advances in mathematical usa lectures on formal and...

Mathematics springer.com/NEWSonline

28

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

Volume 18

S. Kusuoka, Graduate School of Mathematical Sciences, Komaba 3-8-1, Meguro-ku, Japan; T. Maruyama, Keio University Dept. Economics, Tokyo, Japan (Eds)

Advances in Mathematical Economics Volume 18Contents Optimal Control Problems Governed By A Second Order Ordinary Differential Equation With M-Point Boundary Condition (Charles Castaing, C. Godet-Thobie, Le Xuan Truongz, Bianca Satco).- Stochastic Mesh Methods For H¨Ormander Type Diffusion Processes (Shigeo Kusuoka and Yusuke Morimoto).- Turnpike Properties For Nonconcave Problems (Alexander J. Zaslavski).- A Character-ization of Quasi-Concave Function in View of the Integrability Theory (Yuhki Hosoya).

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

Target groupsProfessional/practitioner

Product categoryMonograph

Due April 2014

2014. VI, 100 p. Hardcover7 * € (D) 90,94 | € (A) 93,49 | sFr 113,507 € 84,99 | £76.50ISBN 978-4-431-54833-1

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S. Bosch, Westfälische Wilhelms-Universität Mathematisches Institut, Münster, Germany

Lectures on Formal and Rigid GeometryThe aim of this work is to offer a concise and self-contained ‘lecture-style’ introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader’s level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more exten-sively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster’s Collaborative Research Center “Geometrical Structures in Mathematics”.

Features 7 Provides rapid access to advanced Rigid Geom-etry 7 Offers self-contained content 7 Includes Tate’s classical theory, as well as Raynaud’s ap-proach using formal schemes

Contents Classical Rigid Geometry.- Tate Algebras.- Af-finoid Algebras and their Associated Spaces.- Af-finoid Functions.- Towards the Notion of Rigid Spaces.- Coherent Sheaves on Rigid Spaces.- For-mal Geometry.- Adic Rings and their Associ-ated Formal Schemes.- Raynaud’s View on Rigid Spaces.- More Advanced Stuff.- Appendix.- Refer-ences.- Index.

Fields of interestMathematics, general; Algebraic Geometry; Num-ber Theory

Target groupsResearch


Due June 2014

2014. Approx. 220 p. (Lecture Notes in Mathematics, Volume 2105) Softcover7 approx. * € (D) 48,10 | € (A) 49,45 | sFr 60,007 approx. € 44,95 | £40.99ISBN 978-3-319-04416-3

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K. Burdzy, University of Washington, Seattle, WA, USA

Brownian Motion and its Applications to Mathematical AnalysisÉcole d’Été de Probabilités de Saint‑Flour XLIII – 2013

These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phe-nomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in “deterministic” fields of mathemat-ics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis.

Features 7 Contains interesting examples of cou-plings 7 Gentle introduction to Brownian motion and analysis 7 Heuristic explanations of the main results

Contents 1. Brownian motion.- 2. Probabilistic proofs of classical theorems.- 3. Overview of the “hot spots” problem.- 4. Neumann eigenfunctions and eigen-values.- 5. Synchronous and mirror couplings.- 6. Parabolic boundary Harnack principle.- 7. Scaling coupling.- 8. Nodal lines.- 9. Neumann heat kernel monotonicity.- 10. Reflected Brownian motion in time dependent domains.

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



Due March 2014

2014. X, 141 p. 16 illus., 4 in color. (Lecture Notes in Mathematics / École d’Été de Probabilités de Saint-Flour, Volume 2106) Softcover7 * € (D) 37,44 | € (A) 38,49 | sFr 47,007 € 34,99 | £31.99ISBN 978-3-319-04393-7

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www.springer.com/978-4-431-54833-1



News 2/2014 Mathematics

29

A. d’Onofrio, European Institute of Oncology, Milano, Italy; A. Gandolfi, Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Rome, Italy (Eds)

Mathematical Oncology 2013Working in mathematical oncology is a slow and difficult process, requiring the acquisition of a spe-cial mindset that goes well beyond the usual appli-cations of mathematics and physics. Mathematical Oncology 2013 presents the most significant recent results in the field of mathematical oncol-ogy, highlighting the work of world-class research teams. This innovative volume emphasizes the way different researchers see and approach problems, not just technical results. It covers many of the most important topics related to the mathematical modeling of tumors, including: Free boundaries. Tumors are growing entities, as such their spatial mean field description involves free boundary problems.Constitutive equations. Tumors should be described as nontrivial porous media.Stochastic dynamics. At the end of anti-cancer therapy, a small number of cells remain, whose dynamics is thus inherently stochastic.Noise-induced state transitions. The growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. This may induce phenomena that are mathematically equivalent to phase transi-tions.Stochastic and fractal geometry.

Features 7 Highlights the most significant recent results in the field of mathematical oncology 7 Contains interdisciplinary contributions by bio mathemati-cians, computational and theoretical biologists, biophysicists and biomedical researchers 7 In-cludes contributions that focus on the experimen-tal, clinical and ethical aspects of mathematical oncology

Fields of interestPhysiological, Cellular and Medical Topics; Cancer Research; Biophysics and Biological Physics


Product categoryContributed volume

Due March 2014

2014. X, 250 p. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 approx. * € (D) 85,55 | € (A) 87,95 | sFr 107,507 approx. € 79,95 | £73.00ISBN 978-1-4939-0457-0

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D. G. Figueiredo, Cidade Universitaria Instituto de Matematica, Estatistica e C, Campinas, Brazil; J. M. do Ó, Universidade Federal da Paraíba, João Pessoa, Brazil; C. Tomei, Pontifícia Universidade Católica do Rio, Rio de Janeiro, Brazil (Eds)

Analysis and Topology in Nonlinear Differential EquationsA Tribute to Bernhard Ruf on the Occasion of his 60th Birthday

This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topo-logical methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type.

Features 7 Growing vital area of mathematics 7 Anni-versary volume dedicated to Bernhard Ruf

Contents 27 contributions written by specialists in their field.

Fields of interestPartial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Topology


Product categoryCollection of essays

Due June 2014

2014. Approx. 480 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 402) Hardcover7 approx. * € (D) 116,63 | € (A) 119,90 | sFr 145,507 approx. € 109,00 | £98.50ISBN 978-3-319-04213-8

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D. Finston, Brooklyn College of the City University of New York, Brooklyn, NY, USA; P. Morandi, New Mexico State University, Las Cruces, NM, USA

An Invitation to Abstract Algebra via ApplicationsAn Invitation to Abstract Algebra via Applica-tions seeks to generate an interest in abstract algebra while requiring minimal prerequisites via the use of motivating applications examples, rather than, developing a complete theory of algebraic structures. The thorough and logical presenta-tion starts with concrete topics and applications based on everyday experiences that naturally lead students to algebraic questions and concepts. The consistent, down-to-earth presentation is acces-sible to an audience with no previous knowledge of abstract algebra, paving the way towards more advanced algebra courses.

Features 7 Accessible to students with no prior knowledge of abstract algebra 7 Focuses on a wide variety of daily applications 7 Numerous sample prob-lems and exercises

Contents 1 Identification Numbers and Modular Arith-metic.- 2 Error Correcting Codes.- 3 Rings and Fields.- 4 Linear Algebra and Linear Codes.- 5 Field Extensions and Ruler and Compass Con-structions.- 6 Quotient Rings and Field Exten-sions.- 7 Ideals and Quotient Rings.- 8 Cyclic Codes.- 9 Cryptography and Group Theory.- 10 Symmetry.- Bibliography.- List of Symbols.- Index.

Fields of interestAlgebra; Mathematical Applications in Computer Science; Linear and Multilinear Algebras, Matrix Theory

Target groupsUpper undergraduate

Product categoryUndergraduate textbook

Due March 2014

2014. XVI, 184 p. 24 illus., 18 in color. Hardcover7 approx. * € (D) 42,79 | € (A) 43,99 | sFr 49,507 approx. € 39,99 | £33.99ISBN 978-3-319-04497-2

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30

W. Gander, ETH Zürich, Zürich, Switzerland; M. J. Gander, F. Kwok, Université de Genève, Genève, Switzerland

Scientific Computing – An Introduction using Maple and MATLABScientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathemat-ics, numerical and symbolic/algebraic computa-tions and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic.

Features 7 Equal emphasis on theory, symbolic computa-tion and numerical algorithms 7 Numerous complete, ready-to-run programs in Matlab and Maple, complete with many examples 7 In-depth treatment of many advanced topics, beyond standard undergraduate texts

Contents Why Study Scientific Computing?.- Finite Precision Arithmetic.- Linear Systems of Equa-tions.- Interpolation.- Nonlinear Equations.-Least Squares Problems.- Eigenvalue Problems.- Differ-entiation.- Quadrature.- Numerical Ordinary Dif-ferential Equations.- Iterative Methods for Linear Systems.- Optimization.- Bibliography.- Index.

Fields of interestComputational Mathematics and Numerical Analysis; Algorithms; Computational Science and Engineering

Target groupsUpper undergraduate

Product categoryGraduate/Advanced undergraduate textbook

Due March 2014

2014. Approx. 900 p. (Texts in Computational Science and Engineering, Volume 11) Hardcover7 * € (D) 85,59 | € (A) 87,99 | sFr 106,507 € 79,99 | £72.00ISBN 978-3-319-04324-1

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F. Hiai, Tohoku University, Sendai, Japan; D. Petz, Budapest University of Technology and Economics, Budapest, Hungary

Introduction to Matrix Analysis and ApplicationsMatrices can be studied in different ways. They are a linear algebraic structure and have a topologi-cal/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropri-ate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information.

Features 7 Based on the lectures from the Graduate School of Information Sciences of Tohoku Uni-versity and the Budapest University of Technology and Economics 7 Provides a strong emphasis to various areas of quantum theory, particularly quantum information theory 7 Covers classical topics and recent advances in the field

Contents Fundamentals of operators and matrices.- Map-pings and algebras.- Functional calculus and derivation.- Matrix monotone functions and con-vexity.- Matrix means and inequalities.- Majoriza-tion and singular values.- Some applications.

Field of interestLinear and Multilinear Algebras, Matrix Theory

Target groupsGraduate


Due February 2014

Jointly published with Hindustan Book Agency, New Delhi, India

No distribution rights for India

2014. VIII, 332 p. 3 illus. (Universitext) Softcover7 * € (D) 64,19 | € (A) 65,99 | sFr 80,007 € 59,99 | £39.99ISBN 978-3-319-04149-0

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M. Iannelli, A. Pugliese, Università di Trento, Trento, Italy

An Introduction to Mathematical BiologyThis book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work starts from population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and use it as the area where to understand different types of mathematical mod-eling, and the idea of qualitative agreement with data. Shorter sections are devoted to infectious diseases, to molecular networks, and finally to ex-citable media. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at stu-dents in their fourth year of studies in Mathemat-ics. It can also be used as a reference as we provide up-to-date developments in several areas.

Features 7 Extended overview of applications of Math-ematics to Biology 7 Attention to mathematical rigour in applied and empirical context 7 De-tailed construction of models 7 A collection of problems designed to approach more advanced questions

Fields of interestMathematical and Computational Biology; Theoretical Ecology/Statistics; Applications of Mathematics



Due June 2014

2014. Approx. 350 p. (UNITEXT / La Matematica per il 3+2) Softcover7 approx. * € (D) 64,19 | € (A) 65,99 | sFr 80,007 approx. € 59,99 | £53.99ISBN 978-3-319-03025-8

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31

A. F. Izmailov, Moscow, Russia; M. V. Solodov, Rio de Janeiro, Brazil

Newton-Type Methods for Optimization and Variational ProblemsThis book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frame-works that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associ-ated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se.

Features 7 Offers new approaches to optimization algo-rithms through Newtonian methods 7 Relevant to researchers in Optimization and Variational Analysis 7 Provides a unified view of classi-cal as well as recent developments in the field of Newton-type methods

Contents 1. Elements of optimization theory and variational analysis.- 2. Equations and unconstrained optimi-zation.- 3. Variational problems: local methods.- 4. Constrained optimization: local methods.- 5. Variational problems: globalization of conver-gence.- 6. Constrained optimization: globalization of convergence.- 7. Degenerate problems with non-isolated solutions.- A. Miscellaneous material.

Fields of interestOperations Research, Management Science; Con-tinuous Optimization; Optimization



Due March 2014

2014. XX, 570 p. 30 illus., 1 in color. (Springer Series in Operations Research and Financial Engineering) Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-3-319-04246-6

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J. Jost, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Mathematical Methods in Biology and NeurobiologyMathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phe-nomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biol-ogy and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies: • discrete structures and graph theory • stochastic processes • dynami-cal systems and partial differential equations • optimization and the calculus of variations.

Features 7 Develops the mathematical tools required for modern biology at all levels and scales 7 Pro-vides a survey of mathematics, from graph theory and stochastic processes to dynamical systems and pattern formation 7 Contains biological examples from the molecular to the evolutionary and ecological levels 7 Contains concise, mod-ern introduction to mathematical population ge-netics 7 Written by one of the most experienced and successful authors of advanced mathematical textbooks

Contents Introduction.- Discrete structures.- Stochastic processes.- Pattern formation.- Optimization.- Population genetics.

Fields of interestDynamical Systems and Ergodic Theory; Partial Differential Equations; Complex Systems



Due April 2014

2014. Approx. 215 p. 8 illus. in color. (Universitext) Softcover7 approx. * € (D) 53,49 | € (A) 54,99 | sFr 67,007 approx. € 49,99 | £29.99ISBN 978-1-4471-6352-7

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C. Klüppelberg, D. Straub, I. M. Welpe, Munich University of Technology, Munich, Germany (Eds)

Risk – A Multidisciplinary IntroductionContents Introduction.- Part I. Risk in History and Science: 1.Zachmann, K.: Risk in historical perspective: concepts, contexts, and conjunctions.- 2.Lütge, C., Schnebel, E., Westphal, N.: Risk manage-ment and business ethics: integrating the human factor.- 3.Straub, D., Welpe, I.: Decision-making under risk: a normative and behavioral perspec-tive.- 4.Mainzer, K.: The new role of mathematical modelling and its importance for society.- Part II. Quantitative Risk Methodology: 5.Biagini, F. , Meyer-Brandis, T. and Svindland, G. :The math-ematical concept of risk.- 6.Fasen, V., Klüppelberg, C., Menzel, A.: Quantifying extreme event risk. 7.Schön, C.-C. and Wimmer, V.: Statistical models for the prediction of genetic values.- 8.Brechmann, E. and Czado, C.: Bayesian risk analysis.- 9.Klüp-pelberg, C., Stelzer, R.: Dealing with dependent risks.- 10.Bannör, K. and Scherer, M.: Model risk and uncertainty; illustrated with examples from Mathematical finance.- Part III. Risk Treatment in Various Applications: 11.Roosen, J.: Cost-benefit analysis.- 12.Straub, D.: Engineering risk assessment.- 13.Vogel-Heuser, B.: Integrated modeling of complex production automation systems to increase dependability.- 14.Wiesche, M., Hörmann, S., Schermann, M., Krcmar. H.: Information technology risks: an interdisciplin-ary challenge.- 15.Klinker, G.: Risks in developing novel user interfaces for Human-Computer inter-action.- 16.Ankerst, D., Seifert-Klauss, V., Kiechle, M.: Translational risk models.- 17.Seifert-Klauss, V., Thümer, L., Protzer, U. [...]

Fields of interestProbability Theory and Stochastic Processes; Sta-tistics for Life Sciences, Medicine, Health Sciences; Quality Control, Reliability, Safety and Risk



Due June 2014

2014. XIV, 430 p. 100 illus., 43 in color. Hardcover7 * € (D) 64,19 | € (A) 65,99 | sFr 80,007 € 59,99 | £53.99ISBN 978-3-319-04485-9

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32

S. Koziel, Reykjavik University Engin. Optimization & Modeling Center, Reykjavik, Iceland; S. Ogurtsov, Reykjavik University School of Science and Engineering, Reykjavik, Iceland

Antenna Design by Simulation-Driven OptimizationThis Brief reviews a number of techniques exploit-ing the surrogate-based optimization concept and variable-fidelity EM simulations for efficient optimization of antenna structures. The introduc-tion of each method is illustrated with examples of antenna design.

Features 7 Features cutting-edge research on efficient design optimization of antenna structures 7 Spe-cific examples of antenna design complement descriptions of techniques 7 Useful for electrical engineers working in academia and industry

Contents 1. Introduction.- 2. Antenna Design Using Elec-tromagnetic Simulations.- 3. Surrogate-Based Op-timization.- 4. Methodologies for Variable-Fidelity Optimization of Antenna Structures.- 5. Low-Fidelity Antenna Models.- 6. Simulation-Based UWB Antenna Design.- 7. Optimization of Di-electric Resonator Antennas.- 8. Surrogate-Based Optimization of Microstrip Broadband Antennas.- 9. Simulation-Driven Antenna Array Optimiza-tion.- 10. Antenna Optimization with Surrogates and Adjoint Sensitivities.- 11. Simulation-Based Multi-Objective Antenna Optimization with Sur-rogate Models.- 12. Practical Aspects of Surrogate-Based Antenna Design: Selecting Model Fidelity.- 13. Discussion and Recommendations.

Fields of interestOptimization; Microwaves, RF and Optical Engi-neering; Simulation and Modeling


Product categoryBrief

Due March 2014

2014. X, 120 p. 94 illus., 45 in color. (SpringerBriefs in Optimization) Softcover7 * € (D) 53,49 | € (A) 54,99 | sFr 67,007 € 49,99 | £44.99ISBN 978-3-319-04366-1

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C. J. Larsen, Worcester Polytechnic Institute Dept. Mathematical Sciences, Worcester, MA, USA

A Guide to Special Functions of Bounded Variation and ApplicationsThe space Special Functions of Bounded Variation (SBV) has become critical for many applica-tions, particularly in fracture mechanics and image processing, since its introduction in 1988. Inspite of this increased importance, the current literature on SBV provides a purely mathematical perspective and is written for an audience with a solid background in measure theory. In this book the authors makes SBV more accessible to applied mathematicians and engineers. The mate-rial progresses systematically, beginning with an introduction and motivation and then providing a review of measure theory before moving on to more complex topics. Illustrations and examples are used to enhance the presentation.

Features 7 New book 7 Featuring exciting up-dates 7 An in depth look at special functions of bounded variation

Contents Preface.- Introduction and Motivation for SBV: Free Discontinuity Problems.- Review of Basic Measure Theory.- Relations Between Mea-sures.- BV, Sets of Finite Perimeter, SBV, and Coarea.- Structure Related to Applications.- Ap-plications.- Issues in Quasi-Static Evolution.- Bib-liography.- Index

Fields of interestCalculus of Variations and Optimal Control; Opti-mization; Mechanics; Applications of Mathematics



Due June 2014

2013. 250 p. 30 illus. Hardcover7 approx. * € (D) 57,67 | € (A) 59,29 | sFr 89,507 approx. € 53,90 | £42.99ISBN 978-1-4419-0536-9

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R. Lewandowski, University of Rennes 1, Rennes, France; T. C. Rebollo, University of Seville, Seville, Spain

Mathematical and Numerical Foundations of Turbulence Models and ApplicationsContents PART I.- 1. General modelization from the incom-pressible Navier-Stokes Equations to turbulent models.- PART II.- 2. Some mathematical tools for analysing parabolic and elliptic equations with second hand side in L1.- 3. Theoretical results for the coupling of the Navier-Stokes Equations with eddy viscosity to the equation for the Turbulent kinetic energy: Stationary case with Dirichlet boundary conditions.- 4. Theoretical results for the coupling of the Navier-Stokes Equations with eddy viscosity to the equation for the Turbulent kinetic energy: Evolutionary case with Dirichlet boundary conditions.- 5. The theoretical coupling of two turbulent flows modelized by models with the TKE equation and eddy viscosities and the usual interface condition.- 6. Navier boundary conditions: Notion of suitable solutions and ex-istence result including the estimate for the pres-sure.- PART III.- 7. Finite Element approximation of one-equation turbulence models: Discretiza-tion, stability and convergence analysis. Numerical tests.- 8. Finite Element approximation of coupled two-fluid turbulence models: Discretization, stability and convergence analysis. Numerical tests.- 9. Modeling of turbulent oceanic mixing-layer: Modeling, equilibria states, discretization, convergence of discretizations to equilibria states.- PART IV.- 10. Variational Multi-Scale modeling of turbulence.

Fields of interestPartial Differential Equations; Engineering Fluid Dynamics; Numerical Analysis



Due February 2014

2014. XX, 290 p. 30 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 approx. * € (D) 80,20 | € (A) 82,45 | sFr 105,507 approx. € 74,95 | £66.99ISBN 978-1-4939-0454-9

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33

M. Mursaleen, Aligarh Muslim University, Aligarh, India

Applied Summability MethodsThis short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in re-cent years. The book provides basic definitions of sequence spaces, matrix transformations, regular matrices and some special matrices, making the material accessible to mathematicians who are new to the subject. Among the core items covered are the proof of the Prime Number Theorem using Lambert’s summability and Wiener’s Tauberian theorem, some results on summability tests for singular points of an analytic function, and ana-lytic continuation through Lototski summability.

Features 7 Focuses exclusively on the study of summa-bility methods and their applications 7 Fea-tures self-contained chapters appropriate for researchers and graduate students 7 Includes topics such as proof of the prime number theorem using Lambert's summability and Wiener's Taube-rian theorem

Contents Toeplitz Matrices.- Lambert Summability and the Prime Number Theorem.- Summability Tests for Singular Points.- Lototski Summability and Analytic Continuation.- Summability Methods for Random Variables.- Almost Summability.- Almost Summability of Taylor Series.- Matrix Summabil-ity of Fourier and Walsh-Fourier Series.- Almost Convergence in Approximation Process.- Statisti-cal Summability.- Statistical Approximation.- Ap-plications to fixed point theorems.- Bibliography.- Index.

Fields of interestSequences, Series, Summability; Number Theory; Linear and Multilinear Algebras, Matrix Theory



Due May 2014

2014. IV, 97 p. (SpringerBriefs in Mathematics) Softcover7 approx. * € (D) 42,79 | € (A) 43,99 | sFr 54,507 approx. € 39,99 | £36.99ISBN 978-3-319-04608-2

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H. J. Prömel, Technische Universität Darmstadt, Darmstadt, Germany

Ramsey Theory for Discrete StructuresThis monograph covers some of the most im-portant developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century.

Features 7 First monograph with such an in depth treat-ment of Ramsey Theory 7 Written by one of the leading researchers of the field in the eighties and nineties of the last century 7 Provides a thorough reference on the topic

Contents Foreword by Angelika Steger.- Preface.- Con-ventions.- Part I Roots of Ramsey Theory: 1.1 Ramsey’s theorem.- 1.2 From Hilbert’s cube lemma to Rado’s thesis.- Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Defini-tions and basic examples.- 2.2 Hales-Jewett’s theorem.- 2.3 Graham-Rothschild’s theorem.- 2.4 Canonical partitions.- Part III Back to the Roots: Sets: 3.1 Ramsey numbers.- 3.2 Rapidly growing Ramsey functions.- 3.3 Product theorems.- 3.4 A quasi Ramsey theorem.- 3.5 Partition relations for cardinal numbers.- Part IV Graphs and Hyper-graphs: 4.1 Finite graphs.- 4.2 Infinite graphs.- 4.3 Hypergraphs on parameter sets.- 4.4. Ramsey statements for random graphs.- 4.5 Sparse Ramsey Theorems.- Part V Density Ramsey Theorems: 5.1 Szemerédi’s Theorem.- 5.2 Density Hales-Jewett Theorem.- 5.3 Proof of the density Hales-Jewett theorem.- References.- Index.

Fields of interestCombinatorics; Discrete Mathematics; Discrete Mathematics in Computer Science



Available

2013. XVI, 232 p. 13 illus. Hardcover7 * € (D) 90,94 | € (A) 93,49 | sFr 113,507 € 84,99 | £76.50ISBN 978-3-319-01314-5

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A. Quarteroni, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland; F. Saleri, Politecnico di Milano MOX, Milano, Italy; P. Gervasio, Università degli Studi di Brescia, Brescia, Italy

Scientific Computing with MATLAB and OctaveThis textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The au-thors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using poly-nomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and ap-pealing, the programming environments Matlab and Octave are adopted as faithful companions.

Features 7 Offers a combination of problems, algorithms, programs, exercises, illustrations and numeri-cal solutions 7 Includes 100 examples, 145 solved exercises and 43 Matlab and Octave pro-grams 7 Each chapter opens with representative problems and continues with construction and analysis of algorithms and ad-hoc programs for their implementation

Contents 1. What can’ t be ignored.- 2. Nonlinear equa-tions.- 3. Approximation of functions and data.- 4. Numerical differentiation and integration.- 5. Linear systems.- 6. Eigenvalues and eigenvec-tors.- 7. Numerical optimization.- 8. Ordinary differential equations.- 9. Numerical approxima-tion of boundary-value problems.- 10. Solutions of the exercises.- References.- Index.

Fields of interestComputational Science and Engineering; Numeri-cal and Computational Physics; Computational Intelligence

Target groupsLower undergraduate

Product categoryUndergraduate textbook

Due February 2014

4th ed. 2014. XVIII, 442 p. 188 illus., 172 in color. (Texts in Computational Science and Engineering, Volume 2) Hardcover7 * € (D) 48,14 | € (A) 49,49 | sFr 60,007 € 44,99 | £40.99ISBN 978-3-642-45366-3

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34

I. V. Sergienko, National Academy of Sciences of Ukraine, Kiev, Ukraine

Topical Directions of InformaticsIn Memory of V. M. Glushkov

This work is devoted to the late Ukrainian computer scientist V. M. Glushkov on the 90th anniversary of his birthday. Dr.

Features 7 Features the contributions of V. M. Glushkov to the world of computer science 7 Elucidates new results in the field of mathematical modeling of complicated processes 7 May be used as supple-mentary text for graduate and post-graduate students of computer science

Contents Introduction.- 1. Theoretical and Applied Pro-gramming.- 2. Supercomputers and Intelligent Technologies of High-Performance Computing.- 3. Computer Technologies as Tools for Studying Complicated Processes.- 4. Mathematical Models and Computer Technologies in Investigating Economic Processes.- 5. Mathematical Modeling and Investigation of Complicated Processes.- 6. Optimization Methods for Solving Transcomputa-tional Problems.- 7. Combinatorial Optimization Problems.- 8. Computer Technologies in Medical and Biological Research.

Fields of interestOperations Research, Management Science; Mathematical Applications in Computer Science; Mathematical Models of Cognitive Processes and Neural Networks



Due April 2014

2014. XXIV, 294 p. 90 illus., 7 in color. (Springer Optimization and Its Applications, Volume 78) Hardcover7 approx. * € (D) 85,59 | € (A) 87,99 | sFr 107,507 approx. € 79,99 | £73.00ISBN 978-1-4939-0475-4

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M. Talagrand, Université Paris VI, Paris Cedex 05, France

Upper and Lower Bounds for Stochastic ProcessesModern Methods and Classical Problems

The book develops modern methods and in par-ticular the “generic chaining” to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes.

Features 7 Develops modern methods and in particular the "generic chaining" to bound stochastic pro-cesses 7 Gives applications to stable processes, infinitely divisible processes, matching theorems etc. 7 Gives the complete solution of a number of classical problems

Contents 0. Introduction.- 1. Philosophy and Overview of the Book.- 2. Gaussian Processes and the Generic Chaining.- 3. Random Fourier Series and Trigono-metric Sums, I. - 4. Matching Theorems I.- 5. Ber-nouilli Processes.- 6. Trees and the Art of Lower Bounds.- 7. Random Fourier Series and Trigono-metric Sums, II.- 8. Processes Related to Gaussian Processes.- 9. Theory and Practice of Empirical Processes.- 10. Partition Scheme for Families of Distances.- 11. Infinitely Divisible Processes.- 12. The Fundamental Conjectures.- 13. Convergence of Orthogonal Series; Majorizing Measures.- 14. Matching Theorems, II: Shor’s Matching Theorem. 15. The Ultimate Matching Theorem in Dimension ≥ 3.- 16. Applications to Banach Space Theory.- 17. Appendix: What this Book is Really About.- 18. Appendix: Continuity.- References. Index.

Fields of interestProbability Theory and Stochastic Processes; Functional Analysis



Due March 2014

2014. XII, 616 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Volume 60) Hardcover7 * € (D) 117,69 | € (A) 120,99 | sFr 146,507 € 109,99 | £99.00ISBN 978-3-642-54074-5

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C. Weiß, Goethe University Frankfurt am Main, Frankfurt am Main, Germany

Twisted Teichmüller CurvesThese notes introduce a new class of alge-braic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main proper-ties are described. In particular, the volume of twisted Teichmüller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.

Features 7 Contains a comprehensive introduction to the theory of Teichmüller curves 7 Is kept as self-contained as possible 7 Contains 15 figures and 2 tables

Contents Introduction.- Background.- Teichmüller Curves.- Twisted Teichmüller Curves.- Stabilizer and Maximality.- Calculations for Twisted Teichmül-ler Curves.- Prym Varieties and Teichmüller Curves.- Lyapunov Exponents.- Kobayashi Curves Revisited.- Appendix.- Tables.- List of Symbols.- Index.- Bibliography.

Fields of interestAlgebraic Geometry; Number Theory; Dynamical Systems and Ergodic Theory



Due February 2014

2014. XVI, 166 p. 13 illus., 6 in color. (Lecture Notes in Mathematics, Volume 2104) Softcover7 * € (D) 37,44 | € (A) 38,49 | sFr 47,007 € 34,99 | £31.99ISBN 978-3-319-04074-5

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