G. Amendola, M. Fabrizio, D. Arapura, Purdue University ... · basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius

Mathematics. springer.com/NEWSonline

26

G. Amendola, University of Pisa, Italy; M. Fabrizio, University of Bologna, Italy; J. M. Golden, Dublin Institute of Technology, Ireland

Thermodynamics of Materials with MemoryTheory and Applications

Contents Introduction to Continuum.-Materials with Constitutive Equations That Are Local in Time.- Principles of Thermodynamics.- Free Energies and the Dissipation Principle.-Thermodynamics of Materials with Memory.-A Linear Memory Model.- Viscoelastic Solids and Fluids.- Heat Conductors.- Free Energies on Special Clas-ses of Material.- The Minimum Free Energy.-Representation of the Minimum Free Energy in the Time Domain.- Minimum Free Energy for Viscoelastic Solids, Fluids, and Heat Conductors.- The Minimum Free Energy for a Continuous-Spectrum Material.- The Minimum Free Energy for a Finite-Memory Material.- A Family of Free Energies.- Properties and Explicit Forms of Free Energies for the Case of Isolated Singularities.- Free Energies for Nonlocal Materials.- Existence and Uniqueness.- Controllability of Thermoelastic Systems with Memory.- The Saint-Venant Problem for Viscoelastic Materials.- Exponential Decay.- Semigroup Theory for Abstract Equations with Memory.- Identification Problems for Integro-differential Equations.- Dynamics of Viscoelastic Fluids.- A Conventions and Some Properties of Vector Spaces.- References.- Index.

Fields of interestMathematical Applications in the Physical Sciences; Characterization and Evaluation of Materials; Continuum Mechanics and Mechanics of Materials

Target groupsResearch

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2012. XV, 562 p. 4 illus. Hardcover7 $124.00ISBN 978-1-4614-1691-3

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D. Arapura, Purdue University, West Lafayette, IN, USA

Algebraic Geometry over the Complex NumbersThis is a relatively fast paced graduate level intro-duction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry.

Features 7 Contains a rapid introduction to complex algebraic geometry Includes background material on topology, manifold theory and sheaf theo-ry 7 Analytic and algebraic approaches are developed somewhat in parallel 7 Easy-going style will not intimidate newcomers to algebraic geometry

Contents Preface.- 1. Plane Curves.- 2. Manifolds and Varieties via Sheaves.- 3. More Sheaf Theory.- 4. Sheaf Cohomology.- 5. de Rham Cohomoloy of Manifolds.- 6. Riemann Surfaces.- 7. Simplicial Methods.- 8. The Hodge Theorem for Riemann Manifolds.- 9. Toward Hodge Theory for Complex Manifolds.- 10. Kahler Manifolds.- 11. A Little Al-gebraic Surface Theory.- 12. Hodge Structures and Homological Methods.- 13. Topology of Families.- 14. The Hard Lefschez Theorem.- 15. Coherent Sheaves.- 16. Computation of Coherent Sheaves.- 17. Computation of some Hodge numbers.- 18. Deformation Invariance of Hodge Numbers.- 19. Analogies and Conjectures.- References.- Index.

Fields of interestAlgebraic Geometry; Several Complex Variables and Analytic Spaces; Topology

Target groupsGraduate

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2012. XII, 332 p. 17 illus., 4 in color. (Universitext) Softcover7 approx. $74.95ISBN 978-1-4614-1808-5

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A. Badrikian, J. Hoffmann-Jørgensen, University of Aarhus, Denmark; J. Kuelbs, University of Minnesota, Madison, WI; USA; F. Xavier, Université Louis Pasteur et C.N.R.S., Strasbourg, France

Probability in Banach Spaces at Saint-FlourContents Prolegomenes au calcul des probabilités dans les Banach.- Régularité des trajectoires des fonctions aléatoires Gaussiennes.- Probability in Banach space.- The law of the iterated logarithm and rela-ted strong convergence theorems for Banach space valued random variables.

Fields of interestProbability Theory and Stochastic Processes


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2012. 538 p. WithReprint of lectures originally published in the Lecture Notes in Mathematics volumes 539 (1976), 480 (1975), 589 (1977) and 976 (1983).. (Probability at Saint-Flour) Softcover7 approx. $69.95ISBN 978-3-642-25276-1

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www.springer.com/978-1-4614-1691-3www.springer.com/978-1-4614-1808-5www.springer.com/978-3-642-25276-1

News 11/2011 Mathematics.

27

P. Bangert, algorithmica technologies GmbH, Bremen, Germany (Ed.)

Optimization for Industrial ProblemsIndustrial optimization lies on the crossroads bet-ween mathematics, computer science, engineering and management. This book presents these fields in interdependence as a conversation between theoretical aspects of mathematics and computer science and the mathematical field of optimization theory at a practical level. The 19 case studies that were conducted by the author in real enterprises in cooperation and co-authorship with some of the leading industrial enterprises, including RWE, Vattenfall, EDF, PetroChina, Vestolit, Sasol, and Hella, illustrate the results that may be reasonably expected from an optimization project in a com-mercial enterprise.

Features 7 Presentation of modern methods to solve real and pressing industrial optimization problems in a practical way together with real-life examp-les 7 With examples usually hard to come by or not published at all 7 Presents new methods or new results about existing methods to information science

Contents Overview of Heuristic Optimization.- Statistical Analysis in Solution Space.- Project Manage-ment.- Pre-processing: Cleaning up Data.- Data Mining: Knowledge from Data.- Modeling: Neural Networks.- Optimization: Simulated Annealing.- The Human Aspect in Sustainable Change and Innovation.

Fields of interestOptimization; Operations Research, Management Science

Target groupsProfessional/practitioner

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2012. XXII, 247 p. 60 illus., 24 in color. Softcover7 approx. $99.00ISBN 978-3-642-24973-0

9

R. Berndt, Universität Hamburg, Germany; R. Schmidt, University of Oklahoma, Norman, OK, USA

Elements of the Representation Theory of the Jacobi GroupThe Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta func-tions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation the-ory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger‘s theory for the metaplectic group, complete classification theorems for irreducible representations are obtai-ned. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms.

Features 7 Very well written monograph combining algebraic groups and number theory 7 Recom-mended reading for researchers of modular and automorphic forms 7 Up to date and structured collection of known results

Contents Introduction.- 1 The Jacobi Group.- 2 Basic Re-presentation Theory of the Jacobi Group.- 3 Local Representations: The Real Case.- 4 The Space and its Decomposition.- 5 Local Representations: The p-adic Case.- 6 Spherical Representations.- 7 Global Considerations.- Bibliography.- Index of Notations.- Index.

Fields of interestAlgebraic Geometry; Number Theory; Group Theory and Generalizations


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Reprint of the 1998 edition. XIV, 214 p. (Modern Birkhäuser Classics) Softcover7 $69.95ISBN 978-3-0348-0282-6

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F. Brauer, University of British Columbia, Vancouver, BC, Canada; C. Castillo-Chavez, Arizona State University, Phoenix, AZ, USA

Mathematical Models in Population Biology and EpidemiologyThis textbook provides an introduction to the field of mathematical biology through the integration of classical applications in ecology with more recent applications to epidemiology, particularly in the context of spread of infectious diseases.

Features 7 Free supplementary material available on the author's website involving problems using both Mathematica and Maple 7 Text offers nice ba-lance of theory and application 7 Concentration is on applications in population biology, epide-miology, and resource management

Contents Part I: Simple Single-Species Models. 1. Conti-nuous population models. 2. Discrete population models. 3. Continuous single-species population models with delay.- Part II: Models for Interacting Species. 4. Introduction and mathematical preli-minaries. 5. Continuous models for two inter-acting populations. 6. Harvesting in two-species population models. 7. Multi-species population models.- Part III: Structured Population Models. 8. Models for population with age structure. 9. Models for populations with spatial distribution.

Fields of interestCommunity & Population Ecology


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2nd ed. 2012. X, 518 p. 120 illus., 2 in color. (Texts in Applied Mathematics, Volume 40) Hardcover7 $84.95ISBN 978-1-4614-1685-2

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28

A. E. Brouwer, Eindhoven University of Technology, Netherlands; W. H. Haemers, Tilburg University, Netherlands

Spectra of GraphsThis book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard to-pics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar to-pics. Exercises at the end of each chapter provide practice and vary from easy yet interesting appli-cations of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.

Features 7 Provides an excellent introduction to advanced topics in graph spectral theory 7 Written by experts in this area 7 Includes tables, references, author and subject index

Contents Graph spectrum.- Linear algebra.- Eigenvalues and eigenvectors of graphs.- The second largest eigenvalue.- Trees.- Groups and graphs.- Topolo-gy.- Euclidean representations.- Strongly regular graphs.- Regular two-graphs.- Association sche-mes.- Distance regular graphs. - p-ranks.- Spectral characterizations.- Graphs with few eigenvalues.- References.- Author Index.- Subject Index.

Fields of interestAlgebraic Geometry; Group Theory and Genera-lizations


Discount group P

Due January 2012

2012. XII, 247 p. 26 illus. (Universitext) Hardcover7 approx. $59.95ISBN 978-1-4614-1938-9

9

R. Der, MPI-MIS, Leipzig, Germany; G. Martius, MPI-DS, Göttingen, Germany

The Playful MachineTheoretical Foundation and Practical Realization of Self-Organizing RobotsForeword by: R. Pfeifer, University of Zurich, Switzerland

Autonomous robots may become our closest companions in the near future.

Features 7 This work opens a new field of research 7 The reader learns everything about the self-orga-nization of behavior in robots that is known today 7 A simulation software enables the reader to make immediately contact with the applications and provides the him with the tools to start deve-loping its own variations and ideas quickly

Contents 1.Introduction.- 2.Self-Organization in Nature and Machines.- 3.The Sensorimotor Loop. - 4.Prin-ciples of Self-Regulation - Homeostasis . - 5.A General Approach to Self-Organization - Homeo-kinesis.- 6.From Fixed-Point Flows to Hysteresis Oscillators.- 7.Symmetries, Resonances, and Second Order Hysteresis.- 8.Low Dimensional Robotic Systems.- 9.Model Learning.- 10.High-Dimensional Robotic Systems.- 11.Facing the Unknown - Homeokinesis in a New Represen-tation*.- 12.Guided Self-Organization - A First Realization.- 13.Channeling Self-Organization.- 14.Reward-Driven Self-Organization.- 15.Algo-rithmic Implementation.- 16.The LPZROBOTS Simulator.- 17.Discussion and Perspectives.- List of Figures.- List of Videos.- List of Experiments.- References.- Index.

Fields of interestApplications of Mathematics; Artificial Intelli-gence (incl. Robotics)


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2012. X, 290 p. (Cognitive Systems Monographs, Volume 15) Hardcover7 approx. $129.00ISBN 978-3-642-20252-0

9

R. Durrett, Duke University, Durham, NC, USA; T. M. Liggett, University of California, Los Angeles, CA, USA; F. Spitzer, A.-S. Sznitman, ETH Zürich, Switzerland

Interacting Particle Systems at Saint-FlourContents: Durrett, Rick: Ten lectures on particle systems.- Liggett, T.M.: The stochastic evolution of infinite systems of interacting particles.- Spitzer, Frank L.:Introduction aux processus de Markov à paramètre dans Zυ

Contents Introduction aux processus de Markov à paramèt-re dans Zυ.- The stochastic evolution of infinite systems of interacting particles.- Topics in propa-gation of chaos.- Ten lectures on particle systems.

Fields of interestProbability Theory and Stochastic Processes;


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2012. VIII, 326 p. WithReprint of lectures originally published in the Lecture Notes in Mathematics volumes 1608 (1995), 1464 (1991), 589 (1977), and 390 (1974).. (Probability at Saint-Flour) Softcover7 approx. $49.95ISBN 978-3-642-25297-6

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29

J. S. Golan, University of Haifa, Israel

The Linear Algebra a Beginning Graduate Student Ought to KnowLinear algebra is a living, active branch of mathe-matics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological, and social sciences, and to engineering.

Features 7 Contains a wealth of biographical notes and thumbnail photos 7 Facilitates the transition from concrete exemplification to theoretical abstraction and thus enables a deeper level of un-derstanding for use in a real world context 7 131 exercises have been added to the already extensive collection supplied in the 2nd edition 7 Can be used as a self-study guide, textbook or reference work

Contents Notation and terminology.- Fields.- Vector spaces over a field.- Algebras over a field.- Linear independence and dimension.- Linear transfor-mations.- The endomorphism algebra of a vector space.- Representation of linear transformations by matrices.- The algebra of square matrices.- Sys-tems of linear equations.- Determinants.- Eigen-values and eigenvectors.- Krylov subspaces.- The dual space.- Inner product spaces.- Orthogo-nality.- Selfadjoint Endomorphisms.- Unitary and Normal endomorphisms.- Moore-Penrose pseudoinverses.- Bilinear transformations and forms.- Summary of Notation.-Index to thumbnail photos.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Associative Rings and Algebras; Non-associative Rings and Algebras


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Originally published as volume 27 in the series: Kluwer Texts in the Mathematical Sciences

3rd ed. 2012. XII, 488 p. 201 illus. Softcover7 $69.95ISBN 978-94-007-2635-2

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J. Hilgert, University of Paderborn, Germany; K.-H. Neeb, Friedrich-Alexander Universität Erlangen-Nürnburg, Germany

Structure and Geometry of Lie GroupsThis self-contained text is an excellent introduc-tion to Lie groups and their actions on manifolds.

Features 7 Systematically presents the structure theory of general, unrestricted Lie groups 7 Self-con-tained, with two appendices on covering theory and multilinear algebra 7 Includes abundant classroom-tested exercises 7 Useful as both a graduate text and as a research reference for a broad range of mathematicians

Contents Preface.- 1 Introduction.- Part I Matrix Groups.- 2 Concrete Matrix Groups.- 3 The Matrix Exponen-tial Function.- 4 Linear Lie Groups.- Part II Lie Algebras.- 5 Elementary Structure Theory of Lie Algebras.- 6 Root Decomposition.- 7 Represen-tation Theory of Lie Algebras.- Part III Manifolds and Lie Groups.- 8 Smooth Manifolds.- 9 Basic Lie Theory.- 10 Smooth Actions of Lie Groups.- Part IV Structure Theory of Lie Groups.- 11 Normal Subgroups, Nilpotemt and Solvable Lie Groups.- 12 Compact Lie Groups.- 13 Semisimple Lie Groups.- 14 General Structure Theory.- 15 Complex Lie Groups.- 16 Linearity of Lie Groups.- 17 Classical Lie Groups.- 18 Nonconnected Lie Groups.- Part V Appendices.- A Basic Covering Theory.- B Some Multilinear Algebra.- C Some Functional Analysis.- D Hints to Exercises.- Refe-rences.- Index.

Fields of interestTopological Groups, Lie Groups; Differential Geometry; Algebraic Topology


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2012. X, 744 p. 4 illus. (Springer Monographs in Mathematics) Hardcover7 $129.00ISBN 978-0-387-84793-1

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J. A. Hogan, University of Newcastle, Callaghan, NSW, Australia; J. D. Lakey, New Mexico State University, NM, USA

Duration and Bandwidth LimitingProlate Functions, Sampling, and Applications

Increasingly important in the field of commu-nications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive mono-graph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications enginee-ring, but also to optical engineering, geosciences, planetary sciences, and biomedicine.

Features 7 Combines research and methods from many sources to present an impressively comprehensive analysis 7 Includes ample discussion of both theory and applications 7 Features chapter-by-chapter supplemental material illustrating results in further depth and detail

Contents Preface.- Chapter 1: The Bell Labs Theory.- Chap-ter 2: Numerical Aspects of Time- and Bandlimi-ting.- Chapter 3: Thomson‘s Multitaper Method and Applications to Channel Modeling.- Chapter 4: Time- and Bandlimiting of Multiband Signals.- Chapter 5: Sampling of Bandlimited and Multi-band Signals.- Chapter 6: Time-localized Sampling Approximations.- Appendix: Notation and Mathe-matical Prerequisites.- References.- Index.

Fields of interestFourier Analysis; Communications Engineering, Networks; Abstract Harmonic Analysis


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2012. XVII, 258 p. 14 illus. (Applied and Numerical Harmonic Analysis) Hardcover7 $99.00ISBN 978-0-8176-8306-1

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30

J. Jacod, Université Paris VI, France; P. Protter, Columbia University, New York, NY, USA

Discretization of ProcessesIn applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes.

Features 7 The first and so far the only book in this area 7 Presents the important results in a cohe-rent and unified manner 7 Includes systematic, creative and original ways to use sophisticated (but highly technical) tools

Contents Part I Introduction and Preliminary Material.- 1.Introduction .- 2.Some Prerequisites.- Part II The Basic Results.- 3.Laws of Large Numbers: the Basic Results.- 4.Central Limit Theorems: Technical Tools.- 5.Central Limit Theorems: the Basic Results.- 6.Integrated Discretization Error.- Part III More Laws of Large Numbers.- 7.First Extension: Random Weights.- 8.Second Extension: Functions of Several Increments.- 9.Third Extensi-on: Truncated Functionals.- Part IV Extensions of the Central Limit Theorems.- 10.The Central Limit Theorem for Random Weights.- 11.The Central Limit Theorem for Functions of a Finite Number of Increments.- 12.The Central Limit Theorem for Functions of an Increasing Number of Incre-ments.- 13.The Central Limit Theorem for Trun-cated Functionals.- Part V Various Extensions.- 14.Irregular Discretization Schemes. 15.Higher Order Limit Theorems.- 16.Semimartingales Contaminated by Noise.- Appendix.- References.- Assumptions.- Index of Functionals.- Index.

Fields of interestProbability Theory and Stochastic Processes; Statistics for Business/Economics/Mathematical Finance/Insurance; Econometrics


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2012. XIV, 596 p. (Stochastic Modelling and Applied Probability, Volume 67) Hardcover7 $129.00ISBN 978-3-642-24126-0

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H. Kunze, University of Guelph, ON, Canada; D. La Torre, University of Milan, Italy; F. Mendivil, Acadia University, Wolfville, NS, Canada; E. R. Vrscay, University of Waterloo, ON, Canada

Fractal-Based Methods in AnalysisThe idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics.

Features 7 Extensive coverage of both the theory and the applications of IFS fractals 7 Unified presenta-tion of almost 20 years of research literature, with new viewpoints and results which stimulate the reader and show the state-of-the-art of research in this area 7 The book illustrates a large number of analytical applications of IFS methods 7 In-cludes both direct applications of IFS methods as well as new analytical methods inspired by the IFS fractal framework 7 Self-contained and readable mathematical book with background appendices on topological and metric spaces, measure theory, and basic notions from set-valued analysis, which make the book suitable for self-study or for specia-lized graduate courses

Contents What do we mean by “Fractal-Based Analysis“.- Basic IFS.- IFS on Spaces of Functions.- IFS, Mul-tifunctions, and Measure-Valued Functions. -IFS on Spaces of Measures.-The Chaos Game.-Inverse Problems and Fractal-Based Methods.-Further Developments and Extensions.- References.- In-dex.

Fields of interestDynamical Systems and Ergodic Theory; Mathe-matical Methods in Physics; Approximations and Expansions


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2012. XII, 424 p. 72 illus., 8 in color. Hardcover7 $124.00ISBN 978-1-4614-1890-0

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M. Lifshits, St.Petersburg State University, Russia

Lectures on Gaussian ProcessesGaussian processes can be viewed as a far-re-aching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathema-tics. The first chapters introduce essentials of the classical theory of Gaussian processes and measu-res with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle.

Feature 7 A quick and condensed treatment of the core theory

Contents Preface.- 1.Gaussian Vectors and Distributions.- 2.Examples of Gaussian Vectors, Processes and Distributions.- 3.Gaussian White Noise and Integral Representations.- 4.Measurable Func-tionals and the Kernel.- 5.Cameron-Martin Theorem.- 6.Isoperimetric Inequality.- 7.Measure Concavity and Other Inequalities.- 8.Large Devi-ation Principle.- 9.Functional Law of the Iterated Logarithm.- 10.Metric Entropy and Sample Path Properties.- 11.Small Deviations.- 12.Expansions of Gaussian Vectors.- 13.Quantization of Gaussian Vectors.- 14.Invitation to Further Reading.- Refe-rences.

Fields of interestProbability Theory and Stochastic Processes


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2012. V, 115 p. (SpringerBriefs in Mathematics) Softcover7 approx. $49.95ISBN 978-3-642-24938-9

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31

M. R. Murty, Queen‘s University, Kingston, ON, Canada; V. K. Murty, University of Toronto, ON, Canada

Non-vanishing of L-Functions and ApplicationsThis book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book. One of the most attracti-ve features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point the latest discoveries as are presented in the final chapters can be fully appreciated.

Features 7 Well-written monograph on a difficult but at-tractive subject in number theory 7 Provides an excellent easy-to-read introduction to the modern analytic theory of L-functions 7 Each chapter is accompanied by exercises

Contents Preface.- Introduction.- Chapter 1 The Prime Number Theorem and Generalizations.- Chapter 2 Artin L-functions.- Chapter 3 Equidistribution and L-functions.- Chapter 4 Modular Forms and Dirichlet Series.- Chapter 5 Dirichlet L-functions.- Chapter 6 Non-vanishing of Quadratic Twists of Modular L-functions.- Chapter 7 Selberg‘s Conjectures.- Chapter 8 Suggestions for further reading.- Author index.- Subject index.

Fields of interestNumber Theory; Algebraic Geometry


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Reprint of the 1997 Edition. XII, 196 p. (Modern Birkhäuser Classics) Softcover7 $59.95ISBN 978-3-0348-0273-4

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G. L. Naber, Drexel University, Department of Mathematics, Philadelphia, PA

The Geometry of Minkowski SpacetimeAn Introduction to the Mathematics of the Special Theory of Relativity

This book offers a presentation of the special theo-ry of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addi-tion to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterizati-on of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essen-tially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes.

Features 7 Mathematically rigorous treatment of special relativity with precise statement of the physi-cal interpretation 7 Detailed introduction to the the theory of spinors in Minkowski space-time 7 Thorough treatments of numerous topics not generally discussed at the introductory level

Fields of interestManifolds and Cell Complexes (incl. Diff.Topolo-gy); Classical and Quantum Gravitation, Relativity Theory; Mathematical Methods in Physics


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2nd ed. 2012. X, 330 p. 55 illus. (Applied Mathematical Sciences, Volume 92) Hardcover7 approx. $59.95ISBN 978-1-4419-7837-0

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V. P. Pikulin, Moscow Power Engineering Institute, Russia; S. I. Pohozaev, Steklov Institute of Mathematics, Moscow, Russia

Equations in Mathematical PhysicsA practical courseTransl. Russian: A. Iacob, Ann Arbor, MI, USA

Many physical processes in fields such as mecha-nics, thermodynamics, electricity, magnetism or optics are described by means of partial differen-tial equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In par-ticular, the methods of conformal mappings, Fou-rier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.

Features 7 Presents main methods and tools for solving basic problems from mathematical physics 7 Of-fers quick access to principal facts and valuable tools 7 A very good example of a valuable manual for future engineers and scientists

Contents Preface.- Introduction.- Chapter 1. Elliptic prob-lems.- Chapter 2. Hyperbolic problems.- Chapter 3. Parabolic problems.- References.- Index.

Fields of interestPartial Differential Equations; ; Computational Mathematics and Numerical Analysis


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Reprint of the 1st ed. 2001. 2nd printing 2001. VIII, 207 p. 31 illus. (Modern Birkhäuser Classics) Softcover7 $59.95ISBN 978-3-0348-0267-3

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J. Richter-Gebert, Technische Universität, München, Germany; U. H. Kortenkamp, Pädagogische Hochschule, Karlsruhe, Germany

The Cinderella.2 ManualWorking with The Interactive Geometry Software

Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. It now consists of three connected parts: An enhanced geometry component with new features like trans-formations and dynamic fractals, a simulation laboratory to explore basic laws of Newton me-chanics, and an easy to use scripting language that enables any user to quickly extend the software even further. The Cinderella.2 Manual is the first book to offer complete instruction and techniques for using Cinderella.2. It contains a wealth of ex-amples, in particular for the CindyScript language which interacts smoothly with the geometry and simulation components, and a complete reference. Cinderella.2 is Math in Motion all the way, and this book provides comprehensive documentation from start to finish.

Feature 7 Best geometry and physics simulation and teaching software available

Fields of interestGeometry; Electronics and Microelectronics, Instrumentation; Algorithms

Target groupsLower undergraduate

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2012. XIV, 459 p. 378 illus., 370 in color. Hardcover7 $49.95ISBN 978-3-540-34924-2

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K. Schmidt, Universität Wien, Austria

Dynamical Systems of Algebraic OriginAlthough much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. Howe-ver, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to syste-matic study: the Zd-actions by automorphisms of compact, abelian groups.

Features 7 Beautifully written monograph on an interes-ting topic in ergodic theory 7 First systematic account of the ergodic theory of algebraic Zd-actions 7 Valuable to researchers and graduate students of ergodic theory

Contents Introduction.- Chapter I. Group actions by automorphisms fo compact groups.- Chapter II. Zd-actions on compact abelian groups.- Chap-ter III. Expansive automorphisms of compact groups.- Chapter IV. Periodic points.- Chapter V. Entropy.- Chapter VI. Positive entropy.- Chapter VII. Zero entropy.- Chapter VIII. Mixing.- Chap-ter IX. Rigidity.- Bibliography.- Index.

Fields of interestTopological Groups, Lie Groups; Algebraic Geometry; Probability Theory and Stochastic Processes


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Reprint of the 1995 Edition. XVIII, 310 p. (Modern Birkhäuser Classics) Softcover7 $74.95ISBN 978-3-0348-0276-5

9

V. Shikhman, RWTH Aachen, Germany

Topological Aspects of Nonsmooth OptimizationThis book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the to-pological approach and topological invariants of corresponding feasible sets are investigated. Mo-reover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nons-moothness.

Features 7 Establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness 7 Consi-ders four optimization problems and uses a topo-logical approach 7 Handles various equilibrium optimization problems from the same topological point of view 7 Links ideas from singularity and transversality theory with nonsmooth optimiza-tion

Contents Preface. -Notation.- Introduction.- Mathematical Programming Problems with Complementarity.- Constraints.- General Semi-infinite Programming Problems.- Mathematical Programming Problems with Vanishing Constraints.- Bilevel Optimizati-on.- Impacts on Nonsmooth Analysis.- Appen-dix.- Bibliography.- References.- Index.

Fields of interestOptimization; ; Functional Analysis


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Due November 2011

2012. XI, 189 p. 29 illus. (Springer Optimization and Its Applications / Nonconvex Optimization and Its Applications, Volume 64) Hardcover7 $99.00ISBN 978-1-4614-1896-2

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G. Shimura, Princeton University, NJ, USA

Modular Forms: Basics and BeyondThis is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisen-stein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.

Features 7 Contains advanced material but always reminds the reader of basic facts 7 Features the theory of modular forms of half-integral weight, and the discussion of theta functions and Eisen-stein series of holomorphic and nonholomorphic types 7 Discusses special values of various Dirichlet series associated to one or two modular forms

Contents Preface.- Notation and Terminology.- Chapter I. Preliminaries.- Chapter II. Theta Functions and Factors of Automorphy.- Chapter III. The Rationality and Eisenstein Series.- Chapter IV. The Correspondence between Forms of Integral and Half-integral Weight.- Chapter V. The Arithmeti-city of Critical Values of Dirichlet Series.- Appen-dix.- References.- Index.

Fields of interestNumerical Analysis


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Due November 2011

2012. X, 176 p. (Springer Monographs in Mathematics) Hardcover7 $99.00ISBN 978-1-4614-2124-5

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A. Sorokin, University of Florida, Gainesville, FL, USA; S. Rebennack, Colorado School of Mines, Golden, CO, USA; P. M. Pardalos, University of Florida, Gainesville, FL, USA; N. A. Iliadis, EnerCoRD, Athens, Greece; M. V. Pereira, PSR, Rio de Janeiro, Brazil (Eds)

Handbook of Networks in Power Systems IThe Handbook of Networks in Power Systems has as an objective to include the state-of-the-art developments that occurred in the power systems network, in particular gas, electricity, liquid fuels, freight network and network interactions. It is separated into six sections with different subjects where one scientific paper or more, depending on the importance is included. Each subject is identi-fied following the activity on the domain and the recognition of each subject as an area of research. The scientific papers are authored by a world specialist on the domain. Preliminary.

Features 7 Provides a state-of-the-art overview in the field of networks in power systems 7 Also for non-experts 7 Covers all major fields in power systems networks

Contents Part I.- Electricity.- Network.

Fields of interestCalculus of Variations and Optimal Control; Op-timization; Operation Research/Decision Theory; Energy Technology


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Available

2012. X, 600 p. 147 illus., 87 in color. (Energy Systems) Hardcover7 $239.00ISBN 978-3-642-23192-6

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A. Sorokin, University of Florida, Gainesville, FL, USA; S. Rebennack, Colorado School of Mines, Golden, CO, USA; P. M. Pardalos, University of Florida, Gainesville, FL, USA; N. A. Iliadis, EnerCoRD, Athens, Greece; M. V. Pereira, PSR, Rio de Janeiro, Brazil (Eds)

Handbook of Networks in Power Systems IIThe Handbook of Networks in Power Systems has as an objective to include the state-of-the-art developments that occurred in the power systems network, in particular gas, electricity, liquid fuels, freight network and network interactions. It is separated into six sections with different subjects where one scientific paper or more, depending on the importance is included. Each subject is identi-fied following the activity on the domain and the recognition of each subject as an area of research. The scientific papers are authored by a world specialist on the domain. See Volume 1.

Features 7 Covers all major topics in power systems networks 7 Contains a collection of state-of-the-art review articles 7 Includes topics like natural gas, electricity, liquid fuels, freight and network interactions

Contents Part II Gas Network. - Part III Network Interac-tions.

Fields of interestCalculus of Variations and Optimal Control; Op-timization; Operation Research/Decision Theory; Energy Technology


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2012. X, 580 p. 46 illus., 5 in color. (Energy Systems) (In 2 volumes, not available separately) Hardcover7 $239.00ISBN 978-3-642-23405-7

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34

H. Van Maldeghem, Ghent University, Gent, Belgium

Generalized PolygonsGeneralized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry.

Features 7 Provides a complete introduction to gene-ralized polygons 7 Develops the theory from scratch 7 Provides geometric proofs of algebraic results 7 Serves as an extensive source for references

Contents Preface.- 1 Basic Concepts and Results.- 2 Clas-sical Polygons.- 3 Coordinatization and Further Examples.- 4 Homomorphisms and Automor-phism Groups.- 5 The Moufang Condition.- 6 Characterizations.- 7 Ovoids, Spreads and Self-Dual Polygons.- 8 Projectivities and Projective Embeddings.- 9 Topological Polygons.- Appendi-ces.- A An Eigenvalue Technique.- B The Theorem of Bruck and Kleinfeld.- C Tits Diagrams for Moufang Quadrangles.- D Root Elations of Clas-sical Polygons.- E The Ten Most Famous Open Problems.- Bibliography.- Index.

Fields of interestGeometry; Algebraic Geometry


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Reprint of the 1st ed. 1998. 2nd printing 1998. XVI, 503 p. 25 illus. (Modern Birkhäuser Classics) Softcover7 $84.95ISBN 978-3-0348-0270-3

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E. Wegert, TU Bergakademie Freiberg, Germany

Visual Complex FunctionsThis course on complex functions is distinguished by consistently using phase portraits, a special color representation which visualizes functions as images. The text introduces the basic concepts of complex analysis, and, parallel to a systematic investigation of analytic and meromorphic func-tions, readers learn how properties of a function are reflected in and can be recovered from its pha-se portrait. The approach emphasizes constructive aspects, it is intuitive, and requires only basic knowledge of calculus. More advanced readers will get a fresh view on classical results and may be inspired by the pictures to new and challenging questions.

Features 7 First introduction to complex functions syste-matically using phase portraits (which are expec-ted to become an indispensable tool for exploring complex functions in teaching, mathematical research and applications alike) 7 Reorganizati-on of the traditional material covered by textbooks in complex analysis and emphasis on special as-pects of the topic. 7 A companion to rather than a substitute for existing textbooks on complex analysis, although mostly self-contained 7 En-hances intuitive understanding of basic concepts and special functions by visualizing complex func-tions by phase plots 7 Complete text equipped with color illustrations

Contents Preface.- 1 Introduction.- 2 Complex Functions.- 3 Analytic Functions.- 4 Complex Calculus.- 5 Conformal Mapping.- 6 Special Topics and Applications.- 7 Phase Diagrams.- 8 An Atlas of Functions.

Fields of interestFunctions of a Complex Variable; Special Func-tions


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2012. 200 p. 200 illus. in color. Softcover7 approx. $49.95ISBN 978-3-0348-0179-9

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www.springer.com/978-3-0348-0270-3www.springer.com/978-3-0348-0179-9

Documents

G. Amendola, M. Fabrizio, D. Arapura, Purdue University ... · basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius