ordinary differential equations model based parameter ... · ordinary differential equations unlike...

Mathematics springer.com/NEWSonline

26

W. A. Adkins, M. G. Davidson, Louisiana State University, Baton Rouge, LA, USA

Ordinary Differential EquationsUnlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and de-velop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also inclu-des proofs of several important theorems that are not usually given in introductory texts.

Features 7 Contains numerous helpful examples and exercises that provide motivation for the rea-der 7 Presents the Laplace transform early in the text and uses it to motivate and develop solution methods for differential equations 7 Takes a streamlined approach to linear systems of differen-tial equations 7 Protected instructor solution manual is available on springer.com

Contents Preface.- 1 First Order Differential Equations.- 2 The Laplace Transform.- 3 Second Order Constant Coefficient Linear Differential Equations.- 4 Line-ar Constant Coefficient Differential Equations.- 5 Second Order Linear Differential Equations.- 6 Discontinuous Functions and the Laplace Transform.- 7 Power Series Methods.- 8 Matrices .- 9 Linear Systems of Differential Equations.- A Appendix.- B Selected Answers.- C Tables.- Sym-bol Index.- Index.

Fields of interestOrdinary Differential Equations

Target groupsUpper undergraduate

Discount groupProfessional Non-Medical

Due June 2012

2012. XVI, 706 p. 121 illus. (Undergraduate Texts in Mathematics) Hardcover7 $79.95ISBN 978-1-4614-3617-1

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H. G. Bock, T. Carraro, W. Jäger, S. Körkel, R. Rannacher, J. P. Schlöder, University of Heidelberg, Germany (Eds)

Model Based Parameter EstimationTheory and Applications

Contents Parameter Estimation and Optimum Experimen-tal Design for Differential Equation Models: H.G. Bock, St. Körkel, J.P. Schlöder.- Adaptive Finite Element Methods for Parameter Identification Problems: B. Vexler.- Gauss-Newton Methods for Robust Parameter Estimation: T. Binder, E. Kostina.- An Optimal Scanning Sensor Activation Policy for Parameter Estimation of Distributed Systems: D. Ucínski.- Interaction between Experi-ment, Modeling and Simulation of Spatial Aspects in the JAK2/STAT5 Signaling Pathway: E. Fried-mann, A. C. Pfeifer, R. Neumann, U. Klingmüller , R. Rannacher.- The Importance and Challenges of Bayesian Parameter Learning in Systems Biology: J. Mazur, L. Kaderali.- Experiment Setups and Parameter Estimation in Fluorescence Recovery After Photobleaching Experiments: A Review of Current Practice: J. Beaudouin, M. S. Mommer, H. G. Bock, R. Eils.- Drug Resistance in Infec-tious Diseases: Modeling, Parameter Estimation and Numerical Simulation: Le Thi Thanh An, W. Jäger.- Mathematical Models of Hematopoietic Reconstitution after Stem Cell Transplantation: A. Marciniak-Czochra, Th. Stiehl.- Combustion Chemistry and Parameter Estimation: M. Fischer, U. Riedel.- Numerical Simulation of Catalytic Reactors by Molecular-Based Models: O. Deutsch-mann, St. Tischer.- Model-Based Design of Expe-riments for Estimating Heat-Transport Parameters in Tubular Reactors: A.Badinski, D. Corbett. [...]

Fields of interestsOrdinary Differential Equations; Partial Differen-tial Equations; Numerical Analysis

Target groupsResearch


Available

2012. 331 p. 105 illus., 25 in color. (Contributions in Mathematical and Computational Sciences, Volume 4) Hardcover7 approx. $129.00ISBN 978-3-642-30366-1

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A. Cano, UNAM, Cuernavaca, MO, Mexico; J. P. Navarrete, Universidad Autónoma de Yucatán, YU, Mexico; J. Seade, UNAM, Cuernavaca, MO, Mexico

Complex Kleinian GroupsThis monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discre-te groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?

Features 7 Lays down the foundations of a new field of mathematics including areas as important as real and complex hyperbolic geometry, discrete group actions in complex geometry and the uniformiza-tion problem 7 First book of its kind in the lite-rature 7 Accessible to a wide audience 7 Serves also as an introduction to the study of real and complex hyperbolic geometry

Contents Preface.- Introduction.- Acknowledgments.- 1 A glance of the classical theory.- 2 Complex hyper-bolic geometry.- 3 Complex Kleinian groups.- 4 Geometry and dynamics of automorphisms of P2C.- 5 Kleinian groups with a control group.- 6 The limit set in dimension two.- 7 On the dyna-mics of discrete subgroups of PU(n,1).- 8 Projec-tive orbifolds and dynamics in dimension two.- 9 Complex Schottky groups.- 10 Kleinian groups and twistor theory.- Bibliography.- Index.

Fields of interestsDynamical Systems and Ergodic Theory; Topo-logical Groups, Lie Groups; Several Complex Variables and Analytic Spaces



Available

2013. 300 p. (Progress in Mathematics, Volume 303) Hardcover7 approx. $119.00ISBN 978-3-0348-0480-6

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www.springer.com/978-1-4614-3617-1



News 6/2012 Mathematics

27

V. Capasso, D. Bakstein, University of Milan, Italy

An Introduction to Continuous-Time Stochastic ProcessesTheory, Models, and Applications to Finance, Biology, and Medicine

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-con-tained introduction to the theory of continuous-time stochastic processes.

Features 7 Expanded and revised to include more tho-rough introduction and enhanced coverage of financial modling applications, among other things 7 Fully updated references reflect la-test research in the field 7 Concise, yet rigorous presentation covers a broad range of applica-tions 7 Valuable for students, researchers, and practitioners 7 Minimal background knowledge required

Contents Part I. The Theory of Stochastic Processes.- Fun-damentals of Probability.- Stochastic Proces-ses.- The Itô Integral.- Stochastic Differential Equations.- Part II. The Applications of Stochastic Processes.- Applications to Finance and Insu-rance.- Applications to Biology and Medicine.- Part III. Appendices.- Measure and Integration.- Convergence of Probability Measures on Metric Spaces.- Elliptic and Parabolic Operators.- D Semigroups and Linear Operators.- E Stability of Ordinary Differential Equations.- References.

Fields of interestsProbability Theory and Stochastic Processes; Ma-thematical Modeling and Industrial Mathematics; Quantitative Finance



Due August 2012

2nd ed. 2012. XVIII, 420 p. 14 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 $129.00ISBN 978-0-8176-8345-0

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S.‑s. Chern, Mathematical Sciences Research Institute, Berkeley, CA, USA

Selected PapersVolume 3

In recognition of professor Shiing-shen Chern‘s long and distinguished service to mathematics and to the University of California, the geometers at Berkely held an International Symposium in Global Analysis and Global Geometry in his ho-nor at Berkely in June 1979. The outgrowth of this Symposium was published in a series of three se-parate volumes, comprising approximately a third of Professor Chern‘s total output up to 1979. Later, a fourth volume was published, comprising papers written during the Eighties. This third volume comprises papers written from 1965 until 1979. In making the selections, Professor Chern has given preference to shorter and less accessible papers.

Fields of interestsDifferential Geometry; Algebraic Topology; Sever-al Complex Variables and Analytic Spaces



Available

1st ed. 1989. 2nd printing 1989. XIV, 504 p. 2 illus. Hardcover7 $109.00ISBN 978-0-387-96817-9

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S.‑s. Chern

Selected PapersVolume 1

In recognition of professor Shiing-shen Chern‘s long and distinguished service to mathematics and to the University of California, the geome-ters at Berkely held an International Symposium in Global Analysis and Global Geometry in his honor at Berkely in June 1979. The outgrowth of this Symposium was published in a series of three separate volumes, comprising approximately a third of Professor Chern‘s total output up to 1979. Later, a fourth volume was published, focusing on papers written during the Eighties. This first volume comprises selected papers written from 1932 until 1975. In making the selections, Profes-sor Chern has given preference to shorter and less accessible papers.

Fields of interestsAlgebraic Geometry; Geometry; Differential Geometry



Available

1st ed. 1978. 2nd printing 1978. XXI, 476 p. 2 illus. Cloth bound7 $89.95ISBN 978-0-387-90339-2

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G. Citti, Università di Bologna, Italy; L. Grafakos, University of Missouri, Columbia, MO, USA; C. Pérez, Universidad de Sevilla, Spain; A. Sarti, Università di Bologna, Italy; X. Zhong, University of Jyväskylä, Finland

Harmonic and Geometric AnalysisEditorial coordination: J. Mateu, Universitat Autònoma de Barcelona, Bellaterra, Spain

This book contains an expanded version of lectu-res delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear har-monic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.

Features 7 Contains two surveys of new results on linear and multilinear analysis 7 Offers a very nice presentation of the De Giorgi–Moser–Nash re-sult 7 Contains elegant applications of harmonic analysis to human vision

Contents 1 Models of the Visual Cortex in Lie Groups.- 2 Multilinear Calderón–Zygmund Singular Inte-grals.- 3 Singular Integrals and Weights.- 4 De Giorgi–Nash–Moser Theory.

Fields of interestsAnalysis; Partial Differential Equations

Target groupsGraduate


Available

2013. 190 p. (Advanced Courses in Mathematics - CRM Barcelona) Softcover7 approx. $39.95ISBN 978-3-0348-0407-3

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S. Cobzas, Babes-Bolyai University, Cluj-Napoca, Romania

Functional Analysis in Asymmetric Normed SpacesAn asymmetric norm is a positive definite subline-ar functional p on a real vector space X. The topo-logy generated by the asymmetric norm p is trans-lation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X.

Feature 7 First treatment in book form of basic results on asymmetric normed spaces The presentation fol-lows the ideas from the theory of normed spaces, emphasizing similarities as well as differences with respect to the classical theory Detailed treatment of quasi-metric, quasi-uniform and bitopological spaces, with emphasis on completeness, compact-ness and Baire category

Contents Introduction.- Chapter 1. Quasi-Metric and quasi-Uniform Spaces. 1.1. Topological Properties of quasi-Metric and quasi-Uniform Spaces.- 1.2. Completeness and Compactness in Quasi-metric and Quasi-uniform Spaces.- Chapter 2. Asymme-tric Functional Analysis.- 2.1. Continuous Linear Operators Between Asymmetric Normed Spaces.- 2.2. Hahn-Banach Type Theorems and the Separation of Convex Sets.- 2.3. The Fundamental Principles.- 2.4. Weak Topologies.- 2.5. Applica-tions to Best Approximation.- 2.6. Spaces of semi-Lipschitz Functions.- Bibliography.- Index.

Fields of interestsFunctional Analysis; Approximations and Expan-sions; Operator Theory



Available

2012. X, 170 p. (Frontiers in Mathematics) Softcover7 approx. $69.95ISBN 978-3-0348-0477-6

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T. Dayar

Analyzing Markov Chains using Kronecker ProductsTheory and Applications

Kronecker products are used to define the un-derlying Markov chain (MC) invarious modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform.

Feature 7 First to provide a solely Kronecker product based treatment of Markov chain analysis The subject matter is interdisciplinary and at the intersection of applied mathematics, specifically numerical linear algebra and computational probability, and computer science The exposition is concise and rigorous, yet it tries to be complete and touches almost all relevant aspects without being too technical.

Contents Introduction.- Background.- Kronecker represen-tation.- Preprocessing.- Block iterative methods for Kronecker products.- Preconditioned projec-tion methods.- Multilevel methods.- Decompositi-onal methods.- Matrix analytic methods.

Fields of interestsProbability Theory and Stochastic Processes; Numerical Analysis; Probability and Statistics in Computer Science



Due August 2012

2012. IX, 91 p. 3 illus., 1 in color. (SpringerBriefs in Mathematics) Softcover7 $49.95ISBN 978-1-4614-4189-2

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S. Deng, Nankai University, Tianjin, China

Homogeneous Finsler SpacesHomogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae). This monograph introduces the most recent developments in the study of Lie groups and homogeneous Finsler spaces, leading the reader to directions for further development.

Features 7 Presents the most recent results on the applica-tions of Lie theory to Finsler geometry 7 Provi-des an accessible introduction to Finsler geometry that allows the reader to quickly understand topics and to access related problems 7 Contains related work concerning Randers spaces, making it suitable for readers with a background in biology, as well as various topics for readers with backgrounds in pure algebra

Contents Preface.- Acknowledgements.- 1. Introduction to Finsler Geometry.- 2. Lie Groups and Homo-genous Spaces.- 3. The Group of Isometries.- 4. Homogeneous Finsler Spaces.- 5. Symmetric Finsler Spaces.- 6. Weakly Symmetric Finsler Spaces.- 7. Homogeneous Randers Spaces.- Refe-rences.- Index.

Fields of interestDifferential Geometry



Due August 2012

2012. XIV, 230 p. (Springer Monographs in Mathematics) Hardcover7 approx. $109.00ISBN 978-1-4614-4243-1

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M. Dewar, B. Stevens, Carleton University, Ottawa, ON, Canada

Ordering Block DesignsGray Codes, Universal Cycles and Configuration Orderings

The study of combinatorial block designs is a vibrant area of combinatorial mathematics with connections to finite geometries, graph theory, co-ding theory and statistics. The practice of ordering combinatorial objects can trace its roots to bell ringing which originated in 17th century England, but only emerged as a significant modern research area with the work of F. Gray and N. de Bruijn. These two fascinating areas of mathematics are brought together for the first time in this book. It presents new terminology and concepts which unify existing and recent results from a wide variety of sources.

Features 7 This book provides the first comprehensive introduction to the problem of ordering blocks of designs 7 Includes a large introductory section on relevant design theory and literature on Gray codes and Universal cycles 7 Expands the definition of configuration orderings and uses new language to unify existing material

Contents Abstract.- Acknowledgements.- Introduc-tion.- Background.- Ordering the Blocks of Designs.- Gray Codes and Universal Cycles for Designs.- New Results in Configuration Orde-ring.- Conclusions and Future Work.- Bibliogra-phy.- Index.

Fields of interestsCombinatorics; Mathematics, general; Discrete Mathematics in Computer Science



Due August 2012

2012. XIV, 222 p. 60 illus., 30 in color. (CMS Books in Mathematics) Hardcover7 approx. $69.95ISBN 978-1-4614-4324-7

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P. Drabek, University West Bohemia, Plzen, Czech Republic; J. Milota, Charles University Prague, Czech Republic

Methods of Nonlinear AnalysisApplications to Differential Equations

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method con-sidered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value prob-lems for both ordinary and partial differential equations.

Features 7 Designed as a textbook for advanced under-graduate and graduate students and useful as a handbook for scientists and engineers 7 Two level structure: basic level for the beginners and advanced one for more experienced rea-der 7 Accessible to beginners by avoiding too many technical details and keeping key asser-tions simple 7 Transparent and illustrative examples 7 Exercises are an organic part of the exposition and accompany the reader throughout the book

Contents Preface.- 1 Preliminaries.- 2 Properties of Linear and Nonlinear Operators.- 3 Abstract Integral and Differential Calculus.- 4 Local Properties of Differentiable Mappings.- 5 Topological and Monotonicity Methods.- 6 Variational Methods.- 7 Boundary Value Problems for Partial Differential Equations.- Summary of Methods.- Typical Appli-cations.- Comparison of Bifurcation Results.- List of Symbols.- Index.- Bibliography.

Fields of interestsAnalysis; Functional Analysis; Partial Differential Equations



Available

2nd ed. 2012. X, 710 p. (Birkhäuser Advanced Texts Basler Lehrbücher) Hardcover7 approx. $109.00ISBN 978-3-0348-0386-1

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S. Kislyakov, Steklov Mathematical Institute, St. Petersburg, Russia; N. Kruglyak, Linköping University, Sweden

Extremal Problems in Interpolation Theory, Whitney-Besicovitch Coverings, and Singular IntegralsFeature 7 Quick and concise introduction to several important classical topics of real analysis Expo-sition of powerful results of recent research in a self-contained manner, making them accessible to beginners Presents results not yet available in existing literature Contains descriptions of new techniques which may be useful in other research problems

Contents Preface.- Introduction.- Definitions, notation, and some standard facts.- Part 1. Background.- Chap-ter 1. Classical Calderón–Zygmund decomposi-tion and real interpolation.- Chapter 2. Singular integrals.- Chapter 3. Classical covering theo-rems.- Chapter 4. Spaces of smooth functions and operators on them.- Chapter 5. Some topics in interpolation.- Chapter 6. Regularization for Banach spaces.- Chapter 7. Stability for analytic Hardy spaces.- Part 2. Advanced theory.- Chapter 8. Controlled coverings.- Chapter 9. Construction of near-minimizers.- Chapter 10. Stability of near-minimizers.- Chapter 11. The omitted case of a limit exponent.- Chapter A. Appendix. Near-mini-mizers for Brudnyi and Triebel–Lizorkin spaces.- Notes and remarks.- Bibliography.- Index.

Fields of interestsReal Functions; Approximations and Expansions; Functional Analysis



Available

2013. VIII, 272 p. (Monografie Matematyczne, Volume 74) Hardcover7 approx. $109.00ISBN 978-3-0348-0468-4

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New SeriesDifferential-Algebraic Equations ForumSeries editors: A. Ilchmann, T. Reis

The series „Differential-Algebraic Equations Forum“ is concerned with analytical, algebraic, control theoretic and numerical aspects as well as applications of differential algebraic equations (DAEs). It is aimed to publish survey articles, research monographs, textbooks, and mathe-matically rigorous research articles. Papers are assigned to an Associate Editor, who recommends publication on the basis of a detailed and careful evaluation by at least two referees. Evaluation is based on substance and quality of exposition.

R. Lamour, R. März, Humboldt University of Berlin, Germany; C. Tischendorf, University of Cologne, Germany

Differential-Algebraic Equations: A Projector Based AnalysisFeatures 7 New comprehensive analysis of general nonlinear DAEs 7 First book describing the projector approach for nonlinear, higher-index DAEs 7 Rigorous description, multitude of examples highlighting analytical and numerical challenges in this field 7 Suitable for students, researchers and users from different application fields (e.g. circuit and electromagnetic simulation, mechanical engineering, system biology)

Contents Notations.- Introduction.- Part I. Projector based approach.- 1 Linear constant coefficient DAEs.-.2 Linear DAEs with variable coefficients.- 3 Non-linear DAEs.- Part II. Index-1 DAEs: Analysis and numerical treatment.- 4 Analysis.- 5 Numerical integration.- 6 Stability issues.- Part III. Compu-tational aspects.- 7 Computational linear algebra aspects.- 8 Aspects of the numerical treatment of higher index DAEs.- Part IV. Advanced topics.- 9 Quasi-regular DAEs.- 10 Nonregular DAEs.- 11 Minimization with constraints described by DAEs.- 12 Abstract differential algebraic equa-tions.- A. Linear Algebra – Basics.-.B. Technical Computations.- C Analysis.- References.- Index.

Fields of interestsOrdinary Differential Equations; Applications of Mathematics; Computational Mathematics and Numerical Analysis



Available

2013. XVIII, 660 p. 10 illus., 5 in color. (Differential-Algebraic Equations Forum, Volume 1) Softcover7 approx. $129.00ISBN 978-3-642-27554-8

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U. Ledzewicz, Southern Illinois University,IL, USA; H. Schättler, Washington University, MO, USA; A. Friedman, The Ohio State University, OH, USA; E. Kashdan, Tel Aviv University,Israel (Eds)

Mathematical Methods and Models in BiomedicineContents Spatial aspects of HIV infection.- Basic Principles in Modeling Adaptive Regulation and Immu-nodominance.- Evolutionary Principles In Viral Epitopes.- A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: the Role of Randomness.- Modeling Tumor Blood Vessel Dynamics.- Influence of Blood Rheology and Outflow Boundary Conditions in Nume-rical Simulations of Cerebral Aneurysms.- The Steady State of Multicellular Tumour Spheroids: a Modelling Challenge.- Deciphering Fate Decision in Normal and Cancer Stem Cells – Mathematical Models and Their Experimental Verification..- Data Assimilation in Brain Tumor Models.- Op-timisation of Cancer Drug Treatments Using Cell Population Dynamics.- Tumor Development under Combination Treatments with Antiangioge-nic Therapies.- Saturable Fractal Pharmacokinetics and Its Applications.- A MathematicalModel of Gene Therapy for the Treatment of Cancer.- Epi-demiological Models with Seasonality.- Periodic Incidence in a Discrete-Time SIS Epidemic Model.

Fields of interestsMathematical and Computational Biology; Ma-thematical Modeling and Industrial Mathematics; Life Sciences, general



Due September 2012

2012. IX, 419 p. 94 illus., 64 in color. (Lecture Notes on Mathematical Modelling in the Life Sciences) Softcover7 $89.95ISBN 978-1-4614-4177-9

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X. Li, Xueliang Li, Nankai University, Tianjin, China; Y. Shi, Yongtang Shi, Nankai University, Tianjin, China; I. Gutman, Ivan Gutman, University of Kragujevac, Serbia

Graph EnergyThis book is about graph energy. The authors have included many of the important results on graph energy, such as the complete solution to the con-jecture on maximal energy of unicyclic graphs, the Wagner-Heuberger’s result on the energy of trees, the energy of random graphs or the approach to energy using singular values. It contains an exten-sive coverage of recent results and a gradual de-velopment of topics and the inclusion of complete proofs from most of the important recent results in the area. The latter fact makes it a valuable reference for researchers looking to get into the field of graph energy, further stimulating it with occasional inclusion of open problems. The book provides a comprehensive survey of all results and common proof methods obtained in this field with an extensive reference section. The book is aimed mainly towards mathematicians, both researchers and doctoral students, with interest in the field of mathematical chemistry.

Features 7 One of the first books on this topic 7 Graph energy is a topic within Spectral Graph The-ory and (more generally) Discrete Mathema-tics 7 Graph energy is also of interest to chemists

Contents Preface.- Introduction.- The Chemical Connec-tion.- The Coulson Integral Formula.- Common Proof Methods.- Bounds for the Energy of Graphs.- The Energy of Random Graphs.- Graphs Extremal with with Regard to Energy.- Hyperner-getic and Equienergetic Graphs.- Miscellaneous.- Other Graph Energies.- Bibliography.- Index.

Fields of interestsGraph Theory; Math. Applications in Chemistry; Algebra



Due August 2012

2012. X, 254 p. 60 illus. Hardcover7 approx. $109.00ISBN 978-1-4614-4219-6

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J.‑L. Loday, Université de Strasbourg et CNRS, France; B. Vallette, Université de Nice-Sophia Antipolis, Nice, France

Algebraic OperadsIn many areas of mathematics one can see some “higher operations” popping up. In fact these higher structures have become so important that several projects refer to such expressions. These higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is precisely the operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as: algebraic geometry, mathematical physics, diffe-rential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads.

Features 7 Being the first book on algebraic ope-rads, will be used as a reference work in this field 7 Each chapter contains a list of exercises and a résumé 7 A new and conceptual presenta-tion of the Koszul duality theory is presented

Contents Preface.- 1.Algebras, coalgebras, homology.- 2.Twisting morphisms.- 3.Koszul duality for asso-ciative algebras.- 4.Methods to prove Koszulity of an algebra.- 5.Algebraic operad.- 6 Operadic ho-mological algebra.- 7.Koszul duality of operads.- 8.Methods to prove Koszulity of an operad.- 9.The operads As and A\infty.- 10.Homotopy operadic algebras.- 11.Bar and cobar construction of an algebra over an operad.- 12.(Co)homology of algebras over an operad.- 13.Examples of algebraic operads.- Apendices: A.The symmetric group.- B.Categories.- C.Trees.- References.- Index.- List of Notation.

Fields of interestsCategory Theory, Homological Algebra; Non-as-sociative Rings and Algebras; Algebraic Topology



Available

2012. XIV, 648 p. (Grundlehren der mathematischen Wissenschaften, Volume 346) Hardcover7 approx. $149.00ISBN 978-3-642-30361-6

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M. d. Longueville, Hochschule für Technik und Wirtschaft Berlin, Germany

A Course in Topological CombinatoricsA Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant and the connection between combinatorics and topology often arises as an unexpected surprise.

Features 7 First textbook in the field of topological com-binatorics 7 Covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discre-te geometry 7 Contains many figures that aid in the understanding of concepts and proofs 7 In-cludes an extensive appendix that helps make the book completely self-contained

Contents Preface.- List of Symbols and Typical Notation.- 1 Fair-Division Problems.- 2 Graph-Coloring Problems.- 3 Evasiveness of Graph Properties.- 4 Embedding and Mapping Problems.- A Basic Concepts from Graph Theory.- B Crash Course in Topology.- C Partially Ordered Sets, Order Com-plexes, and Their Topology.- D Groups and Group Actions.- E Some Results and Applications from Smith Theory.- References.- Index.

Fields of interestsCombinatorics; Convex and Discrete Geometry; Graph Theory



Due June 2012

2012. XX, 240 p. 146 illus., 2 in color. (Universitext) Hardcover7 $69.95ISBN 978-1-4419-7909-4

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S. Migórski, Jagiellonian University, Kraków, Poland; A. Ochal, Jagiellonian University in Kraków, Poland; M. Sofonea, Université de Perpignan, France

Nonlinear Inclusions and Hemivariational InequalitiesModels and Analysis of Contact Problems

This book introduces the reader the theory of non-linear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis.

Features 7 Gathers new results on nonlinear inclusions and hemivariational inequalities and provides a unique overview of this topic 7 Deals with new and nonstandard models of contact involving subdifferential of nonconvex functions, including models for the contact of piezoelectric materi-als 7 Intends to represent a bridge between the functional analysis and the mechanics of conti-nua 7 Provides the reader an example of cross fertilization between modelling and applications on one hand, and nonsmooth nonlinear analysis on the other

Contents Preface.- List of Symbols.- 1. Preliminaries.- 2. Function Spaces.- 3. Elements of Nonlinear Analysis.- 4. Stationary Inclusions and Hemiva-riational Inequalities.- 5. Evolutionary Inclusions and Hemivarational Inequalities.- 6. Modeling of Contact Problems.- 7. Analysis of Static Contact Problems.- 8. Analysis of Dynamic Contact Prob-lems.- Bibliographic Notes.- References.- Index.

Fields of interestsPartial Differential Equations; Mechanics; Func-tional Analysis



Due August 2012

2012. XVIII, 294 p. 9 illus. (Advances in Mechanics and Mathematics, Volume 26) Hardcover7 approx. $109.00ISBN 978-1-4614-4231-8

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C. Miller, The Ohio State University, Columbus, OH, USA; J.‑P. Rolin, Université de Bourgogne, Dijon, France; P. Speissegger, McMaster University, Hamilton, ON, Canada (Eds)

Lecture Notes on O-Minimal Structures and Real Analytic Geometry This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute.

Features 7 Presents material produced in conjunction with the Thematic Program in O-minimal Structures and Real Analytic Geometry, held at the Fields Institute 7 Collects material that is elsewhere unavailable or spread across many dif-ferent sources such as research papers, conference proceedings, and PhD theses 7 Reflects original content, such as developments and insights that arose since the original research papers were published

Contents Preface.- Blowings-up of Vector Fields (F. Cano).- Basics of o-Minimality and Hardy Fields (C. Miller).- Construction of o-Minimal Structures from Quasianalytic Classes (J.-P. Rolin).- Course on Non-Oscillatory Trajectories.- F.S. Sánchez).- Pfaffian Sets and o-Minimality (P. Speissegger).- Theorems of the Complement (A. Fornasiero, T. Servi).

Fields of interestsMathematical Logic and Foundations; General Algebraic Systems; Group Theory and Generali-zations



Due August 2012

2012. XVIII, 200 p. 26 illus. (Fields Institute Communications, Volume 62) Hardcover7 approx. $109.00ISBN 978-1-4614-4041-3

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33

P. M. Pardalos, University of Florida, Gainesville, FL, USA; T. F. Coleman, University of Waterloo, ON, Canada; P. Xanthopoulos, University of Central Florida, Orlando, FL, USA (Eds)

Optimization and Data Analysis in Biomedical InformaticsContents Preface.- Novel Biclustering Methods for Re-Ordering Data Matrices (P.A. DiMaggio Jr., A. Subramani, C.A. Floudas).- Clustering Time Series Data with Distance Matrices (O. Şeref, W.A. Chao-valitwongse).- Mathematical Models of Supervised Learning and Application to Medical Diagnosis (R. De Asmundis, M.R. Guarracino).- Predictive Model for Early Detection of Mild Cognitive Im-pairment and Alzheimer’s Disease (E.K. Lee, T.-L. Wu, F. Goldstein, A. Levey).- Strategies for Bias Reduction in Estimation of Marginal Means with Data Missing at Random (B. Chen, R.J. Cook).- Cardiovascular Informatics: A Perspective on Promises and Challenges of IVUS Data Analysis (I.A. Kakadiaris, E.G.M. Ruiz).- An Introduction to the Analysis of Functional Magnetic Resonance Imaging Data (G. Gazzola, C.-A. Chou, M.K. Jeong, W.A. Chaovalitwongse).- Sensory Neurop-rostheses: From Signal Processing and Coding to Neural Plasticity in the Central Nervous System (F. Panetsos, A. Sanchez-Jimenez, C. Herrera-Rincon).- EEG Based Biomarker Identification Using Graph-Theoretic Concepts: Case Study in Alcoholism (V. Sakkalis, K. Marias).- Maximal Connectivity and Constraints in the Human Brain (R.V. Belavkin).

Fields of interestsOptimization; Data Mining and Knowledge Dis-covery; Health Informatics



Due August 2012

2012. X, 150 p. 40 illus., 28 in color. (Fields Institute Communications, Volume 63) Hardcover7 approx. $109.00ISBN 978-1-4614-4132-8

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A. Romano, Università degli Studi di Napoli, Italy

Classical Mechanics with Mathematica®Features 7 Offers a unique and broad approach to me-chanics, integrating linear algebra, analysis, and differential geometry 7 Provides an illuminating historical perspective on the subject, including the models of Newton, Euler, Lagrange and Hamil-ton 7 Gives a treatment of impulsive dynamics, rarely found elsewhere in the literatureIncludes over 200 carefully crafted excercises, frequent-ly making use of Mathematica 7 Suitable for both graduate and advanced undergraduate stu-dents

Contents I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Ten-sors.- 6 Differentiable Manifolds.- 7 One-Para-meter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Diffe-rential Calculus.- 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Prin-ciples of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dyna-mics.- 16 Dynamics of a Rigid Body.- 17 Lagran-gian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrab-le Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics.- A First-Order PDE.- B Fourier’s Series.- References.- Index.

Fields of interestsDifferential Geometry; Mechanics; Mathematical Physics



Due August 2012

2013. XIV, 440 p. 137 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover7 $129.00ISBN 978-0-8176-8351-1

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K. Schmüdgen, University of Leipzig, Germany

Unbounded Self-Adjoint Operators on Hilbert SpaceFeatures 7 Includes important topics which are not yet or not completely presented in a text book 7 Nu-merous well-choosen examples and exercises help the reader to learn dealing with unbounded ope-rators 7 Treats unbounded self-adjoint operators with the emphasis on applications in mathematical physics

Contents I Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Ope-rators.- II Spectral Theory.- 4 Spectral Measures and Spectral Integrals.- 5 Spectral Decomposition of Selfadjoint and Normal Operators.- III Special Topics.- 6 One-Parameter Groups and Semigroups of Operators.- 7 Miscellaneous.- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators.- 8 Perturbations of Selfadjoint Opera-tors.- 9 Trace Class Perturbations of Spectra of Sel-fadjoint Operators.- V Forms and Operators.- 10 Semibounded Forms and Selfadjoint Operators.- 11 Sectorial Forms and m-Sectorial Operators.- 12 Discrete Spectrum of Selfadjoint Operators.- VI Selfadjoint Extention Theory of Symmetric Opera-tors.- 13 Selfajoint Extensions: Cayley Transform and Krein Transform.- 14 Selfadjoint Extensions: Boundary Triplets.- 15 Sturm-Liouville Opera-tors.- One-Dimensional Moment Problem.

Fields of interestsFunctional Analysis; Mathematical Methods in Physics; Operator Theory



Available

2012. XX, 432 p. (Graduate Texts in Mathematics, Volume 265) Hardcover7 $79.95ISBN 978-94-007-4752-4

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34

S. Scholtes

Introduction to Piecewise Differentiable Equations This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piece-wise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathe-matical analysis and to have some familiarity with polyhedral theory.

Feature 7 Introduces the theory of piecewise differen-tiable functions with an emphasis on piecewise differentiable equations Illustrates the relevance of the study via two sample problems

Contents -1. Sample problems for nonsmooth equations. -2. Piecewise affline functions. -3. Elements from nonsmooth analysis. -4. Piecewise differentiable functions. -5. Sample applications.

Fields of interestsAnalysis; Functions of a Complex Variable; Calculus of Variations and Optimal Control; Optimization



Due August 2012

2012. IV, 126 p. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-4339-1

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

Methods of Optimization and Systems Analysis for Problems of Transcomputational ComplexityThis work presents lines of investigation and scientific achievements of the Ukrainian school of optimization theory and adjacent disciplines. These include the development of approaches to mathematical theories, methodologies, methods, and application systems for the solution of applied problems in economy, finances, energy saving, agriculture, biology, genetics, environmental protection, hardware and software engineering, information protection, decision making, pattern recognition, self-adapting control of complicated objects, personnel training, etc.

Features 7 Offers an interesting and rigorous presentation of modern optimization and adjacent discipli-nes 7 Presents research from a well-known school of optimization originating in Ukrai-ne 7 Enables the students of informatics and cybernetics to refine their specialization

Contents Preface.- 1. Science Was the Meaning of His Life.- 2. Optimization Methods and Their Efficient Use.- 3. Mathematical Modeling and Analysis of Complex Processes on Supercomputer Systems.- 4. Problems of Modeling and Analysis of Processes in Economic Cybernetics.- 5. Problems of Solving Complicated Combinatorial Problems.- After-ward.- References.- Index.

Fields of interestsOptimization; Simulation and Modeling; Com-puter Imaging, Vision, Pattern Recognition and Graphics



Due August 2012

2012. XIV, 266 p. 13 illus. (Springer Optimization and Its Applications, Volume 72) Hardcover7 approx. $109.00ISBN 978-1-4614-4210-3

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G. Sirbiladze, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia.

Extremal Fuzzy Dynamic SystemsTheory and Applications

In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems.

Features 7 Presents a new approach for fuzzy modeling of dynamic processes in the systems sciences research 7 Systematica lly organizes the topic by covering theory first and applications later 7 In-troduces a software library which is used to demonstrate the applications

Contents F uzzy Measures and Fuzzy Statistics: Its Proba-bility Representations.- Extended Extremal Fuzzy Measures.- Extended Extremal Fuzzy Measures on Compositional Product of Measurable Spaces.- Modeling of Extremal and Controllable Extremal Fuzzy Processes.- Identification of Fuzzy-Integral Models of Extremal fuzzy Processes.- Optimiza-tion of Continuous Controllable Extremal Fuzzy Processes and the Choice of Decisions.- Problems of States Estimation (Filtration) of Extremal Fuzzy Processes. - Conclusions on the Parts I-VII.- Al-gorithms and software for Discrete Possibilistic EFDS.- Application of the Discrete Possibilistic Model of the EFDS in the Evaluation of Expert Knowledge Streams.- Application: Forecasting of Increasing Financial Risks (Credit Risks) of Georgia-based Organization (LTD-“Fractal”) by the Discrete Possibilistic EFDS’s Finite Mo-del.- General Conclusions.- Bibliography.

Fields of interestsSystems Theory, Control; Simulation and Mode-ling; Artificial Intelligence (incl. Robotics)



Due August 2012

2012. XVIII, 378 p. 26 illus., 1 in color. (IFSR International Series on Systems Science and Engineering, Volume 28) Hardcover7 approx. $129.00ISBN 978-1-4614-4249-3

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35

J. Stix, University of Heidelberg, Germany

Evidence for the Section Conjecture in the Theory of Arithmetic Fundamental GroupsFeatures 7 The first exposition of foundational material on the arithmetic of fundamental groups with respect to the Section Conjecture of anabelian Geometry: from the history of the subject to the state of the art of the conjecture. 7 Numerous approaches to the Section Conjecture are discussed with open questions to stimulate future research. 7 Assu-ming the basics, the more advanced chapters are self contained and can be read independently

Contents Part I Foundations of Sections.- 1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid.- 3 Basic Geometric Operations in Terms of Sections.- 4 The Space of Sections as a Topological Space.- 5 Evaluation of Units.- 6 Cycle Classes in Anabelian Geometry.- 7 Injectivity in the Section Conjecture.- Part II Basic Arithmetic of Sections.- 7 Injectivity in the Section Conjecture.- 8 Reduction of Sections.- 9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers.- Part III On the Passage from Local to Global.- 10 Local Obstructions at a p-adic Place.- 11 Brauer-Manin and Descent Obstructions.- 12 Fragments of Non-abelian Tate–Poitou Duality.- Part IV Analogues of the Section Conjecture.- 13 On the Section Conjecture for Torsors.- 14 Nilpotent Sections.- 15 Sections over Finite Fields.- 16 On the Section Conjecture over Local Fields.- 17 Fields of Coho-mological Dimension 1.- 18 Cuspidal Sections and Birational Analogues.

Fields of interestsAlgebraic Geometry; Number Theory



Available

2012. XII, 234 p. (Lecture Notes in Mathematics, Volume 2054) Softcover7 $59.95ISBN 978-3-642-30673-0

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N. Touzi, École Polytechnique, Palaiseau, France

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic program-ming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary.

Features 7 Provides a self-contained presentation of the recent developments in Stochastic target problems which cannot be found in any other monograph 7 Approaches quadratic backward stochastic differential equations following the point of view of Tevzadze and presented in a way to maximize the ease of understanding 7 Con-tains relevant examples from finance, including the Nash equilibrium example

Contents Preface.- 1. Conditional Expectation and Linear Parabolic PDEs.- 2. Stochastic Control and Dynamic Programming.- 3. Optimal Stopping and Dynamic Programming.- 4. Solving Control Problems by Verification.- 5. Introduction to Viscosity Solutions.- 6. Dynamic Programming Equation in the Viscosity Sense.- 7. Stochastic Target Problems.- 8. Second Order Stochastic Target Problems.- 9. Backward SDEs and Stochas-tic Control.- 10. Quadratic Backward SDEs.- 11. Probabilistic Numerical Methods for Nonlinear PDEs.- 12. Introduction to Finite Differences Methods.- References.

Fields of interestsQuantitative Finance; Probability Theory and Sto-chastic Processes; Partial Differential Equations



Due September 2012

2012. XII, 194 p. (Fields Institute Monographs, Volume 29) Hardcover7 approx. $99.00ISBN 978-1-4614-4285-1

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G. G. Yin, Wayne State University, Detroit, MI, USA; Q. Zhang, University of Georgia, Athens, GA, USA

Continuous-Time Markov Chains and ApplicationsA Two‑Time‑Scale Approach

This book gives a systematic treatment of singular-ly perturbed systems that naturally arise in control and optimization, queueing networks, manufactu-ring systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions.

Features 7 New chapters added on backward equations and LQG control problems 7 Bridges the gap between theory and applications 7 Presents results on asymptotic expansions of the correspon-ding probability distributions

Contents Prologue and Preliminaries: Introduction and overview- Mathematical preliminaries.- Marko-vian models.- Two-Time-Scale Markov Chains: Asymptotic Expansions of Solutions for Forward Equations.- Occupation Measures: Asymptotic Properties and Ramification.- Asymptotic Ex-pansions of Solutions for Backward Equations.- Applications:MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching: Markov Decision Problems.- Stochastic Control of Dynamical Systems.- Numerical Methods for Control and Optimization.- Hybrid LQG Prob-lems.- References.- Index.-

Fields of interestsProbability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization; Operations Research, Management Science



Due September 2012

2nd ed. 2012. X, 433 p. (Stochastic Modelling and Applied Probability, Volume 37) Hardcover7 $129.00ISBN 978-1-4614-4345-2

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