingham State University, Framingham, MA, USA

Pell and Pell-Lucas Numbers with ApplicationsPell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics.

Features 7 Invaluable resource with extensive and in-depth coverage of topic 7 Broad audience of stu-dents and math teachers/instructors at various lev-els, depending on college or university, computer scientists and the mathematically curious 7 Pre-sentation is rigorous yet user-friendly, interweav-ing an engaging historical context 7 Valuable ap-plications to number theory, combinatorics, graph theory, geometry, and interesting math puzzles

Contents Fundamentals.- Pell’s Equation.- Continued Fractions.- Pythagorean Triples. -Triangular Numbers.- Square-Triangular Numbers.- Pell and Pell-Lucas Numbers.- Additional Pell identi-ties.- Pascal’s Triangle and the Pell Family.- Pell Sums and Products.- Generating Functions for the Pell Family.- Pell Walks.- Pell Triangles. - Pell and Pell-Lucas Polynomials.- Pellonometry.- Pell Radicals.- Pell Tilings. -Pell-Fibonacci Bridges. - An Extended Pell Family.- Chebyshev Polynomi-als.- Chebyshev Tilings.- Bibliography.- Appendix

Fields of interestNumber Theory; Mathematical Logic and Founda-tions; History of Mathematical Sciences



Due November 2013

2014. Approx. 400 p. 30 illus. Hardcover7 approx. $59.95ISBN 978-1-4614-8488-2

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R. López, University of Granada, Granada, Spain

Constant Mean Curvature Surfaces with BoundaryThe study of surfaces with constant mean curva-ture (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phe-nomena. Further, as most techniques used in the theory of CMC surfaces not only involve geomet-ric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.

Features 7 Includes set of interesting open prob-lems 7 First comprehensive publication on "compact surfaces with boundary" 7 Gives a state-of-the-art review of the theory

Contents Introduction.- Surfaces with Constant Mean Curvature.- Constant Mean Curvature Embedded Surfaces.-The Flux Formula for Constant Mean Curvature Surfaces.- The Area and the Volume of a Constant Mean Curvature Surface.- Constant Mean Curvature Discs with Circular Boundary.- The Dirichlet Problem of the CMC Equation.- The Dirichlet Problem in Unbounded Domains.- Con-stant Mean Curvature Surfaces in Hyperbolic Space.- The Dirichlet Problem in Hyperbolic Space.- Constant Mean Curvature Surfaces in Lorentz-Minkowski Space.- Appendix: A. The Variation Formula of the Area and the Volume.- B.Open Questions.- References.

Fields of interestDifferential Geometry; Partial Differential Equa-tions; Geometry



Due September 2013

2013. XIV, 286 p. 64 illus. (Springer Monographs in Mathematics) Hardcover7 $109.00ISBN 978-3-642-39625-0

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67

L. Lovász, Eötvös Loránd University, Budapest, Hungary; I. Ruzsa, Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics, Budapest, Hungary; V. T. Sós, Hungarian Academy of Sciences, Budapest, Hungary; D. Palvolgyi, Eötvös University, Budapest, Hungary (Eds)

Erdös CentennialContents Contents.- Preface.- Alon, N.: Paul Erdös and Probabilistic Reasoning.- Benjamini, I.: Euclidean vs. Graph Metric.- Bollobas, B. and Riordan, O.: The Phase Transition in the Erdös–Rényi Random Graph Process.- Bourgain, J.: Around the Sum-product Phenomenon.- Breuillard, E., Green, B. and Tao, T.: Small Doubling in Groups.- Diamond, H. G.: Erdös and Multiplicative Number Theory.- Füredi, Z. and Simonovits, M.: The History of Degenerate (Bipartite) Extremal Graph Problems.- Gowers, W. T.: Erdös and Arithmetic Progres-sions.- Graham, R. L.: Paul Erdös and Egyptian Fractions.- Györy, K.: Perfect Powers in Products with Consecutive Terms from Arithmetic Pro-gressions.- Komjáth, P.: Erdös’s Work on Infinite Graphs.- Kunen, K.: The Impact of Paul Erd˝os on Set Theory.- Mauldin, R. D.: Some Problems and Ideas of Erdös in Analysis and Geometry.- Mont-gomery, H. L.: L2 Majorant Principles.- Nesetril, J.: A Combinatorial Classic – Sparse Graphs with High Chromatic Number.- Nguyen, H. H. and Vu, V. H.: Small Ball Probability, Inverse Theorems, and Applications.- Pach, J.: The Beginnings of Geometric Graph Theory.- Pintz, J.: Paul Erdös and the Difference of Primes.- Pollack, P. and Pomerance, C.: Paul Erdös and the Rise of Statisti-cal Thinking in Elementary Number Theory.- Rödl, V. and Schacht, M.: Extremal Results in Random Graphs.-Schinzel, A.: Erdös’s Work on the Sum of Divisors Function and on Euler’s Func-tion. [...]

Fields of interestCombinatorics; Number Theory; Probability Theory and Stochastic Processes



Due August 2013

2013. Approx. 700 p. (Bolyai Society Mathematical Studies, Volume 25) Hardcover7 $149.00ISBN 978-3-642-39285-6

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F. Lutz, TU Berlin Fak. II Mathematik & Naturwissenschaften, Berlin, Germany

Triangulated ManifoldsWritten from a Computational Topology point-of-view the intention of this book is to provide the reader with an easy and up-to-date access to a wide range of topics concerning topological, com-binatorial, and geometric aspects of triangulated manifolds. As a compendium of many classical results, complemented with new material, the book is equipped with an extensive bibliography. An atlas of small triangulations is also included. The list of topics comprises: classification results, PL structures and Hauptvermutung, recognition techniques, computation of invariants, explicit constructions of examples, enumeration proce-dures, f-vectors of triangulations, vertex-minimal, vertex-transitive, and centrally symmetric examples, realizability issues, polytopality and tightness of triangulations.

Fields of interestAlgorithms; Combinatorics; Global Analysis and Analysis on Manifolds



Due September 2014

2014. Approx. 350 p. Hardcover7 approx. $129.00ISBN 978-3-540-34502-2

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New SeriesAtlantis Studies in Differential EquationsSeries editor: M. Chipot

The “Atlantis Studies in Differential Equations” publishes monographs in the area of differential equations, written by leading experts in the field and useful for both students and researchers. Books with a theoretical nature will be published alongside books emphasizing applications.




68

A. Meirmanov, Kazakh-British Technical University, Almaty, Kazakhstan

Mathematical Models for Poroelastic FlowsThe book is devoted to rigorous derivation of macroscopic mathematical models as a homog-enization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equa-tions). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.

Features 7 For each underground physical process the reader finds a set of mathematical models depend-ing on the dimensionless criteria of the given process and describing the process with different degrees of exactness 7 The reader may apply the suggested approach to solve many other important problems in filtration and acoustics and obtain macroscopic mathematical models, which are as-ymptotically exact 7 First volume in a new series

Fields of interestPartial Differential Equations; Mathematical Methods in Physics; Mechanics



Due November 2013

2014. Approx. 460 p. (Atlantis Studies in Differential Equations, Volume 1) Hardcover7 approx. $129.00ISBN 978-94-6239-014-0

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V. Nazaikinskii, Russian Academy of Sciences, Moscow, Russia; B.‑W. Schulze, Universität Potsdam Inst. Mathematik, Potsdam, Germany; B. Sternin, Peoples’ Friendship Univers. of Russia, Moscow, Russia

The Localization Problem in Index Theory of Elliptic OperatorsContents Preface.- Introduction.- 0.1 Basics of Elliptic Theory .- 0.2 Surgery and the Superposition Principle.- 0.3 Examples and Applications.- Part I Superposition Principle for the Relative Index.- 1 Superposition Principle in Collar Spaces.- 1.1 Collar Spaces and Elliptic Operators.- 1.2 Relative Index Theorem.- 2 K-Theoretic Statement of the Superposition Principle.- 2.1 K-Theory: Short Re-minder.- 2.2 Surgery and the Relative Index.- Part II Applications.- 3 Applications to Operators on Smooth Manifolds.- 3.1 General Construction.- 3.2 Booß–Wojciechowski Theorem.- 3.3 Anghel and Gromov–Lawson Theorems.- 4 Applications to Boundary Value Problems.- 4.1 Preliminaries.- 4.2 Agranovich–Dynin Theorem.- 4.3 Agranovich Theorem.- 4.4 Bojarski Theorem and Its Gener-alizations.- 4.5 Boundary Value Problems with Symmetric Conormal Symbol.- 5 Applications to Operators on Nonsmooth Manifolds .- 5.1 Index of Elliptic Pseudodifferential Operators.- 5.2 Index of Fourier Integral Operators.- A Operators on Manifolds with Singularities.- A.1 Manifolds with Singularities.- A.2 Pseudodifferential Operators.- A.3 Fourier Integral Operators.- Bibliographical Remarks.- References.

Fields of interestGlobal Analysis and Analysis on Manifolds; K-Theory; Functional Analysis



Due November 2013

2014. Approx. 150 p. (Pseudo-Differential Operators, Volume 10) Softcover7 approx. $89.95ISBN 978-3-0348-0509-4

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A. Paprotny, prudsys AG, Berlin, Germany; M. Thess, prudsys AG, Chemnitz, Germany

Realtime Data MiningToward the Self‑Learning Recommendation Engine

Features 7 Specifically addresses recommendation engines from a mathematically rigorous view-point 7 Discusses a control-theoretic framework for recommendation engines 7 Provides applica-tions to a number of areas within engineering and computer science

Contents 1 Brave New Realtime World – Introduction.- 2 Strange Recommendations? – On The Weak-nesses Of Current Recommendation Engines.- 3 Changing Not Just Analyzing – Control Theory And Reinforcement Learning.- 4 Recommenda-tions As A Game – Reinforcement Learning For Recommendation Engines.- 5 How Engines Learn To Generate Recommendations – Adaptive Learning Algorithms.- 6 Up The Down Staircase – Hierarchical Reinforcement Learning.- 7 Breaking Dimensions – Adaptive Scoring With Sparse Grids.- 8 Decomposition In Transition - Adap-tive Matrix Factorization.- 9 Decomposition In Transition Ii - Adaptive Tensor Factorization.- 10 The Big Picture – Towards A Synthesis Of Rl And Adaptive Tensor Factorization.- 11 What Cannot Be Measured Cannot Be Controlled - Gauging Success With A/B Tests.- 12 Building A Recom-mendation Engine – The Xelopes Library.- 13 Last Words – Conclusion.- References.- Summary Of Notation.

Fields of interestComputational Science and Engineering; Math-ematical Applications in Computer Science; Mathematical Software



Due October 2013

2013. XIX, 271 p. 62 illus., 9 in color. (Applied and Numerical Harmonic Analysis) Hardcover7 approx. $119.00ISBN 978-3-319-01320-6

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69

J. P. Pinasco, Universidad de Buenos Aires, Buenos Aires, Argentina

Lyapunov-type InequalitiesWith Applications to Eigenvalue Problems

The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequal-ity for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this can-not happen in linear problems. Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunov-type inequalities in R^n when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for one-dimensional problems.

Features 7 Emphasizes the use of Lyapunov-type inequalities to obtain lower bounds for eigen-values 7 Devoted to more general nonlinear equations, systems of differential equations, or partial differential equations 7 Many inequali-ties intertwined, including Hardy, Sobolev and Poincare inequalities

Contents A short history of Lyapunov inequality.- Lyapunov inequality for p-laplacian operators.- Generaliza-tions.- Lyapunov type inequalities in RN .

Fields of interestOrdinary Differential Equations; Several Complex Variables and Analytic Spaces; Difference and Functional Equations



Due September 2013

2013. X, 120 p. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-1-4614-8522-3

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E. Rosazza Gianin, Università di Milano Bicocca, Milano, Italy; C. Sgarra, Politecnico di Milano, Milano, Italy

Mathematical Finance: Theory Review and ExercisesFrom Binomial Model to Risk Measures

The book collects over 120 exercises on differ-ent subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theo-retical results necessary to solve the exercises.

Features 7 Offers substantially more exercises on continu-ous time than do other textbooks 7 Includes three completely new chapters (one on Arbitrage Theory and Incompleteness, one on Risk Mea-sures, and one on Stochastic Volatility Models and Models with jumps) 7 Presents a middle ground between the stochastic and the analytic approach to option pricing and hedging at a reasonable, but not trivial, mathematical level

Contents 1 Short review of Probability and of Stochastic Processes.- 2 Portfolio Optimization in Discrete time Models.- 3 Binomial Model for Option Pric-ing.- 4 Absence of arbitrage and Completeness of market models.- 5 Itô’s Formula and Stochastic Differential Equations.- 6 Partial Differential Equations in Finance.- 7 Black-Scholes model for Option Pricing and Hedging Strategies.- 8 Ameri-can Options.- 9 Exotic Options.- 10 Interest Rate Models.- 11 Pricing Models beyond Black-Scho-les.- 12 Risk Measures: Value at Risk and beyond.

Fields of interestProbability Theory and Stochastic Processes; Fi-nance/Investment/Banking; Statistics for Business/Economics/Mathematical Finance/Insurance



Due September 2013

2013. Approx. 300 p. (UNITEXT / La Matematica per il 3+2) Softcover7 approx. $69.99ISBN 978-3-319-01356-5

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J.‑P. Serre, College de France Paris Chaire d’Algebre et Geometrie, Paris CX 05, France

Oeuvres - Collected Papers I1949 ‑ 1959

Fields of interestAlgebraic Geometry; Category Theory, Homologi-cal Algebra; Group Theory and Generalizations



Due August 2013

Edition originale publiée en 4 tomes


2003. Reprint 2013 of the 2003 edition. XXIV, 596 p. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-3-642-39815-5

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70

J.‑P. Serre, College de France Paris Chaire d’Algebre et Geometrie, Paris CX 05, France

Oeuvres - Collected Papers IV1985 ‑ 1998

From the reviews of Vol. IV: “This is the fourth volume of J-P. Serre’s Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain “the essence’’ of his work from that period and are devoted to number theory, algebraic ge-ometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the an-nounced results. The letters reproduced, however (in particular to K. Ribet and M.-F. Vignéras), provide indications of some of those proofs. Also included is an interview with J-P. Serre from 1986, revealing his views on mathematics (with the stress upon its integrity) and his own mathemati-cal activity. The volume ends with Notes which complete the text by reporting recent progress and occasionally correct it. The volume is an indis-pensable addition to previous ones and the whole set presents a fine piece of modern mathematics.” Zentralblatt MATH In this softcover edition of volume IV, two recently published articles have been added, one on the life and works of André Weil, the other one on Finite Subgroups of Lie Groups.

Contents Preface.- Papers published between 1985 and 1998.- Notes.-Modifications volumes I-III.- Errata volumes I-III.- Acknowledgements.

Fields of interestNumber Theory; Group Theory and Generaliza-tions; Algebraic Geometry



Due August 2013


2000. Reprint 2013 of the 2000 edition. VIII, 694 p. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-3-642-39839-1

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R. W. Shonkwiler, Georgia Institute of Technology, Atlanta, GA, USA

Finance with Monte CarloThis text introduces upper division undergradu-ate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles.

Features 7 Students will learn by doing; implementing concepts of each chapter into code and experi-menting with the outcome 7 Exploits the great-est virtue of the Monte Carlo method – providing results for exotic probability models 7 Students will learn a lot about options in addition to usage of mathematical models 7 Focus on Monte Carlo methods allows for students to travel a short road from theory to practical applica-tions 7 Presents "standard" models involving Random Walks with GBM but includes other distributions as well

Contents 1. Geometric Brownian Motion and the Efficient Market Hypothesis.- 2. Return and Risk.- 3. For-ward and Option Contracts and their Pricing.- 4. Pricing Exotic Options.- 5. Option Trading Strate-gies.- 6. Alternative to GBM Prices.- 7. Kelly’s Criterion.- Appendices.- A. Some Mathematical Background Topics.- B. Stochastic Calculus.- C. Convergence of the Binomial Method.- D. Vari-ance Reduction Techniques.- E. Shell Sort.- F. Next Day Prices Program.- References.- List of Nota-tion.- List of Algorithms.- Index.

Fields of interestQuantitative Finance; Mathematical Modeling and Industrial Mathematics; Probability Theory and Stochastic Processes



Due September 2013

2013. X, 316 p. 70 illus., 17 in color. (Springer Undergraduate Texts in Mathematics and Technology) Hardcover7 $59.99ISBN 978-1-4614-8510-0

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A. Syropoulos, Xanthi, Greece

Theory of Fuzzy ComputationThe book provides the first full length explora-tion of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It con-tains a detailed literature review and the author includes all proofs to make the presentation accessible. Ideas for future research and explora-tions are also provided. Students and researchers in computer science and mathematics will benefit from this work.

Features 7 First full length work on the subject of Fuzzy Computability 7 Features a review of existing literature 7 Full proofs included

Contents Introduction.- A Précis of Classical Computabil-ity Theory.- Elements of Fuzzy Set Theory.- On Fuzzy Turing Machines.- Other Fuzzy Models of Computation.- Appendix A: Computing with Words.- Appendix B: The Rough Sets Approach.- References.- Subject Index.- Name Index.

Fields of interestComputational Mathematics and Numerical Analysis; Mathematics of Computing



Due September 2013

2013. XI, 159 p. 6 illus. (IFSR International Series on Systems Science and Engineering, Volume 31) Hardcover7 $109.00ISBN 978-1-4614-8378-6

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71

T. Tonietti, University of Pisa, Pisa, Italy

And yet it is heardMusical, Multilingual and Polycultural History of Mathematics, Volume 1

We bring into full light some excerpts on musical subjects which were until now scattered through-out the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.

Features 7 The influence of some musical problems on the development of sciences is shown 7 No biased Eurocentric viewpoint is assumed 7 The numer-ous excerpts from various texts are quoted in their original language

Contents 0. Introduction.- PART I: In the ancient world.- 1. Above all with the Greek alphabet.- 2. In Chinese characters.- 3. In the Sanskrit of sacred Indian texts.-4. Not only in Arabic.- 5. Above all in the Latin alphabet.- Appendices.

Fields of interestMathematics, general; Mathematics in Music; His-tory of Mathematical Sciences



Due November 2013

2014. Approx. 450 p. (Science Networks. Historical Studies, Volume 46) Hardcover7 $169.00ISBN 978-3-0348-0671-8

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And yet it is heardMusical, Multilingual and Polycultural History of Mathematics, Volume 2

We bring into full light some excerpts on musical subjects which were until now scattered through-out the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.


Contents PART II: In the world of the scientific revolu-tion.- 6. Not only in Latin, but also in Dutch, Chinese, Italian and German.- 7. Beyond Latin, French, English, German, Italian and Flemish: the invention of symbolism.- 8. Between Latin, French, English and German: the language of transcendence.- 9. Between Latin and French.- 10. From French to German.- PART III: It is not even heard.- 11. In the language of the Venusians.- 12. Come on, Apophis.- Bibliography.- Index of names and works.




Due November 2013

2014. Approx. 750 p. (Science Networks. Historical Studies, Volume 47) Hardcover7 $229.00ISBN 978-3-0348-0674-9

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And yet it is heardMusical, Multilingual and Polycultural History of Mathematics

We bring into full light some excerpts on musical subjects which were until now scattered through-out the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in.


Contents Volume 1.- 0. Introduction.- PART I: In the ancient world.- 1. Above all with the Greek alphabet.- 2. In Chinese characters.- 3. In the Sanskrit of sacred Indian texts.-4. Not only in Arabic.- 5. Above all in the Latin alphabet.- Ap-pendices.- Volume 2.- PART II: In the world of the scientific revolution.- 6. Not only in Latin, but also in Dutch, Chinese, Italian and German.- 7. Be-yond Latin, French, English, German, Italian and Flemish: the invention of symbolism.- 8. Between Latin, French, English and German: the language of transcendence.- 9. Between Latin and French.- 10. From French to German.- PART III: It is not even heard.- 11. In the language of the Venusians.- 12. Come on, Apophis.- Bibliography.- Index of names and works.




Due November 2013

2013. Approx. 1200 p. (Science Networks. Historical Studies) (2-volume-set)7 $329.00ISBN 978-3-0348-0677-0

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72

W. Wallis, Southern Illinois University, Evansville, IN, USA

Mathematics in the Real WorldMathematics in the Real World is a self-contained, accessible introduction to the world of mathemat-ics for non-technical majors. With a focus on everyday applications and context, the topics in this textbook build in difficulty and are presented sequentially, starting with a brief review of sets and numbers followed by an introduction to elementary statistics, models, and graph theory. Data and identification numbers are then covered, providing the pathway to voting and finance. Each subject is covered in a concise and clear fashion through the use of real-world applications and the introduction of relevant terminology.

Features 7 Ideal textbook for use in a mathematics course for liberal arts majors 7 Covers accessible and applicable topics that other books omit 7 Pres-ents a range of relevant material in a condensed and approachable manner 7 Features numerous examples, writing exercises, and multiple choice questions

Contents Preface.- Part I Introduction.- Math is Every-where.- Numbers and Sets.- Counting.- Part II Statistical Ideas.- Collecting Data.- Measuring Data.- Normal.- Sampling, Predicting.- Multi-variate Situations.- Probability.- Part III Graph Models.- Euler.- Hamilton.- Trees.- Scheduling, Critical Paths.- Coloring, Handshakes.- Part IV Data.- Identification Numbers.- Data Trans-mission.- Encryption; The Hat Game.- Part V Voting.- Voting Systems.- Messing with Systems.- Electing a President.- Part VI The Exponential World.- Finance.- Populations and Radioactivity.

Fields of interestMathematics in the Humanities and Social Sci-ences; Graph Theory; Mathematics, general

Target groupsLower undergraduate


Due September 2013

2013. XVI, 276 p. 233 illus. Hardcover7 $49.99ISBN 978-1-4614-8528-5

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M. Willem, Université catholique de Louvain, Louvain-la-Neuve, Belgium

Functional AnalysisFundamentals and Applications

The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fun-damentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chap-ters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional meth-ods. The epilogue contains a sketch of the history of functional analysis, in relation with integra-tion and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics.

Features 7 Presents the principles of functional analysis in a clear and concise way 7 Most competing titles are out of date 7 Includes very recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis

Contents Preface.- The Integral.- Norm.- Lebesgue Spaces.- Duality.- Sobolev Spaces.- Capacity.- Elliptic Prob-lems.- Appendix.- Epilogue.- References.- Index of Notations.- Index.

Fields of interestFunctional Analysis; Analysis; Partial Differential Equations



Due July 2013

2013. XIII, 213 p. 1 illus. (Cornerstones) Hardcover7 $69.95ISBN 978-1-4614-7003-8

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J.‑Y. Yen, University of Cincinnati Department of Mathematical Sciences, Cincinnati, OH, USA; M. Yor, Université Paris VI CNRS UMR 7599, Paris CX 05, France

Local Times and Excursion Theory for Brownian MotionA Tale of Wiener and Itô Measures

This work introduces both local times for semi-martingales and excursion theory for Brownian paths, and presents applications to topics which are not usually treated with the same tools, e.g. arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.

Features 7 Both local times and excursion theory are usu-ally discussed in much longer texts. We examine these topics in relation to readers’ basic knowledge of stochastic processes 7 Presents interesting applications of excursion theory 7 Similarly with local times of Brownian motion

Contents Prerequisites.- Local times of continuous semi-martingales.- Excursion theory for Brownian paths.- Some applications of Excursion Theory.- Index.

Field of interestProbability Theory and Stochastic Processes



Due September 2013

2013. X, 135 p. 9 illus., 8 in color. (Lecture Notes in Mathematics, Volume 2088) Softcover7 $49.99ISBN 978-3-319-01269-8

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73

M. Zabarankin, Stevens Institute of Technology, Hoboken, NJ, USA; S. Uryasev, University of Florida, Gainesville, FL, USA

Statistical Decision Problems: Selected Concepts and Portfolio Safeguard Case StudiesStatistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems. It introduces state-of-the-art practical decision making through twenty-one case studies from real-life applications. The case studies cover a broad area of topics and the authors include links with source code and data, a very helpful tool for the reader.

Features 7 Presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision prob-lems 7 Discusses basic principles of statistical decision making from optimization perspective in various risk management applications such as optimal hedging, portfolio optimization, portfolio replication, and more 7 Introduces state-of-the-art practical decision making through seventeen case studies from real-life applications

Contents 1. Random Variables.- 2. Deviation, Risk, and Error Measures.- 3. Probabilistic Inequalities.- 4. Maximum Likelihood Method.- 5. Entropy Maxi-mization.- 6. Regression Models.- 7. Classifica-tion.- 8. Statistical Decision Models with Risk and Deviation.- 9. Portfolio Safeguard Case Studies.- Index.- References.

Fields of interestOperations Research, Management Science; Probability Theory and Stochastic Processes; Data Mining and Knowledge Discovery



Due November 2013

2014. XIV, 266 p. 9 illus., 3 in color. (Springer Optimization and Its Applications, Volume 85) Hardcover7 approx. $109.00ISBN 978-1-4614-8470-7

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A. J. Zaslavski, Technion – Israel Institute of Technology, Haifa, Israel

Structure of Approximate Solutions of Optimal Control ProblemsThis title examines the structure of approximate solutions of optimal control problems consid-ered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of opti-mal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any element in a set that is in a countable in-tersection which is open everywhere dense sets in the space of integrands; meaning that the turnpike property holds for most optimal control problems.

Features 7 Establishes the turnpike property for ge-neric optimal control problems 7 Contains an in-depth look at the existence and structure of solutions of infinite horizon optimal control prob-lems 7 Considers applications to linear control systems

Contents Preface.- 1.Introduction.- 2.Turnpike Properties of Optimal Control Problems.- 3.Infinite Horizon Problems.- 4.Linear Control Systems.- References.

Fields of interestCalculus of Variations and Optimal Control; Opti-mization; Systems Theory, Control; Game Theory, Economics, Social and Behav. Sciences



Due August 2013

2013. XII, 112 p. (SpringerBriefs in Optimization) Softcover7 $54.99ISBN 978-3-319-01239-1

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