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Mathematics springer.com/NEWSonline

28

K. Alladi, University of Florida, Gainesville, FL, USA

Ramanujan‘s Place in the World of MathematicsEssays on Ramanujan‘s Work and Impact

Contents Foreword.- Preface.- Part I: Ramanujan and other mathematical luminaries.- Chapter 1: Ramanu-jan - an estimation.- Chapter 2: Ramanujan - the second century.- Chapter 3: L. J. Rogers - a contemporary of Ramanujan.- Chapter 4: P. A. MacMahon - Ramanujan‘s distinguished contem-porary.- Chapter 5: Fermat and Ramanujan - a comparison.- Chapter 6: J. J. Sylvester - Ramanu-jan‘s illustrious predecessor.- Chapter 7: Erdos and Ramanujan - legends of twentieth century math-ematics.- Chapter 8: C. G. J. Jacobi - algorist par-excellence.- Chapter 9: Evariste Galois - founder of group theory.- Chapter 10: Leonhard Euler - most prolific mathematician in history.- Chapter 11: G. H. Hardy - Ramanujan‘s mentor.- Chapter 12: J. E. Littlewood - Ramanujan‘s contemporary and Hardy‘s collaborator.- Chapter 13: Neils Henrik Abel - Norwegian mathematical genius.- Chapter 14: Issai Schur - Ramanujan‘s German contempo-rary.- Chapter 15: Robert Rankin - Scottish link with Ramanujan.- Part II: On some aspects of Ra-manujan‘s mathematics.- Chapter 16: Ramanujan and pi.- Chapter 17: Ramanujan and partitions.- Chapter 18: Major progress on a problem of Ra-manujan.- Part III: Reviews.- Chapter 19: Review of “Srinivasa Ramanujan: The Lost Notebook and other unpublished papers”.- Chapter 20: Review of “The man who knew infinity - book by Robert Kanigel”.- Chapter 21: Review of “Ramanujan: Let-ters and Commentary - book by Bruce Berndt and Robert Rankin”.- Chapter 22: Review of “Ramanu-jan: Essays and Surveys - book by Bruce Berndt and Robert Rankin”. [...]

Fields of interestsMathematics, general; Number Theory; History of Mathematical Sciences

Target groupsPopular/general

Discount groupProfessional Non-Medical

Due October 2012

2013. Approx. 120 p. 23 illus. Hardcover7 approx. $59.95ISBN 978-81-322-0766-5

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M. Bader, Munich Center of Advanced Computing, Garching, Germany

Space-Filling CurvesAn Introduction with Applications in Scientific Computing

The present book provides an introduction to us-ing space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representa-tion of SFC and on resulting algorithms.

Features 7 Connects the different techniques to describe space-filling curves to corresponding algo-rithms 7 Connects space-filling curves and respective orders to regular and adaptive meshes for discretisation 7 Describes parallelisation and cache-efficient algorithms based on space-filling curves 7 Provides a section on references to both pioneering and current research on space-filling curves in scientific computing

Contents Two Motivating Examples.- How to Construct Space-Filling Curves.- Grammar-Based De-scription of Space-Filling Curves.- Arithmetic Representation of Space-Filling Curves.- Approxi-mating Polygons.- Sierpinski Curves.- Further Space-Filling Curves.- Space-Filling Curves in 3D.- Refinement Trees and Space-Filling Curves.- Parallelisation with Space-Filling Curves.- Lo-cality Properties of Space-Filling Curves.- Si-erpinski Curves on Triangular and Tetrahedral Meshes.- Case Study: Cache Efficient Algorithms for Matrix Operations.- Case Study: Numerical Simulation on Spacetree Grids Using Space-Filling Curves.- Further Applications of Space-Filling Curves.- Solutions to Selected Exercises.- Refer-ences.- Index

Fields of interestsComputational Science and Engineering; Algo-rithms; Applications of Mathematics

Target groupsUpper undergraduate


Due September 2012

2012.XIII, 278 p. 357 illus., 323 in color. (Texts in Computational Science and Engineering, Volume 9) Hardcover7 $89.95ISBN 978-3-642-31045-4

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P. Biane, Université Paris-Est, Champs-Sur-Marne, France; A. Guionnet, Ecole Normale Supérieure de Lyon, France; D.‑V. Voiculescu, University of California, Berkeley, CA, USA

Noncommutative Probability and Random Matrices at Saint-FlourBiane, Philippe: Non-commutative stochastic calculus.-Voiculescu, Dan-Virgil: Lectures on free probability.- Guionnet, Alice: Large random matrices: Lectures on macroscopic asymptotics.

Contents Biane, Philippe: Non-commutative stochastic calculus.-Voiculescu, Dan-Virgil: Lectures on free probability.- Guionnet, Alice: Large random matrices: Lectures on macroscopic asymptotics.

Fields of interestsProbability Theory and Stochastic Processes; Functional Analysis; Statistics and Computing/Statistics Programs

Target groupsResearch


Due October 2012

Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 1608 (1995), 1738 (2000) and 1957 (2009).

2013. Approx. 480 p. (Probability at Saint-Flour) Softcover7 approx. $69.95ISBN 978-3-642-32798-8

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www.springer.com/978-81-322-0766-5



News 9/2012 Mathematics

29

B. M. Brown, M. S. Eastham, K. M. Schmidt, Cardiff University, Wales, UK

Periodic Differential OperatorsPeriodic differential operators have a rich math-ematical theory as well as important physical applications. They have been the subject of inten-sive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Features 7 Comprehensive treatment of one-dimensional periodic systems from the differential equation, boundary-value problem and operator-theoretic points of view 7 Unified analysis of periodic Sturm-Liouville- and Dirac-type operators by the use of oscillation methods 7 Study of perturbed periodic problems

Contents Preface.- 1 Floquet Theory.- 2 Oscillations.- 3 Asymptotics.- 4 Spectra.- 5 Perturbations.

Fields of interestsOrdinary Differential Equations; Operator Theory



Due November 2012

2013. VIII, 218 p. (Operator Theory: Advances and Applications, Volume 230) Hardcover7 approx. $119.00ISBN 978-3-0348-0527-8

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A. Capietto, Università di Torino, Italy; P. Kloeden, Universitaet Frankfurt, Germany; J. Mawhin, Université Catholique de Louvain, Belgium; S. Novo, E.T.S. de Ingenieros Industriales de Valladolid, Spain; M. Ortega, Universidad de Granada, Spain

Stability and Bifurcation Theory for Non-Autonomous Differential EquationsCetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera

Scientific editors: R. Johnson, Universitá Firenze, Italy; M. P. Pera, Università degli Studi di Firenze, Italy

This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E.

Features 7 Up-to-date study of ordinary and functional differential equations 7 Use of topological and dynamical methods and comparison of such methods 7 Speakers are all leading experts in the field

Contents The Maslov index and global bifurcation for non-linear boundary value problems.- Discrete-time nonautonomous dynamical systems.- Resonance problems for some non-autonomous ordinary dif-ferential equations.- Non-autonomous functional differential equations and applications.- Twist mappings with non-periodic angles.

Fields of interestsOrdinary Differential Equations; Difference and Functional Equations; Dynamical Systems and Ergodic Theory



Due November 2012

2013. Approx. 315 p. 5 illus. in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2065) Softcover7 $89.95ISBN 978-3-642-32905-0

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Y.‑J. Chiang, University of Mary Washington, Fredericksburg, VA, USA

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills FieldsHarmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose cur-vature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up.

Features 7 Presents the recent crucial developments of harmonic maps into biharmonic maps, of wave maps into biwave maps and of Yang-Mills fields into bi-Yang-Mills fields 7 Discusses exponential harmonic maps, exponential wave maps and ex-ponential Yang-Mills fields 7 Introduces biwave maps (generalizing wave maps) and bi-Yang-Mills fields (generalizing Yang-Mills fields)

Contents Preface. 1 Harmonic Maps.- 2 Wave Maps.-3 Yang-Mills Fields.- 4 Biharmonic Maps.- 5 Biwave Maps.- 6 Bi-Yang-Mills Fields.-7 Exponential Har-monic Maps.-8 Exponential Wave Maps.- Index.

Fields of interestsGlobal Analysis and Analysis on Manifolds; Dif-ferential Geometry; Partial Differential Equations



Due November 2012

2012.Approx. 370 p. (Frontiers in Mathematics) Softcover7 approx. $89.95ISBN 978-3-0348-0533-9

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E. Çınlar, R. J. Vanderbei, Princeton University, Princeton, USA

Real and Convex AnalysisThis book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. In the first three chap-ters, the authors lay the foundational material and cover the all-important “four-C’s”: convergence, completeness, compactness, and continuity. In subsequent chapters, the basic tools of analysis are used to give brief introductions to differential and integral equations, convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.

Features 7 First undergraduate text that provides ac-cessible introduction to real and convex analy-sis 7 Top authors from Princeton University (both published previously successful books) 7 Lots of examples and exercises

Contents Sets and Functions.- Metric Spaces.- Functions on Metric Spaces.- Differential and Integral Equa-tions.- Convexity.-Convex Optimization.- Mea-sure and Integration.- Bibiography.-Index.-

Fields of interestsAnalysis; Appl.Mathematics/Computational Methods of Engineering; Operations Research, Management Science

Target groupsUpper undergraduate


Due November 2012

2013. XII, 163 p. 23 illus., 2 in color. (Undergraduate Texts in Mathematics) Hardcover7 $49.95ISBN 978-1-4614-5256-0

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D. v. Dalen, Utrecht University, Netherlands

Logic and StructureDirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a com-prehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing rec-ognition of constructive methods and principles, intuitionistic logic and Kripke semantics is care-fully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel‘s first incompleteness theorem is self-contained and provides a systematic exposition of the neces-sary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.

Features 7 Features a self-contained introduction into classical and intuitionistic logic using Gentzen’s natural deduction 7 Includes the basics of recur-sion, proof and model theory (including a new section on ultraproducts) 7 Gives a comprehen-sive account of Goedel’s Incompleteness Theorem within the framework of natural deduction

Contents Introduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normaliza-tion.- Gödel‘s theorem.

Fields of interestMathematical Logic and Foundations

Target groupsGraduate


Due November 2012

5th ed. 2013. Approx. 285 p. (Universitext) Softcover7 approx. $59.95ISBN 978-1-4471-4557-8

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A. Deitmar, Universität Tübingen

Automorphic FormsAutomorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles‘s proof of Fermat‘s Last Theorem. This text provides a concise introduc-tion to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essen-tial aspects and restricting it to the ‚base field‘ of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.

Features 7 Presents an elementary introduction that requires only few pre-requisites 7 Introduces a host of different techniques such as representa-tion theory, adeles and ideles, and the methods of Tate's thesis 7 Combines the classical and ana-lytical viewpoint and the modern representation-theoretic approach and reveals their interplay

Contents Doubly periodic functions.-Modular forms for SL2(Z).-Representations of SL2(R).-p-adic numbers.-Adeles and ideles.-Tate’s thesis.-Auto-morphic representations of GL2(A).-Automorphic L-functions.

Fields of interestsMathematics, general; Number Theory; Group Theory and Generalizations



Due October 2012

2013. XII, 252 p. (Universitext) Softcover7 $69.95ISBN 978-1-4471-4434-2

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31

F. den Hollander, University of Leiden, The Netherlands; S. A. Molchanov, The University of North Carolina, Charlotte, NC, USA; O. Zeitouni, Weizmann Institute of Science, Rehovot, Israel

Random Media at Saint-FlourMolchanov, S.: Lectures on random media.- Zeitouni, Ofer: Random walks in random environment.-den Hollander, Frank: Random polymers

Contents Molchanov, S.: Lectures on random media.- Zeitouni, Ofer: Random walks in random environment.-den Hollander, Frank: Random polymers

Fields of interestsProbability Theory and Stochastic Processes; Sta-tistics and Computing/Statistics Programs



Due October 2012

2013. Approx. 570 p. (Probability at Saint-Flour) Softcover7 approx. $69.95ISBN 978-3-642-32948-7

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New SeriesF. Diacu, University of Victoria, BC, Canada

Relative Equilibria of the Curved N-Body ProblemThe guiding light of this monograph is a question easy to understand but difficult to answer: {What is the shape of the universe? In other words, how do we measure the shortest distance between two points of the physical space? Should we follow a straight line, as on a flat table, fly along a circle, as between Paris and New York, or take some other path, and if so, what would that path look like? If you accept that the model proposed here, which assumes a gravitational law extended to a universe of constant curvature, is a good approximation of the physical reality (and I will later outline a few arguments in this direction), then we can answer the above question for distances compa-rable to those of our solar system. More precisely, this monograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, not surprising for such small cosmic scales. Physicists take the flatness of space for granted in regions of that size.

Features 7 Understanding of the geometric shape of the universe 7 New mathematical re-sults 7 Bridges laid between several fields of mathematics 7 Opening of new directions of research 7 Clearly exposed material

Contents Introduction.- Preliminary developments.- Equa-tions of motion.- Isometric rotations.- Relative equilibria (RE).- Fixed Points (FP).- Existence criteria.- Qualitative behavior.- Positive elliptic RE.- Positive elliptic-elliptic RE.- Negative RE.- Polygonal RE.- Lagrangian and Eulerian RE.- Saari’s conjecture.

Fields of interestsDynamical Systems and Ergodic Theory; Ordinary Differential Equations; Mathematics, general


Due August 2012

2012.XIV, 143 p. 9 illus. (Atlantis Series in Dynamical Systems, Volume 1) Hardcover7 $109.00ISBN 978-94-91216-67-1

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F. V. Dolzhansky

Fundamentals of Geophysical HydrodynamicsScientific editors: A. Gledzer, E. Gledzer, Oboukhov Institute of Atmospheric Physics, Moscow, Russia; Transl. English: B. Khesin, University of Toronto, ON, Canada

This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation.

Features 7 Comprehensive treatment of the fundamentals of geophysical hydrodynamics 7 Fairly system-atic exposition 7 Broad range of topics 7 Based on graduate and undergraduate courses at the Moscow Institute of Physics and Technolo-gy 7 Ideal companion to the complexities of the topic for students and researchers in mathematics, physics, meteorology and engineering

Contents Preface.- Part I Main Principles and Laws of Mo-tion of an Ideal Fluid.- Part II Quasi-geostrophic Approximations of the Equations of Motion of Rotating Barotropic and Baroclinic Fluids.- Part III Hydrodynamic Stability and Atmospheric Dy-namics.- Part IV Friction in Geophysical Bound-ary Layers and Their Models.- Part V Mechanical Prototypes of Equations of Motion of a Rotating Stratified Fluid and a Toy Model of Atmospheric Circulation.- Part VI Appendices.- Index

Fields of interestsMathematical Applications in the Physical Sci-ences; Geophysics and Environmental Physics; Hydrogeology



Due November 2012

2013. XIV, 294 p. 35 illus. (Encyclopaedia of Mathematical Sciences, Volume 103) Hardcover7 $139.00ISBN 978-3-642-31033-1

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32

G. Gentili, University of Firenze, Italy; I. Sabadini, Politecnico di Milano, Italy; M. Shapiro, Michigan State University, East Lansing, MI, USA; F. Sommen, University of Gent, Belgium; D. C. Struppa, Chapman University, Orange, CA, USA (Eds)

Advances in Hypercomplex AnalysisFeatures 7 New trends in mathematics 7 Applied math-ematics 7 International leading specialists

Contents C. Bisi, C. Stoppato: Regular vs. classical Mobius transformations of the quaternionic unit ball.- F. Brackx, H. De Bie, Hennie De Schepper: Distributional Boundary Values of Harmonic Potentials in Euclidean Half-space as Fundamental Solutions of Convolution Operators in Clifford Analysis.- F. Colombo, J.O. Gonzalez-Cervantes, M.E. Luna-Elizarraras, I. Sabadini, M. Shapiro: On two approaches to the Bergman theory for slice regular functions.- C. Della Rocchetta, G. Gentili, G. Sarfatti: A Bloch- Landau Theorem for slice regular functions.- M. Ku, U. Kahler, P. Cerejeiras: Dirichlet-type problems for the iterated Dirac operator on the unit ball in Clifford analysis.- A. Perotti: Fueter regularity and slice regularity: meeting points for two function theories.- D.C. Struppa: A note on analytic functionals on the complex light cone.- M.B. Vajiac: The S-spectrum for some classes of matrices.- F. Vlacci: Regular Composition for SliceRegular Functions of Qua-ternionic Variable.

Fields of interestsMathematics, general; Analysis

Target groupsProfessional/practitioner


Due November 2012

2013. X, 240 p. (Springer INdAM Series) Hardcover7 approx. $119.00ISBN 978-88-470-2444-1

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B. Goldengorin, Nizhny Novgorod, Russia; P. Pardalos, University of Florida, Gainesville, FL, USA

Data Correcting Algorithms in Combinatorial Optimization Data Correcting Algorithms in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinato-rial optimization problems. Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Travel-ing Salesman Problem and its variations, Maxi-mum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis as well as some classes of Scheduling Problems.

Features 7 Focuses on algorithmic applications of well known polynomially solvable special cases of computationally intractable problems 7 Dis-cusses design of practically efficient algorithms for solving wide classes of combinatorial optimization problems 7 Presents a new approach to study optimization problems both from theoretical and practical points of view

Contents -1. Introduction. -2. Maximization of Submodu-lar Functions: Theory and Algorithms. -3. Data Correcting Approach for the Maximization of Submodular Functions. -4. Data Correcting Ap-proach for the Simple Plant Location Problem. –References.

Fields of interestsGraph Theory; Optimization; Data Structures



Due September 2012

2012.VIII, 116 p. 41 illus. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-5285-0

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C. C. Graham, University of British Columbia, Vancouver, BC, Canada; K. E. Hare, University of Waterloo, ON, Canada

Interpolation and Sidon Sets for Compact GroupsUnderstanding special sets of integers was clas-sically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets. It is a unique book, aimed at both new and experienced researchers. In particular, this is the only book in English which features a complete treatment of the Pisier-Bour-gain results on Sidon sets, many of which were originally in French, in hard to access publica-tions. Applications of the P-B results, due to Pisier, Bourgain, Ramsey, and the authors are included. The book introduces the reader to a wealth of methods important in mathematics today: topo-logical, probabilistic, algebraic, combinatoric and analytic.

Features 7 Only book on interpolation sets 7 Only book in English with Pisier-Bourgain results 7 Brings together results from topology, probability, combi-natorics, algebra and analysis

Contents Preface .- Introduction .- Hadamard Sets.- $\epsilon$-Kronecker sets.- Sidon sets: Introduction and decomposition properties.- Characterizations of $I_0$ sets.- Proportional characterizations of Sidon sets.- Decompositions of $I_0$ sets.- Sizes of thin sets.- Sets of zero discrete harmonic den-sity.- Related results.-Open problems.- Appendices (Groups, Probability, Combinatoric results,...).- Bibliography.- Author index.- Subject index.- In-dex of notation.

Fields of interestsAbstract Harmonic Analysis; Fourier Analysis; Functional Analysis



Due December 2012

2013. XII, 256 p. 60 illus., 30 in color. (CMS Books in Mathematics) Hardcover7 approx. $109.00ISBN 978-1-4614-5391-8

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33

G. R. Grimmett, Cambridge University, UK; H. Kesten, Cornell University, Ithaca, NY, USA

Percolation Theory at Saint-FlourGrimmett, Geoffrey: Percolation and disordered systems.- Kesten, Harry: Aspects of first passage percolation.

Contents Introduction.- Grimmett, Geoffrey: Percolation and disordered systems.- Kesten, Harry: Aspects of first passage percolation.

Fields of interestsProbability Theory and Stochastic Processes; Sta-tistics and Computing/Statistics Programs



Due October 2012

Originally published in the Lecture Notes in Mathematics volumes 1180 (1986) and 1665 (1997).

2012.Approx. 305 p. (Probability at Saint-Flour) Softcover7 approx. $49.95ISBN 978-3-642-32508-3

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M. H. Holmes, Rensselaer Polytechnic Institute, Troy, NY, USA

Introduction to Perturbation MethodsThis introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied math-ematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as bound-ary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equa-tions. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new mate-rial on transcedentally small terms, Kummer‘s function, weakly coupled oscillators and wave interactions.

Features 7 Lots of examples and exercises 7 Class test for over 20 years 7 Includes delay equations

Contents Preface.- Preface to Second Edition.- Introduction to Asymptotic Approximations.- Matched Asymp-totic Expansions.- Multiple Scales.- The WKB and Related Methods.- The Method of Homogeniza-tion- Introduction to Bifurcation and Stability.- References.- Index.

Fields of interestsPartial Differential Equations; Ordinary Differen-tial Equations; Analysis



Due December 2012

2nd ed. 2013. X, 430 p. (Texts in Applied Mathematics, Volume 20) Hardcover7 approx. $74.95ISBN 978-1-4614-5476-2

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L. Lakatos, Eötvös Loránd University, Budapest, Hungary; L. Szeidl, Széchenyi István University, Győr, Hungary; M. Telek, Technical University of Budapest, Hungary

Introduction to Queueing Systems with Telecommunication ApplicationsThe book is composed of two main parts: math-ematical background and queueing systems with applications. The mathematical background is a self containing introduction to the stochastic processes of the later studies queueing systems. It starts with a quick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes.

Features 7 Examples from modern communication system 7 Accurately established mathematical background (part 1), with intuitive explanations for queueing applications (part 2 Guidelines for application of queueing theory in practice.

Contents Preface.- Introduction to probability theory.- Introduction to stochastic processes.- Markov chains.- Renewal and regenerative processes.- Markov chains with special structures.- Introduc-tion to queueing systems.- Markovian queueing systems.- Non-Markovian queueing systems.- Queueing systems with structured Markov chains.- Queueing networks.- Applied queueing systems.- Functions and transforms.- Exercises.- References.-

Fields of interestsProbability Theory and Stochastic Processes; Op-erations Research, Management Science; System Performance and Evaluation



Due November 2012

2013. VI, 331 p. 30 illus. Hardcover7 approx. $74.95ISBN 978-1-4614-5316-1

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34

M. L. Lapidus, University of California, Riverside, CA, USA; M. van Frankenhuijsen, Utah Valley State College, Orem, UT, USA

Fractal Geometry, Complex Dimensions and Zeta FunctionsGeometry and Spectra of Fractal Strings

Features 7 The Riemann hypothesis is given a natural geometric reformulation in the context of vibrat-ing fractal strings 7 Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with frac-tal boundary 7 Numerous theorems, examples, remarks and illustrations enrich the text

Contents Preface.- Overview.- Introduction.- 1. Complex Dimensions of Ordinary Fractal Strings.- 2. Com-plex Dimensions of Self-Similar Fractal Strings.- 3. Complex Dimensions of Nonlattice Self-Similar Strings.- 4. Generalized Fractal Strings Viewed as Measures.- 5. Explicit Formulas for General-ized Fractal Strings.- 6. The Geometry and the Spectrum of Fractal Strings.- 7. Periodic Orbits of Self-Similar Flows.- 8. Fractal Tube Formulas.- 9. Riemann Hypothesis and Inverse Spectral Prob-lems.- 10. Generalized Cantor Strings and their Oscillations.- 11. Critical Zero of Zeta Functions.- 12 Fractality and Complex Dimensions.- 13. Re-cent Results and Perspectives.- Appendix A. Zeta Functions in Number Theory.- Appendix B. Zeta Functions of Laplacians and Spectral Asymptot-ics.- Appendix C. An Application of Nevanlinna Theory.- Bibliography.- Author Index.- Subject Index.- Index of Symbols.- Conventions.- Ac-knowledgements.

Fields of interestsNumber Theory; Measure and Integration; Partial Differential Equations



Due October 2012

2nd ed. 2013. XXII, 568 p. 73 illus. (Springer Monographs in Mathematics) Hardcover7 $89.95ISBN 978-1-4614-2175-7

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A. B. Levy, Bowdoin College, Brunswick, ME, USA

Stationarity and Convergence in Reduce-or-Retreat MinimizationStationarity and Convergence in Reduce-or-Re-treat Minimization presents and analyzes a unify-ing framework for a wide variety of numerical methods in optimization. The author’s “reduce-or-retreat” framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two general-izations of classic derivative-based methods which accommodate non-smooth objectives, and the lat-ter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method.

Features 7 Analyzes an innovative unifying framework for a wide variety of numerical methods in optimi-zation 7 Inspires new convergence analyses for existing methods in numerical optimiza-tion 7 Extends and broadens the traditional convergence analyses

Contents -1. A Framework for Reduce-or-Retreat Minimi-zation. -2. Particular Reduce-or-Retreat Methods. -3. Scenario Analysis.

Fields of interestsAlgorithms; Optimization; Computational Math-ematics and Numerical Analysis



Due September 2012

2012.XIV, 61 p. 3 illus., 1 in color. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-4641-5

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P. Manfredi, University of Pisa, Italy; A. d‘Onofrio, European Institute of Oncology, Milan, Italy (Eds)

Modeling the Interplay Between Human Behavior and the Spread of Infectious DiseasesContents Behavioral epidemiology of infectious diseases: an overview (C. Bauch et al.). -Part 1. Field data on behaviour. -Survey on the likely behavioural changes of the general public in 4 European coun-tries during the 2009/2010 pandemic (C. Rizzo et al.). -Factors influencing infant and adolescent vaccine uptake in Flanders, Belgium (H. Theeten et al). -Part 2. Modeling behaviour change in re-sponse to epidemic threats. -Modeling the Impact of Behavior Changes on the Spread of Pandemic Influenza (S.Y. Del Valle et al.). -Uncoordinated human responses during epidemic outbreaks (P. Poletti et al.). -The talk of the town: modelling the spread of information and changes in behavior (S. Funk and V. Jansen). -Modeling contact and mobility based social response to the spreading of infectious diseases (N. Perra and A. Vespignani). -Incorporating human behaviour in epidemic dy-namics: a modelling perspective (Istvan Z. Kiss). -Risk perception, heuristics and epidemic spread (P. Liò et al.). -The mechanism and phenomena of adaptive human behavior during an epidemic and the role of information (E.P. Fenichel and X. Wang). -Part 3. Modeling vaccinating behaviour. -The Economic approach to modeling self-protective behaviour in epidemiology (F. Chen). -Mathematical epidemiology and welfare econom-ics (M. Gersovitz). -Modeling influenza vaccina-tion behaviour via inductive reasoning games (R. Vardavas and C.S. Marcum). [...]

Fields of interestsPhysiological, Cellular and Medical Topics; Im-munology; Math. Applications in Chemistry



Due December 2012

2013. XII, 350 p. 120 illus., 30 in color. Hardcover7 approx. $129.00ISBN 978-1-4614-5473-1

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35

J. Mashreghi, Université Laval, Québec, QC, Canada; E. Fricain, Université Claude Bernard Lyon 1, Villeurbanne, France (Eds)

Blaschke Products and Their ApplicationsContents Preface. - Applications of Blaschke products to the spectral theory of Toeplitz operators (Grudsky, Shargorodsky). -A survey on Blaschke-oscillatory differential equations, with updates (Heittokan-gas.). - Bi-orthogonal expansions in the space L2(0,1) ( Boivin, Zhu). - Blaschke products as solutions of a functional equation (Mashreghi.). - Cauchy Transforms and Univalent Functions( Cima, Pfaltzgraff). - Critical points, the Gauss curvature equation and Blaschke products (Kraus, Roth). - Growth, zero distribution and factoriza-tion of analytic functions of moderate growth in the unit disc, (Chyzhykov, Skaskiv). - Hardy means of a finite Blaschke product and its deriva-tive ( Gluchoff, Hartmann). -Hyperbolic deriva-tives determine a function uniquely (Baribeau). - Hyperbolic wavelets and multiresolution in the Hardy space of the upper half plane (Feichtinger, Pap). - Norm of composition operators induced by finite Blaschke products on Mobius invariant spaces (Martin, Vukotic). - On the computable theory of bounded analytic functions (McNich-oll). - Polynomials versus finite Blaschke products ( Tuen Wai Ng, Yin Tsang). -Recent progress on truncated Toeplitz operators (Garcia, Ross).

Fields of interestsFunctions of a Complex Variable; Functional Analysis; Difference and Functional Equations



Due November 2012

2013. X, 330 p. 2 illus., 1 in color. (Fields Institute Communications, Volume 65) Hardcover7 approx. $129.00ISBN 978-1-4614-5340-6

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R. Melnik, I. S. Kotsireas, Wilfrid Laurier University, Waterloo, ON, Canada (Eds)

Advances in Applied Mathematics, Modeling, and Computational ScienceContents Preface.-Interconnected Challenges and New Perspectives in Applied Mathematical and Com-putational Sciences (Melnik, Korsireas).-Dynamic Blocking Problems for a Model of Fire Propaga-tion (Bressan).-Inverse Lax-Wendroff Procedure for Numerical Boundary Conditions of Hyper-bolic Equations: Survey and New Developments (Tan, Shu).-Illiptic Curves Over Finite Fields (Shparlinski).-Random Matrix Theory and its Innovative (Edelman, Wang).-Boundary Closures for Sixth-Order Energy-Stable Weighted Essen-tially Non-Oscillatory Finite-Difference Schemes (Carpenter, Yamaleev, Fisher).-A Multiscale Meth-od Coupling Network and Continuum Models in Porous Media II—Single- and Two-Phase Flows (Chu, Engquist, Prodanovic, Tsai).-Statistical Geometry and Topology of the Human Placenta (Seong, Getreuer, Li, Girardi, Salafia, Vvedensky).-Illustrating Optimal Control Applications with Discrete and Continuous Features (Lenhart, Bodine, Zhong, Joshi).

Fields of interestsMathematical Modeling and Industrial Mathemat-ics; Applications of Mathematics; Mathematical and Computational Biology



Due November 2012

2013. VIII, 240 p. 62 illus., 36 in color. (Fields Institute Communications, Volume 66) Hardcover7 approx. $109.00ISBN 978-1-4614-5388-8

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I. Mitrea, Temple University, Philadelphia, PA, USA; M. Mitrea, University of Missouri, Columbia, MI, USA

Multi-Layer Potentials and Boundary Problemsfor Higher‑Order Elliptic Systems in Lipschitz Domains

Many phenomena in engineering and mathemati-cal physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure tech-niques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g.

Features 7 Aimed at people working in different areas of mathematics with different levels of exper-tise, and with different goals in mind 7 The topics are new and mathematically sophisticated Readable, self-contained and has pedagogical value 7 Comprehensive range of topics makes a suitable and much needed reference for mathema-ticians and engineers

Contents 1 Introduction.- 2 Smoothness scales and Calde-ón-Zygmund theory in the scalar-valued case.- 3 Function spaces of Whitney arrays.- 4 The double multi-layer potential operator.- 5 The single multi-layer potential operator.- 6 Functional analytic properties of multi-layer potentials and boundary value problems.

Fields of interestsPotential Theory; Partial Differential Equations; Integral Equations



Due November 2012

2013. X, 398 p. (Lecture Notes in Mathematics, Volume 2063) Softcover7 $89.95ISBN 978-3-642-32665-3

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36

P. Pardalos, P. G. Georgiev, University of Florida, Gainesville, FL, USA; P. Papajorgji, National Agency for Exams, Tirana, Albania; B. Neugaard, James A. Haley Vetrans Hospital, Tampa, FL, USA (Eds)

Systems Analysis Tools for Better Health Care DeliveryFeatures 7 Presents the most recent systems engineer-ing and mathematical tools for health care and its applications 7 Shows and promotes the increased need for partnership between engineers and health care professionals 7 State of the art contents from leaders in the field

Contents Optimization Methods for Large-scale Radio-therapy Problems, Dionne M. Aleman, Hamid R. Ghaffari, Velibor V. Misic, Michael B. Sharpe, Mark Ruschin, and David A. Jaffray. -Portable Asset Management in Hospitals, Nebil Buyurgan, Nabil Lehlou, and Ashraf Hajiyev. -Clinical Data Mining to Discover Optimal Treatment Patterns, Patricia Cerrito. - Stochastic Integer Programming in Health Care Delivery, Camilo Mancilla and Robert H. Storer. - An Expository Discourse of E-health, Anastasius Moumtzoglou and Anastasia Kastania. - Nurse Scheduling Problem: An Integer Programming Model with a Practical Application, F. Neng, S. Mujahid, J. Zhang, P. Georgiev, P. Papa-jorgji, I. Radziukyniene, and P.M. Pardalos. - Ex-ploring the Parallels Between a Hospital Pharmacy and a Distribution Center, Jennifer A. Pazour and Russell D. Meller. - Automatic scheduling of nurses: What does it take in practice? Elina Rön-nberg, Torbjörn Larsson, and Ann Bertilsson

Fields of interestsOptimization; Operations Research, Management Science; Health Administration



Due November 2012

2013. IV, 185 p. 57 illus., 39 in color. (Springer Optimization and Its Applications, Volume 74) Hardcover7 $129.00ISBN 978-1-4614-5093-1

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K. D. Pham, The Air Force Research Laboratory,Kirtland Air Force Base, NM, USA

Linear-Quadratic Controls in Risk-Averse Decision MakingPerformance‑Measure Statistics and Control Decision Optimization

Features 7 Provides 'Statements of Statistical Opti-mal Control' which provide complete problem formulations composed of unique notations, terminologies ,definitions and theorems 7 In-cludes 'Problem Descriptions' in which basic assumptions related to the state space models are discussed 7 Provides a complete description of statistical optimal control

Contents -1. Introduction. -2. Risk-Averse Control of Linear-Quadratic Tracking Problems. -3. Overtak-ing Tracking Problems in Risk-Averse Control. -4. Performance Risk Management in Servo Systems. -5. Risk-Averse Control Problems in Model-Fol-lowing Systems. -6. Incomplete Feedback Design in Model-Following Systems. -7. Reliable Control for Stochastic Systems with Low Sensitivity. -8. Output Feedback Control for Stochastic Systems with Low Sensitivity. -9. Epilogue. –Index.

Fields of interestsCalculus of Variations and Optimal Control; Op-timization; Computational Science and Engineer-ing; Statistical Theory and Methods



Due November 2012

2013. XV, 144 p. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-5078-8

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S. T. Rachev, Stonybrook University, NY, USA; L. B. Klebanov, Charles University, Prague, Czech Republic; S. Stoyanov, EDHEC Business School, EDHEC-Risk Institute, Singapore; F. Fabozzi, EDHEC Business School, Singapore

The Methods of Distances in the Theory of Probability and StatisticsContents Main directions in the theory of probability met-rics.- Probability distances and probability met-rics: Definitions.- Primary, simple and compound probability distances, and minimal and maximal distances and norms.- A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms.- Quantitative relationships between minimal distances and minimal norms.- K-Minimal metrics.- Relations between minimal and maximal distances.- Moment problems related to the theory of probability metrics: Rela-tions between compound and primary distances.- Moment distances.- Uniformity in weak and vague convergence.- Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle.- Stability of queueing systems.-Optimal quality usage.- Ideal metrics with respect to summation scheme for i.i.d. random variables.- Ideal metrics and rate of convergence in the CLT for random motions.- Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory.- How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements.- Ideal metrics and stability of characterizations of probability distributions. [...]

Fields of interestsProbability Theory and Stochastic Processes; Statistical Theory and Methods; Approximations and Expansions



Due December 2012

2013. X, 550 p. Hardcover7 approx. $79.95ISBN 978-1-4614-4868-6

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37

T. Rylander, Chalmers University of Technology, Göteborg, Sweden; P. Ingelström, Chalmer University of Technology, Sweden; A. Bondeson

Computational ElectromagneticsComputational Electromagnetics is a young and growing discipline, expanding as a result of the steadily increasing demand for software for the design and analysis of electrical devices. This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element meth-od and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell‘s equations, using, for example, „staggered grids“ and „edge elements.“ The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions.

Features 7 Describes most popular computational methods used to solve problems in electromagnet-ics 7 Matlab code is included throughout, so that the reader can implement the various tech-niques discussed 7 Extensive computer projects included in this new edition

Contents Introduction.- Convergence.- Finite Differences.- Eigenvalues.- The Finite-Difference Time-Domain Method.- The Finite Element Method.- The Meth-od of Moments.- Summary and Overview.- Large Linear Systems.- Krylov Methods.

Fields of interestsComputational Science and Engineering; Electri-cal Engineering; Numerical Analysis



Due November 2012

2nd ed. 2013. XXI, 292 p. 81 illus. (Texts in Applied Mathematics, Volume 51) Hardcover7 approx. $84.95ISBN 978-1-4614-5350-5

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Z. Zhang, Chinese Academy of Sciences, Beijing, China

Variational, Topological, and Partial Order Methods with their ApplicationsContents 1 Preliminaries.- Sobolev spaces and embed-ding theorems.- Critical point.- Cone and partial order.- Brouwer Degree.- Compact map and Leray-Schauder Degree.- Fredholm operators.- Fixed point index.- Banach‘s Contract Theorem, Implicit Functions Theorem.- Krein-Rutman theo-rem.- Bifurcation theory.- Rearrangements of sets and functions.- Genus and Category.- Maximum principles and symmetry of solution.- Compari-son theorems.- 2 Cone and Partial Order Meth-ods.- Increasing operators.- Decreasing opera-tors.- Mixed monotone operators.- Applications of mixed monotone operators.- Further results on cones and partial order methods.- 3 Minimax Methods.- Mountain Pass Theorem and Mini-max Principle.- Linking Methods.- Local linking Methods.- 4 Bifurcation and Critical Point.- Intro-duction.- Main results with parameter.- Equations without the parameter.- 5 Solutions of a Class of Monge-Ampère Equations.- Introduction.- Mov-ing plane argument.- Existence and non-existence results.- Bifurcation and the equation with a parameter.- Appendix.- 6 Topological Methods and Applications.- Superlinear system of integral equations and applications.- Existence of posi-tive solutions for a semilinear elliptic system.- 7 Dancer-Fučik Spectrum.- The spectrum of a self-adjoint operator.- Dancer-Fučik Spectrum on bounded domains.- Dancer-Fučik point spectrum on RN.- Dancer-Fučik spectrum and asymptoti-cally linear elliptic problems.- 8 Sign-changing Solutions.- Sign-changing solutions for superlin-ear Dirichlet problems. [...]

Fields of interestFunctional Analysis



Due November 2012

2013. XII, 320 p. 3 illus. (Developments in Mathematics, Volume 29) Hardcover7 $129.00ISBN 978-3-642-30708-9

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