advances in mathematical mastering the discrete fourier ... · muhle-karbe); and numerical methods...

Mathematics springer.com/NEWSonline

82

Advances in Mathematical EconomicsSeries editors: S. Kusuoka, R. Anderson, C. Castaing, F. H. Clarke, E. Dierker, D. Duffie, L. C. Evans, T. Fujimoto, N. Hirano, T. Ichiishi, A. Ioffe, S. Iwamoto, K. Kamiya, K. Kawamata, H. Matano, M. K. Richter, Y. Takahashi, J.‑M. Grandmont, T. Maruyama, M. Yano, A. Yamazaki, K. Nishimura

Volume 17

S. Kusuoka, T. Maruyama (Eds)

Advances in Mathematical Economics Volume 17A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispens-able machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Features 7 International scientific association that aims to promote research activities in mathematical economics 7 This series is designed to bring together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research 7 This series is published once a year under the auspices of the Research Center for Mathematical Economics

Fields of interestGame Theory, Economics, Social and Behav. Sciences; Probability Theory and Stochastic Pro-cesses; Applications of Mathematics

Target groupsProfessional/practitioner

Discount groupProfessional Non-Medical

Due May 2013

2013. V, 174 p. 12 illus., 3 in color. Hardcover7 $109.00ISBN 978-4-431-54323-7

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K. Alladi, University of Florida, Gainesville, FL, USA; M. Bhargava, Princeton University, NJ, USA; D. Savitt, P. H. Tiep, University of Arizona, Tucson, AZ, USA (Eds)

Quadratic and Higher Degree FormsIn the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School.

Features 7 Provides survey lectures, also accessible to non-experts 7 Introduction summarizes current research on quadratic and higher degree forms with a presentation of the necessary background material 7 Contains expositions on the latest advances on some famous mathematical problems

Contents Preface.- Toy Models for D. H. Lehmer’s Con-jecture II (E. Bannai, T. Miezaki).- On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich).- Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch).- Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Komin-ers).- Quadratic and Automorphic Forms (J. Hanke).- Integral Positive Ternary Quadratic Forms (W. Jagy).- Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala).- On the Length of Binary Forms (B. Reznick).- Represen-tation of Quadratic Forms by Integral Quadratic Forms (R. Schulze-Pillot).- Identifying the Matrix Ring (J. Voight).

Fields of interestNumber Theory; Combinatorics; Special Func-tions

Target groupsResearch


Due June 2013

2013. VIII, 288 p. (Developments in Mathematics, Volume 31) Hardcover7 $109.00ISBN 978-1-4614-7487-6

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I. Amidror, Ecole Polytechnique Fédérale de Lausanne, Switzerland

Mastering the Discrete Fourier Transform in One, Two or Several DimensionsPitfalls and Artifacts

The discrete Fourier transform (DFT) is an ex-tremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations.

Features 7 Written in an informal style using a picto-rial, intuitive approach rather than a rigorous mathematical treatment, intentionally avoid-ing a purist's approach based on theorems and proofs 7 Teaches how to correctly interpret the DFT results, and how to distinguish between true spectral contents and the various artifacts that are only due to DFT 7 Contains information on subjects rarely covered in literature, such as practi-cal questions regarding the correct interpretation of the DFT results

Contents Introduction.- Background and basic notions.- Data reorganizations for the DFT and the IDFT.- True units along the axes when plotting the DFT.- Issues related to aliasing.- Issues related to leakage.- Issues related to resolution and range.- Miscellaneous issues.- Appendices.

Fields of interestFourier Analysis; Mathematical Applications in Computer Science; Visualization



Due May 2013

2013. XII, 374 p. 120 illus., 3 in color. (Computational Imaging and Vision, Volume 43) Hardcover7 $129.00ISBN 978-1-4471-5166-1

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www.springer.com/978-4-431-54323-7



News 5/2013 Mathematics

83

T. D. Andrews, R. Balan, J. J. Benedetto, W. Czaja, K. A. Okoudjou, University of Maryland, College Park, MD, USA (Eds)

Excursions in Harmonic Analysis, Volume 2The February Fourier Talks at the Norbert Wiener Center

Contents Part V Measure Theory.- Absolute Continuity and Singularity of Measures Without Measure Theory.- Visible and Invisible Cantor Sets.- Convolution Inequalities for Positive Borel Measures on R^d and Beurling Density.- Positive Operator-Valued Measures: A General Setting for Frames.- Part VI Filtering.- Extending Wavelet Filters, Infinite Di-mensions, the Non-Rational Case, and Indefinite-Inner Product Spaces.- On the Group-Theoretic Structure of Lifted Filter Banks.- Parametric Optimization of Biorthogonal Wavelets and Fil-terbanks via Pseudoframes for Subspaces.- On the Convergence of Iterative Filtering Empirical Mode Decomposition.- Wavelet Transforms by Nearest Neighbor Lifting.- Part VII Operator Theory.- On the Heat Kernel of a Left Invariant Elliptic Operator.- Mixed-Norm Estimates for the k-Plane Transform.- Representation of Linear Operators by Gabor Multipliers.- Extensions of Berezin-Lieb Inequalities.- Bilinear Calderon-Zygmund Opera-tors.- Weighted Inequalities and Dyadic Harmonic Analysis.- Part VIII Biomathematics.- Enhance-ment and Recovery in Atomic Force Micosopy Images.- Numerical Harmonic Analysis and Diffu-sions on the 3D-Motion Group.- Quantification of Retinal Chromophores Through Autofluorescence Imaging to Identify Precursors of Age-Related Macular .- Simple Harmonic Oscillator Based Re-construction and Estimation for One-Dimensional q-Space Magnetic Resonance (1D-SHORE). [...]

Fields of interestFourier Analysis; Signal,Image and Speech Pro-cessing; Abstract Harmonic Analysis



Available

2013. XIX, 456 p. 56 illus., 21 in color. (Applied and Numerical Harmonic Analysis) Hardcover7 $129.00ISBN 978-0-8176-8378-8

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N. Bellomo, Politecnico di Torino, Italy; G. Ajmone Marsan, Organization for Economic Cooperation and Development, Paris, France; A. Tosin, Consiglio Nazionale delle Ricerche, Rome, Italy

Complex Systems and SocietyModeling and Simulation

This work aims to foster the interdisciplinary dialogue between mathematicians and socio-eco-nomic scientists. Interaction among scholars and practitioners traditionally coming from different research areas is necessary more than ever in order to better understand many real-world problems we face today. On the one hand, mathematicians need economists and social scientists to better address the methodologies they design in a more realistic way; on the other hand, economists and social scientists need to be aware of sound math-ematical modelling tools in order to understand and, ultimately, solve the complex problems they encounter in their research.

Features 7 Contents look ahead to a new approach to modelling and simulation of real-world sys-tems 7 Introduces models of individual behav-iours in the social and economic sciences 7 Ex-amines recently developed modelling approaches using stochastic game theory

Contents 1. The Role of Individual Behaviors in Socio-Economic Sciences.- 2. Mathematical Tools for Modeling Social Complex Systems.- 3. Modeling Cooperation and Competition in Socio-Economic Systems.- 4. Welfare Policy: Applications and Simulations.- 5. Forward Look at Research Per-spectives.- References.

Fields of interestMathematical Modeling and Industrial Math-ematics; Game Theory/Mathematical Methods; Complex Systems



Due May 2013

2013. X, 100 p. 12 illus. in color. (SpringerBriefs in Mathematics) Softcover7 $49.95ISBN 978-1-4614-7241-4

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F. E. Benth, University of Oslo, Norway; D. Crisan, Imperial College London, United Kingdom; P. Guasoni, Dublin City University, Ireland; P. Protter, Columbia University, New York, NY, USA

Paris-Princeton Lectures on Mathematical Finance 2013Scientific editors: V. Henderson, Oxford University, UK; R. Sircar, Princeton University, USA

The current volume presents four chapters touch-ing on some of the most important and modern areas of research in Mathematical Finance: asset price bubbles (by Philip Protter); energy mar-kets (by Fred Espen Benth); investment under transaction costs (by Paolo Guasoni and Johannes Muhle-Karbe); and numerical methods for solving stochastic equations (by Dan Crisan, K. Mano-larakis and C. Nee).The Paris-Princeton Lecture Notes on Mathematical Finance, of which this is the fifth volume, publish cutting-edge research in self-contained, expository articles from renowned specialists. The aim is to produce a series of articles that can serve as an introductory reference source for research in the field.

Feature 7 Presents cutting-edge research in Mathematical Finance

Contents Preface: Vicky Henderson & Ronnie Sircar.- Philip Protter: A Mathematical Theory of Financial Bub-bles.- Fred Espen Benth: Stochastic Volatility and Dependency in Energy Markets – Multi-Factor Modelling.- Paolo Guasoni: Portfolio Choice with Transaction Costs: a User’s Guide.- Dan Crisan: Cubature Methods and Applications.

Fields of interestGame Theory, Economics, Social and Behav. Sci-ences; Financial Economics



Due June 2013

2013. Approx. 200 p. (Lecture Notes in Mathematics, Volume 2081) Softcover7 $49.99ISBN 978-3-319-00412-9

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84

A. Borovkov, Sobolev Institute of Mathematics, Novosibirsk, Russia

Probability TheoryProbability theory is an actively developing branch of mathematics. It has applications in many areas of science and technology and forms the basis of mathematical statistics. This self-contained, com-prehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into.

Features 7 Presents a wide range of results in logic and computational complexity 7 Explains the topic informally and then in more detail for the advanced reader 7 Presents the ideas behind the theoretical concepts

Contents Discrete Spaces of Elementary Events.- An Arbitrary Space of Elementary Events.- Random Variables and Distribution Functions.- Numerical Characteristics of Random Variables.- Sequences of Independent Trials with Two Outcomes.- On Convergence of Random Variables and Distribu-tions.- Characteristic Functions.- Sequences of Independent Random Variables. Limit Theo-rems.- Large Deviation Probabilities for Sums of Independent Random Variables.- Renewal Processes.- Properties of the Trajectories of Ran-dom Walks. Zero-One Laws.- Random Walks and Factorisation Identities.- Sequences of Dependent Trials. Markov Chains.- Information and Entropy.- Martingales.- Stationary Sequences.- Stochastic Recursive Sequences.- Continuous Time Random Processes.- Processes with Independent Incre-ments.- Functional Limit Theorems.- Markov Pro-cesses.- Processes with Finite Second Moments. Gaussian Processes.- Appendices.

Field of interestProbability Theory and Stochastic Processes

Target groupsGraduate


Due June 2013

2013. Approx. 745 p. 22 illus. (Universitext) Softcover7 $99.00ISBN 978-1-4471-5200-2

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C. Brezinski, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France; A. Sameh, Purdue University, West Lafayette, IN, USA (Eds)

Walter Gautschi, Volume 1Selected Works with Commentaries

Walter Gautschi has written extensively on top-ics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomi-als, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts.

Features 7 Collection of original and influential papers by Walter Gautschi on a wide range of relevant topics and techniques 7 Includes historical essays on Euler and Chrisoffel, as well as biographical essays on several influential 20th-century numerical analysts, relating their work to Gautschi's 7 Inte-grates powerful software packages for orthogonal polynomials and their applications

Contents Preface.- Part I Walter Gautschi.- Biography of Walter Gautschi.- A brief summary of my scientific work and highlights of my career.- Pub-lications.- Part II Commentaries.- Numerical conditioning.- Special functions.- Interpolation and approximation.- Part III Reprints.- Numerical conditioning.- Special functions.- Interpolation and approximation.

Fields of interestNumerical Analysis; Mathematics of Computing; Approximations and Expansions



Due July 2013

2013. XIV, 655 p. 4 illus. in color. (Contemporary Mathematicians) Hardcover7 approx. $179.00ISBN 978-1-4614-7033-5

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C. Brezinski, Université des Sciences et technologies de Lille, Villeneuve d’Ascq, France; A. Sameh, Purdue University, West Lafayette, IN, USA (Eds)



Features 7 Collection of original and influential papers by Walter Gautschi on a wide range of relevant topics and techniques 7 Includes historical essays on Euler and Christoffel, as well as biographical es-says on several influential 20th-century numerical analysts, relating their work to Gautschi's 7 Inte-grates powerful software packages for orthogonal polynomials and their applications

Contents Part I Commentaries.- Orthogonal polynomials on the real line.- Polynomials orthogonal on the semicircle.- Chebyshev quadrature.- Kronrod and other quadratures.- Gauss-type quadrature.- Part II Reprints.- Orthogonal polynomials on the real line.- Polynomials orthogonal on the semicircle.- Chebyshev quadrature.- Kronrod and other quadratures.- Gauss-type quadrature.




Due July 2013


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85

C. Brezinski, Université des Sciences et Technologies de Lille, Villeneuce d’Ascq, France; A. Sameh, Purdue University, West Lafayette, IN, USA (Eds)



Features 7 Collection of original and influential papers by Walter Gautschi on a wide range of relevant topics and techniques 7 Includes historical essays on Euler and Christoffel, as well as biographical es-says on several influential 20th-century numerical analysts, relating their work to Gautschi's 7 Inte-grates powerful software packages for orthogonal polynomials and their applications

Contents Part I Commentaries.- Linear recurrence rela-tions.- Ordinary differential equations.- Computer algorithms and software packages.- History and biography.- Miscellanea.- Part II Reprints.- Lin-ear difference equations.- Ordinary differential equations.- Computer algorithms and software packages.- History and biography.- Miscellanea.- Part III Werner Gautschi.- Publications.- Obituar-ies.- Recording.




Due July 2013


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T. Chan, W. J. Cook, E. Hairer, J. Hastad, A. Iserles, H. P. Langtangen, C. Le Bris, P. L. Lions, C. Lubich, A. J. Majda, J. McLaughlin, R. M. Nieminen, J. ODEN, P. Souganidis, A. Tveito (Eds)

Encyclopedia of Applied and Computational MathematicsEditor-in-chief: B. Engquist, University of Texas at Austin, TX, USA and Royal Institute of Technology (KTH), Stockholm, Sweden

EACM is a comprehensive reference work cover-ing the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications.

Fields of interestComputational Mathematics and Numerical Analysis; Applications of Mathematics; Mathemat-ics of Computing



Due January 2014

Print

2013. 3000 p. 7 approx. $1600.00ISBN 978-3-540-70528-4

9<HTOFPA=hafcie> eReference

2013. 7 approx. $1600.00ISBN 978-3-540-70529-1

9<HTOFPA=hafcjb> Print + eReference

2013. 3000 p. (2-volume-set)7 approx. $2050.00ISBN 978-3-540-70530-7

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M. Cicognani, Università di Bologna, Italy; F. Colombini, Università di Pisa, Italy; D. Del Santo, Università di Trieste, Italy (Eds)

Studies in Phase Space Analysis with Applications to PDEsFeatures 7 Provides both surveys and recent advances in phase space analysis for PDEs 7 Distinguished mathematicians address current work of impor-tance 7 Encompasses applications to a wide range of areas in mathematics and physics

Contents Preface.- The water-waves equations: from Zakha-rov to Euler.- On the characterization of pseudo-differential operators (old and new).- Improved multipolar Hardy inequalities.- The role of spectral anisotropy in the resolution of the three-dimen-sional Navier-Stokes equations.- Schrödinger equations in modulation spaces.- New maximal regularity results for the heat equation in exterior domains, and applications.- Cauchy problem for some 22 hyperbolic systems of pseudo-differential equations with nondiagonalisable principal part.- Scattering problem for quadratic nonlinear Klein-Gordon equation in 2d.- Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system with rough density.- The Cauchy problem for the Euler-Poisson system and derivation of the Zakharov-Kuznetsov equation.- L1 estimates for oscillating integrals related to structural damped wave models.- On the Cauchy problem for nonef-fectively hyperbolic operators, a transition case.- References.

Fields of interestPartial Differential Equations; Dynamical Systems and Ergodic Theory; Mathematical Physics



Available

2013. XVII, 379 p. 4 illus., 1 in color. (Progress in Nonlinear Differential Equations and Their Applications, Volume 84) Hardcover7 $169.00ISBN 978-1-4614-6347-4

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86

C. Donati‑Martin, Université de Versailles-St Quentin, France; A. Lejay, INRIA, Vandoeuvre-les-Nancy, France; A. Rouault, Université de Versailles-St Quentin, France (Eds)

Séminaire de Probabilités XLVContents Special Course: I. Nourdin: Lectures on Gaussian approximations with Malliavin calculus.- Other Contributions: V. Prokaj: Some sufficient condi-tions for the ergodicity of the Lévy-transforma-tion.- S. Laurent: Vershik’s intermediate level standardness criterion and the scale of an auto-morphism.- C. Dellacherie and M. Émery: Filtra-tions indexed by ordinals; application to a conjec-ture of S. Laurent.- M. Émery: A planar Borel set which divides every Borel product.- J. Brossard et C. Leuridan: Characterising Ocone local martin-gales with reflections.- H. Hashimoto: Approxima-tion and stability of solutions of SDEs driven by a symmetric a stable process with non-Lipschitz coefficients.- C. Cuchiero and Josef Teichman: Path properties and regularity of affine processes on general state spaces.- E. Jacob: Langevin pro-cess reflected on a partially elastic boundary II.- R. Doney and S. Vakeroudis: Windings of planar stable processes.- A. Sokol: Elementary proof that the first hitting time of an open set by a jump pro-cess is a stopping time.- L. Döring and M. Roberts: Catalytic branching processes via spine techniques and renewal theory.- S. Bourgain and C. Tudor: Malliavin calculus and self normalized sums.- P. Catuogno, D. Ledesma and P. Ruffino: A note on stochastic calculus in vector bundles.- G. Pagès: Functional co-monotony of processes with an application to peacocks.- S. Noreddine: Fluctua-tions of the traces of complex-valued iid random matrices.- J. Ortmann: Functionals of the Free Brownian motion.- L. Miclo and P. Monmarche´: Étude de processus moins indécis que les autres.- F. Barthe and C. [...]




Due June 2013

2013. X, 520 p. 16 illus., 12 in color. (Lecture Notes in Mathematics / Séminaire de Probabilités, Volume 2078) Softcover7 $119.00ISBN 978-3-319-00320-7

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A. d’Onofrio, European Institute of Oncology, Milan, Italy (Ed)

Bounded Noises in Physics, Biology, and EngineeringContents Introduction.- Part I : Modeling of Bounded Nois-es and Their Applications in Physics.- On Bound-ed Stochastic Processes.- Dynamics of Systems With Randomly Disordered Periodic Excitations.- Noise-Induced Phenomena: Effects of Noises Based on Tsallis Statistics.- Dynamical Systems Driven by Dichotomous Noise.- Stochastic Oscil-lator : Brownian Motion With Adhesion.- Nu-merical Study of Energetic Stability For Harmonic Oscillator With Fluctuating Damping Param-eter.- A Moment-Based Approach to Bounded Non-Gaussian Colored Noise.- Spatiotemporal Bounded Noises, and Their Application to the Ginzburg-Landau Equation.- Part II: Bounded Noises in the Framework of Discrete and Continu-ous Random Dynamical Systems.- Bifurcations of Random Differential Equations With Bounded Noise.- Effects of Bounded Random Perturbations on Discrete Dynamical Systems.- Part III: Bound-ed Stochastic Fluctuations in Biology.- Bounded Stochastic Perturbations May Induce Non-Genetic Resistance to Anti-Tumor Chemotherapy.- Inter-play Between Cross Correlation and Delays in the Sine-Wienernoise-Induced Transitions.- Bounded Extrinsic Noises Affecting Biochemical Networks With Low Molecule Numbers.- Part IV: Bounded Noises: Applications in Engineering.- Almost Sure Stability of Fractional Viscoelastic Systems Driven By Bounded Noises.- Model Selection for Random Functions With Bounded Range. Applications in Science and Engineering.- From Model-Based to Data-Driven Filter Design.

Fields of interestMathematical Modeling and Industrial Mathemat-ics; Mathematical and Computational Biology; Theoretical, Mathematical and Computational Physics



Due July 2013

2013. XVI, 263 p. 87 illus., 39 in color. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 approx. $124.00ISBN 978-1-4614-7384-8

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Y. Giga, T. Kobayashi (Eds)

What Mathematics Can Do for YouEssays and Tips from Japanese Industry Leaders

Contents Toshiyuki Kobayashi and Fujio Cho (Chairman, TOYOTA), A Dialogue between a Mathemati-cian and TOYOTA’s Chairman: Think, think, and think again. Yusuke Yasuda (BNP Paribas Tokyo), Reasons Why Mathematics Is Important to Our Company. Yasuchika Hasegawa (CEO, Takeda Pharma) Are Numbers Useful? Acknowledging the Contribution of Mathematical Modeling to Corporate Management. Norio Wada (Chairman, NTT), Mathematics Drives the Economy. Kenichi Watanabe (CEO, Nomura Holdings), The Role of Mathematics in Finance: Applied Mathematics and Risk. Atsushi Horiba (CEO, HORIBA), Math-ematics Is the Starting Point of Corporate Culture.Eisuke Masada (President, RTRI), Mathematics Supports Development of Railway System Tech-nology.Hirobumi Kawano (President, JOGMEC), The role of mathematics in the petroleum and nat-ural gas exploitation industry in Japan.Waro Iwane (President, Iwane Labo), Mathematics in Our Company: What does it describe? Kaoru Yosano (Former Minister of Finance, Japan), Mathematics and I. Masahiro Yamamoto (Professor, U Tokyo), Mathematics for industry - principle, reality, prac-tice, from a viewpoint of a mathematician. Masato Wakayama (Director, Math-for-Industry, Japan), Importance and Unpredictable Effectiveness of Mathematics in the Real World and for Industry. Hiroshi Fujita (Professor Emeritus, U Tokyo), Mathematics for Business and Business Leaders Based on Mathematical Intelligence.

Fields of interestMathematics, general; Mathematical Modeling and Industrial Mathematics; Mathematics Educa-tion

Target groupsProfessional/practitioner


Due April 2013

2013. VIII, 144 p. 57 illus., 35 in color. Hardcover7 $59.95ISBN 978-4-431-54345-9

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87

H. Glöckner, University of Paderborn, Germany; K.‑H. Neeb, TU Darmstadt, Germany

Infinite-dimensional Lie Groups. General Theory and Main ExamplesInfinite-dimensional Lie Groups provides a com-prehensive introduction to this important subject by developing a global infinite-dimensional Lie theory on the basis that a Lie group is simply a manifold modeled on a locally convex space, equipped with a group structure with smooth group operations.

Features 7 Provides a comprehensive introduction to this important subject, examining the basic structure theory of infinite-dimensional Lie groups 7 Essentially self-contained, provides all necessary background, excepting modest prerequisites 7 Clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material

Contents Preface.- Introduction.- Infinite-dimensional Calculus.- Infinite-dimensional Manifolds.- Lie Groups.- Locally Exponential Lie Groups.- Linear Lie Groups.- Direct Limits of Lie Groups.- Groups of Maps.- Groups of Diffeomorphisms.- Appen-dix A: Tools from Topology.- Appendix B: Basic Theory of Locally Convex Spaces.- Appendix C: Finite-dimensional Lie Algebras.- Appendix D: Calculus in Banach Spaces.- Appendix E: Smooth Maps into non-Lie Groups.- Appendix F: Co-homology of Lie Algebras.- Bibliography.- Index.

Fields of interestTopological Groups, Lie Groups; Group Theory and Generalizations; Linear and Multilinear Alge-bras, Matrix Theory



Due December 2014

2015. 350 p. 10 illus. (Graduate Texts in Mathematics, Volume 935) Hardcover7 approx. $69.95ISBN 978-0-387-09444-1

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D. J. Grynkiewicz, Karl-Franzens-Universität Graz, Austria

Structural Additive Theory Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing sub-ject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory.

Features 7 Focuses on areas of Additive Theory that have not been treated in detail in book form 7 Re-quires little pre-requisite apart from a solid background in undergraduate mathematics and graduate-level introductory algebra 7 Contains detail-rich proofs, making the material more ac-cessible to newcomers in the field

Contents 1. Abelian Groups and Character Sums.- 2. Introduction to Sumsets.- 3. Simple Results for Torsion-Free Abelian Groups.- 4. Basic Results for Sumsets with an Infinite Summand.- 5. The Pigeonhole and Multiplicity Bounds.- 6. Periodic Sets and Kneser’s Theorem.- 7. Compression, Complements and the 3k–4 Theorem.- 8. Additive Energy.- 9. Kemperman’s Critical Pair Theory.- 10. Zero-Sums, Setpartitions and Subsequence Sums.- 11. Long Zero-Sum Free Sequences over Cyclic Groups.- 12. Pollard’s Theorem for General Abelian Groups.- 13. The DeVos–Goddyn–Mohar Theorem.- 14. The Partition Theorem I.- 15. The Partition Theorem II.- 16. The Ψ-Weighted Gao Theorem.- 17. Group Algebras.- 18. Character and Linear Algebraic Methods.- 19. Character Sum and Fourier Analytic Methods.- 20. Freiman Ho-momorphisms Revisited.- 21. The Isoperimetric Method.- 22. The Polynomial Method.- Index.

Fields of interestNumber Theory; Sequences, Series, Summability; Order, Lattices, Ordered Algebraic Structures



Due June 2013

2013. XII, 424 p. (Developments in Mathematics, Volume 30) Hardcover7 $129.00ISBN 978-3-319-00415-0

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H. Han, Tsinghua University, Beijing, China; X. Wu, Hong Kong Baptist University, Hong Kong

Artificial Boundary Method“Artificial Boundary Method” systematically intro-duces the artificial boundary method for the nu-merical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrödinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for researchers working in the fields of computa-tional mathematics and mechanical engineering. Prof. Houde Han works at Tsinghua University, China; Prof. Xiaonan Wu works at Hong Kong Baptist University, China.

Features 7 Artificial boundary method 7 Numerical solution of partial differential equations on un-bounded domains 7 High effect computational schemes 7 Detailed theoretical analysis

Contents Global artificial boundary conditions of second order elliptic differential equations.- Global artificial boundary conditions of Navie Equations and Stokes Equations.- Global artificial bound-ary conditions of heat equation and Schrodinger Equation.- Fully absorbing boundary conditions of wave equations, Klein-Gordan Equation and linear KdV Equation.- Discrete artificial boundary conditions.- Local artificial boundary conditions.- Implicit artificial boundary conditions.- Nonlinear artificial boundary conditions.- Applications.

Fields of interestComputational Mathematics and Numerical Analysis; Computational Science and Engineering; Appl.Mathematics/Computational Methods of Engineering



Due May 2013

Jointly published with Tsinghua University Press. Original Chinese edition published by Tsinghua University Press, 2009.

Distribution rights in China: Tsinghua University Press.

2013. Approx. 300 p. 30 illus. Hardcover7 approx. $109.00ISBN 978-3-642-35463-2

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88

A. Huckleberry, Ruhr-Universität Bochum, Germany; I. Penkov, Jacobs University Bremen, Germany; G. Zuckerman, Yale University, CT, USA (Eds)

Lie Groups: Structure, Actions, and RepresentationsIn Honor of Joseph A. Wolf on the Occasion of his 75th Birthday

Contents Preface.- Real group orbits on flag manifolds.- Complex connections with trivial holonomy.- Indefinite harmonic theory and harmonic spinors.- Twistor theory and the harmonic hull.- Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets.- Propagation of the multiplicity-free-ness property for holomorphic vector bundles.- Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains.- Cent(U(n)), cascade of orthogonal roots, and a construction of Lipsman–Wolf.- Weakly harmonic Maaß forms and the principal series for SL(2,R).- Holomorphic realization of unitary representa-tions of Banach-Lie groups.- The Segal–Bargmann transform on compact symmetric spaces and their direct limits.- Analysis on flag manifolds and Sobolev inequalities.- Boundary value problems on Riemannian symmetric spaces of noncompact type.- One step spherical functions of the pair (SU(n + 1), U(n)).- Chern–Weil theory for certain infinite-dimensional Lie groups.- On the structure of finite groups with periodic cohomology.

Fields of interestTopological Groups, Lie Groups; Associative Rings and Algebras; Functional Analysis



Due June 2013

2013. XV, 367 p. (Progress in Mathematics, Volume 306) Hardcover7 $129.00ISBN 978-1-4614-7192-9

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A. Ilchmann, Technische Universität Ilmenau, Germany; T. Reis, Universität Hamburg, Germany (Eds)

Surveys in Differential-Algebraic Equations IThe need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to the strong relation to (ordinary) differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in - Controllability for linear DAEs - Port-Hamiltonian differential-algebraic systems - Robustness of DAEs - Solution concepts for DAEs - DAEs in circuit modeling. The results in the individual chapters are presented in an acces-sible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Features 7 A collection of survey articles, covering a broad spectrum of areas related to DAEs, each of which presented in an individual chap-ter 7 Unique in the sense that other books provide rather an introduction to the principles of DAEs 7 Suitable not only for graduate students for self-study but also for active researchers by dealing with specific aspects of particular fields of DAEs

Fields of interestOrdinary Differential Equations; Numerical Analysis; Systems Theory, Control



Available

2013. VII, 231 p. 13 illus. (Differential-Algebraic Equations Forum) Softcover7 $109.00ISBN 978-3-642-34927-0

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M. Joswig, Fachbereich Mathematik, Algorithmische diskrete Mathematik, Technische Universität Darmstadt, 64293 Darmstadt, Germany

Essentials of Tropical CombinatoricsThe goal of this book is to explain, at the graduate student level, how tropical geometry can be ac-cessed via geometric combinatorics. This way the book offers a viable path to a topic of very active research. At the same time the reader learns how a number of seemingly unrelated combinatorial results fall into place, once viewed through the “tropical lens”. No attempt is made to cover the entire field of tropical geometry, which has been evolving too rapidly anyway to be covered by a book so small.

Features 7 Offers a viable path to a topic of very active re-search 7 Focuses on the polyhedral and combi-natorial aspects while requiring less prerequisites in algebraic geometry and commutative algebra, thus making the book more accessible to a wider audience 7 Uses tropical convexity as a general language to study classical subjects in combinato-rial optimization

Contents Preface.- Contents.- Introduction.- 1 Tropical Arithmetic and Polynomials.- 2 Puiseux Series and Tropicalization.- 3 Graph Algorithms and the Tropical Determinant.- 4 Tropical Polytopes.- 5 Products of Simplices.- 6 Tropical Halfspaces.- 7 Polytropes.- 8 Resolutions of Monomial Ideals.- 9 Tropical Linear Spaces.- 10 Matroid Subdivisions of Hypersimplices.- 11 Buildings.- 12Using poly-make.- Appendix A Ordinary Convex Polytopes.- Appendix B Matroids and Oriented Matroids.- Appendix C Gröbner Bases.- Bibliography.- Index

Fields of interestAlgebraic Geometry; Convex and Discrete Geom-etry; Field Theory and Polynomials



Due March 2014

2014. XX, 180 p. 50 illus. Hardcover7 approx. $49.95ISBN 978-1-4419-8365-7

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89

A. Kirillov, University of Pennsylvania, Philadelphia, PA, USA

A Tale of Two FractalsSince Benoit Mandelbrot’s pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. De-spite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve wide-spread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once ac-cessible to beginners and sufficiently rigorous for serious mathematicians.

Features 7 First book to provide a rigorous study of fractals usable by undergraduates 7 Written by a renowned authority in the field and expert at communicating mathematical ideas to stu-dents 7 An excellent means for young mathema-ticians to acquire basic tools from many different areas 7 Abundant figures and exercises provide valuable clarity and practice

Contents Introduction.- Part 1. The Sierpiński Gasket.- Definition and General Properties.- The Laplace Operator on the Sierpiński Gasket.- Harmonic Functions on the Sierpiński Gasket.- Part 2. The Apollonian Gasket.- Introduction.- Circles and Disks on Spheres.- Definition of the Apollonian Gasket.- Arithmetic Properties of Apollonian Gaskets.- Geometric and Group-Theoretic Ap-proach.- Many-Dimensional Apollonian Gaskets.- Bibliography.

Fields of interestVisualization; Special Functions; Geometry

Target groupsUpper undergraduate


Due April 2013

2013. XII, 128 p. 42 illus., 4 in color. Hardcover7 $39.95ISBN 978-0-8176-8381-8

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S. Koziel, L. Leifsson, Engineering Optimization & Modeling Center, School of Science and Engineering, Reykjavik University, Iceland (Eds)

Surrogate-Based Modeling and OptimizationApplications in Engineering

Contents Space Mapping for Electromagnetic-Simulation-Driven Design Optimization, Slawomir Koziel, Leifur Leifsson, and Stanislav Ogurtsov.- Sur-rogate-Based Circuit Design Centering, Abdel-Karim S.O. Hassan and Ahmed S.A. Mohamed.- Simulation-Driven Antenna Design Using Surrogate-Based Optimization, Slawomir Koziel, Stanislav Ogurtsov, and Leifur Leifsson.- Practical Application of Space Mapping Techniques to the Synthesis of CSRR-based Artificial Transmission Lines, Ana Rodríguez, Jordi Selga, Ferran Martín and Vicente E. Boria.- The Efficiency of Difference Mapping on Space Mapping Based Optimization, Murat Simsek, Neslihan Serap Sengor.- Bayesian Support Vector Regression Modeling of Micro-wave Structures for Design Applications, J. Pieter Jacobs, Slawomir Koziel, Leifur Leifsson.- Arti-ficial Neural Networks and Space Mapping For EM-Based Modelling and Design of Microwave Circuits, José Ernesto Rayas-Sánchez.- Model-Based Variation-Aware Integrated Circuit Design, Ting Zhu, Mustafa Berke Yelten, Michael B. Steer, and Paul D. Franzon.- Computing Surrogates for Gas Network Simulation using Model Order Reduction, Sara Grundel, Nils Hornung, Bernhard Klaassen, Peter Benner, and Tanja Clees.- Aero-dynamic Shape Optimization by Space Mapping, Leifur Leifsson, Slawomir Koziel, Eirikur Jonsson, Stanislav Ogurtsov. [...]

Fields of interestMathematical Modeling and Industrial Math-ematics; Aerospace Technology and Astronautics; Control



Due June 2013

2013. VIII, 422 p. 60 illus., 10 in color. Hardcover7 $129.00ISBN 978-1-4614-7550-7

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A. T. Layton, Duke University, Durham, NC, USA; A. Edwards, Centre de Recherche des Cordeliers, Paris, France

Mathematical Modeling in Renal PhysiologyWith the availability of high speed computers and advances in computational techniques, the ap-plication of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical mod-eling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physi-ology. The models presented describe the main homeostatic functions performed by the kidney, including blood filtration, excretion of water and salt, maintenance of electrolyte balance, and regu-lation of blood pressure. Each chapter includes an introduction to the basic relevant physiology, a derivation of the essential conservation equations, and then a discussion of a series of mathemati-cal models, with increasing level of complexity. This volume will be of interest to biological and mathematical scientists, as well as physiologists and nephrologists, who would like an introduction to mathematical techniques that can be applied to renal transport and function. The material is written for students who have had college-level calculus, but can be used in modeling courses in applied mathematics at all levels through early graduate courses.

Features 7 Written by experts in academia 7 Provides the mathematical and biological basis needed to understand transport phenomena in the kid-ney 7 First book of this kind on the market

Fields of interestPhysiological, Cellular and Medical Topics; Math-ematical and Computational Biology



Due April 2013

2013. XII, 188 p. (Lecture Notes on Mathematical Modelling in the Life Sciences) Hardcover7 approx. $59.95ISBN 978-3-642-27366-7

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90

S. E. Louridas, Athens, Greece; M. T. Rassias, ETH Zurich, Switzerland

Problem-Solving and Selected Topics in Euclidean GeometryIn the Spirit of the Mathematical Olympiads

“Problem-Solving and Selected Topics in Euclid-ean Geometry: in the Spirit of the Mathemati-cal Olympiads” contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geom-etry. Before the complete solution of every prob-lem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given.

Features 7 The book teaches in practice methods of analy-sis, synthesis, construction, and proof with specific problems, examples, and applications 7 Teaches mathematical thinking presented in the most elementary possible form for the solution or proof of every problem or statement of theo-rem 7 Presents main theorems of Euclidean Geometry with a discussion of the central ideas behind their proofs 7 Provides approximately 25 problems proposed by leading mathematicians or given in IMO's or short lists for IMO's or BMO's

Contents Foreword.- Preface.- Basic Concepts and Theorems of Euclidean Geometry.- Methods of Analysis, Synthesis, Construction and Proof.-Geometrical Constructions.- Geometrical Loci.- Problems of Olympiad Caliber.- Solutions of the Problems.- Bibliography.- Index.

Fields of interestGeometry; Algebraic Geometry; Mathematics, general

Target groupsLower undergraduate


Due May 2013

2013. X, 254 p. 134 illus. Hardcover7 $49.99ISBN 978-1-4614-7272-8

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K. Luoto, University of British Columbia,Vancouver, BC, Canada; S. Mykytiuk, York University,Toronto, ON, Canada; S. van Willigenburg, University of British Columbia, Vancouver, BC, Canada

An Introduction to Quasisymmetric Schur FunctionsHopf Algebras, Quasisymmetric Functions, and Young Composition Tableaux

An Introduction to Quasisymmetric Schur Func-tions is aimed at researchers and graduate students in algebraic combinatorics. This book introduces readers to the algebra of quasisymmetric functions and its fundamental theory. Results and relevant new contributions are included which pertains to the dynamic new basis of quasisymmetric Schur functions. A state-of-the-art summary is included with respect to an exciting new basis of alge-bra, which is the basis of quasisymmetric Schur functions, whose combinatorics is analogous to that of the renowned Schur functions.

Features 7 Comprehensive introduction to quasisym-metric functions for non-specialists 7 First summary of results in the blossoming field of quasisymmetric 7 Schur functions using Young composition tableaux, which generalize Young tableaux

Contents 1. Introduction.- 2. Classical combinatorial con-cepts.- 3. Hopf algebras.- 4. Compsition tableaux and further combinatorial concepts.- 5. Quasisym-metric Schur functions.- References.- Index.

Fields of interestAlgorithms; Topological Groups, Lie Groups; Ap-plications of Mathematics



Due May 2013

2013. XIII, 91 p. 75 illus. (SpringerBriefs in Mathematics) Softcover7 $49.99ISBN 978-1-4614-7299-5

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E. Mahmudov, Istanbul Technical University, Turkey

Single Variable Differential and Integral CalculusMathematical Analysis

The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced.

Features 7 Treatment of countable and uncountable sets, the cardinality of the continuum; Dedekind completeness theorem for the set of real num-bers 7 Coverage of polynomials and inter-polation, Lagrange and Newton interpolation formulas 7 Inclusion of Lebesgue measure and Lebesgue integrals 7 Interesting applications: potential and kinetic energy, a body in the earth’s gravitational field, escape 7 At the end of each chapter, many of challenging of problems with answers

Contents Introduction to Numbers and Set Theory.- Se-quences and Series.- Limits and Continuity of Functions.- Differential Calculus.- Some Basic Properties of Differentiable Functions.- Polynomi-als and Interpolations.- Applications of Differen-tial Calculus to Limit Calculations and Extremum Problems.- The Indefinite Integral.- The Definite Integral.- Applications of the Definite Integral.

Fields of interestAnalysis; Ordinary Differential Equations

Target groupsUpper undergraduate


Available

2013. XVI, 373 p. 41 illus. Hardcover7 $79.95ISBN 978-94-91216-85-5

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91

P. Major, Hungarian Academy of Sciences Budapest, Hungary

On the Estimation of Multiple Random Integrals and U-StatisticsThis work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The esti-mation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation.

Contents 1 Introduction.- 2 Motivation of the investigation. Discussion of some problems.- 3 Some estimates about sums of independent random variables.- 4 On the supremum of a nice class of partial sums.- 5 Vapnik– Červonenkis classes and L2-dense classes of functions .- 6 The proof of Theorems 4.1 and 4.2 on the supremum of random sums.- 7 The completion of the proof of Theorem 4.1.- 8 Formulation of the main results of this work.- 9 Some results about U-statistics.- 10 MultipleW-iener–Itô integrals and their properties.- 11 The diagram formula for products of degenerate U-statistics.- 12 The proof of the diagram formula for U-statistics.- 13 The proof of Theorems 8.3, 8.5 and Example 8.7.- 14 Reduction of the main result in this work.- 15 The strategy of the proof for the main result of this work.- 16 A symmetrization argument.- 17 The proof of the main result.- 18 An overview of the results and a discussion of the literature.




Due May 2013

2013. X, 276 p. 11 illus. (Lecture Notes in Mathematics, Volume 2079) Softcover7 $59.99ISBN 978-3-642-37616-0

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A. Marica, E. Zuazua, BCAM – Basque Center for Applied Mathematics, Derio, Spain

Symmetric Discontinuous Galerkin Approximations of 1-D WavesFourier Analysis, Propagation, Observability and Applications

This work describes the propagation proper-ties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spec-tral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropri-ate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm.

Contents -1. Preliminaries. -2. Discontinuous Galerkin approximations and main results. -3. Bibliographi-cal notes. -4. Fourier analysis of the DG methods. -5. Non-uniform observability for DG approxi-mations of waves. -6. Filtering mechanisms. -7. Extensions to other numerical approximation schemes. -8. Comments and open problems. –A technical proof. –References.

Fields of interestNumerical Analysis; Fourier Analysis; Approxima-tions and Expansions



Due April 2013

2013. XII, 91 p. 15 illus. in color. (SpringerBriefs in Mathematics) Softcover7 approx. $49.95ISBN 978-1-4614-5810-4

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V. Maz’ya, Linköping University, Sweden; A. Movchan, University of Liverpool, UK; M. Nieves, Liverpool John Moores University, UK

Green’s Kernels and Meso-Scale Approximations in Perforated DomainsContents Part I: Green’s functions in singularly perturbed domains: Uniform asymptotic formulae for Green’s functions for the Laplacian in domains with small perforations.- Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green’s kernels.- Green’s function for the Dirichlet boundary value problem in a domain with several inclusions.- Numerical simulations based on the asymptotic approximations.- Other examples of asymptotic approximations of Green’s functions in singularly perturbed domains.- Part II: Green’s tensors for vector elasticity in bodies with small defects: Green’s tensor for the Dirichlet boundary value problem in a domain with a single inclu-sion.- Green’s tensor in bodies with multiple rigid inclusions.- Green’s tensor for the mixed boundary value problem in a domain with a small hole.- Part III Meso-scale approximations. Asymptotic treat-ment of perforated domains without homogeni-zation: Meso-scale approximations for solutions of Dirichlet problems.- Mixed boundary value problems in multiply-perforated domains.

Fields of interestPartial Differential Equations; Approximations and Expansions



Due May 2013

2013. X, 264 p. 17 illus., 10 in color. (Lecture Notes in Mathematics, Volume 2077) Softcover7 $59.99ISBN 978-3-319-00356-6

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92

V. Obukhovskii, Voronezh State Pedagogical University, Russia; P. Zecca, Università di Firenze, Italy; N. Van Loi, PetroVietNam University, Ha Noi, Vietnam; S. Kornev, Voronezh State Pedagogical University, Russia

Method of Guiding Functions in Problems of Nonlinear AnalysisThis book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary dif-ferential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in ap-plied mathematics, the engineering sciences and physics.

Features 7 May serve as the convenient introduction into intensively developing and interesting branches of contemporary nonlinear analysis, theory of differential equations and inclusions and control theory 7 The presentation is self-contained and directed to a non-specialist Contains interesting applications of the theory in control theory, theory of bifurcations and physics

Contents 1 Background.- 2 MGF in Finite-Dimensional Spaces.- 3 Guiding Functions in Hilbert Spaces.- 4 Second-Order Differential Inclusions.- 5 Nonlin-ear Fredholm Inclusions.

Fields of interestMathematics, general; Operator Theory; Game Theory, Economics, Social and Behav. Sciences



Due April 2013

2013. XIII, 177 p. (Lecture Notes in Mathematics, Volume 2076) Softcover7 $49.95ISBN 978-3-642-37069-4

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A. A. Roytvarf, Rishon LeZion, Center District, Israel

Thinking in ProblemsHow Mathematicians Find Creative Solutions

This concise, self-contained textbook gives an in-depth look at problem-solving from a math-ematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem.

Features 7 Introduces key problem-solving techniques in depth 7 Provides the reader with a range of methods that are used in numerous math-ematical fields 7 Each self-contained chapter builds on the previous one, allowing the reader to uncover new approaches and prepare creative solutions 7 Corresponding hints, explanations, and full solutions are supplied for each prob-lem 7 The difficulty level for all examples are indicated throughout the book

Contents Preface.- Using the Stars on Problems.- Under-standing the Advanced Skill Requirements.- Ac-knowledgements.- Jacobi Identities and Related Combinatorial Formulas.- A Property of Recursive Sequences.- A Combinatorial Algorithm in Multi-exponential Analysis.- A Frequently Encountered Determinant.- A Dynamical System with a Strange Attractor.- Polar and Singular Value Decomposi-tion Theorems.- 2x2 Matrices Which Are Roots of Unity.- A Property of Orthogonal Matrices.- Con-vexity and Related Classical Inequalities.- One-Pa-rameter Groups of Linear Transformations.- Some Problems in Combinatorics and Analysis that can be Explored using Generating Functions.- Least Squares and Chebyshev Systems.- References.- In-dex of Terms.

Fields of interestAlgebra; Analysis; Combinatorics



Available

2013. XXXVII, 405 p. 14 illus. Hardcover7 $79.95ISBN 978-0-8176-8405-1

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A. I. Saichev, ETH Zürich, Switzerland; W. A. Woyczynski, Case Western Reserve University, Cleveland, OH, USA

Distributions in the Physical & Engineering Sciences, Volume 2Partial Differential Equations and ProbabilityVolume 2

Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering prob-lems. It is written from the unifying viewpoint of distribution theory and enriched with many mod-ern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis.

Features 7 Application oriented exposition of distribu-tional (Dirac delta) methods in the theory of partial differential equations 7 Includes a large number of exercises and solutions expanding on themes developed in the main text 7 Clear explanations, motivations, and illustration of all necessary mathematical concepts

Contents III POTENTIALS, DIFFUSIONS AND WAVES.- 9 Potential Theory and Fundamental Solutions of Elliptic Equations.- 10 Diffusions and Parabolic Evolution Equations.- 11 Waves and Hyperbolic Equations.- 12 First Order Nonlinear PDEs and Conservation Laws.- 13 Generalized Solutions of First Order Nonlinear PDEs.- 14 Nonlinear waves and growing interfaces: 1-D Burgers-KPZ models.- 15 Other Standard Nonlinear Models of Higher Order.- Appendix A: Answers and Solu-tions.- Appendix B: Bibliographical Notes.

Field of interestMathematics, general



Due July 2013

2013. XX, 370 p. 110 illus., 15 in color. (Applied and Numerical Harmonic Analysis) Hardcover7 approx. $79.99ISBN 978-0-8176-3942-6

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93

K. Sakai

Geometric Aspects of General TopologyThis book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with vari-ous fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomologi-cal dimension; a dimension raising cell-like map; and a non-AR metric linear space.

Features 7 The perfect book for acquiring fundamental knowledge of simplicial complexes and the theo-ries of dimension and retracts 7 Many proofs are illustrated by figures or diagrams for easier un-derstanding 7 Fascinating problems in the final chapter enable readers to understand how deeply related the theories of dimension and retracts are

Fields of interestTopology; Convex and Discrete Geometry; Geometry



Due May 2013

2013. XII, 534 p. 79 illus. (Springer Monographs in Mathematics) Hardcover7 $149.00ISBN 978-4-431-54396-1

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S. Schewe, University of Liverpool, UK

Synthesis of Distributed SystemsDistributed and parallel systems have an increas-ing influence on our lives. Defective systems can endanger our lives or health (e.g., in the control of airbags) and cause considerable costs (e.g., transactions processing). For computer science this implies the challenge to establish a sound mathematical foundation for the development of such systems. This book provides a central contribution in this field: It presents a solution to the synthesis problem of distributed systems, that is, for automatically deriving an implementation from its specification.

Features 7 Excellently written overview of an area of interest in logic and theoretical computer sci-ence 7 Makes a central contribution to the mathematical foundation for the development of distributed systems 7 Model checking has become a hot topic also in other fields such as biology

Contents Introduction.- Parity Games.- Solving Parity Games in Big Steps.-Optimal Strategy Improve-ment.- Logics & Automata.- Satisfiability of ATµC.- ATL* Satisfiability is 2EXPTIME-com-plete.- Open & Distributed Synthesis.- Uniform Distributed Synthesis.- Bounded Synthesis.- Ex-cursion: Probabilistic Environments.- Semi-Auto-matic Synthesis.- Asynchronous Systems.- Sum-mary & Conclusions.

Fields of interestSystems Theory, Control; Mathematical Logic and Foundations; Mathematical Logic and Formal Languages



Due May 2013

2013. 300 p. (Progress in Computer Science and Applied Logic, Volume 26) Hardcover7 approx. $109.00ISBN 978-3-0348-0242-0

9<HTOAOE=iaceca>

B. Simeon, Technische Universität Kaiserslautern

Computational Flexible Multibody DynamicsA Differential‑Algebraic Approach

This monograph, written from a numerical analy-sis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this field permanently and rapidly growing, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actual computations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this book should benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales.

Features 7 First comprehensive treatment of mathematical models and numerical methods in the field of flex-ible multibody dynamics 7 Detailed discussion of state-of-the-art numerical methods both from a theoretical and practical viewpoint 7 Author is a renowned expert in the field

Contents A Point of Departure.- Rigid Multibody Dynam-ics.- Elastic Motion.- Flexible Multibody Dynam-ics.- Spatial Discretization.- Stiff Mechanical Systems.- Time Integration Methods.- Numerical Case Studies.

Fields of interestNumerical Analysis; Mechanics; Ordinary Dif-ferential Equations



Due July 2013

2013. Approx. 250 p. (Differential-Algebraic Equations Forum) Softcover7 approx. $119.00ISBN 978-3-642-35157-0

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94

S. Stepanov, Dneropetrovsk, Ukraine

Stochastic WorldThis authored monograph presents an introduc-tion to the Ito calculus techniques used to handle stochastic differential equations. The book covers a broad spectrum of techniques which are useful for working with stochastic equations. Two chapters are devoted to corresponding applications in physics, biology and finance. The target audience primarily comprises professionals in the applica-tion fields but the book may also be beneficial for graduate students.

Features 7 Requires only minimum prior knowledge of probability theory 7 Ideally suited for profes-sionals who want to quickly grasp the mate-rial 7 Contains problems with detailed solutions in the appendix 7 Written by an expert in the field

Fields of interestProbability Theory and Stochastic Processes; Numeric Computing; Mathematical Methods in Physics



Due May 2013

2013. 350 p. 70 illus., 20 in color. Hardcover7 approx. $179.00ISBN 978-3-319-00070-1

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E. Tonti, Università di Trieste, Italy

The Mathematical Structure of Classical and Relativistic PhysicsA General Classification Diagram

Features 7 Presents an original mathematical analysis of the underlying analogies in diverse branches of physics 7 Provides a novel classification of physical variables 7 A valuable resource across many disciplines in applied mathematics, physics, and engineering 7 Clear exposition includes hundreds of figures to enhance under-standing 7 Useful for both advanced students and professional researchers

Contents 1 Introduction.- Part I Analysis of variables and equations.- 2 Terminology revisited.- 3 Space and time elements and their orientation.- 4 Cell complexes.- 5 Analysis of physical variables.- 6 Analysis of physical equations.- 7 Algebraic topol-ogy.- 8 The birth of the classification diagrams.- Part II Analysis of physical theories.- 9 Particle dynamics.- 10 Electromagnetism.- 11 Mechanics of deformable solids.- 12 Mechanics of fluids.- 13 Other physical theories.- Part III Advanced analy-sis.- 14 General structure of the diagrams.- 15 The mathematical structure.- Part IV Appendices.- A Affine vector fields.- B Tensorial notation.- C On observable quantities.- D History of the dia-gram.- D.1 Historical remarks.- E List of physical variables.- F List of symbols used in this book.- G List of diagrams.- References.

Fields of interestMathematical Physics; Mathematical Methods in Physics; Partial Differential Equations



Due June 2013

2013. XVI, 540 p. 151 illus., 13 in color. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 $149.00ISBN 978-1-4614-7421-0

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A. Tveito, Simula Research Laboratory, Lysaker, Norway; A. M. Bruaset, Simular Research Laboratory, Lysaker, Norway (Eds)

Conversations About Challenges in ComputingInterview by: K. Aspaas, Oslo, Norway; D. Mackenzie, Santa Cruz, CA, USA

Contents Part I: Communications Systems: 1 The Nature of the Beast: An interview with Olav Lysne.- 2 Ignit-ing the New Internet: An interview with Keith Marzullo.- 3 The Internet of Things: An interview with Heinrich Stüttgen.- Part II: Computational Science: 4 The Mathematics of the Mind: An interview with Hans Petter Langtangen.- 5 Solving Puzzle Earth by Adaptive Mesh Refinement: An interview with Carsten Burstedde.- 6 Compu-tational Inverse Problems Can Drive a Big Data Revolution: An interview with Omar Ghattas.- 7 Towards the ‘Google Heart’: Aninterview with Natalia Trayanova.- 8 As Simple as Possible, but Not Simpler: An interview with Alfio Quarteroni.- Part III: Software Engineering.- 9 A Caring Critic: An interview with Magne Jørgensen.- 10 Through the Looking Glass into Digital Space: An interview with Paola Inverardi.- 11 Harmonizing the Babel of Voices: An interview with Martin Shepperd.- 12 Mediating between Man and Machine: An inter-view with Bashar Nuseibeh.

Fields of interestComputational Science and Engineering; Partial Differential Equations; Mathematical Modeling and Industrial Mathematics

Target groupsPopular/general


Due May 2013

2013. Approx. 130 p. 12 illus. in color. Hardcover7 $29.99ISBN 978-3-319-00208-8

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95

D. Wu, The Hong Kong University of Science & Technology, Hong Kong, China

Foundations of Text AlignmentStatistical Machine Translation Models from Bitexts to Bigrammars

This book provides a systematic, foundational introduction to automatic alignment of parallel texts, a family of essential corpus analysis tech-niques for computing and learning the mappings between corresponding parts of the texts. Bitext alignment lies at the heart of all data-driven machine learning approaches to automatic transla-tion, and the rapid research progress on alignment during the past two decades underlies the success of statistical machine translation approaches. Alignment is used across a wide range of resource acquisition applications including word sense dis-ambiguation, terminology extraction, and gram-mar induction, as well as in translation memories and biconcordances for translators’ assistants, bilingual lexicographers, and computer assisted language learners.

Features 7 The book provides a systematic, foundational introduction to automatic alignment of parallel texts 7 It surveys a wide variety of fundamental alignment techniques including: IBM and HMM alignment models, techniques for aligning compa-rable corpora and learning of phrasal bilexicons, more recent alignment techniques such as greedy/competitive approaches and LTG models 7 Use-ful for both practitioners and researchers in machine translation, natural language processing, bilingual lexicography, and computer assisted language learners

Fields of interestApplications of Mathematics; Language Transla-tion and Linguistics; Probability and Statistics in Computer Science



Due May 2013

2012. X, 90 p. (Theory and Applications of Natural Language Processing) Hardcover7 $29.95ISBN 978-3-642-25843-5

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A. J. Zaslavski, Technion - Israel Institute of Technology, Haifa, Israel

Nonconvex Optimal Control and Variational ProblemsNonconvex Optimal Control and Variational Problems is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations.

Features 7 Presents progress in the studies of nonconvex optimal control and variational problems 7 Em-ploys the Baire category approach to consider problems that do not satisfy convexity assump-tions 7 Establishes the well-posedness of a typical optimal control problem without convexity assumptions

Contents Preface.- 1. Introduction.- 2. Well-posedness of Optimal Control Problems.- 3. Well-posedness and Porosity.- 4. Well-posedness of Nonconvex Variational Problems.- 5. Gerenic Well-posedness result.- 6. Nonoccurrence of the Lavrentiev Phe-nomenon for Variational Problems.- 7. Nonoccur-rence of the Lavrentiev Phenomenon in Optimal Control.- 8. Generic Nonoccurrence of the Lavrentiev phenomenon.- 9. Infinite Dimensional Linear Control Problems.- 10. Uniform Bound-edness of Approximate Solutions of Variational Problems.- 11. The Turnpike Property for Ap-proximate Solutions.- 12. A Turnpike Result For Optimal Control Systems. - References.- Index.

Fields of interestCalculus of Variations and Optimal Control; Opti-mization; Optimization



Due June 2013

2013. XII, 240 p. (Springer Optimization and Its Applications, Volume 82) Hardcover7 $129.00ISBN 978-1-4614-7377-0

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