mathematical modeling and quasi-stationary...

Mathematics springer.com/NEWSonline

20

R. Azencott, University of Houston, TX, USA; M. I. Freidlin, University of. Maryland, College Park, MD, USA; S. S. Varadhan, New York University, NY, USA

Large Deviations at Saint-FlourContents: Azencott, R. : Large deviations and applications.- Freidlin, Mark I. Semi-linear PDE’s and limit theorems for large deviations- Varadhan, Srinivasa R.S.: Large deviations and applications.

Contents Azencott, R. : Large deviations and applications.- Freidlin, Mark I. Semi-linear PDE’s and limit theorems for large deviations- Varadhan, Srinivasa R.S.: Large deviations and applications.

Fields of interestProbability Theory and Stochastic Processes; Partial Differential Equations

Target groupsResearch

Discount groupProfessional Non-Medical

Due October 2012

Based on original French edition: “Ecole d’Ete de Probabilites de Saint-Flour VIII”, 1978

2013. Approx. 400 p. (Probability at Saint-Flour) Softcover7 $69.95ISBN 978-3-642-33199-2

9<HTOGPC=ddbjjc>

J. Batzel, Medical University of Graz, Austria; M. Bachar, King Saud University, Riyadh, Saudi Arabia; F. Kappel, University of Graz, Austria (Eds)

Mathematical Modeling and Validation in PhysiologyApplications to the Cardiovascular and Respiratory Systems

Features 7 Focused study of modeling from model design to model identifiability and validation 7 Written by current leading experts in the field and includ-ing topics of current research interest in state of the art questions and methods 7 Focus on interdisciplinary (physiological and mathemati-cal) collaboration and applications of modeling with clinical relevance 7 Presentation of key theoretical ideas and current areas of research interest through clear and motivated examples of application and implementation

Contents 1 Merging Mathematical and Physiological Knowledge: Dimensions and Challenges.- 2 Math-ematical Modeling of Physiological Systems.- 3 Pa-rameter Selection Methods in Inverse Problem Formulation.- 4 Application of the Unscented Kalman Filtering to Parameter Estimation.- 5 Inte-grative and Reductionist Approaches to Modeling of Control of Breathing.- 6 Parameter Identifica-tion in a Respiratory Control System Model with Delay.- 7 Experimental Studies of Respiration and Apnea.- 8 Model Validation and Control Issues in the Respiratory System.- 9 Experimental Studies of the Baroreflex.- 10 Development of Patient Spe-cific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges.- 11 Parameter Estimation of a Model for Baroreflex Control of Unstressed Volume.

Fields of interestMathematical and Computational Biology; Hu-man Physiology; Computer Appl. in Life Sciences



Due November 2012

2013. X, 290 p. 83 illus., 34 in color. (Lecture Notes in Mathematics / Mathematical Biosciences Subseries, Volume 2064) Softcover7 $89.95ISBN 978-3-642-32881-7

9<HTOGPC=dciibh>

P. Collet, Ecole Polytechnique, Paris, France; S. Martínez, J. San Martín, University of Chile, Santiago, Chile

Quasi-Stationary DistributionsMarkov Chains, Diffusions and Dynamical Systems

Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present the QSDs as the ones that allow describing the long-term behavior conditioned to not being killed. Studies in this re-search area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. The authors provide the expo-nential distribution property of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever. For birth-and-death chains and diffusions, the existence of a single or a continuum of QSDs is described. They study the convergence to the extremal QSD and give the classification of the survival process.

Features 7 Deals with an area that has received a lot of attention in last decades 7 Provides numerous examples 7 Focuses on selected topics

Contents 1.Introduction.- 2.Quasi-stationary Distributions: General Results.- 3.Markov Chains on Finite Spaces.- 4.Markov Chains on Countable Spaces.- 5.Birth and Death Chains.- 6.Regular Diffusions on [0,∞).- 7.Infinity as Entrance Boundary.- 8.Dy-namical Systems.- References.- Index.- Table of Notations.- Citations Index.

Fields of interestProbability Theory and Stochastic Processes; Dynamical Systems and Ergodic Theory; Genetics and Population Dynamics



Due December 2012

2013. XVIII, 342 p. 14 illus., 12 in color. (Probability and Its Applications) Hardcover7 $129.00ISBN 978-3-642-33130-5

9<HTOGPC=ddbdaf>

www.springer.com/978-3-642-33199-2



News 10/2012 Mathematics

21

D. V. Cruz-Uribe, Trinity College, Hartford, CT, USA; A. Fiorenza, University of Naples, Italy

Variable Lebesgue SpacesFoundations and Harmonic Analysis

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their con-nection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Leb-esgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces.

Features 7 Proofs are developed in detail, illustrating the standard techniques used in the field 7 Acces-sible for research mathematicians as well as gradu-ate students 7 Provides a thorough and up to date bibliographic treatment that makes clear the history and development of the field

Contents 1 Introduction.- 2 Structure of Variable Leb-esgue Spaces.- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity.- 5 Extrapolation in the Variable Lebesgue Spaces.- 6 Basic Properties of Variable Sobolev Spaces.- Ap-pendix: Open Problems.- Bibliography.- Symbol Index.- Author Index.- Subject Index.

Fields of interestAbstract Harmonic Analysis; Functional Analysis; Global Analysis and Analysis on Manifolds



Due January 2013

2013. X, 316 p. (Applied and Numerical Harmonic Analysis) Hardcover7 $129.00ISBN 978-3-0348-0547-6

9<HTOAOE=iafehg>

C. A. de Moura, Rio de Janeiro State University, RJ, Brazil; C. S. Kubrusly, Catholic University of Rio de Janeiro, RJ, Brazil (Eds)

The Courant–Friedrichs–Lewy (CFL) Condition80 Years After its Discovery

This volume comprises a carefully selected col-lection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, cel-ebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition.

Features 7 All articles carefully selected and written by well-known experts 7 Provides a survey of the current state of the field 7 Includes original research results

Contents Foreword.- Stability of Different Schemes.- Math-ematical Intuition: Poincaré, Pólya, Dew-ey.- Three-dimensional Plasma Arc Simulation using Resistive MHD.- A Numerical Algorithm for Ambrosetti-Prodi Type Operators.- On the Quadratic Finite Element Approximation of 1-D Waves: Propagation, Observation, Control, and Numerical Implementation.- Space-Time Adap-tive Mutilresolution Techniques for Compressible Euler Equations.- A Framework for Late-time/stiff Relaxation Asymptotics.- Is the CFL Condition Sufficient? Some Remarks.- Fast Chaotic Artificial Time Integration.- Appendix A.- Hans Lewy’s Recovered String Trio.- Appendix B.- Appendix C.- Appendix D.

Fields of interestComputational Mathematics and Numerical Analysis; Partial Differential Equations; Theory of Computation



Due December 2012

2013. X, 250 p. 53 illus., 37 in color. Hardcover7 $109.00ISBN 978-0-8176-8393-1

9<HTLIMH=gidjdb>

W. Ebeling, Leibniz Universität Hannover

Lattices and CodesA Course Partially Based on Lectures by Friedrich Hirzebruch

The purpose of coding theory is the design of effi-cient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surpris-ingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numer-ous corrections and improvements have been made and the text has been updated.

Features 7 Master course on the relationship between coding theory and the 7 theory of integral lat-tices 7 Linking classical mathematics to modern aspects in the design of codes 7 With many examples and connections to number theory and geometry

Contents Lattices and Codes.- Theta Functions and Weight Enumerators.- Even Unimodular Lattices.- The Leech Lattice.- Lattices over Integers of Number Fields and Self-Dual Codes.

Fields of interestMathematics, general; Algebra

Target groupsGraduate


Due September 2012

3rd ed. 2012. XVI, 167 p. 50 illus. (Advanced Lectures in Mathematics) Softcover7 $59.95ISBN 978-3-658-00359-3

9<HTOGQI=aadfjd>





22

D. Futer, Temple University, Philadelphia, PA, USA; E. Kalfagianni, Michigan State University, East Lansing, MI, USA; J. Purcell, Brigham Young University, Provo, UT, USA

Guts of Surfaces and the Colored Jones PolynomialThis monograph derives direct and concrete rela-tions between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagram-matic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coef-ficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots.

Features 7 Relates all central areas of modern 3-dimen-sional topology 7 The first monograph which initiates a systematic study of relations between quantum and geometric topology 7 Appeals to a broad audience of 3-dimensional topologists: combines tools from mainstream areas of 3-di-mensional topology

Contents 1 Introduction.- 2 Decomposition into 3–balls.- 3 Ideal Polyhedra.- 4 I–bundles and essential product disks.- 5 Guts and fibers.- 6 Recognizing essential product disks.- 7 Diagrams without non-prime arcs.- 8 Montesinos links.- 9 Applications.- 10 Discussion and questions.

Fields of interestManifolds and Cell Complexes (incl. Diff.Topol-ogy); Hyperbolic Geometry



Due December 2012

2013. X, 173 p. 63 illus., 46 in color. (Lecture Notes in Mathematics, Volume 2069) Softcover7 $59.95ISBN 978-3-642-33301-9

9<HTOGPC=dddabj>

G. Gentili, University of Florence, Italy; C. Stoppato, University of Milan, Italy; D. C. Struppa, Chapman University, Orange, CA, USA

Regular Functions of a Quaternionic VariableThe theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research com-munity. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one com-plex variable and its wide variety of applications are a strong motivation for the study of its analogs in higher dimensions.

Features 7 The book is entirely devoted to a new theory 7 Presents a state of the art survey of the theory of slice regular functions 7 The theory presented in the book is the basis for the solution to an outstanding problem, the construction of functional calculus in non commutative settings

Contents Introduction.- 1.Definitions and Basic Results.- 2.Regular Power Series.- 3.Zeros.- 4.Infinite Products.- 5.Singularities.- 6.Integral Represen-tations.- 7.Maximum Modulus Theorem and Applications.- 8.Spherical Series and Differen-tial.- 9.Fractional Transformations and the Unit Ball.- 10.Generalizations and Applications.- Bibli-ography.- Index.

Fields of interestFunctions of a Complex Variable; Sequences, Series, Summability; Functional Analysis



Due December 2012

2013. XVI, 188 p. 4 illus., 3 in color. (Springer Monographs in Mathematics) Hardcover7 $109.00ISBN 978-3-642-33870-0

9<HTOGPC=ddihaa>

F. Herzberg, University of Bielefeld, Germany

Stochastic Calculus with InfinitesimalsStochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well.

Features 7 A demonstrably consistent use of infinitesi-mals permits a radically simplified approach to stochastic calculus 7 Chapters on asset pricing, Lévy processes and the Feynman path integral introduce readers to applications 7 Appendixes explore the relationship with Internal Set Theory and Robinsonian nonstandard analysis

Contents 1 Infinitesimal calculus, consistently and acces-sibly.- 2 Radically elementary probability theory.- 3 Radically elementary stochastic integrals.- 4 The radically elementary Girsanov theorem and the diffusion invariance principle.- 5 Excursion to nancial economics: A radically elementary approach to the fundamental theorems of asset pricing.- 6 Excursion to financial engineering: Volatility invariance in the Black-Scholes model.- 7 A radically elementary theory of Itô diffusions and associated partial differential equations.- 8 Excursion to mathematical physics: A radically elementary definition of Feynman path integrals.- 9 A radically elementary theory of Lévy process-es.- 10 Final remarks.

Fields of interestMathematical Logic and Foundations; Probability Theory and Stochastic Processes; Game Theory, Economics, Social and Behav. Sciences



Due November 2012

2013. X, 120 p. (Lecture Notes in Mathematics, Volume 2067) Softcover7 $49.95ISBN 978-3-642-33148-0

9<HTOGPC=ddbeia>





23

A. M. Hinz, Ludwigs-Maximilians Universität München, Germany; S. Klavžar, University of Ljubljana, Slovenia; U. Milutinović, University of Maribor, Slovenia; C. Petr, Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

The Tower of Hanoi – Myths and MathsThis is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the histori-cal development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology.

Features 7 The first comprehensive monograph on the topic 7 Thorough presentation of the histori-cal development 7 Numerous attractive figures and original photos 7 Connections to various mathematical fields and applications to fields like computer science and psychology 7 Exercises with hints and solutions 7 No special knowl-edge of advanced mathematics assumed from the reader

Contents Foreword by Ian Stewart.- Preface.- 0 The Begin-ning of the World.- 1 The Chinese Rings.- 2 The Classical Tower of Hanoi.- 3 Lucas’s Second Prob-lem.- 4 Sierpinski Graphs.- 5 The Tower of Hanoi with More Pegs.- 6 Variations of the Puzzle.- 7 The Tower of London.- 8 Tower of Hanoi Variants with Oriented Disc Moves.- 9 The End of the World.- A Hints and Solutions to Exercises.- Glossary.- Bib-liography.- Name Index.- Subject Index.- Symbol Index.

Fields of interestMathematics, general; History of Mathematical Sciences; Sequences, Series, Summability

Target groupsUpper undergraduate


Due October 2012

2012. XII, 331 p. Hardcover7 approx. $89.95ISBN 978-3-0348-0236-9

9<HTOAOE=iacdgj>

S. Jeschke, I. Isenhardt, F. Hees, K. Henning, RWTH Aachen University, Germany (Eds)

Automation, Communication and Cybernetics in Science and Engineering 2011/2012Contents Foreword.- List of Contributors.- Part 1: Agile and Turbulence-Suitable Processes for Knowledge and Technology Intensive Organizations.- Part 2: Next-Generation Teaching and Learning Concepts for Universities and the Economy.- Part 3: Cognitive IT-Supported Processes for Hetero-geneous and Cooperative Systems.- Part 4: Target Group-Adapted User Models for Innovation and Technology Development Processes.- Part 5: Semantic Networks and Ontologies for Complex Value Chains and Virtual Environments.- Appen-dix: Monographs and Published Books from IMA/ZLW & IfU.

Fields of interestComputational Science and Engineering; Artificial Intelligence (incl. Robotics); Robotics and Auto-mation



Due December 2012

2013. 1200 p. Hardcover7 $189.00ISBN 978-3-642-33388-0

9<HTOGPC=dddiia>

D. Jungnickel, University of Augsburg, Germany

Graphs, Networks and AlgorithmsFrom the reviews of the previous editions 7 The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained ... 7 K.Engel, Mathematical Reviews 2002

Features 7 Thoroughly revised new edition 7 Further material added 7 Additional exercises 7 Addi-tional references

Contents Prefaces.- Basic Graph Theory.- Algorithms and Complexity.- Shortest Paths.- Spanning Trees.- The Greedy Algorithm.- Flows.- Combinatorial Applications.- Connectivity and Depth First Search.- Colorings.- Circulations.- The Network Simplex Algorithm.- Synthesis of Networks.- Matchings.- Weighted Matchings.- A Hard Prob-lem: The TSP.- Appendix A: Some NP-Complete Problems.- Appendix B: Solutions.- Appendix C: List of Symbols.- References.- Index.

Fields of interestCombinatorics; Optimization; Mathematics of Computing



Due November 2012

4th ed. 2013. XXII, 678 p. 211 illus. (Algorithms and Computation in Mathematics, Volume 5) Hardcover7 $89.95ISBN 978-3-642-32277-8

9<HTOGPC=dcchhi>





24

Y. I. Karlovich, Universidad Autónoma del Estado de Morelos, Cuernavaca, MO, Mexico; L. Rodino, University of Torino, Italy; B. Silbermann, Technical University Chemnitz, Germany; I. M. Spitkovsky, College of William and Mary, Williamsburg, VA, USA (Eds)

Operator Theory, Pseudo-Differential Equations, and Mathematical PhysicsThe Vladimir Rabinovich Anniversary Volume

This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabi-novich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinov-ich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and con-volution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich’s research interests. Many of them are written by participants of the International workshop “Analysis, Opera-tor Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.

Features 7 Wide spectrum of important problems in operator theory, PDEs, mathematical physics and numerical analysis 7 Modern methods and ap-proaches 7 Dedicated to Vladimir Rabinovich

Contents Preface.- Contributions by renowned scientists.- References.

Fields of interestPartial Differential Equations; Operator Theory



Due November 2012

2013. XXVI, 408 p. 12 illus. in color. (Operator Theory: Advances and Applications, Volume 228) Hardcover7 approx. $169.00ISBN 978-3-0348-0536-0

9<HTOAOE=iafdga>

M. G. Larson, F. Bengzon, Umeå University, Umea, Sweden

The Finite Element Method: Theory, Implementation, and ApplicationsThis book gives an introduction to the finite ele-ment method as a general computational method for solving partial differential equations approxi-mately.

Features 7 Introduction to finite elements only based on calculus and linear algebra 7 Covers theory, implementation and applications. Focus on basic mathematical principles and consequent use of the same approach in different applications 7 Matlab programs included 7 Wide range of applications including solid mechanics, electromagnetics, and fluid mechanics 7 Covers modern topics such as adaptivity based on duality arguments

Contents 1. Piecewise Polynomial Approximation in 1D.- 2. The Finite Element Method in 1D.- 3. Piecewise Polynomial Approximation in 2D.- 4. The Finite Element Method in 2D.- 5. Time-dependent Prob-lems.- 6. Solving Large Sparse Linear Systems.- 7. Abstract Finite Element Analysis.- 8. The Finite Element.- 9. Non-linear Problems.- 10. Transport Problems.- 11. Solid Mechanics.- 12. Fluid Me-chanics.- 13. Electromagnetics.- 14. Discontinuous Galerkin Methods.- A. Some Additional Matlab Code.- References.

Fields of interestComputational Science and Engineering; Partial Differential Equations; Theoretical and Applied Mechanics



Due December 2012

2013. XVI, 372 p. 86 illus., 49 in color. (Texts in Computational Science and Engineering, Volume 10) Hardcover7 $79.95ISBN 978-3-642-33286-9

9<HTOGPC=ddcigj>

L. Lebedev, Universidad Nacional de Colombia, Bogota, Colombia; M. Cloud, Lawrence Technological University, MI, USA; I. I. Vorovich

Functional Analysis in MechanicsThis book offers a brief, practically complete, and relatively simple introduction to functional analy-sis. It also illustrates the application of functional analytic methods to the science of continuum me-chanics. Abstract but powerful mathematical no-tions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value prob-lems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis.

Features 7 The mathematical material is treated in a non-abstract manner and is fully illuminated by the underlying mechanical ideas 7 The presenta-tion is concise but complete, and is intended for specialists in continuum mechanics who wish to understand the mathematical underpinnings of the discipline 7 Exercises and examples are included throughout with detailed solutions pro-vided in the appendix

Contents Introduction.- Metric, Banach, and Hilbert Spaces.- Mechanics Problems from the Functional Analysis Viewpoint.- Some Spectral Problems of Mechanics.- Elements of Nonlinear Functional Analysis.- Summary of Inequalities and Imbed-dings.- Hints for Selected Problems.- References.- In Memoriam: Iosif I. Vorovich.- Index.-

Fields of interestFunctional Analysis; Partial Differential Equa-tions; Mechanics



Due December 2012

2nd ed. 2013. X, 307 p. (Springer Monographs in Mathematics) Hardcover7 $129.00ISBN 978-1-4614-5867-8

9<HTMERB=efighi>





25

E. Lord, Bangalore

Symmetry and Pattern in Projective GeometrySymmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on ho-mogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The em-phasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed through-out the text.

Features 7 Provides a self-contained and easy-to-read introduction to projective geometry 7 Com-pares and contrasts both analytic and synthetic methods 7 Makes accessible subjects and theorems which are often considered quite com-plicated 7 Compares and contrasts both analytic and synthetic methods 7 Makes accessible subjects and theorems which are often considered quite complicated 7 Makes accessible subjects and theorems which are often considered quite complicated

Contents Foundations: the Synthetic Approach.- The Analytic Approach.- Linear Figures.- Quadratic Figures.- Cubic Figures.- Quartic Figures.- Finite Geometries.

Fields of interestProjective Geometry; Symbolic and Algebraic Manipulation; Mathematics, general



Due September 2012

2013. XII, 212 p. 103 illus., 20 in color. Softcover7 $49.95ISBN 978-1-4471-4630-8

9<HTMEPH=begdai>

A. Malyarenko, Mälardalen University, Västerås, Sweden

Invariant Random Fields on Spaces with a Group ActionForeword by: N. Leonenko, Cardiff University, Wales, UK

The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including Probability Theory, Differential Geom-etry, Harmonic Analysis, and Special Functions. The present volume unifies many results scattered throughout the mathematical, physical, and engi-neering literature, as well as it introduces new re-sults from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of Stochastic Pro-cesses, Statistics, Functional Analysis, Astronomy, and Engineering.

Features 7 Highly interdisciplinary nature 7 Fills a gap in the literature 7 Many new results, and practi-cal applications as for example in cosmology and earthquake engineering

Contents 1.Introduction.- 2.Spectral Expansions.- 3.L2 Theory of Invariant Random Fields.- 4.Sample Path Properties of Gaussian Invariant Random Fields.- 5.Applications.- A.Mathematical Back-ground.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes; Mathematical Applications in the Physical Sci-ences; Cosmology



Due December 2012

2013. XVIII, 246 p. (Probability and Its Applications) Hardcover7 $109.00ISBN 978-3-642-33405-4

9<HTOGPC=ddeafe>

J. Mashreghi, Université Laval, Quebec, QC, Canada

Derivatives of Inner Functions Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will allow researchers to get acquainted with essentials on inner functions, and it is self-contained, which makes it accessible to graduate students.

Features 7 Includes a comprehensive list of results on integral means taken from several research papers 7 Text is concise and self-contained, making it easily accessible to graduate stu-dents 7 Provides rapid access to the frontiers of research in this field

Contents Preface.-1. Inner Functions.-2. The Exceptional Set of an Inner Function.-3. The Derivative of Finite Blaschke Products.-4. Angular Deriva-tive.-5. Hp-Means of S’.-6. Bp-Means of S’.-7. The Derivative of a Blaschke Product.-8. Hp-Means of B’.-9. Bp-Means of B’.-10. The Growth of Integral Means of B’.-References.-Index.

Fields of interestFunctions of a Complex Variable; Functional Analysis; Several Complex Variables and Analytic Spaces



Due November 2012

2013. XI, 169 p. (Fields Institute Monographs, Volume 31) Hardcover7 $109.00ISBN 978-1-4614-5610-0

9<HTMERB=efgbaa>





26

V. Moretti, Università di Trento, Italy

Spectral Theory and Quantum Mechanicswith an Introduction to the Algebraic Formulation of Quantum Theories

Features 7 Most chapters are accompanied by exercises, many of which solved explicitly 7 At any rate several examples of the physical formalism are presented 7 Many of these aspects have been known for a long time but are scattered in the specialistic literature

Contents Introduction and mathematical backgrounds.- Normed and Banach spaces, examples and appli-cations.- Hilbert spaces and bounded operators.- Families of compact operators on Hilbert spaces and fundamental properties.- Densely-defined un-bounded operators on Hilbert spaces.- Phenom-enology of quantum systems and Wave Mechanics: an overview.- The first 4 axioms of QM: proposi-tions, quantum states and observables.- Spectral Theory I: generalities, abstract C -algebras and operators in B(H).- Spectral theory II: unbounded operators on Hilbert spaces.- Spectral Theory III: applications.- Mathematical formulation of non-relativistic Quantum Mechanics.- Introduction to Quantum Symmetries.- Selected advanced topics in Quantum Mechanics.- Introduction to the Algebraic Formulation of Quantum Theories.- Or-der relations and groups.- Elements of differential geometry.

Fields of interestApplications of Mathematics; Theoretical, Math-ematical and Computational Physics; Mathemati-cal Methods in Physics



Due October 2012

2013. Approx. 600 p. 100 illus. (UNITEXT / La Matematica per il 3+2) Softcover7 approx. $69.95ISBN 978-88-470-2834-0

9<HTTIPH=acidea>

I. Nourdin, Université de Lorraine, Nancy, France

Selected Aspects of Fractional Brownian MotionFractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brown-ian motion and semimartingales, and others classically used in probability theory. As a cen-tered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental im-portance for financial data and in internet traffic.

Features 7 Except for very few exception, every result stated in this book is proved in details: the book is then perfectly tailored for self-learning 7 My guiding thread was to develop only the most aesthetic topics related to fractional Brownian motion: the book will appeal to readers who are not necessarily familiar with fractional Brownian motion and who like beautiful mathematics 7 A special chapter on a recent link between fractional Brownian motion and free probability introduces the reader to a new and promising line of research

Contents 1. Preliminaries.- 2. Fractional Brownian motion.- 3. Integration with respect to fractional Brownian motion.- 4. Supremum of the fractional Brownian motion.- 5. Malliavin calculus in a nutshell.- 6. Central limit theorem on the Wiener space.- 7. Weak convergence of partial sums of station-ary sequences.- 8. Non-commutative fractional Brownian motion.

Fields of interestProbability Theory and Stochastic Processes; Quantitative Finance



Due November 2012

2013. Approx. 140 p. (Bocconi & Springer Series) Hardcover7 approx. $119.00ISBN 978-88-470-2822-7

9<HTTIPH=acicch>

C. Pechstein

Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale ProblemsTearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to give a detailed and self-contained presentation of these methods, including the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed that have not been covered in any monograph yet: the coupling of finite and bound-ary elements within the tearing and interconnect-ing framework including exterior problems, and the case of highly varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book offers a detailed view to an active and up-to-date area of research.

Features 7 Detailed derivation of the methods and their analysis 7 Includes algorithms and implemen-tation issues 7 Special chapter on multiscale problems at the cutting edge of research 7 Both finite and boundary elements are covered, as well as exterior problems

Contents Preliminaries.- One-level FETI/BETI Methods.- Multiscale Problems.- Unbounded Domains.- Dual-Primal Methods.- References.- Index.- List of Symbols

Fields of interestNumerical Analysis; Computational Science and Engineering



Due November 2012

2013. XVI, 304 p. 51 illus., 1 in color. (Lecture Notes in Computational Science and Engineering, Volume 90) Hardcover7 $129.00ISBN 978-3-642-23587-0

9<HTOGPC=cdfiha>





27

L. Rüschendorf, University of Freiburg, Germany

Mathematical Risk AnalysisDependence, Risk Bounds, Optimal Allocations and Portfolios

The author’s particular interest in the area of risk measures is to combine this theory with the analy-sis of dependence properties.

Features 7 Up-to-date treatment of the main concepts and techniques used in mathematical risk analysis 7 Clearly structured guide 7 Gives orientation and help to acquire a solid fundament for working in this area

Contents Preface.-Part I: Stochastic Dependence and Extremal Risk.-1 Copulas, Sklar’s Theorem, and Distributional Transform.- 2 Fréchet Classes, Risk Bounds, and Duality Theory.- 3 Convex Order, Excess of Loss, and Comonotonicity.- 4 Bounds for the Distribution Function and Value at Risk of the Joint Portfolio.- 5 Restrictions on the Depen-dence Structure.- 6 Dependence Orderings of Risk Vectors and Portfolios.- Part II: Risk Measures and Worst Case Portfolios.- 7 Risk Measures for Real Risks.- 8 Risk Measures for Portfolio Vectors.- 9 Law Invariant Convex Risk Measures on L_d^p and Optimal Mass Transportation.- Part III: Optimal Risk Allocation.- 10 Optimal Allocations and Pareto Equilibrium.- 11 Characterization and Examples of Optimal Risk Allocations for Convex Risk Functionals.- 12 Optimal Contingent Claims and (Re)Insurance Contracts.- Part IV: Optimal Portfolios and Extreme Risks.- 13 Optimal Portfo-lio Diversification w.r.t. Extreme Risks.- 14 Order-ing of Multivariate Risk Models with Respect to Extreme Portfolio Losses.- References.- List of Symbols.- Index.

Fields of interestProbability Theory and Stochastic Processes; Quantitative Finance; Actuarial Sciences

Target groupsProfessional/practitioner


Due December 2012

2013. XVIII, 446 p. 12 illus., 1 in color. (Springer Series in Operations Research and Financial Engineering) Hardcover7 $129.00ISBN 978-3-642-33589-1

9<HTOGPC=ddfijb>

M. Senechal, Smith College, Northampton, MA, USA (Ed)

Shaping SpaceExploring Polyhedra in Nature, Art, and the Geometrical Imagination

Contents Preface.- I First Steps.-1 Introduction to the Poly-hedron Kingdom. Marjorie Senechal- 2 Six Reci-pes for Making Polyhedra. Marion Walter; Jean Pedersen; MagnusWenninger; Doris Schattsch-neider; Arthur Loeb; and Eric Demaine, Martin Demaine and Vi Hart.- 3 Regular and Semiregular Polyhedra. H. S. M. Coxeter.- 4 Milestones in the History of Polyhedra. Joseph Malkevitch.- 5 Poly-hedra: Surfaces or Solids? Arthur Loeb.- 6 Dürer’s Problem. Joseph O’Rourke.- II Polyhedra in Na-ture and Art.- 7 Exploring the Polyhedron King-dom. Marjorie Senechal.- 8 Spatial Perception and Creativity. Janos Baracs.- 9 Goldberg Polyhedra. George Hart.- 10 Polyhedra and Crystal Struc-tures. Chung Chieh.- 11 Polyhedral Molecular Ge-ometries. Magdolna Hargittai and Istvan Hargit-tai.- 12 Form, Function, and Functioning. George Fleck.- III Polyhedra in the Geometrical Imagina-tion.- 13 The Polyhedron Kingdom Tomorrow. Marjorie Senechal.- 14 Paneled and Molecular Polyhedra: How Stable Are They? Ileana Streinu.- 15 Duality of Polyhedra. Banko Grünbaum and G. C. Shephard.- 16 Combinatorial Prototiles. Egon Schulte.- 17 Polyhedra Analogues of the Platonic Solids. Jörg M. Wills.- 18 Convex Polyhedra, Dirichlet Tessellations, and Spider Webs. Walter Whiteley with Peter Ash, Ethan Bolker, and Henry Crapo.- 19 Uniform Polyhedra from Diophantine Equations. Barry Monson.- 20 Torus Decomposi-tions of Regular Polytopes in 4-space. Thomas F. Banchoff.- 21 Tensegrities and Global Rigidity. Robert Connelly.- 22 Ten Problems in Geometry. Günter Ziegler and Moritz Schmitt. [...]

Fields of interestGeometry; Crystallography; Design, general

Target groupsPopular/general

Discount groupTrade

Due December 2012

2013. XIV, 480 p. 400 illus., 31 in color. Hardcover7 approx. $39.95ISBN 978-0-387-92713-8

9<HTLDTH=jchbdi>

E. Spodarev, University of Ulm, Germany (Ed)

Stochastic Geometry, Spatial Statistics and Random FieldsAsymptotic Methods

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Features 7 Comprises introductory material as well as advances topics with a significant number of proofs 7 Numerous images ease the understand-ing of complex mathematical notions 7 Includes a large number of excercises for active reading Provides vast research bibliography

Contents 1 Foundations of stochastic geometry and theory of random sets.- 2 Introduction into integral geometry and stereology.- 3 Spatial point patterns – models and statistics.- 4 Asymptotic methods in statistics of random point processes.- 5 Random tessellations and Cox processes.- 6 Asymptotic methods for random tessellations.- 7 Random polytopes.- 8 Limit theorems in discrete stochastic geometry.- 9 Introduction to random fields.- 10 Central limit theorems for weakly dependent random fields.- 11 Strong limit theorems for incre-ments of random fields.- 12 Geometry of large random trees: SPDE approximation.

Fields of interestConvex and Discrete Geometry; Probability Theory and Stochastic Processes; Statistical Theory and Methods



Due December 2012

2013. XXIV, 430 p. 118 illus., 28 in color. (Lecture Notes in Mathematics, Volume 2068) Softcover7 $89.95ISBN 978-3-642-33304-0

9<HTOGPC=dddaea>





28

S. M. Srivastava, Indian Statistical Institute, Kolkata, India

A Course on Mathematical LogicThis is a short, modern, and motivated introduc-tion to mathematical logic for upper undergradu-ate and beginning graduate students in mathemat-ics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and comput-ability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text.

Features 7 New edition extensively revised and up-dated 7 Includes a new chapter on model theory, and several new sections on topics such as ultraproducts, quantifier eliminations, real closed and algebraically closed fields, definability, partial elementary maps, and homogenous struc-tures 7 Contains numerous exercises, examples, and applications such as Chevalley's theorem, Hil-bert's Nullstellensatz, and the solution to Hilbert's 17th problem 7 Employs Gödel’s completeness and incompleteness theorems to motivate the entire text

Contents Preface.- 1 Syntax of First-Order Logic.- 2 Seman-tics of First-Order Languages.- 3 Propositional Logic.- 4 Completeness Theorem for First-Order Logic.- 5 Model Theory.- 6 Recursive Functions and Arithmetization of Theories.- 7 Incomplete-ness Theorems and Recursion Theory.- Refer-ences.- Index.

Fields of interestMathematical Logic and Foundations; Mathemati-cal Logic and Formal Languages; Algebra



Due January 2013

2nd ed. 2013. XII, 206 p. (Universitext) Softcover7 $69.95ISBN 978-1-4614-5745-9

9<HTMERB=efhefj>

K. Vajravelu, R. A. Van Gorder, University of Central Florida, Orlando, FL 32816-1364, USA

Nonlinear Flow Phenomena and Homotopy AnalysisFluid Flow and Heat Transfer

Since most of the problems arising in science and engineering are nonlinear, they are inher-ently difficult to solve. Traditional analytical ap-proximations are valid only for weakly nonlinear problems, and often fail when used for prob-lems with strong nonlinearity. “Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer” presents the current theo-retical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method.

Features 7 A powerful analytical method for strongly non-linear differential equations 7 Latest develop-ments in theory and applications 7 Varieties of very recent and interesting applications in science and engineering

Contents Part I: Theoretical Considerations.- Principles of the Homotopy Analysis Method.- Methods for the Control of Convergence in Obtained Solutions.- Additional Techniques. Part II: Applications to Physical Problems.- Application of the Homotopy Analysis Method to Fluid Flow Problems.- Appli-cation of the Homotopy Analysis Method to Heat Transfer Problems.- Application of the Homotopy Analysis Method to More Advanced Problems.

Fields of interestComputational Mathematics and Numerical Analysis; Engineering Fluid Dynamics; Theoreti-cal, Mathematical and Computational Physics



Due October 2012

Jointly published with Higher Education Press

Distribution rights in China: Higher Education Press

2013. Approx. 250 p. 40 illus. Hardcover7 approx. $109.00ISBN 978-3-642-32101-6

9<HTOGPC=dcbabg>

X. Wang, South China Normal University, Guangzhou, China; D. Pei, Guangzhou University, China

Modular Forms with Integral and Half-Integral Weights“Modular Forms with Integral and Half-Integral Weights” focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series.

Features 7 The first book available on modular forms dealing with integral and half-integral weights in a unified framework 7 The first book dealing with in detail Eisenstein series with half-integral weights 7 Includes all necessary basic material for reading modern research literature on modular forms with half-integral weights 7 Offers some very beautiful applications of modular forms of half-integral weights to some arithmetic problems of definite positive quadratic forms

Contents Theta Functions and Their Transformation For-mulae.- Eisenstein Series.- The Modular Group and Its Subgroups.- Modular Forms with Integral Weight or Half-integral Weight.- Operators on the Space of Modular Forms.- New Forms and Old Forms.-Construction of Eisenstein Series.- Weil Representation and Shimura Lifting.- Trace For-mula.- Integers Represented by Positive Definite Quadratic Forms.

Fields of interestNumber Theory; Algebraic Geometry; Functions of a Complex Variable



Available

Distribution rights in China: Science Press Ltd

2013. Approx. 400 p. 3 illus. Hardcover7 $129.00ISBN 978-3-642-29301-6

9<HTOGPC=cjdabg>




mathematical modeling and quasi-stationary...

Documents