cairo university, giza, egypt; caversham, reading, uk gems ......dynamical systems the book treats...

News 7/2012 Mathematics

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M. H. Annaby, Cairo University, Giza, Egypt; Z. S. Mansour, King Saud University, Riyadh, Kingdom of Saudi Arabia

q-Fractional Calculus and EquationsThis nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with ele-mentary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, lea-ding to systems of equations with retarded argu-ments. Regular q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi.

Features 7 First detailed rigorous study of q-calcu-li 7 First detailed rigorous study of q-difference equations 7 First detailed rigorous study of q-fractional calculi and equations 7 Proofs of many classical unproved results are given 7 Il-lustrative examples and figures helps readers to digest the new approaches

Contents 1 Preliminaries.- 2 q-Difference Equations.- 3 q-Sturm Liouville Problems.- 4 Riemann–Liou-ville q-Fractional Calculi.- 5 Other q-Fractional Calculi.- 6 Fractional q-Leibniz Rule and Applica-tions.- 7 q-Mittag–Leffler Functions.- 8 Fractio-nal q-Difference Equations.- 9 Applications of q-Integral Transforms.

Fields of interestsAnalysis; Difference and Functional Equations; Functions of a Complex Variable

Target groupsResearch

Discount groupProfessional Non-Medical

Available

2012. X, 322 p. 6 illus. (Lecture Notes in Mathematics, Volume 2056) Softcover7 $89.95ISBN 978-3-642-30897-0

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R. Balakrishnan, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India; K. Ranganathan

A Textbook of Graph TheoryGraph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph the-ory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This textbook provides a solid background in the basic topics of graph theory, and is intended for an advanced undergraduate or beginning gra-duate course in graph theory. This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homo-morphisms and colorings and the uniqueness of the Mycielskian up to isomorphism.

Features 7 New edition extensively revised and up-dated 7 Includes two new chapters, one on domination in graphs and another on spectral properties of graphs 7 Contains a discussion on graph energy, a topic of current interest in spectral graph theory

Contents Preface to the Second Edition.- Preface to the First Edition.- 1 Basic Results.- 2 Directed Graphs.- 3 Connectivity.- 4 Trees.- 5 Independent Sets and Matchings.- 6 Eulerian and Hamiltonian Graphs.- 7 Graph Colorings.- 8 Planarity.- 9 Triangulated Graphs.- 10 Domination in Graphs.- 11 Spectral Properties of Graphs.- Bibliography.- Index.

Fields of interestGraph Theory

Target groupsGraduate


Due September 2012

2nd ed. 2012. XI, 471 p. 183 illus. (Universitext) Softcover7 $69.95ISBN 978-1-4614-4528-9

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J. Barnes, Caversham, Reading, UK

Gems of GeometryBased on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author‘s infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein‘s Theories of Relativity. Equally suitable as a gift for a youngs-ter or as a nostalgic journey back into the world of mathematics for older readers, John Barnes‘ book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment. In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

Features 7 Enjoyable book with a huge amount of colou-red figures, some produced in stereo 7 Brings new perspectives to even the most familiar of shapes 7 Also considers common artistic and literary interpretations of geometric figu-res 7 Detailed description of recommended further reading

Contents 1 The Golden Number.- 2 Shapes and Solids.- 3 The Forth Dimension.- 4 Projective Geometry.- 5 Topology.- 6 Bubbles.- 7 Harmony of the Spheres.- 8 Chaos and Fractals.- 9 Relativity.- 10 Finale.- A More on Four.- B Crystals.- C Stability.- D Stereo Images.- E Schlegel Images.- F Stability.- G Fano-land.- Bibliography.- Index.

Fields of interestGeometry

Target groupsProfessional/practitioner


Available

2nd ed. 2012. Approx. 440 p. 337 illus., 139 in color. Hardcover7 approx. $59.95ISBN 978-3-642-30963-2

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www.springer.com/978-3-642-30897-0



Mathematics springer.com/NEWSonline

24

P. Cardaliaguet, Université Paris-Dauphine, Paris, France; R. Cressman, Wilfrid Laurier University, Waterloo, ON, Canada (Eds)

Advances in Dynamic GamesTheory, Applications, and Numerical Methods for Differential and Stochastic Games

Contents Part I Evolutionary Games.- 1 Some Generali-zations of a Mutual Mate Choice Problem with Age Preferences.- 2 Signalling Victory to Ensure Dominance: A Continuous Model.- 3 Evolutionary Games for Multiple Access Control.- 4 Join Forces or Cheat: Evolutionary Analysis of a Consumer-Resource System.- Part II Dynamic and Differen-tial Games: Theoretical Developments.- 5 Strong Strategic Support of Cooperative Solutions in Differential Games.- 6 Characterization of Feed-back Nash Equilibrium for Differential Games.- 7 Nash Equilibrium Payoffs in Mixed Strategies.- 8 A Penalty Method Approach for Open-Loop Vari-ational Games with Equality Constraints.- 9 Nash Equilibrium Seeking for Dynamic Systems with Non-Quadratic Payoffs.- 10 A Uniform Tauberian Theorem in Optimal Control.- 11 E-equilibria for Multicriteria Games.- 12 Mean Field Games with Quadratic Hamiltonian: A Constructive Sche-me.- Part III Pursuit-Evasion Games and Search Games.- 13 Differential Game-Theoretic Approach to a Spatial Jamming Problem.- 14 Study of Linear Game with Two Pursuers and One Evader: Dif-ferent Strength of Pursuers.- 15 Salvo Enhanced No Escape Zone.- 16 One Method of Solving Differential Games Under Integrally Constrained Controls.- 17 Anglers‘ Fishing Problem.- 18 A Nonzero-Sum Search Game with Two Competiti-ve Searchers and a Target. [...]

Fields of interestsGame Theory, Economics, Social and Behav. Sciences; Game Theory/Mathematical Methods; Applications of Mathematics



Due September 2012

2013. IV, 332 p. 15 illus. in color. (Annals of the International Society of Dynamic Games, Volume 12) Hardcover7 $129.00ISBN 978-0-8176-8354-2

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A. N. Carvalho, Universidade de São Paulo, São Carlos , Brazil; J. A. Langa, Universidad de Sevilla, España; J. C. Robinson, University of Warwick, Mathematics InstituteCoventry, UK

Attractors for infinite-dimensional non-autonomous dynamical systemsThe book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of proces-ses to impose the minimum of restrictions on the nature of the non-autonomous dependence.

Features 7 Key Researcher 7 Obtains new results on the characterization of global attractors for processes and their perturbations 7 An up-to-date sum-mary of the field

Contents The pullback attractor.- Existence results for pull-back attractors.- Continuity of attractors.- Finite-dimensional attractors.- Gradient semigroups and their dynamical properties.- Semilinear Differential Equations.- Exponential dichoto-mies.- Hyperbolic solutions and their stable and unstable manifolds.- A non-autonomous compe-titive Lotka-Volterra system.- Delay differential equations.-The Navier–Stokes equations with non-autonomous forcing.- Applications to parabolic problems.- A non-autonomous Chafee–Infante equation.- Perturbation of diffusion and conti-nuity of attractors with rate.- A non-autonomous damped wave equation.- References.- Index.-

Fields of interestsPartial Differential Equations; Dynamical Systems and Ergodic Theory; Manifolds and Cell Comple-xes (incl. Diff.Topology)



Due September 2012

2012. XXIV, 412 p. 12 illus., 4 in color. (Applied Mathematical Sciences, Volume 182) Hardcover7 $129.00ISBN 978-1-4614-4580-7

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F. Cazals, P. Kornprobst, INRIA Sophia-Antipolis-Méditerranée, France (Eds)

Modeling in Computational Biology and BiomedicineA Multidisciplinary Endeavor

Foreword by: O. Faugeras, INRIA Sophia Antipolis - Méditerranée, France; J. Janin, Université Paris-Sud, France

Contents Foreword by Olivier Faugeras.- Foreword by Joël Janin.- Preface.- Part I Bioinformatics.- 1.Mo-deling Macro-molecular Complexes: a Journey Across Scales. F.Cazals, T.Dreyfus, and C.H. Robert.- 1.1.Introduction.- 1.2.Modeling Atomic Resolution.- 1.3.Modeling Large Assemblies.- 1.4.Outlook.- 1.5.Online Resources.- Referen-ces.- 2.Modeling and Analysis of Gene Regula-tory Networks. G.Bernot, J-P.Comet, A.Richard, M.Chaves, J-L.Gouzé, and F.Dayan.- 2.1.Intro-duction.- 2.2.Continuous and Hybrid Models of Genetic Regulatory Networks.- 2.3.Discrete Models of GRN.- 2.4.Outlook.- 2.5.Online Re-sources.- 2.6.Acknowledgments.- References.- Part II Biomedical Signal and Image Analysis.- 3.No-ninvasive Cardiac Signal Analysis Using Data Decomposition Techniques. V.Zarzoso, O.Meste, P.Comon, D.G.Latcu, and N.Saoudi.- 3.1.Preli-minaries and Motivation.- 3.2.T-Wave Alternans Detection via Principal Component Analysis.- 3.3.Atrial Activity Extraction via Independent Component Analysis.- 3.4.Conclusion and Outlook.- 3.5.Online Resources.- References.- 4.Deconvolution and Denoising for Confocal Microscopy. P.Pankajakshan, G.Engler, L.Blanc-Féraud, and J.Zerubia.- 4.1.Introduction.- 4.2.De-velopment of the Auxiliary Computational Lens.- 4.3.Outlook.- 4.4.Selected Online Resources. [...]

Fields of interestsMathematical and Computational Biology; Appli-cations of Mathematics; Computational Biology/Bioinformatics



Available

2012. X, 270 p. Hardcover7 approx. $119.00ISBN 978-3-642-31207-6

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A. Cegielski, University of Zielona Góra, Poland

Iterative Methods for Fixed Point Problems in Hilbert SpacesIterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define itera-tive methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from ge-neral properties of some classes of operators and from some general convergence theorems.

Features 7 The projection methods for fixed point prob-lems are presented in a consolidated way 7 Over 60 figures help to understand the properties of important classes of algorithmic operators 7 The convergence properties of projection methods follow from a few general convergence theorems presented in the monograph

Contents 1 Introduction.- 2 Algorithmic Operators.- 3 Convergence of Iterative Methods.- 4 Algorithmic Projection Operators.- 5 Projection methods.

Fields of interestsOptimization; Functional Analysis; Calculus of Variations and Optimal Control; Optimization



Available

2012. X, 318 p. 61 illus., 3 in color. (Lecture Notes in Mathematics, Volume 2057) Softcover7 $89.95ISBN 978-3-642-30900-7

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M. A. Clements, Illinois State University, Normal, IL, USA; A. J. Bishop, Monash University, Clayton, VIC, Australia; C. Keitel, Freie Universität Berlin, Germany; J. Kilpatrick, University of Georgia, Athens, GA, USA; F. K. Leung, The University of Hong Kong, Hong Kong (Eds)

Third International Handbook of Mathematics EducationContents Past, present and future dimensions of mathema-tics education: Introduction to the Third Interna-tional Handbook of Mathematics Education: M. A. (Ken) Clements.- VOLUME ONE.- SECTION A: SOCIAL, POLITICAL AND CULTURAL DI-MENSIONS IN MATHEMATICS EDUCATION.- Introduction to Section A: Social, Political and Cultural Dimensions in Mathematics Education: Christine Keitel.- 1. From the few to the many: Historical perspectives on who should learn ma-thematics: M. A. (Ken) Clements, C. Keitel, Alan J. Bishop, Jeremy Kilpatrick and Frederick Leung.- 2 Theories for studying social, political and cultural dimensions of mathematics education: Eva Jab-lonka, David Wagner and Margaret Walshaw.- 3. Understanding and overcoming “disadvantage” in learning mathematics : Lulu Healey and Arthur B. Powell.- 4. Beyond deficit models of learning mathematics: Sociocultural directions for change and research: Cristina Frade, Nadja Acioly-Régnier and Li Jun.- 5. Studying learners in intercultural contexts: Yoshinori Shimizu and Gaye Williams.- 6. Learners in transition between contexts: Tamsin Meaney and Troels Lange.-7. Critical perspectives on adults’ mathematics education: Jeff Evans, Tine Wedege and Keiko Yasukawa.- 8. The politics of equity and access in teaching and learning ma-thematics: Neil A. Pateman and Chap Sam Lim.- SECTION B: MATHEMATICS EDUCATION AS A FIELD OF STUDY. [...]

Fields of interestsMathematics, general; Educational Policy and Poli-tics; Social Sciences, general



Due September 2012

2012. XXV, 881 p. 113 illus., 67 in color. (Springer International Handbooks of Education, Volume 27) Hardcover7 approx. $539.00ISBN 978-1-4614-4683-5

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S. Cohen, Université Paul Sabatier, Toulouse, France; A. Kuznetsov, York University, Toronto, ON, Canada; A. E. Kyprianou, The University of Bath, UK; V. Rivero, CIMAT A.C., Guanajuato, Mexico

Lévy Matters IIRecent Progress in Theory and Applications: Functional Lévy Fields, and Scale Functions

This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which has been published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The expository articles in this second volume cover two impor-tant topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Levy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuz-netsov, Andreas E.

Features 7 Over the past 10-15 years, we have seen a re-vival of general Lévy processes theory as well as a burst of new applications 7 There is a lively and growing research community in this area 7 Ex-pository articles help to disseminate important theoretical and applied research to other resear-chers and in particular to young researchers like PhD students and Postdocs 7 Chapters attract different focus groups of readers

Contents Fractional Lévy Fields.- The Theory of Scale Func-tions for Spectrally Negative Lévy Processes

Fields of interestsMathematics, general; Probability Theory and Stochastic Processes



Available

2012. Approx. 185 p. 8 illus., 1 in color. (Lecture Notes in Mathematics / Lévy Matters, Volume 2061) Softcover7 $49.95ISBN 978-3-642-31406-3

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L. Cohen, City University of New York, NY, USA

The Weyl Operator and its GeneralizationThe discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of asso-ciating ordinary functions with non-commuting operators. Methods were proposed by Born/Jor-dan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been genera-lized and developed to a high degree.

Features 7 Numerous examples are worked, out illustra-ting each result 7 The applications to various fields are discussed in elementary fashion 7 The methods are extended to operators other than the standard ones

Contents Introduction.- The Fundamental Idea, Termino-logy, and Operator Algebra.- The Weyl Operator.- The Algebra of the Weyl Operator.- Product of Operators, Commutators, and the Moyal Sin Bra-cket.- Some Other Ordering Rules.- Generalized Operator Association.- The Fourier, Monomial, and Delta Function Associations.- Transformation Between Associations.- Path Integral Approach.- The Distribution of a Symbol and Operator.- The Uncertainty Principle.- Phase-Space Distribu-tions.- Amplitude, Phase, Instantaneous Frequen-cy, and the Hilbert Transform.- Time - Frequency Analysis.- The Transformation of Differential Equations into Phase Space.- The Representation of Functions.- The N Operator Case.

Fields of interestsPartial Differential Equations; Operator Theory; Mathematical Physics



Available

2013. 250 p. (Pseudo-Differential Operators, Volume 9) Softcover7 approx. $79.95ISBN 978-3-0348-0293-2

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G. Fasano, Thales Alenia Space Italia S.p.A, Turin, Italy; J. D. Pintér, Pintér Consulting Services Inc, Halifax, NS, Canada (Eds)

Modeling and Optimization in Space EngineeringContents Model Development and Optimization for Space Engineering: Concepts, Tools, Applications and Perspectives. János D. Pintér and Giorgio Fasano. -Practical Direct Collocation Methods for Compu-tational Optimal Control. Victor M. Becerra. - For-mation Flying Control for Satellites: Anti-windup Based Approach. Josep Boada, Christophe Prieur, Sophie Tarbouriech, Christelle Pittet and Cathe-rine Charbonnel. - The ESA NLP Solver WORHP. Christof Büskens and Dennis Wassel. -Global Optimization Approaches for Optimal Trajectory Planning. Andrea Cassioli, David Di Lorenzo, Marco Locatelli and Fabio Schoen. -Indirect Methods for the Optimization of Spacecraft Tra-jectories. Guido Colasurdo and Lorenzo Casalino. -Trajectory Optimization – Launch and Re-entry Vehicles. Francesco Cremaschi. -Global Optimiza-tion of Interplanetary Transfers with Deep Space Manoeuvres using Differential Algebra. Pierluigi Di Lizia, Roberto Armellin, Francesco Topputo, Franco Bernelli-Zazzera, and Martin Berz. -A Traffic Model for the International Space Station: An MIP Approach. Giorgio Fasano. -Global Opti-mization Approaches to Sensor Placement: Model Versions and Illustrative Results. Giorgio Fasano and János D. Pintér. -Space Module On-Board Sto-wage Optimization Exploiting Container Empty Volumes. Giorgio Fasano and Maria Chiara Vola. -Optimization Models for the Three-dimensional Container Loading Problem with Practical Cons-traints. [...]

Fields of interestsOptimization; Aerospace Technology and Astro-nautics; Mathematical Modeling and Industrial Mathematics



Due September 2012

2012. XV, 395 p. 145 illus., 88 in color. (Springer Optimization and Its Applications, Volume 73) Hardcover7 $129.00ISBN 978-1-4614-4468-8

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A. Guerraggio, University of Bocconi, Milano, Italy; G. Paolini, University of Rome, Italy

Vito Volterra

Transl. Italian: K. Williams, Turin, Italy

Vito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterra’s most important contributions to mathe-matics and their applications, as well as his out-standing organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theory and population dynamics (Lotka-Volterra model). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He became involved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche, CNR).

Features 7 Biography of famous mathematician 7 Great insights into the development of science in Italy 7 Life of Volterra in the context of Italian history

Contents I. Chronicles of Italian life.- II. Professor in Pisa.- III. The cats of Torino.- IV. Rome, public appoint-ments, the politician.- V. Days of firing from a dirigible.- VI. From war to peace: Italy’s National Research Council.- VII. The end of freedom.- VIII. After the cats, fish.- IX. Time runs out. [...].

Fields of interestHistory of Mathematical Sciences

Target groupsPopular/general


Available

2013. 240 p. 23 illus. Hardcover7 approx. $69.95ISBN 978-3-642-27262-2

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A. Gulisashvili, Ohio University, Athens, OH, USA

Analytically Tractable Stochastic Stock Price ModelsAsymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochas-tic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility.

Features 7 Comprehensive in scope 7 Results dis-cussed appear for the first time in a mathematical monograph 7 Unique source of information about analytically tractable stochastic volatility models

Contents Preface.- Aknowledgements.- 1.Volatility Pro-cesses.- 2.Stock Price Models with Stochastic Volatility.- 3.Realized Volatility and Mixing Dis-tributions.- 4.Integral Transforms of Distribution Densities.- 5.Asymptotic Analysis of Mixing Dis-tributions.- 6.Asymptotic Analysis of Stock Price Distributions.- 7.Regularly Varying Functions and Pareto Type Distributions.- 8.Asymptotic Analysis of Option Pricing Functions.- 9.Asymptotic Analysis of Implied Volatility.- 10.More Formulas for Implied Volatility.- 11.Implied Volatility in Models Without Moment Explosions.- Bibliogra-phy.- Index .

Fields of interestsQuantitative Finance; Analysis; Probability Theory and Stochastic Processes



Available

2012. V, 375 p. (Springer Finance) Hardcover7 approx. $99.00ISBN 978-3-642-31213-7

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A. Gut, University of Uppsala, Sweden

ProbabilityA Graduate Course

Like its predecessor, Probability starts from the premise that rather than being a purely mathema-tical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequa-lities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the itera-ted logarithm. After a discussion of generalizations and extensions, the book concludes with an ex-tensive chapter on martingales. The new edition is comprehensively updated, including scores of new problems and exercises, as well as new sections in the Inequalities and Random Variables chapters.

Features 7 Covers probability from a very applied per-spective 7 Many exercises involve mathematical modeling of random phenomena in very practical fields, including insurance/actuarial and the life sciences/biomedicine 7 Second edition compre-hensively updated, including all new exercises

Contents Preface to the First Edition.- Preface to the Second Edition.- Outline of Contents.- Notation and Sym-bols.- Introductory Measure Theory.- Random Va-riables.- Inequalities.- Characteristic Functions.- Convergence.- The Law of Large Numbers.- The Central Limit Theorem.- The Law of the Iterated Logarithm.- Limited Theorems.- Martingales.- Some Useful Mathematics.- References.- Index.

Fields of interestsProbability Theory and Stochastic Processes; Stati-stical Theory and Methods; Statistics, general



Due July 2012

2nd ed. 2013. X, 593 p. (Springer Texts in Statistics, Volume 75) Hardcover7 $89.95ISBN 978-1-4614-4707-8

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W. Ingram, Missouri University of Science and Technology, Rolla, MO, USA

An Introduction to Inverse Limits with Set-valued FunctionsInverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical sys-tems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful.

Feature 7 Provides a quick introduction to the subject of inverse limits with set-valued function Contains numerous examples and models of the inverse limits Several of the examples in this volume have not appeared elsewhere in print

Contents 1. Basics.- 2. Connectedness.- 3. Mapping verses Set-valued Functions.- 4. Mapping Theorems.- 5. Dimension.- 6. Problems.–Index.

Fields of interestsDynamical Systems and Ergodic Theory; Ordinary Differential Equations; Game Theory, Economics, Social and Behav. Sciences



Due September 2012

2012. XV, 102 p. 2 illus. (SpringerBriefs in Mathematics) Softcover7 $49.95ISBN 978-1-4614-4486-2

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28

T. Jager, Institut für Technologie, Karlsruhe, Germany

Black-Box Models of Computation in CryptologyGeneric group algorithms solve computational problems defined over algebraic groups without exploiting properties of a particular representation of group elements. This is modeled by treating the group as a black-box. The fact that a computati-onal problem cannot be solved by a reasonably restricted class of algorithms may be seen as support towards the conjecture that the problem is also hard in the classical Turing machine model. Moreover, a lower complexity bound for certain algorithms is a helpful insight for the search for cryptanalytic algorithms. Tibor Jager addresses several fundamental questions concerning alge-braic black-box models of computation: Are the generic group model and its variants a reasonable abstraction? What are the limitations of these models? Can we relax these models to bring them closer to the reality?

Feature 7 Black-Box Models of Computation

Contents Black-Box Models of Computation.- On Black-Box Ring Extraction and Integer Factorization.- On the Analysis of Cryptographic Assumptions in the Generic Ring Model.- The Generic Composite Residuosity Problem.- Semi-Generic Groups and Their Applications.

Fields of interestComputational Mathematics and Numerical Analysis



Available

2012. XII, 86 p. Softcover7 $89.95ISBN 978-3-8348-1989-5

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C. Laurent-Gengoux, Université de Metz, France; A. Pichereau, Université St Etienne, France; P. Vanhaecke, Université de Poitiers, Futuroscope Chasseneuil, France

Poisson StructuresPoisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and repre-sentation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases.

Features 7 First book about Poisson structures giving a comprehensive introduction as well as solid foundations to the theory 7 Unique structure of the volume tailored to graduate students or advanced researchers 7 Provides examples and exercises

Contents Introduction.- Part I Theoretical background.- 1.Poisson structures: basic definitions.- 2.Poisson structures: basic constructions.- 3.Multi-deriva-tions and Kähler forms.- 4.Poisson (co)homolo-gy.-5.Reduction.- Part II Examples.- 6.Constant Poisson structures, regular and symplectic manifolds.- 7.Linear Poisson structures and Lie algebras.- 8.Higher degree Poisson structu-res.- 9.Poisson structures in dimensions two and three.- 10.R-brackets and r-brackets.- 11.Poisson-Lie groups.- Part III Applications.- 12.Liouville integrable systems.- 13.Deformation quantizati-on.- 14.Appendix: Multilinear algebra.- Bibliogra-phy.- Index.- List of Notations.

Fields of interestsNon-associative Rings and Algebras; Differential Geometry; Topological Groups, Lie Groups



Available

2012. X, 460 p. (Die Grundlehren der mathematischen Wissenschaften, Volume 347) Hardcover7 approx. $129.00ISBN 978-3-642-31089-8

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J. Mallet-Paret, Brown University, Providence, RI, USA; J. Wu, York University, Toronto, ON, Canada; Y. Yi, Georgia Institute of Technology, Atlanta, GA, USA; H. Zhu, York University, Toronto, ON, Canada (Eds)

Infinite Dimensional Dynamical SystemsContents Preface.- Persistence of Periodic Orbits for Per-turbed Dissipative Dynamical Systems (J. Hale, G. Raugel).- Spectral Theory for Forward Nonau-tonomus Parabolic Equations and Applications (J. Mierczynski, W. Shen).- A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition (H. Fan, X. Lin).- Instabi-lity of Radially-Symmetric Spikes in Systems with Conserved Quantity (A. Pogan, A. Scheel).- Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays (M. Li, J. Wei).- Instabili-ty of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozel (W. Liu, M. Oh).- A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit (A. Hoffman, G. Wayne).- Littlewood Problem for a Singular Subquadratic Potential (X. Li, Y. Yi).- Semiflows for Neutral Equations with State-dependent Delay (H.-O. Walther).- Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations (Y. Chen, J. Wu).- Differential Equations with Random Delay (T.S. Doan, S. Siegmund).- Beyond Diffusion: Conditio-nal Dispersal in Ecological Models (C. Cosner).- Global Attractor of a Coupled Two-Cell Brussela-tor Model (Y. You).- Projectors on the Generalized Eigenspaces for Partial Differential Equations with Time Delay (A. Ducrot, P. Magal, S. Ruan). [...]

Fields of interestsDynamical Systems and Ergodic Theory; Partial Differential Equations; Ordinary Differential Equations



Due September 2012

2012. XII, 396 p. 15 illus., 2 in color. (Fields Institute Communications) Hardcover7 $129.00ISBN 978-1-4614-4522-7

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29

H. Marubayashi, Tokushima Bunri University, Japan; F. Van Oystaeyen, University of Antwerp, Belgium

Prime Divisors and Noncommutative Valuation TheoryClassical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for cur-ves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become po-pular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective cal-culations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras.

Features 7 Describes different generalizations of valua-tions from the common generalized concept of primes in algebras 7 Combines the arithmetic of finite dimensional central simple algebras with new theory for infinite dimensional ones 7 Mi-xing methods concerning value functions, valua-tion filtrations and orders over valuation rings for the study of new classes of algebras, e.g. quantized algebras, Weyl algebras and Hopf algebras

Contents 1. General Theory of Primes.- 2. Maximal Orders and Primes.- 3. Extensions of Valuations to some Quantized Algebras

Fields of interestsAlgebra; Geometry; Algebraic Geometry



Available

2012. Approx. 230 p. (Lecture Notes in Mathematics, Volume 2059) Softcover7 $59.95ISBN 978-3-642-31151-2

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M. A. Matt, Mannheim, Germany

Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary SmoothnessMichael A. Matt constructs two trivariate local Lagrange interpolation methods which yield opti-mal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation me-thod is based on cubic C1 splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahed-ron is divided into four subtetrahedra, and the Worsey-Farin split, where each tetrahedron is divided into twelve subtetrahedra, of a tetrahedral partition.

Feature 7 Two trivariate local Lagrange interpolation methods are constructed which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition

Contents Lagrange Interpolation on Type-4 Partitions.- Trivariate Lagrange Interpolation with C² Splines.- Cr Macro-Element over the Clough-Tocher Split.- Cr Macro-Element over the Alfeld Split.- Cr Macro-Element over the Worsey Farin Split.

Fields of interestApplications of Mathematics



Available

2012. XVI, 370 p. 87 illus., 2 in color. Softcover7 $109.00ISBN 978-3-8348-2383-0

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T. Nau, Konstanz, Germany

Lp-Theory of Cylindrical Boundary Value ProblemsAn Operator-Valued Fourier Multiplier and Functional Calculus Approach

Tobias Nau addresses initial boundary value problems in cylindrical space domains with the aid of modern techniques from functional analysis and operator theory. In particular, the author uses concepts from Fourier analysis of functions with values in Banach spaces and the operator-valued functional calculus of sectorial operators. He applies abstract results to concrete problems in cylindrical space domains such as the heat equati-on subject to numerous boundary conditions and equations arising from fluid dynamics.

Contents Fourier Transform and Fourier Series.- Operator-valued Fourier multipliers and functional calcu-lus.- Maximal Lp-Regularity.- Parameter-Elliptic Boundary Value Problems in Cylindrical Do-mains.- Periodic and Mixed Dirichlet-Neumann Boundary Conditions for the Laplacian.- Stokes Problem and Helmholtz Projection in Rectangular Cylinders.

Fields of interestFourier Analysis



Available

2012. XVI, 188 p. 14 illus. in color. Softcover7 $99.00ISBN 978-3-8348-2504-9

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30

J.-P. Penot, Université de Pau et des Pays de l‘Adour, Pau, France

Calculus Without DerivativesCalculus Without Derivatives expounds the foun-dations and recent advances in nonsmooth analy-sis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular opti-mization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, va-riational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of diffe-rential calculus and includes a section about the calculus of variations.

Features 7 Includes all necessary preliminary mate-rial 7 Introduces fundamental aspects of nonsmooth analysis that impact many applica-tions 7 Presents a balanced picture of the most elementary attempts to replace a derivative with a one-sided generalized derivative called a subdiffe-rential 7 Includes references, notes, exercises and supplements that will give the reader a thorough insight into the subject

Contents Preface.- 1 Metric and Topological Tools.- 2 Elements of Differential Calculus.- 3 Elements of Convex Analysis.- 4 Elementary and Viscosity Subdifferentials.- 5 Circa-Subdifferentials, Clarke Subdifferentials.- 6 Limiting Subdifferentials.- 7 Graded Subdifferentials, Ioffe Subdifferentials.- References.- Index .

Fields of interestsAnalysis; Real Functions; Optimization



Due September 2012

2012. XIV, 488 p. (Graduate Texts in Mathematics, Volume 266) Hardcover7 $89.95ISBN 978-1-4614-4537-1

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A. Plakhov, University of Aveiro, Portugal

Exterior BilliardsSystems with Impacts Outside Bounded Domains

A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections from the boundary of a domain. Exterior Billiards presents billiards in the complement of domains and their applications in aerodynamics and geometrical optics. This book distinguishes itself from existing literature by presenting billiard dynamics outside bounded do-mains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chap-ters 2 and 3 are focused on problems of minimal resistance and Newton’s problem in media with positive temperature.

Features 7 Examines properties of billiard dynamics outside bounded domains 7 Includes topics such as scattering, resistance, invisibility and retro-reflection 7 Useful for mathematicians working in dynamical systems

Contents -Notation and synopsis of main results. -Problem of minimum resistance to translational motion of bodies. -Newton’s problem in media with positive temperature. -Scattering in billiards. -Problems of optimal mass transportation. -Problems on opti-mization of mean resistance. -Magnus effect and dynamics of a rough disc. -On invisible bodies. –Retroreflectors.

Fields of interestsDynamical Systems and Ergodic Theory; Calculus of Variations and Optimal Control; Optimization; Mathematical Modeling and Industrial Mathe-matics



Due September 2012

2012. XVI, 370 p. 104 illus., 57 in color. Hardcover7 $109.00ISBN 978-1-4614-4480-0

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E. R. Rodrigues, UNAM, Instituto de Matemáticasm, Mexico; J. A. Achcar, Universidade de São Paulo, Departamento de Medicina Social, Brazil

Applications of Discrete-time Markov Chains and Poisson Processes to Air Pollution Modeling and Studies In this brief we consider some stochastic models that may be used to study problems related to en-vironmental matters, in particular, air pollution. The impact of exposure to air pollutants on people‘s health is a very clear and well docu-mented subject. Therefore, it is very important to obtain ways to predict or explain the behaviour of pollutants in general. Depending on the type of question that one is interested in answering, there are several of ways studying that problem. Among them we may quote, analysis of the time series of the pollutants‘ measurements, analysis of the information obtained directly from the data, for instance, daily, weekly or monthly averages and standard deviations. Another way to study the behaviour of pollutants in general is through mathematical models.

Feature 7 Focused volume on some stochastic models used to study problems related to environmental matters.

Contents Introduction.- Discrete-time Markov chain models.- Poisson models and their application to ozone data.- Some counting processes and ozone air pollution.- Comments.- Acknowledge-ments.- References .

Fields of interestsProbability Theory and Stochastic Processes; Monitoring/Environmental Analysis; Atmospheric Protection/Air Quality Control/Air Pollution



Due October 2012

2012. X, 99 p. (SpringerBriefs in Mathematics) Softcover7 $49.95ISBN 978-1-4614-4644-6

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31

D. A. Tran, University of Massachusetts, Boston, MA, USA

Data Storage for Social NetworksA Socially Aware Approach

Evidenced by the success of Facebook, Twitter, and LinkedIn, online social networks (OSNs) have become ubiquitous, offering novel ways for people to access information and communicate with each other. As the increasing popularity of social networking is undeniable, scalability is an important issue for any OSN that wants to serve a large number of users. Storing user data for the entire network on a single server can quickly lead to a bottleneck, and, consequently, more servers are needed to expand storage capacity and lower data request traffic per server. Adding more servers is just one step to address scalability. The next step is to determine how best to store the data across multiple servers. This problem has been widely-studied in the literature of distributed and database systems. OSNs, however, represent a different class of data systems.

Features 7 Discusses existing storage solutions for today's most popular online social networks (OSNs). 7 Hot topic of social networks will appeal to a broad readership 7 Fuses existing literature and new methods

Contents 1. Introduction (Amazon’s Dynamo, Google’s BigTable, Apache Cassandra).-2. Social Locality in Data Storage (Perfect vs. Imperfect Social Locality, Assumptions and Notations, Optimization Objec-tives, Multi-Objective Optimization).- 3. S-PUT (Approach, Algorithm, Numerical Results, Notes).- 4. S-CLONE (Approach, Algorithm, Numerical Results, Notes)- 5. Epilogue. –References.

Fields of interestsOptimization; Database Management



Due September 2012

2012. VIII, 46 p. 12 illus., 10 in color. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-4635-4

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A.-V. Vuong, Kaiserslautern, Germany

Adaptive Hierarchical Isogeometric Finite Element Methods Isogeometric finite elements combine the nu-merical solution of partial differential equations and the description of the computational domain given by rational splines from computer aided geometric design. This work gives a well-founded introduction to this topic and then extends isogeometric finite elements by a local refinement technique, which is essential for an efficient adap-tive simulation. Thereby a hierarchical approach is adapted to the numerical requirements and the relevant theoretical properties of the basis are ensured. The computational results suggest the increased efficiency and the potential of this local refinement method.

Feature 7 publication in the field of natural and mathe-matical sciences

Contents Introduction.– Prerequisites from Applied Geo-metry and Spline Theory. – Mathematical Models and Finite Element Analysis. – Isogeometric Analysis. – Local Refinement for Isogeometric Analysis. – Conclusions.

Fields of interestMathematics, general



Available

2012. XX, 128 p. 63 illus., 20 in color. Softcover7 $89.95ISBN 978-3-8348-2444-8

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Z. Xu, PLA University of Science and Technology, Nanjing, China

Linguistic Decision MakingTheory and Methods

„Linguistic Decision Making: Theory and Me-thods“ is the first monograph which mainly deals with the interdisciplinary subject of computing with words, information fusion and decision analysis. It provides a thorough and systematic introduction to the linguistic aggregation opera-tors, linguistic preference relations, and various models for and approaches to multi-attribute decision making with linguistic information. It also offers various practical examples with tables and figures to illustrate the theory and methods discussed. Researchers and professionals engaged in the relevant fields will find it a useful reference book. Professor Zeshui Xu, senior member of the IEEE, works at the PLA University of Science and Techology, China.

Features 7 The first monograph published on linguistic decision making: theory and methods 7 A systematic survey of various types of linguistic ag-gregation operators 7 A comprehensive coverage of distinct structures of linguistic preference relations 7 Detailed introduction and insights into a variety of models and approaches for multi-attribute decision making under linguistic assessments

Contents Linguistic Evaluation Scales.- Linguistic Aggrega-tion Operators.- Linguistic Preference Relations.- Approaches to Linguistic Multi-Attribute Decision Making.

Fields of interestsApplications of Mathematics; Computing Metho-dologies; Operation Research/Decision Theory



Available

Jointly published with Science Press

Distribution rights in China: Science Press

2013. 300 p. 41 illus. Hardcover7 $109.00ISBN 978-3-642-29439-6

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32

Z. Xu, PLA University of Science and Technology, Nanjing, China; X. Cai, The Chinese University of Hong Kong, China

Intuitionistic Fuzzy Information AggregationTheory and Applications

„Intuitionistic Fuzzy Information Aggregation: Theory and Applications“ is the first book to provide a thorough and systematic introduction to intuitionistic fuzzy aggregation methods, the correlation, distance and similarity measures of in-tuitionistic fuzzy sets and various decision-making models and approaches based on the above-menti-oned information processing tools.

Features 7 First monograph published on intuitionistic fuzzy information aggregation theory and applica-tions 7 Presents a comprehensive and in-depth knowledge of the latest research results 7 Offers numerous practical examples for better understan-ding of the described theory and methods

Contents Intuitionistic Fuzzy Information Aggregation.- Interval-Valued Intuitionistic Fuzzy Information Aggregation.- The Correlation, Distance and Similarity Measures of Intuitionistic Fuzzy Sets.- Intuitionistic Fuzzy Clustering Algorithms.- The Decision-Making Models and Approaches Based on Intuitionistic Preference Relations.- Projection Models-Based Approaches to Intuitionistic Fuzzy Multi-Attribute Decision-Making.- Dynamic Intuitionistic Fuzzy Multi-Attribute Decision-Making.- Nonlinear Optimization Models for Multiple Attribute Group Decision Making with Intuitionistic Fuzzy Information.

Fields of interestsOperations Research, Management Science; Computing Methodologies; Appl.Mathematics/Computational Methods of Engineering



Available

Jointly published with Science Press

Distribution rights in China: Science Press

2013. Approx. 450 p. 97 illus. Hardcover7 $129.00ISBN 978-3-642-29583-6

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cairo university, giza, egypt; caversham, reading, uk gems ......dynamical systems the book treats...

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