lévy processes and their applications in reliability and ... · tography.- appendix a: some...

News 9/2013 Mathematics

63

M. Abdel-Hameed, United Arab Emirates University, Al Ain, Utd.Arab.Emir.

Lévy Processes and Their Applications in Reliability and Storage This book covers Lévy processes and their ap-plications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degrada-tion; estimating the parameters of the degradation process is also discussed, as is the maintenance of dams subject to Lévy input.

Features 7 Provides a concise and comprehensive account of Lévy processes 7 Clearly discusses applica-tions of Lévy processes in reliability, with special attention to life distributions and the maintenance of devices subject to degradation, as well estimat-ing the parameters of the degradation pro-cess 7 Discusses applications of Lévy processes in storage, with special emphasis on monitoring dams subject to Lévy input

Contents Preface.- Notation and Terminology.- Lévy Processes and Their Characteristics.- Degrada-tion Processes.- Storage Models: Control of Dams Using PMλ,τ Policies.- Appendix: Preliminaries.- Index.

Fields of interestProbability Theory and Stochastic Processes; Industrial and Production Engineering; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences

Target groupsResearch

Product categoryBrief

Due January 2014

2014. Approx. 125 p. (SpringerBriefs in Statistics) Softcover7 approx. $69.99ISBN 978-3-642-40074-2

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M. R. Adhikari, Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC), Kolkata, India; A. Adhikari, University of Calcutta, Kolkata, India

Basic Modern Algebra with ApplicationsThe book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are inter-ested in supplementary reading at a higher level. The text is designed in such a way that it encour-ages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.

Features 7 Presents self-contained algebra text for independent study 7 Provides problem-solving techniques for better grasp of the topic 7 Dis-cusses applications of algebra to number theory, primality testing, cryptography, geometry and topology

Contents Prerequisites: Basics of Set Theory and Inte-gers.- Groups: Introductory Concepts.- Actions of Groups, Topological Groups and semigroups.- Rings: Introductory Concepts.- Ideals of Rings: Introductory concepts.- Factorization in Integral Domains and in Polynomial Rings.- Rings with Chain Conditions.- Vector Spaces.- Modules.- Algebraic Aspects of Number Theory.- Algebraic Numbers.- Introduction to Mathematical Cryp-tography.- Appendix A: Some Aspects of Semir-ings.- Appendix B: Category Theory.- Appendix C: A Brief Historical Note.

Fields of interestAlgebra; Commutative Rings and Algebras; Group Theory and Generalizations

Target groupsUpper undergraduate

Product categoryGraduate/Advanced undergraduate textbook

Due October 2013

2013. XVIII, 545 p. 55 illus. Hardcover7 $79.99ISBN 978-81-322-1598-1

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S. Almezel, University of Tabuk, Tabuk, Saudi Arabia; Q. H. Ansari, Aligarh Muslim University, Aligarh, India; M. A. Khamsi, University of Texas at El Paso, El Paso, TX, USA (Eds)

Topics in Fixed Point TheoryThe purpose of this contributed volume is to pro-vide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces.

Features 7 Compiles new research in fixed point theory in one book 7 Introduces topics in an introduc-tory manner 7 Covers most aspects of fixed point theory and its applications

Contents 1 Introduction to Metric Fixed Point Theory. M.A. Khamsi.- 2 Banach Contraction Principle and its Generalizations. Abdul Latif.- 3 Ekeland’s Variational Principle and Its Extensions with Ap-plications. Qamrul Hasan Ansari.- 4 Fixed Point Theory in Hyperconvex Metric Spaces. Rafael Espínola and Aurora Fernández-León.- 5 An Introduction to Fixed Point Theory in Modular Function Spaces. W. M. Kozlowski.- 6 Fixed Point Theory in Ordered Sets from the Met-ric Point of View. M. Z. Abu-Sbeih and M. A. Khamsi.- 7 Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps. Hichem Ben-El-Mechaiekh.- 8 Some Iterative Methods for Fixed Point Problems. Q. H. Ansari and D. R. Sahu.- Index.

Fields of interestAnalysis; Functional Analysis; Operator Theory


Product categoryContributed volume

Due October 2013

2013. X, 300 p. Hardcover7 $129.00ISBN 978-3-319-01585-9

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www.springer.com/978-3-642-40074-2



Mathematics springer.com/NEWSonline

64

P. Amster, FCEN-Universidad de Buenos Aires, Buenos Aires, Argentina

Topological Methods in the Study of Boundary Value ProblemsThis textbook is devoted to the study of some sim-ple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are pres-ent in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems.

Features 7 Some simple but representative problems in nonlinear analysis are studied 7 Only basic knowledge of main topics in general analysis is needed, making the book easy-to-understand for non-specialists too 7 Concise and informal style, thus allowing also undergraduate students to enjoy some of the beauties of this interesting field of Mathematics

Contents Introduction.- Shooting type methods.- The Ban-ach Fixed Point Theorem.- Schauder’s Theorem and applications.- Topological degree: an intro-duction.- Applications.- Basic facts on metric and normed spaces.- Brief review of ODE’s.- Hints and Solutions to Selected Exercises.

Fields of interestAnalysis; Ordinary Differential Equations; Partial Differential Equations

Target groupsGraduate


Due November 2013

2014. X, 250 p. (Universitext) Softcover7 $69.99ISBN 978-1-4614-8892-7

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M. Audin, M. Damian, IRMA Université Louis Pasteur, Strasbourg Cedex, France

Morse Theory and Floer HomologyThis book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the ‘Arnold conjecture’, which asserts that the number of 1-periodic trajec-tories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thor-ough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part.

Features 7 Translation of the popular French text-book 7 Provides a unified presentation of Morse theory and Floer homology that is unique in the English language 7 Explains all the required background on symplectic geometry, differential geometry, algebraic topology and analysis

Contents Introduction to Part I.- Morse Functions.- Pseudo-Gradients.- The Morse Complex.- Morse Homology, Applications.- Introduction to Part II.- What You Need To Know About Symplectic Geometry.- The Arnold Conjecture and the Floer Equation.- The Maslov Index.- Linearization and Transversality.- Spaces of Trajectories.- From Floer To Morse.- Floer Homology: Invariance.- Elliptic Regularity.- Technical Lemmas.- Exercises for the Second Part.- Appendices: What You Need to Know to Read This Book.

Fields of interestGeometry; Differential Geometry; Algebraic Topology



Due September 2013

Original French edition published by EDP Sciences, Les Ulis Cedex A, 2010

Distribution rights for France: EDP Sciences, Les Ulis Cedex A, France

2013. XVI, 618 p. 110 illus. (Universitext) Softcover7 $89.99ISBN 978-1-4471-5495-2

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G. F. Birkenmeier, University of Louisiana, Lafayette, Lafayette, LA, USA; J. K. Park, Busan National University Dept. of Mathematics, Busan, Korea, Republic of (South Korea); S. T. RIZVI, The Ohio State University, Lima, OH, USA

Extensions of Rings and ModulesThe focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions. The first four chapters of the book discuss rings and modules which generalize injectivity (e.g., extend-ing modules), or for which certain annihilators become direct summands (e.g., Baer rings).

Features 7 First research monograph to explore in detail the "extensions" of rings and modules 7 Begins with basic notions, terminology, definitions and a description of the classes of rings and modules covered in this book 7 Mathematical interdisci-plinary applications covered throughout, includ-ing C*-algebras 7 Notes and exercises at the end of each chapter, and open problems at the end of each part, lend text accessible to students

Contents Preliminaries and Basic Results.- Injectivity and Some of Its Generalizations.- Baer, Rickart, and Quasi-Baer Rings.- Baer, Quasi-Baer Modules, and Their Applications.- Triangular Matrix Repre-sentations and Triangular Matrix Extensions.- Ma-trix, Polynomial, and Group Ring Extensions.- Es-sential Overring Extensions - Beyond the Maximal Ring of Quotients.- Ring and Module Hulls.- Hulls of Ring Extensions.- Applications to Rings of Quotients and C* Algebras.- Open Problems and Questions.- References.- Index.

Fields of interestAlgebra; Functional Analysis; Linear and Multilin-ear Algebras, Matrix Theory



Available

2013. XX, 432 p. Hardcover7 $79.99ISBN 978-0-387-92715-2

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65

F. Borceux, Université catholique de Louvain, Louvain-la-Neuve, Belgium

An Axiomatic Approach to GeometryGeometric Trilogy I

Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Histori-cally, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra.

Features 7 Focuses on historical aspects 7 Supports con-temporary approaches of the three aspects of axiomatic geometry: Euclidean, non-Euclidean and projective 7 Includes full solutions to all famous historical problems of classical geometry and hundreds of figures

Contents Introduction.- Preface.- 1.The Prehellenic Antiquity.- 2.Some Pioneers of Greek Geometry.- 3.Euclid’s Elements.- 4.Some Masters of Greek Geometry.- 5.Post-Hellenic Euclidean Geom-etry.- 6.Projective Geometry.- 7.Non-Euclidean Geometry.- 8.Hilbert’s Axiomatics of the Plane.- Appendices: A.Constructibily.- B.The Three Classical Problems.- C.Regular Polygons.- Index.- Bibliography.

Fields of interestGeometry; History of Mathematical Sciences; Projective Geometry


Product categoryMonograph

Due October 2013

2013. XIV, 440 p. 287 illus. Hardcover7 $129.00ISBN 978-3-319-01729-7

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F. Borceux, Université catholique de Louvain, Louvain-la-Neuve, Belgium

An Algebraic Approach to GeometryGeometric Trilogy II

This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems.

Features 7 Unified treatment of the various algebraic ap-proaches of geometric spaces 7 Provides a full treatment, perfectly accessible at a bachelor level, of all algebraic ingredients necessary to develop all the major aspects of the theory of algebraic curves 7 Pays attention to the geometric figures of higher degree

Contents Introduction.- Preface.- 1.The Birth of Analytic Geometry.- 2.Affine Geometry.- 3.More on Real Affine Spaces.- 4.Euclidean Geometry.- 5.Hermi-tian Spaces.- 6.Projective Geometry.- 7.Algebraic Curves.- Appendices: A.Polynomials Over a Field.- B.Polynomials in Several Variables.- C.Homogenous Polynomials.- D.Resultants.- E.Symmetric Polynomials.- F.Complex Numbers.- G.Quadratic Forms.- H.Dual Spaces.- Index.- Bibliography.

Fields of interestGeometry; Projective Geometry; History of Math-ematical Sciences



Due November 2013

2014. 450 p. Hardcover7 $129.00ISBN 978-3-319-01732-7

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F. Borceux, Court-Saint-Etienne, Belgium

A Differential Approach to GeometryGeometric Trilogy III

This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary ap-proaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topol-ogy, providing an integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz de-veloped differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials.

Features 7 Pays particular attention to historical develop-ment and preliminary approaches that support the contemporary geometrical notions 7 Links clas-sical surface theory in the three dimensional real space to modern Riemannian geometry 7 Can be used to teach classical differential geometry up to an advanced level

Contents Introduction.- Preface.- 1.The Genesis of Differ-ential Methods.- 2.Plane Curves.- 3.A Museum of Curves.- 4.Skew Curves.- 5.Local Theory of Sur-faces.- 6.Towards Riemannian Geometry.- 7.Ele-ments of Global Theory of Surfaces.- Appendices: A.Topology.- B.Differential Equations.- Index.- Bibliography.

Fields of interestGeometry; Differential Geometry; History of Mathematical Sciences



Due November 2013

2014. Approx. 480 p. Hardcover7 $129.00ISBN 978-3-319-01735-8

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66

F. Borceux, University of Louvain Institute of Research, Louvain-la-Neuve, Belgium

Geometric TrilogyAxiomatic, Algebraic and Differential Approaches to Geometry

The Trilogy intends to introduce the reader to the multiple complementary aspects of geom-etry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geom-etry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves.

Features 7 Focuses on historical aspects 7 Supports con-temporary approaches of the three aspects of axiomatic geometry: Euclidean, non-Euclidean and projective 7 Includes full solutions to all famous historical problems of classical geometry and hundreds of figures

Fields of interestGeometry; History of Mathematical Sciences



Due December 2013

2013. 1350 p. (3-volume-set)7 $339.00ISBN 978-3-319-01804-1

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J. Blot, Université Paris 1 Panthéon-Sorbonne, Paris, France; N. Hayek, Université Paris 2 Panthéon-Assas, Paris, France

Infinite-Horizon Optimal Control in the Discrete-Time Framework In this book the authors take a rigorous look at the infinite-horizon discrete-time optimal control the-ory from the viewpoint of Pontryagin’s principles. Several Pontryagin principles are described which govern systems and various criteria which define the notions of optimality, along with a detailed analysis of how each Pontryagin principle relate to each other. The Pontryagin principle is examined in a stochastic setting and results are given which generalize Pontryagin’s principles to multi-criteria problems.

Features 7 Examines the Pontryagin principle using a Karush-Kuhn-Tucker theorem in ordered Banach spaces 7 Includes findings on the finite-horizon setting based on the Boltyanski and Michel re-sults 7 Uses various tools of nonlinear functional analysis to analyze the first Pontryagin principle

Contents 1. Presentation of the problems and tools of the finite horizon.- 2. Infinite horizon theorems.- 3. The special case of the bounded processes.- Re-lated topics. Appendix A : Sequences.- Appendix B: Static optimization.- References.

Fields of interestCalculus of Variations and Optimal Control; Opti-mization; Dynamical Systems and Ergodic Theory; Nonlinear Dynamics



Due October 2013

2013. VI, 124 p. (SpringerBriefs in Optimization) Softcover7 $54.99ISBN 978-1-4614-9037-1

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A. Braides, Università di Roma Tor Vergata, Roma, Italy

Local Minimization, Variational Evolution and Γ-ConvergenceThis book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of no-tions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the defini-tion of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions.

Features 7 Provides connections between topics of active current research 7 Presents the subjects with examples from the main areas that have made Gamma-convergence so successful 7 Proposes numerous examples of directions of further research

Contents Introduction.- Global minimization.- Parameter-ized motion driven by global minimization.- Local minimization as a selection criterion.- Conver-gence of local minimizers.- Small-scale stability.- Minimizing movements.- Minimizing movements along a sequence of functionals.- Geometric minimizing movements.- Different time scales.- Stability theorems.- Index.

Fields of interestApplications of Mathematics; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization



Due October 2013

2013. XII, 155 p. 36 illus. (Lecture Notes in Mathematics, Volume 2094) Softcover7 $49.99ISBN 978-3-319-01981-9

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67

P. C. Bressloff, University of Utah, Salt Lake City, UT, USA

Waves in Neural MediaFrom Single Neurons to Neural Fields

Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlin-ear analysis, Evans functions and wave stabil-ity, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable.

Features 7 Covers an extensive array of topics ranging from sub-cellular to tissue level biology 7 Can serve as an entry point for biologists wishing to learn about mathematical modeling 7 Provides an excellent introduction to mathematical neuro-science from the perspective of dymanical systems

Contents Preface.- Part I Neurons.- Single Neuron Model-ing.- Traveling Waves in One-Dimensional Excitable Media.- Wave Propagation Along Spiny Dendrites.- Calcium Waves and Sparks.- Part II Networks.- Waves in Synaptically-Coupled Spik-ing Networks.- Population Models and Neural Fields.- Waves in Excitable Neural Fields.- Neural Field Model of Binocular Rivalry Waves.- Part III Development and Disease.- Waves in the Develop-ing and the Diseased Brain.- Index.

Fields of interestMathematical Models of Cognitive Processes and Neural Networks; Physiological, Cellular and Medical Topics; Neurosciences



Due October 2013

2013. XV, 445 p. 150 illus., 19 in color. (Lecture Notes on Mathematical Modelling in the Life Sciences) Softcover7 $129.00ISBN 978-1-4614-8865-1

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M. Burger, University of Münster, Münster, Germany; A. Mennucci, Scuola Normale Superiore, Pisa, Italy; S. Osher, University of California, Los Angeles, Los Angeles, CA, USA; M. Rumpf, University of Bonn, Bonn, Germany

Level Set and PDE Based Reconstruction Methods in ImagingCetraro, Italy 2008, Editors: Martin Burger, Stanley Osher

This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edge-sharpening image reconstruction and denoising, segmentation and shape analysis in im-ages, and image matching.

Features 7 Examines a very timely subject at the core of mathematical imaging, a field growing at enor-mous speed 7 State of the art methods in image analysis, image reconstruction and shape analysis, combining analysis, computation, and applica-tions will attract researchers from a broad range of fields (mathematics, computer sciences, engineer-ing,...) 7 There is no comparable volume on the subjects covered

Contents A Guide to the TV Zoo.- EM-TV methods for inverse problems with Poisson noise.- Variational Methods in Image Matching and Motion Extrac-tion.- Metrics of Curves in Shape Optimization and Analysis.

Fields of interestPartial Differential Equations; Computational Mathematics and Numerical Analysis; Image Processing and Computer Vision



Due October 2013

2013. X, 326 p. 83 illus., 40 in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2090) Softcover7 $59.99ISBN 978-3-319-01711-2

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F. Cakoni, D. Colton, University of Delaware, Newark, DE, USA

A Qualitative Approach to Inverse Scattering TheoryInverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scatter-ing problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques.

Features 7 Provides a basic introduction to direct and inverse scattering theory 7 Introduces the main themes of the new qualitative approach to inverse scattering theory 7 Provides a systematic ap-proach to the theory of transmission eigenvalues which at this time is an extremely active area of research in inverse scattering theory 7 Offers a basic introduction to the advanced mathematics needed to understand current research papers in inverse scattering theory

Contents 1. Functional Analysis and Sobolev Spaces.- 2. Ill-Posed Problems.- 3. Scattering by Imperfect Conductors.- 4. Inverse Scattering Problems for Imperfect Conductors.- 5. Scattering by Ortho-tropic Media.- 6. Inverse Scattering Problems for Orthotropic Media.- 7. Factorization Methods.- 8. Mixed Boundary Value Problems.- 9. Inverse Spectral Problems for Transmission Eigenvalues.- 10. A Glimpse at Maxwell’s Equations.

Fields of interestPartial Differential Equations; Electrical Engineer-ing; Theoretical, Mathematical and Computational Physics



Due November 2013

2014. VIII, 287 p. 15 illus. (Applied Mathematical Sciences, Volume 188) Hardcover7 $129.00ISBN 978-1-4614-8826-2

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68

L. C. Ciungu, University of Iowa Department of Mathematics, Iowa City, IA, USA

Non-commutative Multiple-Valued Logic AlgebrasThis monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divis-ible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be de-veloped into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.

Features 7 First monograph which treats unitary the non-commutative multiple-valued logic algebras from general to particular; that is, from pseudo-BCK algebras to pseudo-MV algebras 7 Explains the development of the field over the past few decades 7 Presents a fresh view on new trends in logic and algebra

Contents Pseudo-BCK algebras.- Pseudo-hoops.- Residuat-ed lattices.- Other non-commutative multiple-val-ued logic algebras.- Classes of non-commutative residuated structures.- States on multiple-valued logic algebras.- Measures on pseudo-BCK alge-bras.- Generalized states on residuated structures.- Pseudo-hoops with internal states.

Fields of interestMathematical Logic and Foundations; Order, Lattices, Ordered Algebraic Structures; Probability Theory and Stochastic Processes



Due September 2013

2013. XIV, 276 p. 8 illus. (Springer Monographs in Mathematics) Hardcover7 $129.00ISBN 978-3-319-01588-0

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A. Dasgupta, University of Detroit Mercy, Detroit, MI, USA

Set TheoryWith an Introduction to Real Point Sets

Contents Part 0 Preliminaries.- 1 Sets, Relations, and Functions.- Part I Dedekind: Numbers.- 2 The Dedekind-Peano Axioms.- 3 Dedekind’s Theory of the Continuum.- Postscript I: What Exactly Are the Natural Numbers?.- Part II Cantor: Cardinals, Order, and Ordinals.- 4 Cardinals: Finite, Count-able, and Uncountable.- 5 Cardinal Arithmetic and the Cantor Set.- 6 Orders and Order Types.- 7 Dense and Complete Orders.- 8 Well-Orders and Ordinals.- 9 Alephs, Cofinality, and the Axiom of Choice.- 10 Posets, Zorn’s Lemma, Ranks, and Trees.- Postscript II: Infinitary Combinatorics.- Part III Real Point Sets.- 11 Interval Trees and Generalized Cantor Sets.- 12 Real Sets and Func-tions.- 13 The Heine-Borel and Baire Category Theorems.- 14 Cantor-Bendixson Analysis of Countable Closed Sets.- 15 Brouwer’s Theorem and Sierpinski’s Theorem.- 16 Borel and Analytic Sets.- Postscript III: Measurability and Projec-tive Sets.- Part IV Paradoxes and Axioms.- 17 Paradoxes and Resolutions.- 18 Zermelo-Fraenkel System and von Neumann Ordinals.- Postscript IV: Landmarks of Modern Set Theory.- Appendi-ces.- References.- List of Symbols and Notations.- Index.

Fields of interestMathematical Logic and Foundations; Analysis; Algebra


Product categoryUndergraduate textbook

Due October 2013

2013. XXII, 400 p. 1 illus. in color. Hardcover7 $59.99ISBN 978-1-4614-8853-8

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C. Ding, Lawrence Berkeley National Laboratory Computational Research Division, Berkeley, CA, USA; H. Zha, Penn State University Department of Computer Science, State College, PA, USA

Spectral Clustering, Ordering and RankingStatistical Learning with Matrix Factorizations

Contents Part 1 Basic Theory and Algorithms: Introduc-tion.- K-means clustering and spectral relaxation.- Spectral graph clustering.- Multi-way spectral clustering.- Bipartite graph clustering.- Part 2 Advanced Spectral Clustering and Ordering: Per-turbation analysis of spectral clustering.- Green’s function.- Random walk and probabilistic spectral clustering.- Semi-definite programming solution for spectral clustering.- Spectral data order-ing.- Part 3 Related unsupervised learning topics: Spectral ranking.- Further developments on PCA and SVD.- Nonlinear embedding/representation.- Other low-dimension embedding.- Nonnegative matrix representation.- Spectral relaxations for other combinatorial optimization problems.- Level sets based clustering.- Constrained clustering.- subspace clustering.- Part 4 Applications in web, text, bioinformatics: Web and text clustering.- Clustering in genomics.- Other applications.- Ap-pendix

Fields of interestComputational Science and Engineering; Manage-ment of Computing and Information Systems; Math Applications in Computer Science



Due January 2014

2013. 250 p. 60 illus., 20 in color. Hardcover7 approx. $79.95ISBN 978-0-387-30448-9

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69

X. Feng, O. Karakashian, Y. Xing, University of Tennessee, Knoxville, TN, USA (Eds)

Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations2012 John H Barrett Memorial Lectures

Contents A quick tutorial on discontinuous Galerkin methods for elliptic problems.- Discontinuous Galerkin methods for time dependent problems: survey and recent developments.- Adaptivity and error estimation for discontinuous Galerkin methods.- $C^0$ interior penalty methods for 4th order problems.- Devising superconvergent discontinuous Galerkin methods.- A local time stepping Runge-Kutta discontinuous Galerkin method for hurricane storm surge modeling.- An overview of the discontinuous Petrov-Galerkin method.- Discontinuous Galerkin methods for radiative transport equations.- Error control for discontinuous Galerkin methods for first order hyperbolic problems.- Virtual elements and discontinuous Galerkin methods.- Time-discrete higher order ALE formulations: a DG approach.- Discontinuous finite element methods for coupled surface-subsurface flow and transport problems .

Fields of interestNumerical Analysis; Partial Differential Equations; Analysis



Due November 2013

2014. XV, 278 p. 72 illus., 58 in color. (The IMA Volumes in Mathematics and its Applications, Volume 157) Hardcover7 $109.00ISBN 978-3-319-01817-1

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K. Hart, Technische Universiteit, Delft, The Netherlands; P. Simon, Charles University, Prague, Czech Republic; J. v. Mill, Free University, Amsterdam, The Netherlands (Eds)

Recent Progress in General Topology IIIThe book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 20002. The following areas experienced significant develop-ments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Features 7 Authoritative surveys by leading ex-perts 7 Coverage of newly developing ar-eas 7 Third volume in prestigious series giving a panoramic view of the field

Fields of interestTopology; Topological Groups, Lie Groups; Func-tional Analysis



Due September 2013

2013. VII, 882 p. 34 illus., 1 in color. Hardcover7 $189.00ISBN 978-94-6239-023-2

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N. Lerner, Université Pierre et Marie Curie Paris VI, UMR 7586, Paris, France

A Course on Integration TheoryIncluding more than 150 exercises with detailed answers

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolu-tion inequalities, such as Young’s inequality and Hardy-Littlewood-Sobolev inequality are proven.

Features 7 Includes over 150 exercises with detailed solutions 7 Requires no prior knowledge of advanced mathematics although the results proven in the book are not elementary 7 Is self-contained, providing detailed arguments for each statement 7 Includes a helpful appendix to recall basic notions

Contents 1 Introduction.- 2 General theory of integration.- 3 Construction of the Lebesgue measure on R^d.- 4 Spaces of integrable functions.- 5 Integration on a product space.- 6 Diffeomorphisms of open subsets of R^d and integration.- 7 Convolution.- 8 Complex measures.- 9 Harmonic analysis.- 10 Classical inequalities.

Fields of interestReal Functions; Measure and Integration



Due December 2013

2013. Approx. 450 p. Softcover7 approx. $89.99ISBN 978-3-0348-0693-0

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70

M. Mursaleen, Aligarh Muslim University, Aligarh, India; S. A. Mohiuddine, King Abdulaziz University, Jeddah, Saudi Arabia

Convergence Methods for Double Sequences and ApplicationsThis book exclusively deals with the study of almost convergence and statistical convergence of double sequences. The notion of “almost conver-gence” is perhaps the most useful notion in order to obtain a weak limit of a bounded non-conver-gent sequence.

Features 7 Studies double sequences or sequences of matrices by using non-matrix methods 7 Dem-onstrates the concept in use with numerical double sequences 7 Demystifies the concept of double sequences with the help of suitable examples 7 Highlights the application of double sequences in several areas of pure and applied mathematics such as mathematical analysis, probability, fixed-point theory and statistics, and approximation theory

Contents Chapter 1: Almost and statistical convergence of ordinary sequences: A preview.- Chapter 2: Al-most convergence of double sequences.- Chapter 3: Almost regular matrices.- Chapter 4: Absolute almost convergence of double sequences.- Chap-ter 5: Almost convergence and core theorems.- Chapter 6: Application of almost convergence in approximation theorems for functions of two vari-ables.- Chapter 7: Statistical convergence of double sequences.- Chapter 8: Statistical approximation of positive linear operators.- Chapter 9: Double series and convergence tests.- References.

Fields of interestSequences, Series, Summability; Approximations and Expansions; Analysis



Due September 2013


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H. R. Noori, Institute for Psychopharmacology, Mannheim, Germany

Hysteresis Phenomena in BiologyThe occurrence of hysteresis phenomena has been traditionally associated with mechanical and magnetic properties of materials. However, recent studies on the dynamics of biological processes suggest switch-like behavior that could be de-scribed by mathematical models of hysteresis. This book presents the milestones and perspectives of biological hysteresis and provides a comprehen-sive and application-oriented introduction to this subject. The target audience primarily comprises researchers but the book may also be beneficial for graduate students.

Features 7 First book to address the interface between mathematics of hysteresis and biological process-es 7 Well-balanced between theoretical models and applications 7 Provides a view towards computational realizations of biological switches

Fields of interestPhysiological, Cellular and Medical Topics; Bio-medical Engineering; Biophysics and Biological Physics



Due January 2014

2014. 70 p. 10 illus. (SpringerBriefs in Applied Sciences and Technology) Softcover7 approx. $69.95ISBN 978-3-642-38217-8

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M. J. Ostwald, The University of Newcastle, Callaghan, Australia; K. Williams, Torino, Italy (Eds)

Architecture and Mathematics from Antiquity to the FutureVolume I: Antiquity to the 1500s

The aim of this collection of essays is to present a broad portrait of the ways in which two seem-ingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrates the affinity between architecture and mathematics. As the almost 100 papers presented in this two-volume publication show, every age and every culture has relied on principles of mathematics incorporated in their works of architecture to imbue their built environment with meaning and order.

Features 7 The most complete anthology addressing a broad panorama of topics regarding relationships between architecture and mathematics 7 Rep-resents the state of the art of multidisciplinary scholarship in architecture and mathemat-ics 7 Sections dealing with specific historical periods are interspersed with sections regarding theory pertinent to those periods 7 Hard-to-find essays collected in a single work 7 Comprehen-sive introductory essays to both volumes by the editors providing a guide to the discipline

Contents Part I: Introduction.- Part II: From 2000 BC to 300AD.- Part III: Theories of Measurement and Structure.- Part IV: From 1100 AD to 1400 AD.- Part V: Theories of Proportion, Symmetry, Periodicity.- Part VI: From 1500 AD to 1600 AD.- Index.- Acknowledgements.

Fields of interestMathematics in Art and Architecture; History of Mathematical Sciences


Product categoryCollection of essays

Due December 2013

2014. Approx. 700 p. Hardcover7 approx. $149.00ISBN 978-3-319-00136-4

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71

S. Padhi, S. Pati, Birla Institute of Technology, Mesra, Ranchi, India

Theory of Third-Order Differential EquationsThis book discusses the theory of third-order dif-ferential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differ-ential equations. These findings are old, and new techniques have since been developed and new results obtained.

Features 7 Highlights the results that hold good for constant coefficient equations of third order linear differential equations 7 Contains all the latest results, with the reasons for their importance in the present context 7 Furthers the studies of M. Gregus, who first studied third order linear dif-ferential equations

Contents Preface.- Chapter 1: Introduction.- Chapter 2: Behaviour of Solutions of Linear Homogeneous Differential Equations of Third Order.- Chapter 3: Oscillation of Solutions of Linear Nonhomo-geneous Differential Equations of Third Order.- Chapter 4: Oscillation and Nonoscillation of Homogeneous Third-order Nonlinear Differential Equations.- Chapter 5: Oscillation and Nonoscil-lation of Nonlinear Nonhomogeneous Differential Equations of Third Order.- Chapter 6: Oscillatory and Asymptotic Behavior of Solutions of Third Order Delay Differential Equations.- Chapter 7: Stability of Third Order Differential Equations.- References.

Fields of interestOrdinary Differential Equations; Analysis; Differ-ence and Functional Equations



Due October 2013


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I. M. Pelayo, School of Agricultural Engineering of Barcelona, Barcelona, Spain

Geodesic Convexity in Graphs Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most st udied param-eters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester gradu-ate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.

Features 7 Geodesic Convexity in Graphs is a self-contained monograph which is devoted to geo-desic convexity on finite, simply connected graphs 7 Includes specific definitions, discussion and examples, results, proofs, exercises and open problems on geodesic convexity 7 Examines results obtained during the past 15 years, relating cardinality of minimum geodetic and hull sets

Fields of interestGraph Theory; Differential Geometry; Partial Dif-ferential Equations



Due September 2013

2013. VIII, 112 p. 41 illus. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-1-4614-8698-5

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L. S. Pitsoulis, Aristotle University of Thessaloniki School of Engineering, Thessaloniki, Greece

Topics in Matroid TheoryTopics in Matroid Theory provides a brief intro-duction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the ana-lytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axi-omatic definition of matroids along with other necessary concepts such as duality, minors, con-nectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

Features 7 Provides a sollid introduction to matroid theory 7 Present results in matroid theory as they appear in the context of combinatorial optimization 7 Contains a strong emphasis on algorithmic consequences of matroid theory

Contents 1.Introduction.- 2.Graph Theory, Vector Spaces and Transversals.- 3.Definition of Matroids.- 4.Representability, Duality, Minors, and Connectivity.- 5. Decomposition of Graphic Matroids.- 6.Signed-Graphic Matroids.- List of Symbols.- Index.

Fields of interestContinuous Optimization; Algorithms; Combi-natorics



Due September 2013

2013. XII, 133 p. 46 illus. (SpringerBriefs in Optimization) Softcover7 $54.99ISBN 978-1-4614-8956-6

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72

M. A. Sainz, J. Armengol, R. Calm, Escola Politecnica Superior, University of Girona, Girona, Spain; P. Herrero, Imperial College London, London, UK; L. Jorba, Facultad de Economia y Empresa, Universitat de Barcelona, Barcelona, Spain; J. Vehi, Escola Politecnica Superior, University of Girona, Girona, Spain

Modal Interval AnalysisNew Tools for Numerical Information

This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals through the inclusion of the sets of predicates they accept. This modal approach in-troduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equiva-lences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results.

Features 7 Develops of a new interval theory 7 Presents several sample applications 7 Includes many examples to illustrate the main results

Contents Intervals.- Modal Intervals.- Modal interval exten-sions.- Interpretability and optimality.- Interval arithmetic.- Equations and systems.- Twins and f -star algorithm.- Marks.- Intervals of marks.- Some related problems.

Fields of interestAnalysis; Control; Numeric Computing



Due November 2013

2014. Approx. 300 p. 34 illus., 4 in color. (Lecture Notes in Mathematics, Volume 2091) Softcover7 $59.99ISBN 978-3-319-01720-4

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J.-P. Serre, College de France Paris Chaire d’Algebre et Geometrie, Paris CX 05, France

Oeuvres - Collected Papers III1972 - 1984

The impact and influence of Jean-Pierre Serre’s work have been notable ever since his doctoral thesis on homotopy groups. The abundance of significant results and deep insight contained in his research and survey papers ranging through topology, several complex variables, and algebraic geometry to number theory, group theory, com-mutative algebra and modular forms, continues to provide inspiring reading for mathematicians working in these areas, in their research and their teaching. Characteristic of Serre’s publications are the many open questions he formulated suggesting further research directions. Four volumes specify how he has provided comments on and correc-tions to most articles, and described the present status of the open questions with reference to later results. Jean-Pierre Serre is one of a few math-ematicians to have won the Fields medal, the Abel prize, and the Wolf prize.

Contents Extensions de corps ordonnes.- (avec A Borel) Impossibilite de fibrer un espace euclidien par des fibres compactes.- Cohomologie des extensions de groupes.- Homologie singuliere des espaces fibres. I. La suite spectrale.- Homologie singuliere des espaces fibres. II. Les espaces de lacets.

Fields of interestNumber Theory; Algebraic Geometry; Category Theory, Homological Algebra


Product categoryCollected works

Available

Edition originale publiée en 4 tomes

Only available in print

2003. Reprint 2013 of the 2003 edition. VI, 731 p. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-3-642-39837-7

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J.-P. Serre, College de France Paris Chaire d’Algebre et Geometrie, Paris CX 05, France

Oeuvres - Collected Papers IV1985 - 1998

From the reviews of Vol. IV: “This is the fourth volume of J-P. Serre’s Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain “the essence’’ of his work from that period and are devoted to number theory, algebraic ge-ometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the an-nounced results. The letters reproduced, however (in particular to K. Ribet and M.-F. Vignéras), provide indications of some of those proofs. Also included is an interview with J-P. Serre from 1986, revealing his views on mathematics (with the stress upon its integrity) and his own mathemati-cal activity. The volume ends with Notes which complete the text by reporting recent progress and occasionally correct it. The volume is an indis-pensable addition to previous ones and the whole set presents a fine piece of modern mathematics.” Zentralblatt MATH In this softcover edition of volume IV, two recently published articles have been added, one on the life and works of André Weil, the other one on Finite Subgroups of Lie Groups.

Contents Preface.- Papers published between 1985 and 1998.- Notes.-Modifications volumes I-III.- Errata volumes I-III.- Acknowledgements.

Fields of interestNumber Theory; Group Theory and Generaliza-tions; Algebraic Geometry


Product categoryCollected works

Available

Only available in print

2000. Reprint 2013 of the 2000 edition. VIII, 694 p. (Springer Collected Works in Mathematics) Softcover7 approx. $89.99ISBN 978-3-642-39839-1

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73

T. C. Sideris, University of California, Santa Barbara, CA, USA

Ordinary Differential Equations and Dynamical SystemsThis book is a mathematically rigorous introduc-tion to the beautiful subject of ordinary differen-tial equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for com-pleteness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invari-ant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the im-plicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.

Features 7 Proofs are presented with complete mathemati-cal details 7 Extensive use of the implicit func-tion theorem as a unifying approach to perturba-tive analysis 7 Exercises are included at the end of each chapter permit use as a textbook

Field of interestOrdinary Differential Equations



Due October 2013

2013. IX, 218 p. 11 illus. (Atlantis Studies in Differential Equations, Volume 2) Hardcover7 $109.00ISBN 978-94-6239-020-1

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J. Stillwell, University of San Francisco, San Francisco, CA, USA

The Real NumbersAn Introduction to Set Theory and Analysis

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory – uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focus-ing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis – the study of infinite processes on the real numbers.

Features 7 Fills a gap in the standard curriculum by linking analysis to set theory 7 Contains background, history, examples, and explanatory remarks 7 Includes (almost) two courses for the price of one by providing a unified treatment of analysis and set theory

Contents The Fundamental Questions.- From Discrete to Continuous.- Infinite Sets.- Functions and Limits.- Open Sets and Continuity.- Ordinals.- The Axiom of Choice.- Borel Sets.- Measure Theory.- Reflec-tions.- Bibliography.- Index.

Fields of interestReal Functions; Mathematical Logic and Founda-tions; History of Mathematical Sciences


Product categoryUndergraduate textbook

Due October 2013

2013. X, 280 p. 62 illus. (Undergraduate Texts in Mathematics) Hardcover7 $49.99ISBN 978-3-319-01576-7

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D. W. Stroock, Massachusetts Institute of Technology, Cambridge, MA, USA

An Introduction to Markov ProcessesThis book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineer-ing, economics, physics, and biology. Topics cov-ered are: Doeblin’s theory, general ergodic proper-ties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm. The corrected and enlarged 2nd edition contains a new chapter in which the author develops com-putational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson’s algo-rithm and Kirchoff ’s formula for spanning trees in a connected graph.

Features 7 Corrected and enlarged 2nd edition 7 Writ-ten by an expert 7 Includes new material

Contents Preface.- Random Walks, a Good Place to Begin.- Doeblin’s Theory for Markov Chains.- Stationary Probabilities.- More about the Ergodic Theory of Markov Chains.- Markov Processes in Continuous Time.- Reversible Markov Processes.- A minimal Introduction to Measure Theory.- Notation.- Ref-erences.- Index.

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



Due October 2013

2nd ed. 2013. XX, 190 p. (Graduate Texts in Mathematics, Volume 230) Hardcover7 $69.99ISBN 978-3-642-40522-8

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74

A. Vasil’ev, University of Bergen, Bergen, Norway (Ed)

Harmonic and Complex Analysis and its ApplicationsFeatures 7 Representative collection of modern develop-ments in the subject written by leading special-ists and members of the Steering Committee of the HCAA network which united 27 universities and 51 senior researchers across the European Research Area 7 Acessible for both senior researchers and Ph.D. students 7 Highlights the results and perspectives of the future development created within the network and in collaboration with other analogous organizations

Contents L.D. Abreu, H.G. Feichtinger: Function spaces of polyanalytic functions.- F. Bracci, M.D. Contre-ras, S. Díaz-Madrigal,A. Vasil’ev: Classical and stochastic Löwner-Kufarev equations.- M. Elin, F. Jacobzon, M. Levenshtein, D. Shoikhet: The Schwarz Lemma. Rigidity and Dynamics.- H.G. Feichtinger, M. Pap: Coorbit theory and Berg-man spaces.- S.J. Gardiner, T. Sjödin: Quadrature domains and their two-phase counterparts.- B. Gustafsson: Exponential transforms, resultants and moments.- M. Schlichenmaier: From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond.

Fields of interestCommutative Rings and Algebras; Non-associa-tive Rings and Algebras; Functions of a Complex Variable


Product categoryCollection of essays

Due November 2013

2014. IV, 324 p. 47 illus., 11 in color. (Trends in Mathematics) Hardcover7 $169.00ISBN 978-3-319-01805-8

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J. Wei, The Chinese University of Hong Kong, Hong Kong, Hong Kong SAR; M. Winter, Brunel University, Uxbridge, UK

Mathematical Aspects of Pattern Formation in Biological SystemsFeatures 7 Self-contained and includes rigorous proofs, of-ten supported by numerical simulations 7 Con-tains an introduction to mathematical methods in nonlinear functional analysis and partial differen-tial equations; Liapunov-Schmidt reduction and nonlocal eigenvalue problems 7 Includes links to biological applications; hydra development and regeneration, patterns on animal skins, embryo development, insect leg segmentation, left-right asymmetry of organisms, self-organisation of mat-ter and consumer chains

Contents Introduction.- Existence of spikes for the Gierer-Meinhardt system in one dimension.- The Nonlocal Eigenvalue Problem (NLEP).- Stability of spikes for the Gierer-Meinhardt system in one dimension.- Existence of spikes for the shadow Gierer-Meinhardt system.- Existence and stability of spikes for the Gierer-Meinhardt system in two dimensions.- The Gierer-Meinhardt system with inhomogeneous coefficients.- Other aspects of the Gierer-Meinhardt system.- The Gierer-Meinhardt system with saturation.- Spikes for other two-com-ponent reaction-diffusion systems.- Reaction-dif-fusion systems with many components.- Biological applications.- Appendix.

Fields of interestPartial Differential Equations; Mathematical and Computational Biology; Genetics and Population Dynamics



Due October 2013

2013. XII, 260 p. 20 illus. (Applied Mathematical Sciences, Volume 189) Hardcover7 $109.00ISBN 978-1-4471-5525-6

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W. Zeng, Florida International University, Miami, FL, USA; X. D. Gu, Stony Brook University, Stony Brook, NY, USA

Ricci Flow for Shape Analysis and Surface RegistrationTheories, Algorithms and Applications

Ricci Flow for Shape Analysis and Surface Reg-istration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate cal-culus, readers can deduce all the major theorems in surface Ricci flow by themselves. The authors adapt the Ricci flow theory to practical compu-tational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricci flow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network.

Features 7 Presents Ricci flow analysis in a simplified discrete setting 7 Illustrates applications from engineering and medicine that represent state-of-the-art and new exciting challenges 7 Written by experts in the field

Contents 1. Introduction.- 2. Computational.- 3. Compu-tational Geometry.- 4. Differential Geometry of Surface.- 5. Riemann Surface.- 6. Ricci Flow.- 7. Topological Algorithms.- 8. Harmonic Maps.- 9. Discrete Ricci Flow.- 10. Shape Analysis.- 11. Surface Diffeomorphism.- 12. Medical Imag-ing Applications.- 13. Computer Vision Applica-tions.- 14. Computer Graphics Applications.- 15. Network Applications.

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



Due October 2013

2013. X, 140 p. 69 illus., 49 in color. (SpringerBriefs in Mathematics) Softcover7 $54.99ISBN 978-1-4614-8780-7

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lévy processes and their applications in reliability and ... · tography.- appendix a: some...

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