Ramanujan’s Lost Notebook Stochastic Differential Geometry...

News 11/2012 Mathematics

29

A. Ancona, Université Paris Sud, Orsay, France; K. D. Elworthy, University of Warwick, Coventry, UK; M. Emery, Université Louis Pasteur, Strasbourg, France; H. Kunita, Kyushu University, Fukuoka, Japan

Stochastic Differential Geometry at Saint-FlourKunita, H.:Stochastic differential equations and stochastic flows of diffeomorphisms.-Elworthy, D.: Geometric aspects of diffusions on manifolds.-Ancona, A.:Théorie du potential sur les graphs et les variétiés.-Emery, M.:Continuous martingales in differentiable manifolds.

Contents Kunita, H.:Stochastic differential equations and stochastic flows of diffeomorphisms.- Elworthy, D.: Geometric aspects of diffusions on manifolds.- Ancona, A.: Théorie du potential sur les graphes et les variétés.- Emery, M.:Continuous martingales in differentiable manifolds.

Fields of interestProbability Theory and Stochastic Processes; Global Analysis and Analysis on Manifolds; Potential Theory

Target groupsResearch

Product categoryContributed volume

Due November 2012

Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 1097 (1984), 1362 (1988), 1427 (1990) and 1738 (2004).

2013. Approx. 500 p. (Probability at Saint-Flour) Softcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-3-642-34170-0

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G. E. Andrews, The Pennsylvania State University, University Park, PA, USA; B. C. Berndt, University of Illinois at Urbana-Champaign, Urbana, IL, USA

Ramanujan’s Lost NotebookPart IV

Contents Preface.- 1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov’s Formula and Guinand’s Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler’s Constant.- 7 Problems in Diophantine Approxi-mation.- 8 Number Theory.- 9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manu-script on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta Functions adn Gauss Sums.- 15 Functional Equations for Products of Mellin Transforms.- 16 Infinite Products.- 17 A Preliminary Version of Ramanujan’s Paper, On the Integral ∫_0^x tan^(-1)t)/t dt.- 18 A Partial Manu-script Connected with Ramanujan’s Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis.- 20 Elementary Results.- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide.- Provenance.- References.- Index.

Fields of interestNumber Theory; Analysis; Fourier Analysis


Product categoryMonograph

Due February 2013

2013. XIV, 436 p. Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-1-4614-4080-2

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J.‑P. Aubin, University of Paris-Dauphine, France; P. Bernhard, INRIA Sophia Antipolis-Méditerraneé, Sophia Antipolis, France; J. C. Engwerda, Tilburg University, The Netherlands; V. Kolokoltsov, University of Warwick, Warwick, UK; B. Roorda, University of Twente, Enschede, The Netherlands; J. Schumacher, Tilburg University, The Netherlands; P. Saint‑Pierre, University of Paris-Dauphine, France

The Interval Market Model in Mathematical FinanceGame‑Theoretic Methods

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance.

Features 7 First book on the market to highlight the interval market model in mathematical fi-nance 7 Combines several related paths of research into a single source, while providing numerous unpublished results 7 Presented in a manner accessible to readers specializing in both mathematics and finance 7 Includes many features to clarify concepts and facilitate referenc-ing, such as figures, tables, biographical data, and subject, author, and notation indices

Contents General introduction.-Part 1: Revisting two classical problems in dynamic portfolio manage-ment.- Part 2: Hedging in interval models.- Part 3: Robust control approach to option pricing.- Part 4: Game-theoretic analysis of rainbow options in incomplete markets.- Part V Viability approach to complex options pricing and portfolio insur-ance.- References.- Index.

Fields of interestGame Theory, Economics, Social and Behav. Sciences; Game Theory/Mathematical Methods; Quantitative Finance



Due December 2012

2013. XIII, 346 p. 55 illus. (Static & Dynamic Game Theory: Foundations & Applications) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-0-8176-8387-0

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www.springer.com/978-3-642-34170-0



Mathematics springer.com/NEWSonline

30

F. Boyer, Universite Paul Cezanne, Marseille, France; P. Fabrie, Universite Bordeaux I, Talence, France

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related ModelsThe objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others.

Features 7 The book is self-contained 7 The methods presented in the book can be applied to a wide range of domains in nonlinear analysis 7 Some very recent research results are presented along with more classical ones 7 The first chapter of the book presents, with details, the derivation of the equations of fluid mechanics

Contents Preface.- Contents.- The equations of fluid mechanics.- Analysis tools.- Sobolev spaces.- Steady Stokes equations.- Navier-Stokes equations for homogeneous fluids.- Nonhomogeneous fluids.- Boundary conditions modeling.- Classic differential operators.- Thermodynamics supple-ment.- References.- Index.-

Fields of interestPartial Differential Equations; Engineering Fluid Dynamics; Fluid- and Aerodynamics

Target groupsGraduate


Due December 2012

2013. X, 533 p. 12 illus., 1 in color. (Applied Mathematical Sciences, Volume 183) Hardcover7 * € (D) 117,65 | € (A) 120,95 | sFr 146,507 € 109,95 | £99.00ISBN 978-1-4614-5974-3

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M. Breuß, Brandenburg Technical University, Cottbus, Germany; A. Bruckstein, Technion, Haifa, Israel; P. Maragos, National Technical University of Athens, Greece (Eds)

Innovations for Shape AnalysisModels and Algorithms

Contents Part I Discrete Shape Analysis: 1 Modeling Three-Dimensional Morse and Morse-Smale Complexes by L. Čomić et al.- 2 Geodesic Regression and its Application to Shape Analysis by P.Th.Fletcher.- 3 Segmentation and Skeletonization on Arbitrary Graphs Using Multiscale Morphology and Active Contours by P.Maragos and K.Drakopoulos.- 4 Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods by P.Peter and M.Breuß.- 5 Nested Sphere Statistics of Skeletal Models by S.M.Pizer et al.- 6 3D Curve Skeleton Computation and Use for Discrete Shape Analysis by G.Sanniti di Baja and C.Arcelli.- 7 Orientation and Anisotropy of Multi-component Shapes by J. Žunić and P.L.Rosin.- Part II Partial Differential Equations for Shape Analysis: 8 Stable semi-local features for non-rigid shapes by R.Litman et al.- 9 A brief survey on semi-Lagrang-ian schemes for image processing by E.Carlini et al.- 10 Shape reconstruction of symmetric surfaces using Photometric Stereo by R.Mecca and S.Tozza.- 11 Remeshing by Curvature Driven Diffusion by S.Morigi and M.Rucci.- 12 Group-valued Regularization for Motion Segmentation of Articulated Shapes by G.Rosman et al.- 13 Point Cloud Segmentation and Denoising via Constrained Nonlinear Least Squares Normal Estimates by E.Castillo et al.- 14 Distance Images and the Enclosure Field: Applications in Interme-diate-Level Computer and Biological Vision by S.W.Zucker. [...]

Fields of interestVisualization; Computer Imaging, Vision, Pattern Recognition and Graphics; Computational Math-ematics and Numerical Analysis



Due December 2012

2013. IX, 500 p. 228 illus., 171 in color. (Mathematics and Visualization) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-3-642-34140-3

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F. Buekenhout, Brussels, Belgium; A. M. Cohen, University of Technology, Eindhoven, The Netherlands

Diagram Geometryrelated to classical groups and buildings

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geom-etry is motivated by polarities on diagram geome-tries and the complete classification of those polar geometries whose projective planes are Desargue-sian is given. It differs from Tits’ comprehensive treatment in that it uses Veldkamp’s embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams.

Features 7 A basic reference book on diagram geom-etry 7 Treats group theory, matroid theory, Coxeter goups and buildings from a diagrammatic perspective 7 Graph theorists will find many highly regular graphs 7 The book contains many examples

Contents 1. Geometries.- 2. Diagrams.- 3. Chamber Systems.- 4. Thin Geometries.- 5. Linear Ge-ometries.- 6. Projective and Affine Spaces.- 7. Polar Spaces.- 8. Projective Embeddings of Polar Spaces.- 9. Embedding Polar Spaces in Absolutes.- 10. Classical Polar Spaces.- 11. Buildings.- Bibliog-raphy.- Index.

Field of interestGeometry



Due December 2012

2013. X, 640 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics, Volume 57) Hardcover7 * € (D) 117,65 | € (A) 120,95 | sFr 146,507 € 109,95 | £99.00ISBN 978-3-642-34452-7

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31

F. Clarke, Université Claude Bernard Lyon 1,France

Functional Analysis, Calculus of Variations and Optimal ControlFunctional analysis owes much of its early impetus to problems that arise in the calculus of varia-tions. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis.

Features 7 A self-contained in-depth introduction to functional analysis and the related fields of optimal control and the calculus of variations that is unique in its coverage 7 Written in a lively and engaging style by a leading special-ist 7 Includes a short course on optimization and nonsmooth analysis 7 Gives complete proofs of advanced versions of the Pontryagin maximum principle that appear for the first time in a textbook 7 Contains hundreds of exercises of an original nature, with solutions or hints in many cases

Contents Normed Spaces.- Convex sets and functions.- Weak topologies.- Convex analysis.- Banach spaces.- Lebesgue spaces.- Hilbert spaces.- Ad-ditional exercises for Part I.- Optimization and multipliers.- Generalized gradients.- Proximal analysis.- Invariance and monotonicity.- Addi-tional exercises for Part II.- The classical theory.- Nonsmooth extremals.- Absolutely continuous solutions.- The multiplier rule.- Nonsmooth La-grangians.- Hamilton-Jacobi methods.- Additional exercises for Part III.- Multiple integrals.- Neces-sary conditions.- Existence and regularity.- Induc-tive methods.- Differential inclusions.- Additional exercises for Part IV.

Fields of interestFunctional Analysis; Calculus of Variations and Optimal Control; Optimization; Continuous Optimization


Product categoryGraduate/Advanced undergraduate textbook

Due January 2013

2013. XIV, 594 p. 14 illus., 8 in color. (Graduate Texts in Mathematics, Volume 264) Hardcover7 * € (D) 74,85 | € (A) 76,95 | sFr 93,507 € 69,95 | £62.99ISBN 978-1-4471-4819-7

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B. Cordani, Universitá degli Studi, Milan, Italy

Geography of Order and Chaos in MechanicsInvestigations of Quasi‑Integrable Systems with Analytical, Numerical, and Graphical Tools

This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces.

Features 7 Offers a unique approach to the dynamics of quasi-integrable Hamiltonian systems 7 Pro-vides a rare opportunity for readers to ex-periment with and fully conceptualize recent numerical tools via customized MATLAB applications 7 Gives a rigorous but clean and uncluttered presentation of perturbaton theory, including clear proofs of the KAM and Nekhoro-shev theorems 7 Fully describes new, sophisti-cated techniques for reducing two paradigmatic problems the field to normal forms

Contents Preface.- List of Figures.- 1 Introductory Survey.- 2 Analytical Mechanics and Integrable Systems.- 3 Perturbation Theory.- 4 Numerical Tools I: ODE Integration.- 5 Numerical Tools II: Detecting Order, Chaos, and Resonances.- 6 The Kepler Problem.- 7 The KEPLER Program.- 8 Some Perturbed Keplerian Systems.- 9 The Multi-Body Gravitational Problem.- Bibliography.- Index.

Fields of interestMathematical Physics; Differential Geometry; Nonlinear Dynamics



Available

2013. XVIII, 332 p. 75 illus., 27 in color. (Progress in Mathematical Physics, Volume 64) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-0-8176-8369-6

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O. L. Costa, University of São Paulo, SP, Brazil; M. D. Fragoso, M. G. Todorov, National Laboratory for Scientific Computing, Petrópolis, RJ, Brazil

Continuous-Time Markov Jump Linear SystemsIt is important to introduce mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures.

Features 7 Introduces an active and interesting research area 7 Presents a unified and rigorous treatment of recent results in control theory 7 Numerous applications in safety critical and high-integrity systems including robotics, economics and wire-less communication

Contents 1.Introduction.- 2.A Few Tools and Notations.- 3.Mean Square Stability.- 4.Quadratic Optimal Control with Complete Observations.- 5.H2 Optimal Control With Complete Observations.- 6.Quadratic and H2 Optimal Control with Partial Observations.- 7.Best Linear Filter with Unknown (x(t), θ(t)).- 8.H_$infty$ Control.- 9.Design Techniques.- 10.Some Numerical Examples.- A.Coupled Differential and Algebraic Riccati Equations.- B.The Adjoint Operator and Some Auxiliary Results.- References. - Notation and Conventions.- Index.

Fields of interestProbability Theory and Stochastic Processes; Systems Theory, Control; Dynamical Systems and Ergodic Theory



Due February 2013

2013. Approx. 290 p. (Probability and Its Applications) Hardcover7 * € (D) 90,90 | € (A) 93,45 | sFr 113,507 € 84,95 | £76.50ISBN 978-3-642-34099-4

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32

D. v. Dalen, Utrecht University

L.E.J. Brouwer – Topologist, Intuitionist, PhilosopherHow Mathematics Is Rooted in Life

Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and phi-losopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intu-ition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathemati-cians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foun-dation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics.

Features 7 The only comprehensive biography of L.E.J. Brouwer, the famous Dutch mathematician and philosopher 7 Contains background infor-mation on the beginnings of algebraic topol-ogy 7 Explores how mathematics was affected by the conflicts of the twentieth century

Contents Child and Student.- Mathematics and Mysticism.- The Dissertation.-Cantor-Schoenflies Topology.- The New Topology.- Making a Career.- The War Years.- Mathematics after the War.- Politics and Mathematics.- The Breakthrough.- The Fathers of Dimension.- Progress, Recognition, and Fric-tions.- From Berlin to Vienna.- The Three Battles.- The Thirties.- War and Occupation.- Post-War Events.- The Restless Emeritus.

Fields of interestHistory of Mathematical Sciences; Topology; Mathematical Logic and Foundations

Target groupsPopular/general

Product categoryBiography

Due December 2012

First edition published in two volumes as “Mystic, Geometer, and Intuitionist: The Life of L.E.J. Brouwer” by Oxford University Press in 1999 and 2004

2013. X, 930 p. 97 illus., 19 in color. Hardcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £24.95ISBN 978-1-4471-4615-5

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A. Detinko, D. Flannery, National University of Ireland, Galway, Ireland; E. O’Brien, University of Auckland, New Zealand (Eds)

Probabilistic Group Theory, Combinatorics, and ComputingLectures from the Fifth de Brún Workshop

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computa-tional and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a fo-rum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.

Features 7 Unique selection of frontier results which are not available in any other sources 7 Authors are world leading researchers 7 Each chapter is a ready-made graduate lecture course

Contents Martin W. Liebeck: Probabilistic and asymptotic aspects of finite simple groups.- Alice C. Nie-meyer, Cheryl E. Praeger, Ákos Seress: Estimation problems and randomised group algorithms.- Leonard H. Soicher: Designs, groups and comput-ing.

Fields of interestGroup Theory and Generalizations; Symbolic and Algebraic Manipulation



Due January 2013

2013. XIII, 110 p. (Lecture Notes in Mathematics, Volume 2070) Softcover7 * € (D) 37,40 | € (A) 38,45 | sFr 47,007 € 34,95 | £31.99ISBN 978-1-4471-4813-5

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J. H. Dshalalow, Florida Institute of Technology, Melbourne, FL, USA

Foundations of Abstract AnalysisFoundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience.

Features 7 Systematic presentation with cutting edge clas-sical themes in point-set topology and measure/integration 7 Fills a gap between basic and advanced texts through rigorous and yet detailed treatment of topics 7 Includes solutions to hundreds of problems which help reinforce the text 7 Key analytical formations preceded by blueprints and discussions 7 Many historical and biographical inserts on subjects and people

Contents Set-Theoretic and Algebraic Preliminaries.- Analysis of Metric Spaces.- Elements of Point-Set Topology.-Measurable Spaces and Measurable Functions.- Measures.- Integration in Abstract Spaces.- Solutions to Selected Problems.- Bibliography.-List of Symbols.-Index of Names and Terms.

Fields of interestAnalysis; Functional Analysis; Numerical Analysis

Target groupsUpper undergraduate


Due November 2012

2nd ed. 2013. X, 748 p. 29 illus., 21 in color. Hardcover7 * € (D) 85,55 | € (A) 87,95 | sFr 106,507 € 79,95 | £72.00ISBN 978-1-4614-5961-3

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33

W. Freeden, M. Gutting, University of Kaiserslautern, Germany

Special Functions of Mathematical (Geo-)PhysicsSpecial functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understand-ing of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.

Features 7 Presents special functions as essential tools contributing to solutions for geoscientific prob-lems 7 Attractive textbook for the education in geomathematics 7 Addresses mathematicians, physicists, geo-engineers and geoscientists

Contents 1 Introduction: Geomathematical Motiva-tion.- Part I: Auxiliary Functions.- 2 The Gamma Function.- 3 Orthogonal Polynomials.- Part II: Spherically Oriented Functions.- 4 Scalar Spheri-cal Harmonics in R^3.- 5 Vectorial Spherical Harmonics in R^3.- 6 Spherical Harmonics in R^q.- 7 Classical Bessel Functions.- 8 Bessel Functions in R^q.- Part III: Periodically Oriented Functions.- 9 Lattice Functions in R.- 10 Lattice Functions in R^q.- 11 Concluding Remarks.- Ref-erences.- Index.

Fields of interestSpecial Functions; Mathematical Physics; Geo-physics/Geodesy



Due January 2013

2013. XVI, 465 p. 36 illus., 18 in color. (Applied and Numerical Harmonic Analysis) Hardcover7 approx. * € (D) 64,15 | € (A) 65,95 | sFr 80,007 approx. € 59,95 | £53.99ISBN 978-3-0348-0562-9

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A. Fruchard, Université de Haute Alsace, France; R. Schäfke, Université de Strasbourg, France

Composite Asymptotic ExpansionsThe purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and func-tions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however.

Features 7 Presents a comprehensive theory of infinite composite asymptotic expansions (CAsEs), an alternative to the method of matched asymptotic expansions 7 Generalizes the classical theory of Gevrey asymptotic expansions to such CAsEs, thus establishing a new powerful tool for the study of turning points of singularly perturbed ODEs 7 Using CAsEs, especially their versions of Gevrey type, to obtain new results for three classical problems in the theory of singularly perturbed ODEs

Contents Four Introductory Examples.- Composite Asymptotic Expansions: General Study.- Com-posite Asymptotic Expansions: Gevrey Theory.- A Theorem of Ramis-Sibuya Type.- Composite Expansions and Singularly Perturbed Differential Equations.- Applications.- Historical Remarks.- References.- Index.

Fields of interestApproximations and Expansions; Ordinary Differ-ential Equations; Sequences, Series, Summability



Due December 2012

2013. X, 161 p. 21 illus. (Lecture Notes in Mathematics, Volume 2066) Softcover7 * € (D) 37,40 | € (A) 38,45 | sFr 47,007 € 34,95 | £31.99ISBN 978-3-642-34034-5

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D. J. Galiffa, Penn State Erie, Erie,PA, USA

On the Higher-Order Sheffer Orthogonal Polynomial SequencesOn the Higher-Order Sheffer Orthogonal Poly-nomial Sequences sheds light on the existence/non-existence of B-Type 1 orthogonal polynomi-als. This book presents a template for analyzing potential orthogonal polynomial sequences including additional higher-order Sheffer classes. This text not only shows that there are no OPS for the special case the B-Type 1 class, but that there are no orthogonal polynomial sequences for the general B-Type 1 class as well. Moreover, it is quite provocative how the seemingly subtle transition from the B-Type 0 class to the B-Type 1 class leads to a drastically more difficult characterization problem.

Features 7 Addresses preliminary insights regarding the characterization of Orthogonal Polynomial Sequences 7 Gives a concise and informative overview of the development of the B- Type 0 Or-thogonal Polynomail Sequences 7 Functions as a template for which other polynomial sequences can be analyzed

Contents 1. The Sheffer A-Type 0 Orthogonal Polynomial Sequences and Related Results.- 2. Some Applica-tions of the Sheffer A-Type 0 Orthogonal Poly-nomial Sequences.- 3. A Method for Analyzing a Special Case of the Sheffer B-Type 1 Polynomial Sequences.

Fields of interestLinear and Multilinear Algebras, Matrix Theory; Computational Science and Engineering


Product categoryBrief

Due January 2013

2013. XVI, 100 p. 2 illus. (SpringerBriefs in Mathematics) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4614-5968-2

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34

J. Gallier, University of Pennsylvania, Philadelphia, PA, USA; D. Xu, Bryn Mawr College, PA, USA

A Guide to the Classification Theorem for Compact SurfacesThis welcome boon for students of algebraic topol-ogy cuts a much-needed central path between other texts whose treatment of the classifica-tion theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The au-thors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example.

Features 7 Student-centred guide offering comprehensiv – and comprehensible – treatment of the classifica-tion theorem for compact surfaces 7 A short proof using graph theory (due to Thomassen) that every compact surface can be triangulated 7 Accessible to upper level under-graduate students without assuming too much background

Contents The Classification Theorem: Informal Presen-tation.- Surfaces.- Simplices, Complexes, and Triangulations.- The Fundamental Group, Orient-ability.- Homology Groups.- The Classification Theorem for Compact Surfaces.- Viewing the Real Projective Plane in R3.- Proof of Proposition 5.1.- Topological Preliminaries.- History of the Classification Theorem.- Every Surface Can be Triangulated.- Notes .

Fields of interestTopology; Manifolds and Cell Complexes (incl. Diff.Topology); Algebraic Topology


Product categoryUndergraduate textbook

Due January 2013

2013. VII, 176 p. 40 illus., 20 in color. (Geometry and Computing, Volume 9) Hardcover7 * € (D) 42,75 | € (A) 43,95 | sFr 53,507 € 39,95 | £35.99ISBN 978-3-642-34363-6

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F. Brezzi, Istituto Universitario di Studi Superiori (IUSS), Pavia, Italy; P. Colli Franzone, U. Gianazza, G. Gilardi, Università degli Studi di Pavia, Italy (Eds)

Analysis and Numerics of Partial Differential EquationsContents Part I A Historical Perspective.- Personal Memo-ries.- Some Aspects of the Research of Enrico Magenes in Partial Differential Equations.- En-rico Magenes and the Dam Problem.- Inverse Problems in Electrocardiology.- Stefan Problems and Numerical Analysis.- Enrico Magenes and the Teaching of Mathematics.- List of Mathematical Works Authored or Edited by Enrico Magenes.- Part II Recent Developments.- Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case.- Spaces of Finite Element Differential Forms.- A Priori Bounds for Solutions of a Nonlocal Evolu-tion PDE.- On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems.- A Theory and Challenges for Coarsening in Micro-structure.- A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation.- Analysis and Numerics of Some Fractal Boundary Value Problems.- AFEM for Geometric PDE: The Laplace-Beltrami Opera-tor.- Generalized Reduced Basis Methods and n-Width Estimates for the Approximation of the Solution Manifold of Parametric PDEs.- Varia-tional Formulation of Phase Transitions with Glass Formation.

Fields of interestPartial Differential Equations; Computational Mathematics and Numerical Analysis; Calculus of Variations and Optimal Control; Optimization



Due December 2012

2013. Approx. 400 p. (Springer INdAM Series, Volume 4) Hardcover7 approx. * € (D) 101,60 | € (A) 104,45 | sFr 126,507 approx. € 94,95 | £85.50ISBN 978-88-470-2591-2

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M. I. Gil’, Ben Gurion University of the Negev, Beer Sheva, Israel

Stability of Vector Differential Delay EquationsDifferential equations with delay naturally occur in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings.

Features 7 Well-written systematic and comprehensive exposition 7 Presents a solution of the Aizer-man‐Myshkis problem 7 Develops the Hill method for functional differential equations with period coefficients

Contents Preface.- 1. Preliminaries.- 2. Some Results of the Matrix Theory.- 3. General Linear Systems.- 4. Time-Invariant Linear Systems with Delay.- 5. Properties of Characteristic Values.- 6. Equations Close to Autonomous and Ordinary Differential Ones.- 7. Periodic Systems.- 8. Linear Equations with Oscillating Coefficients.- 9. Linear Equations with Slowly Varying Coefficients.- 10. Nonlinear Vector Equations.- 11. Scalar Nonlinear Equa-tions.- 12. Forced Oscillations in Vector Semi-Linear Equations.- 13. Steady States of Differential Delay Equations.- 14. Multiplicative Representa-tions of Solutions.- Appendix A. The General Form of Causal Operators.- Appendix B. Infinite Block Matrices.- Bibliography.- Index.

Fields of interestOrdinary Differential Equations; Difference and Functional Equations; Systems Theory, Control



Due March 2013

2013. X, 272 p. (Frontiers in Mathematics) Softcover7 approx. * € (D) 53,45 | € (A) 54,95 | sFr 66,507 approx. € 49,95 | £44.99ISBN 978-3-0348-0576-6

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35

W. Han, The University of Iowa, Iowa City, IA, USA; B. D. Reddy

PlasticityMathematical Theory and Numerical Analysis

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with harden-ing assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis.

Features 7 Book bridging mechanics and mathemat-ics 7 Provides a comprehensive and unified treatment of the mathematical theory and numeri-cal analysis 7 Focuses on theoretical aspects of the small-strain theory of hardening elastoplastic-ity

Contents Preface to the Second Edition.- Preface to the First Edition.-Preliminaries.- Continuum Me-chanics and Linearized Elasticity.- Elastoplastic Media.- The Plastic Flow Law in a Convex-Analytic Setting.- Basics of Functional Analysis and Function Spaces.- Variational Equations and Inequalities.- The Primal Variational Problem of Elastoplasticity.- The Dual Variational Problem of Classical Elastoplasticity.- Introduction to Finite Element Analysis.- Approximation of Variational Problems.- Approximations of the Abstract Prob-lem.- Numerical Analysis of the Primal Problem.- References.- Index.-

Fields of interestNumerical Analysis; Theoretical and Applied Mechanics; Continuum Mechanics and Mechanics of Materials



Due November 2012

2nd ed. 2013. X, 425 p. 41 illus. (Interdisciplinary Applied Mathematics, Volume 9) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-1-4614-5939-2

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T. Johnson, Editions75, Paris, France; F. Jedrzejewski, CEA Saclay, Gif-sur-Yvette, France

Looking at NumbersNumbers are part of nature. Observing them, looking at them, thinking about them, is a way of understanding our relationship to nature. But when we do this in a technical professional way, we sometimes overlook the basic appearances, the things we can understand by simply “looking at numbers.” Everyone talks about the beauty of mathematics, but almost no one observes that this beauty is largely a result of the symmetries that emerge from simple combinations of natural num-bers. One sees this clearly in Looking at Numbers.

Features 7 Mathematics and music from a platonic point of view 7 Numbers as Pythagoras might have seen them 7 Numbers producing images and music too

Contents Introduction.- 1. Permutations.- 1.1 Symmetric Group.- 1.2 Bruhat Order.- 1.3 Euler Charac-teristic.- 1.4 Group Action.- 1.5 Permutohedra and Cayley Graphs.- 1.6 Coxeter Groups.- 1.7 Homometric Sets.- 2. Sums.- 2.1 Integer Parti-tions.- References.- 3. Subsets.- 3.1 Combinatorial Designs.- 4 Kirkman’s Ladies, a Combinatorial Design.- 4.1 Steiner and Kirkman Systems.- 5. Twelve.- 5.1 (12,4,3).- 6. (9,4,3).- 6.1 Decomposi-tion of Block Designs.- 7. 55 Chords.- 7.1 Chords and Designs.-8. Clarinet Trio.- 8.1 Strange Fractal Sequences.- 9. Loops.- 9.1 Self-Replicating Melo-dies.- 9.2 Rhythmic Canons.-10. Juggling.- 10.1 Juggling, Groups, and Braids.- 11. Unclassified.- 11.1 Some Other Designs.- A Figures.- References.

Fields of interestGraph Theory; Mathematics, general; Mathemat-ics in Music



Due February 2013

2013. Approx. 200 p. 100 illus. With online files/update. Softcover7 approx. * € (D) 53,45 | € (A) 54,95 | sFr 66,507 approx. € 49,95 | £44.99ISBN 978-3-0348-0553-7

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R. P. Kanwal, [deceased]

Linear Integral EquationsTheory & Technique

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathemat-ics, theoretical mechanics, and mathematical physics. This uncorrected soft cover reprint of the second edition places the emphasis on applications and presents a variety of techniques with extensive examples.Originally published in 1971, Linear Integral Equations is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems also makes the book useful to researchers in many applied fields.

Features 7 Affordable reprint of a classic graduate text-book 7 Emphasis on applications to theoretical mechanics, mathematical physics, and applied mathematics 7 Presents a variety of techniques with extensive examples

Contents Introduction.- Integral Equations with Separable Kernels.- Method Of Successive Approxima-tions.- Classical Fredholm Theory.- Applications of Ordinary Differential Equations.- Applications of Partial Differential Equations.- Symmetric Kernels.- Singular Integral Equations.- Integral Transformation Methods.- Applications to Mixed Boundary Value Problems.- Integral Equations Perturbation Methods.- Appendix.- Bibliography.- Index.

Fields of interestIntegral Equations; Applications of Mathematics; Ordinary Differential Equations



Due November 2012

2013. XI, 318 p. 12 illus. (Modern Birkhäuser Classics) Softcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-1-4614-6011-4

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36

V. V. Kozlov, Steklov Mathematical Institute, Moscow, Russia; S. D. Furta, Russian Academy of National Economy & Public Administration, Moscow, Russia

Asymptotic Solutions of Strongly Nonlinear Systems of Differential EquationsTransl. Russian: L. Senechal, Mount Holyoke College, South Hadley, MA, USA

The book is dedicated to the construction of par-ticular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method.

Features 7 Monograph by leading researchers in the theory of dynamical systems 7 Book can be used for a graduate course or seminar 7 Pedagogic approach, contains many examples

Contents Preface.- Semi-quasihomogeneous systems of or-dinary differential equations.- 2. The critical case of purely imaginary kernels.- 3. Singular prob-lems.- 4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems.- Appendix A. Nonexponential asymptotic solutions of systems of functional-differential equations.- Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi-quasihomogeneous systems of ordinary di¤erential equations.- Bibliography.

Fields of interestOrdinary Differential Equations; Dynamical Sys-tems and Ergodic Theory; Mathematical Methods in Physics



Due December 2012

2013. X, 280 p. 2 illus. (Springer Monographs in Mathematics) Hardcover7 * € (D) 90,90 | € (A) 93,45 | sFr 113,507 € 84,95 | £76.50ISBN 978-3-642-33816-8

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J. Li, University of Nevada, Las Vegas, NV, USA; Y. Huang, Xiangtan University, PR China

Time-Domain Finite Element Methods for Maxwell’s Equations in MetamaterialsThe purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design.

Features 7 First book on mathematical modeling and numerical analysis of Maxwell's equations involv-ing metamaterials 7 Complete MATLAB source code on edge elements developed for solving Max-well's equations 7 Introduce the-state-of-the-art of computational methods for wave propagation in metamaterials

Contents Introduction to Metamaterials.- Introduction to Finite Element Methods.- Time-Domain Finite El-ement Methods for Metamaterials.- Discontinuous Galerkin Methods for Metamaterials.- Supercon-vergence Analysis for Metamaterials.- A Poste-riori Error Estimation.- A Matlab Edge Element Code.- Perfectly Matched Layers.- Simulation of Metamaterials.- References.- Index.

Fields of interestComputational Science and Engineering; Appl.Mathematics/Computational Methods of Engi-neering; Simulation and Modeling



Due December 2012

2013. XIV, 292 p. 39 illus., 29 in color. (Springer Series in Computational Mathematics, Volume 43) Hardcover7 * € (D) 90,90 | € (A) 93,45 | sFr 113,507 € 84,95 | £76.50ISBN 978-3-642-33788-8

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A. Lunardi, University of Parma, Italy

Analytic Semigroups and Optimal Regularity in Parabolic ProblemsThe book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equa-tions. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel per-spective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equa-tions and in parabolic partial differential equations and systems.

Features 7 Systematic treatment of the basic theory of an-alytic semigroups and abstract parabolic equations in general Banach spaces 7 Known Theorems are presented from a novel perspective 7 Teach-es how to exploit basic techniques 7 Addresses PhD students as well as researchers

Contents Introduction.- 0 Preliminary material: spaces of continuous and Hölder continuous functions.- 1 Interpolation theory.- Analytic semigroups and in-termediate spaces.- 3 Generation of analytic semi-groups by elliptic operators.- 4 Nonhomogeneous equations.- 5 Linear parabolic problems.- 6 Linear nonautonomous equations.- 7 Semilinear equa-tions.- 8 Fully nonlinear equations.- 9 Asymptotic behavior in fully nonlinear equations.- Appendix: Spectrum and resolvent.- Bibliography.- Index.

Fields of interestPartial Differential Equations; Operator Theory; Functional Analysis



Due November 2012

Originally published as volume 16in the series: Progress in Nonlinear Differential Equations and Their Applications series

2013. XIV, 424 p. 1 illus. (Modern Birkhäuser Classics) Softcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-3-0348-0556-8

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37

R. Magnanini, Università di Firenze, Italy; S. Sakaguchi, Tohoku University, Sendai, Japan; A. Alvino, Università di Napoli “Federico II”, Italy (Eds)

Geometric Properties for Parabolic and Elliptic PDE’sContents Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations.- Elvise Berchio, A family of Hardy-Rellich type inequalities involving the L2-norm of the Hessian matrices.- Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains.- Lorenzo Brasco and Rolando Magnanini, The heart of a convex set.- Giulio Ciraolo, A viscos-ity equation for minimizers of a class of very degenerate elliptic functionals.- Adele Ferone, Kato’s inequality in the half space: an alternative proof and relative improvements.- Ilaria Fragalà, Filippo Gazzola and Jimmy Lamboley, Sharp bounds for the p-torsion of convex planar do-mains.- Giovanni Franzina and Enrico Valdinoci, Geometric analysis of fractional phase transition interfaces.- Antonio Greco, Existence of solutions to some classical variational problems.- Norihisa Ikoma, Existence of minimizers for some coupled nonlinear Schrödinger equations.- Kazuhiro Ishige and Yoshitsugu Kabeya, Decay rate of Lq norms of critical Schrödinger heat semigroups.- Shuichi Jimbo, Hadamard variation for electromagnetic frequencies.- Toru Kan, Global structure of the so-lution set for a semilinear elliptic problem related to the Liouville equation on an annulus.- Anna Mercaldo, A priori estimates and comparison principle for some nonlinear elliptic equations.- Takeyuki Nagasawa, Existence and uniqueness of the n-dimensional Helfrich flow.- Bernhard Ruf and Federica Sani, Ground states for elliptic equa-tions in R2 with exponential critical growth. [...]

Fields of interestAnalysis; Partial Differential Equations; Func-tional Analysis



Due January 2013

2013. VIII, 300 p. 11 illus. (Springer INdAM Series, Volume 2) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-88-470-2840-1

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A. M. Marr, Southwestern University, Georgetown, TX, USA; W. Wallis, Southern Illinois University, Carbondale, IL, USA

Magic GraphsMagic squares are among the more popular math-ematical recreations. Over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. Recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: · a new chapter on magic labeling of directed graphs · applica-tions of theorems from graph theory and interest-ing counting arguments · new research prob-lems and exercises covering a range of difficulties · a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergradu-ate text for courses in mathematics or computer science, and as reference for the researcher.

Features 7 Only book of its kind in the area of magic la-belings 7 Features numerous exercises and their solutions 7 Includes updates on new research in the field

Contents Preface.- List of Figures.- Preliminaries.- Edge-Magic Total Labelings.- Vertex-Magic Total Labelings.- Totally Magic Labelings.- Magic Type Labeling of Digraphs.- Notes on the Research Problems.- References.- Bibliography.- Answers to Selected Exercises.- Index.

Fields of interestCombinatorics; Discrete Mathematics in Com-puter Science; Applications of Mathematics



Due November 2012

2nd ed. 2013. XVI, 186 p. 34 illus. Hardcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-0-8176-8390-0

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V. Michel, University of Siegen, Germany

Lectures on Constructive ApproximationFourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on clas-sical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.

Features 7 Combines an explanation of classical and mod-ern approximation methods for Euclidean and spherical geometries 7 Detailed explanations and illustrations included to optimize the under-standing of topics 7 Concentrates on the es-sentials for a course 7 Uses examples of data sets to explain the tasks, challenges, advantages, and disadvantages of the methods presented 7 First work that explicitly treats approximation methods on the ball

Contents Introduction: the Problem to be Solved.- Part I Basics.- Basic Fundamentals—What You Need to Know.- Approximation of Functions on the Real Line.- Part II Approximation on the Sphere.- Basic Aspects.- Fourier Analysis.- Spherical Splines.- Spherical Wavelet Analysis.- Spherical Slepian Functions.- Part III Approximation on the 3D Ball.- Orthonormal Bases.- Splines.- Wavelets for Inverse Problems on the 3D Ball.- The Regularized Functional Matching Pursuit (RFMP).- Refer-ences.- Index.

Fields of interestApproximations and Expansions; Special Func-tions; Fourier Analysis



Due November 2012

2013. XV, 322 p. 82 illus., 54 in color. (Applied and Numerical Harmonic Analysis) Hardcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-0-8176-8402-0

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38

M. Nagasawa, University of Zurich, Switzerland

Schrödinger Equations and Diffusion TheorySchrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the Schrödinger equation and diffu-sion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles.

Features 7 Self-contained and well-organized introduc-tion to the theory of diffusion processes and applications 7 Recommended to researchers and graduate students in probability theory, functional analysis and quantum dynamics 7 Excellent ad-dition to the literature in probability theory

Contents Preface.- I Introduction and Motivation.- II Dif-fusion Processes and their Transformations.- III Duality and Time Reversal of Diffusion Process-es.- IV Equivalence of Diffusion and Schrödinger Equations.- V Variational Principle.- VI Diffusion Processes in q-Representation.- VII Segregation of a Population.- VIII The Schrödinger Equation can be a Boltzmann Equation.- IX Applications of the Statistical Model for Schrödinger Equations.- X Relative Entropy and Csiszar’s Projection.- XI Large Deviations.- XII Non-Linearity Induced by the Branching Property.- Appendix.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes; Par-tial Differential Equations; Mathematical Physics



Due November 2012

Originally published as volume 86 in the Monographs in Mathematics series

1993 1993. XII, 319 p. 7 illus. (Modern Birkhäuser Classics) Softcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-3-0348-0559-9

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K. Parthasarathy, Indian National Science Academy, New Delhi, India

An Introduction to Quantum Stochastic CalculusAn Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynam-ics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unifica-tion. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito’s correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semi-groups as well as classical Markov semigroups are realised through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.

Features 7 One of the first systematic attempts to weave classical probability theory into the quantum framework 7 Self-contained introduction to the Fock space quantum stochastic calculus in its basic form 7 A large number of stimulating exercises make the text invaluable to students

Contents Preface.- I Events, Observables and States.- II Ob-servables and States in Tensor Products of Hilbert Spaces.- III Stochastic Integration and Quantum Ito’s Formula.- References.- Index.- Author Index.

Fields of interestProbability Theory and Stochastic Processes; Mathematical Physics; Functional Analysis



Due November 2012


2013. IX, 289 p. 2 illus. (Modern Birkhäuser Classics) Softcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-3-0348-0565-0

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I. Peeva, Cornell University, Ithaca, NY, USA (Ed)

Commutative AlgebraExpository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday

Contents Marian Aprodu: Lazarfeld-Mukai bundles and ap-plications to syzygies.- Paul Aspinwall: Some Ap-plications of Commutative Algebra to String Theo-ry.- Angelica Benito, Eleonore Faber, and Karen Smith: F-threshold: a characteristic p analog of the log canonical threshold.- Christine Berkesch, Daniel Erman, and Manoj Kumini: Pure resolu-tions and generalizations.- Manuel Blickle and Karl Schwede: p1 linear maps: from local behavior to vanishing theorems.- Markus Brodmann, Cao Luy Linh, and Maria-Helena Seiler: Castelnuovo-Mumford Regularity of Annihilators, Ext-Modules and Tor-Modules.- David Buchsbaum: Selections From the Letter-Place Panoply.- Aldo Conca, Emanuella DeNegri, and Maria-Evelina Rossi: Bounds for the Castelnuovo-Mumford regularity and Koszul algebras.- Marc Chardin: Regularity.- Hailong Dao: Ext and Tor over complete intersec-tions.- Christopher Francisco, Huy Tai Ha, and Jeffrey Mermin: Resolutions of edge ideals.- Gra-ham Evans and Phillip Griffith: A Brief History of Order Ideals.- Laurent Gruson, Steven Sam, and Jerzy Weyman: Lectures on GIT quotients related to Abelian varieties.- Melvin Hochster: Origins of the study of F-purity and F-splitting.- Craig Huneke: Hilbert-Kunz multiplicity.- Juan Migliore, Uwe Nagel, and Fabrizio Zanello : Pure O-sequences.- Jason McCullough and Alexandra Seceleanu: Bounds on projective dimension.- Gra-ham Leuschke and Roger Wiegand: Brauer-Thrall theorems and direct-sum decompositions over local rings. [...]

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



Due November 2012

2013. VI, 607 p. 18 illus. Hardcover7 * € (D) 117,65 | € (A) 120,95 | sFr 146,507 € 109,95 | £99.00ISBN 978-1-4614-5291-1

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39

M. A. Picardello, Università di Roma “Tor Vergata”, Italy (Ed)

Trends in Harmonic AnalysisFeatures 7 An unusually wide scope of developments in Harmonic Analysis 7 Contributions by leading experts in each area 7 A unique panorama of the development of italian harmonic Analysis, a plus for the new INdAM-Springer collection 7 Dedi-cated to a famous mathematician in the occasion of his retirement

Contents The shifted wave equation on Damek–Ricci spaces and on homogeneous trees.- Invariance of capacity under quasisymmetric maps of the circle: an easy proof.- A Koksma–Hlawka inequality for simpli-ces.- A dual interpretation of the Gromov–Thur-ston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices.- The algebras generated by the Laplace operators in a semi-homogeneous tree.- Surjunctivity and reversibility of cellular automata over concrete categories.- Pointwise convergence of Boch-ner–Riesz means in Sobolev spaces.- Sub-Finsler geometry and finite propagation speed.- On the boundary behavior of holomorphic and harmonic functions.- Constructing Laplacians on limit spaces of self-similar groups.- Some remarks on generalized Gaussian noise.- Eigenvalues of the vertex set Hecke algebra of an affine building.- A Liouville type theorem for Carnot groups: a case study.- Stochastic properties of Riemannian manifolds and applications to PDE’s.- Character-ization of Carleson measures for Besov spaces on homogeneous trees.- Atomic and maximal Hardy spaces on a Lie group of exponential growth.- The maximal singular integral: estimates in terms of the singular integral.

Field of interestMathematics, general



Due January 2013

2013. XVIII, 442 p. 24 illus. (Springer INdAM Series, Volume 3) Hardcover7 * € (D) 101,60 | € (A) 104,45 | sFr 126,507 € 94,95 | £85.50ISBN 978-88-470-2852-4

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S. Salsa, F. Vegni, A. Zaretti, P. Zunino, Politecnico di Milano, Italia

A Primer on PDEsModels, Methods, Simulations

This book is designed as an advanced undergradu-ate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.

Features 7 This minimal knowledge on numerical ap-proximation schemes represents an useful tool for training on model applications 7 Numerical simulations help to put into action and visualize the theoretical properties of the models that will be analysed 7 Each chapter ends with a brief introduction to numerical approximation tech-niques for the specific problem at hand

Contents Introduction.- Scalar Conservation Laws.- Diffu-sion.- The Laplace Equation.- Reaction-diffusion models.- Waves and vibrations.- Elements of Functional Analysis.- Variational formulation of elliptic problems.- Weak formulation of evolution problems.- Solutions.- Fourier Series.- Notes on ordinary differential equations.- Finite difference approximation of time dependent problems.- Identities and Formulas.

Fields of interestMathematics, general; Partial Differential Equa-tions; Analysis


Product categoryUndergraduate textbook

Due November 2012

2013. Approx. 480 p. (UNITEXT / La Matematica per il 3+2) Softcover7 approx. * € (D) 48,10 | € (A) 49,45 | sFr 60,007 approx. € 44,95 | £40.99ISBN 978-88-470-2861-6

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H. Sohr, University Paderborn, Germany

The Navier-Stokes EquationsAn Elementary Functional Analytic Approach

The primary objective of this monograph is to de-velop an elementary and self-contained approach to the mathematical theory of a viscous, incom-pressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical gener-ality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces.

Features 7 Elementary and selfcontained approach to the mathematical theory of the viscous incompressible Navier-Stokes equations 7 Requires familiarity with the basic functional analytic tools in Hilbert and Banach spaces only 7 Fills a gap by provid-ing a systematic treatment of the subject

Contents Preface.- I Introduction.- II Preliminary Results.- III The Stationary Navier-Stokes Equations.- IV The Linearized Nonstationary Theory.- V The Full Nonlinear Navier-Stokes Equations.- Bibliogra-phy.- Index.

Fields of interestPartial Differential Equations; Mathematical Phys-ics; Functional Analysis



Due November 2012

Originally published in the Birkhäuser Advanced Texts Basler Lehrbücher series

2013. VI, 367 p. (Modern Birkhäuser Classics) Softcover7 * € (D) 48,10 | € (A) 49,45 | sFr 60,007 € 44,95 | £40.99ISBN 978-3-0348-0550-6

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40

H. Triebel, Friedrich-Schiller-University Jena, Germany

The Structure of FunctionsThis book deals with the constructive Weierstras-sian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equa-tions. The book is self-contained, although some parts may be considered as a continuation of the author’s book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particu-lar, how they are interrelated. - - - The book under review can be regarded as a continuation of [his book on “Fractals and spectra”, 1997] (...) There are many sections named: comments, prepara-tions, motivations, discussions and so on.

Features 7 Self-contained, i.e. the main ideas can be understood independently of the existing litera-ture 7 Summarizes the results of the author and his co-workers in recent years 7 The material is presented in such a way that the main ideas can be understood independently of the existing litera-ture 7 Addresses mathematicians and (theoreti-cal) physicists

Contents Preface.- I Decompositions of Functions.- II Sharp Inequalities.- III Fractal Elliptic Operators.- IV Truncations and Semi-linear Equations.- Refer-ences.- Symbols.- Index.

Fields of interestFunctional Analysis; Measure and Integration; Abstract Harmonic Analysis



Due November 2012


2013. XII, 425 p. 7 illus. (Modern Birkhäuser Classics) Softcover7 * € (D) 64,15 | € (A) 65,95 | sFr 80,007 € 59,95 | £53.99ISBN 978-3-0348-0568-1

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S. S. Varadhan R. Bhatia, A. Bhatt, K. Parthasarathy (Eds)

Collected Papers IVParticle Systems and Their Large Deviations

Contents Volume 4: Particle Systems and their Large Devia-tions.- Nonlinear diffusion limit for a system with nearest neighbor interaction.- Hydrodynamics and large deviation for simple exclusion pro-cesses.- Large deviations from a hydrodynamic scaling limit.- On the derivation of conservation laws for stochastic dynamics .- Scaling limits for interacting diffusions .- Scaling limit for inter-acting Ornstein-Uhlenbeck processes.- Entropy methods in hydrodynamical scaling .- Hydrody-namical limit for a Hamiltonian system with weak noise.- Nonlinear diffusion limit for a system with nearest neighbor interactions II.- Regularity of self-diffusion coefficient .- Entropy methods in hy-drodynamic scaling .- Spectral gap for zero-range dynamics.- The complex story of simple exclusion .- Non-gradient models in hydrodynamic scaling .- Relative entropy and mixing properties of inter-acting particle systems.- Diffusive limit of lattice gas with mixing conditions.- Large deviations for the symmetric simple exclusion process in dimensions d > 3.- Large deviations for interact-ing particle systems .- Infinite particle systems and their scaling limits .- Lectures on hydrodynamic scaling .- Scaling limits of large interacting sys-tems .- Asymptotic behavior of a tagged particle in simple exclusion processes.- Large deviation and hydrodynamic scaling .- Symmetric simple exclusion process: regularity of the self-diffusion coefficient.- Finite-dimensional approximation of the self-diffusion coefficient for the exclusion pro-cess.- Large deviations for the asymmetric simple exclusion process . [...]

Fields of interestProbability Theory and Stochastic Processes; Mathematical Physics; Partial Differential Equa-tions


Product categoryCollected works

Due October 2012

Jointly published with Hindustan Book Agency, New Delhi, India

2012. 838 p. Hardcover7 * € (D) 107,00 | € (A) 110,00 | sFr 133,507 € 100,00 | £90.00ISBN 978-3-642-33547-1

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V. V. Volchkov, V. V. Volchkov, Donetsk National University, Ukraine

Offbeat Integral Geometry on Symmetric SpacesThe book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group.

Features 7 Covers over twenty years of extensive research on local aspects of integral geometry on sym-metric spaces and the Heisenberg group in one condensed text 7 Highlights significant and previously unpublished results 7 Includes nu-merous new problems

Contents Preface.- Part 1. Analysis on Symmetric Spaces. 1 Preliminaries.- 2 The Euclidean case.- 3 Symmet-ric spaces of the non-compact type.-4 Analogies for compact two-point homogeneous Spaces.- 5 The phase space associated to the Heisenberg group.-Part 2. Offbeat Integral Geometry.- 1 Func-tions with zero ball means on Euclidean space.- 2 Two-radii theorems in symmetric spaces.- 3 The problem of finding a function from its ball means.- 4 Sets with the Pompeiu property.- 5 Functions with zero integrals over polytopes.-6 Ellipsoidal means.- 7 The Pompeiu property on a sphere.- 8 The Pompeiu transform on symmetric spaces and groups.-9 Pompeiu transforms on manifolds.- Bib-liography.- Index.- Basic notation.

Fields of interestSpecial Functions; Abstract Harmonic Analysis; Integral Transforms, Operational Calculus



Due February 2013

2013. X, 562 p. Hardcover7 approx. * € (D) 117,65 | € (A) 120,95 | sFr 146,507 approx. € 109,95 | £99.00ISBN 978-3-0348-0571-1

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41

K. Wang, Wuhan Institute of Physics and Mathematics, Hubei, P.R. China

Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential EquationsThis thesis is devoted to the study of the asymptot-ic behavior of singularly perturbed partial differ-ential equations and some related free boundary problems arising from these two problems. We study the free boundary problems in the singulary limit and give some characterizations, and use this to study the dynamical behavior of competing spe-cies when the competition is strong. These results have many applications in physics and biology.

Features 7 Devoted to the study of the asymptotic behav-ior of singularly perturbed differential equations and some related free boundary problems arising from these two problems 7 The results of this thesis have many applications in Physics and Biol-ogy 7 Nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis

Contents Foreword.- Acknowledgements.- Introduction.- Uniqueness, Stability and Uniform Lipschitz Estimates.- Uniqueness in the Singular Limit.- The Dynamics of One Dimensional Singular Limit-ing Problem.- Approximate Clean Up Lem-ma.- Asymptotics in Strong Competition.- The Limited Equation of a Singular Perturbed System.- Reference.- Index.

Fields of interestPartial Differential Equations; Functional Analysis


Product categoryPh.D. Thesis

Due December 2012

2013. Approx. 120 p. (Springer Theses) Hardcover7 approx. * € (D) 106,95 | € (A) 109,95 | sFr 133,507 approx. € 99,95 | £90.00ISBN 978-3-642-33695-9

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P. Xanthopoulos, University of Central Florida, Orlando, FL, USA; P. M. Pardalos, University of Florida, , Gainesville, FL,USA; T. B. Trafalis, University of Oklahoma, Norman,OK, USA

Robust Data MiningData uncertainty is a concept closely related with most real life applications that involve data collec-tion and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques. Integration of robust optimization in the existing data mining techniques aim to create new algorithms resilient to error and noise. This work encapsulates all the latest applications of robust optimization in data mining. This brief contains an overview of the rap-idly growing field of robust data mining research field and presents the most well known machine learning algorithms, their robust counterpart formulations and algorithms for attacking these problems. This brief will appeal to theoreticians and data miners working in this field.

Features 7 Summarizes the latest applications of robust optimization in data mining 7 An essential ac-companiment for theoreticians and data miners

Contents 1. Introduction.- 2. Least Squares Problems.- 3. Principal Component Analysis.- 4. Linear Dis-criminant Analysis.- 5. Support Vector Machines.- 6. Conclusion.

Fields of interestOptimization; Data Mining and Knowledge Dis-covery; Software Engineering/Programming and Operating Systems


Product categoryBrief

Due January 2013

2013. XII, 64 p. 12 illus., 7 in color. (SpringerBriefs in Optimization) Softcover7 * € (D) 53,45 | € (A) 54,95 | sFr 66,507 € 49,95 | £44.99ISBN 978-1-4419-9877-4

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