d. ambrosi, remembering sofya mathematical...

MathematicsNews 9/2011

131

D. Ambrosi, Politecnico di Milano, Italy; A. Quarteroni, Ecole Polytechnique Federale De Lausanne, Switzerland; G. Rozza, Ecole Polytechnique Federale de Lausanne, Switzerland (Eds)

Modelling of Physiological Flows

Contents Assumptions in modelling of large artery hemody-namics by D.A. Steinman. - Simplified blood flow model with discontinous vessel properties by E.F. Toro and S. Siviglia. - Blood coagulation: a puzzle for biologists, a maze for mathematicians by A. Fasano et al. - Numerical simulation of electrocar-diagrams by J.F. Gerbeau et al. - Mathematical and numerical methods for reaction-diffusion models in electrocardiology by P. Colli-Franzone et al. - Structurally motivated damage models for arterial walls by A.M. Robertson et al. - Arterial growth and remodelling is driven by hemodynamics by L. Cardamone and J.D. Humphrey. - The VPH-Physiome Project: standards, tools and database for multi-scale physiological modelling by P. Hunter et al. - Role of the variational formulation in the dimensionally-heterogeneous modelling of the human cardiovascular system by P. Blanco and R. Feijoo. - Multiscale modelling of hematologic disorders by G.E. Karniadakis et al. - Multiscale computational analysis of degradable polymers by P. Zunino et al. - Applications of variational data assimilitation in computational hemodynamics by A. Veneziani et al. - Quality open source mesh generation for cardiovascular flow simulations by E. Marchandise et al.

Fields of interestsComputational Mathematics and Numerical Ana-lysis; Human Physiology; Mathematical Modeling and Industrial Mathematics

Target groupsResearch

Product CategoryMonograph

Due September 2011

2011 2011. X, 240 p. 151 illus., 1 in color. (MS&A, Volume 5) Hardcover7 $109.00ISBN 978-88-470-1934-8

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H. Ammari, École Normale Supérieure, Paris, France (Ed.)

Mathematical Modeling in Biomedical Imaging IIOptical, Ultrasound, and Opto-Acoustic Tomographies

This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.

Features 7 The first book to cover ultrasound, optic, and opto-acoustic tomographies and to report the most recent mathematical and computational developments in these fields. 7 The contribu-tions are written by leading experts in the field of mathematical imaging. 7 The contributions are comprehensible to non-experts.

Contents Direct Reconstruction Methods in Optical Tomography.- Direct Reconstruction Methods in Ultrasound Imaging of Small Anomalies.- Photoacoustic Imaging for Attenuating Acoustic Media.- Attenuation Models in Photoacoustics.- Quantitative Photoacoustic Tomography.

Fields of interestsApplications of Mathematics; Imaging / Radiolo-gy; Mathematical Methods in Physics

Target groupsGraduate

Product CategoryContributed volume

Due October 2011

2012. X, 158 p. 43 illus., 38 in color. (Lecture Notes in Mathematics / Mathematical Biosciences Subseries, Volume 2035) Softcover7 $49.95ISBN 978-3-642-22989-3

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M. Audin, Université de Strasbourg, France

Remembering Sofya KovalevskayaSofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in be-coming arguably the first woman to have a profes-sional university career in the way we understand it today. This memoir, written by a mathematician who specialises in symplectic geometry and integrable systems, is a personal exploration of the life, the writings and the mathematical achieve-ments of a remarkable woman. It emphasises the originality of Kovalevskaya’s work and assesses her legacy and reputation as a mathematician and scientist. Her ideas are explained in a way that is accessible to a general audience, with diagrams, marginal notes and commentary to help explain the mathematical concepts and provide context.

Features 7 The first biography to be written about Sofya Kovalevskaya by a renowned mathema-tician 7 Offers a well-rounded narrative that incorporates literature, mathematics and personal biography 7 May also appeal to those doing general feminist studies

Contents Sofya’s chronology.- Sofya’s names.- Stories.- The thesis of Sofya, the Cauchy–Kovalevskaya theorem.- The Solid.- A letter to Mittag-Leffler.- Stockholm.- A letter to Vollmar.- The Bordin prize and Sofya’s reputation.- The women of Men of mathematics.- I remember Sofya, by George, Gösta, Julia and all the rest.- I too remember Sofya.- Bibliography.

Fields of interestsHistory of Mathematical Sciences; Theoretical and Applied Mechanics; Gender Studies

Target groupsPopular/general

Product CategoryPopular science

Available

2011. IX, 284 p. 97 illus., 47 in color. Hardcover7 $49.95ISBN 978-0-85729-928-4

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www.springer.com/978-88-470-1934-8



Mathematics springer.com/NEWSonline

132

V. Barbu, University Al.I. Cuza, Iasi, Romania; T. Precupanu, University Al.I.Cuza, Iasi, Romania

Convexity and Optimization in Banach SpacesAn updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and func-tions in infinite-dimensional spaces. The main em-phasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and applica-tion. This edition has been updated to include new results pertaining to advanced concepts of sub-differential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research con-cerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems.

Features 7 This book provides a strong emphasis on the link between abstract theory and applications to convex optimization 7 Chapters end with an informative ‘bibliographic notes’ section for further reading 7 Includes fundamental results of infinite-dimensional convex analysis

Contents Fundamentals of Functional Analysis.- Convex Functions.- Convex Programming.- Convex Con-trol Problems in Banach Spaces.

Fields of interestOptimization



Due December 2011

3rd rev. and enlarged ed. 2012. XII, 352 p. (Springer Monographs in Mathematics) Hardcover7 $124.00ISBN 978-94-007-2246-0

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S. Benenti, Università di Torino, Italy

Hamiltonian Structures and Generating FamiliesThis book is an enhanced version of an earlier Russian edition. Besides thorough revisions, more emphasis was put on reordering the topics accor-ding to a category-theoretical view. This allows the mathematical results to be stated, proved, and un-derstood in a much easier and elegant way. From the reviews of the Russian edition: „The main ac-cent is shifted to the application . . . in geometrical optics, thermostatics and control theory, and not to the Hamiltonian mechanics only. . . . To make the book fairly self-contained, full details of basic definitions and all proofs are included. In this way, the majority of the text can be read without the prerequisite of a course in geometry.

Features 7 Enhanced version of Russian first editi-on 7 Focuses on Hamiltonian mechanics, as well as the application of modern mathematical methods of symplectic geometry and topology in geometrical optics, thermostatics and control theory 7 Self-contained with full details of basic notions of calculus on manifolds in the first two chapters

Contents Preface.- Basic Notions of Calculus on Ma-nifolds.- Relations.- Symplectic Relations on Symplectic Manifolds.- Symplectic Relations on Cotangent Bundles.- Canonical Lift on Cotangent Bundles.-The Geometry of the Hamilton-Jacobi Equation.- Hamiltonian Optics in Euclidean Spaces.- Control of Static Systems.- Supplementa-ry Topics.- Global Hamilton Principal Functions on S2 and H2.- References.- Index.

Fields of interestsGlobal Analysis and Analysis on Manifolds; Sys-tems Theory, Control; Mathematical Applications in the Physical Sciences


Product CategoryGraduate/Advanced undergraduate textbook

Due October 2011

2011. XIV, 258 p. 49 illus. (Universitext) Softcover7 $59.95ISBN 978-1-4614-1498-8

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K. Berglund, University of Helsinki, Finland

The Vexing Case of Igor Shafarevich, a Russian Political ThinkerFeatures 7 “The Shafarevich case” discussed in this study created a large controversy in the mathematics community at the beginning of the 1990s about a fundamental ethical principle: Can scientific ho-norary societies make demands to their members concerning their non-scientific views? 7 Ano-ther, even bigger problem in Shafarevich’s case is that, as this study shows, he was condemned wrongly, on the basis of superficial groundwork and tendentious reading of his texts. This study will hopefully set off Shafarevich’s belated reha-bilitation. Mathematicians are often fascinating personalities and Shafarevich is no exception.

Contents 1 igor shafarevich, a lightning rod for controver-sy.- 2 shafarevich’s early years in the young soviet state.- 3 shafarevich, the human rights activist.- 4 the first disputes about the soviet – and russian – future.- 5 from under the rubble, shafarevich’s and solzhenitsyn’s joint project.- 6 shafarevich’s addresses until the early 1980s.- 7 shafarevich’s first statements during the era of glasnost.- 8 rus-sophobia.- 9 the rapid political changes of the late 1980s early 1990s.- 10 critique of techno-scientific civilisation .- 11 some conclusions.- sources and literature.- index of personal names.

Fields of interestMathematics in the Humanities and Social Sci-ences



Due November 2011

2012. VIII, 549 p. Hardcover7 $129.00ISBN 978-3-0348-0214-7

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133

S. Bianchini, SISSA, Trieste, Italy; E. A. Carlen, Rutgers University, Piscataway NJ, USA; A. Mielke, WIAS, Berlin, Germany; C. Villani, Université de Lyon, France

Nonlinear PDE’s and ApplicationsC.I.M.E. Summer School, Cetraro, Italy 2008, Editors: Luigi Ambrosio, Giuseppe Savaré

This volume collects the notes of the CIME course „Nonlinear PDE’s and applications“ held in Cetra-ro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers Universi-ty), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching fin-dings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry.

Features 7 A broad overview on some deep results and new exciting developments 7 Contribution of leading experts 7 Accessible introduction to new theories and results

Contents Transport Rays and Applications to Hamilton-Jacobi Equations.- Functional Inequalities and Dynamics.- Differential, Energetic, and Metric Formulations for Rate-independent Processes.- Optimal Transport and Curvature.

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



Available

2011. XIII, 224 p. 8 illus., 7 in color. (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries, Volume 2028) Softcover7 $59.95ISBN 978-3-642-21718-0

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V. Blomer, University of Toronto, ON, Canada; P. Mihăilescu, University of Gottingen, Germany (Eds)

Contributions in Analytic and Algebraic Number TheoryFestschrift for S. J. Patterson

Features 7 Contributed volume is dedicated to Samual J. Patterson, and many of the articles in this volume were presented at the conference “Patterson 60++” at the University of Göttingen in July 2009 on the occasion of his 60th birthday 7 This volume covers a broad range of topics within the vast field of number theory and appeals to a broad reader-ship 7 Contributions to the book are the work of an international and select group of first-rate experts in the field of analytic number theory

Contents Preface.- The Density of Rational Points on a Certain Threefold (V. Blomer, J. Brüdern).- Affine Gindikin-Karpelevich Formula via Uhlenbech Spaces (A. Braverman, M. Finklberg, D. Kazh-dan).- Daniel’s Twists of Hooley’s Delta Function (J. Brüdern).- Coefficients of the n-fold Theta Function and Weyl Group Multiple (B. Brubaker, D. Bump, S. Friedberg, J. Hoffstein).- Towards the Trace Formula for Convex-cocompact Groups (U. Bunkhe, M. Olbrich).- Double Dirichlet Series and Theta Functions (G. Chinta, S. Friedberg, J. Hoffstein).- The Patterson Measure: Classics, Variations, and Applications (M. Denker, B. O. Stratmann).- Moments for L-functions for GLr x GLr–1 (A. Diaconu, P. Garrett, D. Goldfeld).- Further Remarks on the Exponent of Convergence and the Hausdorff Dimension of the Limit Set of Kleinian Groups (M. R. Hille).- A Note on the Algebraic Growth Rate of Poinecaré Series for Kleinian Groups (M. Kesselböhmer, B. O. Strat-mann).- References.

Fields of interestNumber Theory



Due December 2011

2012. XXII, 284 p. (Springer Proceedings in Mathematics, Volume 9) Hardcover7 $149.00ISBN 978-1-4614-1218-2

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J. Blowey, M. Jensen, Durham University, UK (Eds)

Frontiers in Numerical Analysis - Durham 2010This book contains detailed lecture notes on four topics at the forefront of current research in com-putational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathema-tics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are gi-ven. This book is also suitable for professional ma-thematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Features 7 Current research areas are introduced on the right level for first-year graduate students 7 To-pics are usually not covered in text books 7 Au-thors are distinguished scientists in their field

Fields of interestComputational Mathematics and Numerical Analysis



Due November 2011

2012. X, 280 p. 38 illus., 2 in color. (Lecture Notes in Computational Science and Engineering, Volume 85) Hardcover7 $59.95ISBN 978-3-642-23913-7

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134

V. L. Boginski, University of Florida, Gainesville, FL, USA; C. Commander, Eglin AFB, FL, USA; P. M. Pardalos, University of Florida, Gainesville, FL, USA; Y. Ye, Stanford University, CA, USA (Eds)

Sensors: Theory, Algorithms, and Applications

Contents Preface.- On Enhancing Fault Tolerance of Virtual Backbone in a Wireless Sensor Network with Unidirectional Links (R. Tiwari, M.T. Thai).- Constrained Node Placement and Assignment in Mobile Backbone Networks (E.M. Craparo).- Ca-nonical Dual Solutions to Sum of Fourth-Order Polynomials Minimization Problems with Appli-cations to Sensor Network Localization (D.Y. Gao, N. Ruan, P.M. Pardalos).- Optimal Estimation of Multidimensional Data with Limited Measure-ments (W. MacKunis, J. W. Curtis, P.E.K. Berg-Yuen).- Informational Patterns in Discrete-Time Linear-Quadratic Dynamic Games (M. Pachter, K.D. Pham).- The Design of Dynamical Inquiring Systems: A Certainty Equivalent Formalization (L. Di Giacomo, G. Patrizi).- Sensors in Transportati-on and Logistics Networks (C. Vogiatzis).- Study of Mobile Mixed Sensing Networks in an Automo-tive Context (A. Chakravarthy, K. Song, J. Peraire, E. Feron).- Navigation in Difficult Environments: Multi-Sensor Fusion Techniques (A. Soloviev, M. M. Miller).- A Spectral Clustering Approach for Modeling Connectivity Patterns in Electroence-phalogram Sensor Networks (P. Xanthopoulos, A. Arulselvan, P. M. Pardalos.).

Fields of interestsOptimization; Circuits and Systems; Algorithms



Due December 2011

2011. X, 244 p. 73 illus., 56 in color. (Springer Optimization and Its Applications, Volume 61) Hardcover7 $124.00ISBN 978-0-387-88618-3

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P. Brändén, Royal Institute of Technology, Stockholm, Sweden; M. Passare, Stockholm University, Sweden; M. Putinar, University of California, Santa Barbara, CA, USA (Eds)

Notions of Positivity and the Geometry of PolynomialsThe book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contribu-tions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.

Feature 7 At the interface between positivity and the geo-metry, combinatorics or analysis of polynomials of one or several variables solicited articles from a select group of mathematicians and physicists dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician

Fields of interestAnalysis



Due September 2011

2011. XX, 404 p. 16 illus., 2 in color. (Trends in Mathematics) Hardcover7 $149.00ISBN 978-3-0348-0141-6

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G. S. Chirikjian, Johns Hopkins University, Baltimore, MD, USA

Stochastic Models, Information Theory, and Lie Groups, Volume 2Analytic Methods and Modern Applications

Contents Lie Groups I: Introduction and Examples.- Lie Groups II: Differential Geometric Properties.- Lie Groups III: Integration, Convolution, and Fourier Analysis.- Variational Calculus on Lie Groups.- Statistical Mechanics and Ergodic The-ory.- Parts Entropy and the Principal Kinematic Formula.- Estimation and Multivariate Analysis in R^n.- Information, Communication, and Group Therapy.- Algebraic and Geometric Coding Theory.- Information Theory on Lie Groups.- Stochastic Processes on Lie Groups.- Numerical Group Representation Theory.-Rotational and Rigid-Body Diffusion.- Kinematic Covariance Propagation.- Biomolecular Conformation and Information Theory.- Infotaxis.- A Survey of Additional Applications.- Summary.- Inequalities, Convexity, and Rearrangements.- Index.

Fields of interestsApplications of Mathematics; Appl.Mathematics/Computational Methods of Engineering; Differen-tial Geometry



Due December 2011

2012. XXII, 453 p. 10 illus. (Applied and Numerical Harmonic Analysis) Hardcover7 approx. $59.95ISBN 978-0-8176-4943-2

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135

S. Coen, Università di Bologna, Italy (Ed.)

Mathematicians in Bologna 1861–1960The scientific personalities of L.Cremona, E. Beltrami, S. Pincherle, F. Enriques, Beppo Levi, G. Vitali, L. Tonelli, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861–1960 are examined by different authors, in some cases providing different view points. Most contributions in the volume are historical; they reproduce original documents, or they study the original works and their impact on later research. The achievements of other mathe-maticians are investigated for their present-day importance.

Features 7 First book devoted to the study of the influence of the two world wars, 7 Fascism and the setting up of the Italian Republic on scientific studies in Italy based on the scientific legacies of members of a single academic environment 7 Significant and valuable contributions to algebraic geometry, differential geometry, operator and integration theory, real and complex analysis, mathematical physics are studied in a unique historical con-text 7 Ample account of the mathematical scien-tific milestones made at the University of Bologna, established in 1088, during the first century of the Italian state, 1861–1960

Fields of interestHistory of Mathematical Sciences



Due December 2011

2012. XII, 550 p. 6 illus. Hardcover7 $179.00ISBN 978-3-0348-0226-0

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Z. Cvetkovski, European University R. Macedonia, Skopje, Macedonia

InequalitiesTheorems, Techniques and Selected Problems

Features 7 Contains 458 problems on Algebra-Inequali-ties 7 Detailed solutions are given 7 Theore-tical background and techniques for proving in-equalities are provided 7 Ideal for participants of national and international mathematical contests

Contents Basic (elementary) inequalities and their ap-plication.- Inequalities between means, (with two and three variables).- Geometric (triangle) inequalities.- Bernoulli’s inequality, the Cau-chy–Schwarz inequality, Chebishev’s inequality, Surányi’s inequality.- Inequalities between means (general case).- Points of incidence in applications of the AM–GM inequality.- The rearrangement inequality.- Convexity, Jensen’s inequality.- Trigo-nometric substitutions and their application for proving algebraic inequalities.- The most usual forms of trigonometric substitutions.- Charac-teristic examples, using trigonometric substitu-tions.- Hölder’s inequality, Minkowski’s inequality and their generalizations.- Generalizations of the Cauchy–Schwarz inequality, Chebishev’s inequality and the mean inequalities.- Newton’s inequality, Maclaurin’s inequality.- Schur’s inequality, Muirhead’s inequality.- Two theorems from differential calculus, and their applications for proving inequalities.- One method of proving symmetric inequalities with three variables.- Me-thod for proving symmetric inequalities with three variables defined on set of real numbers.

Fields of interestsAlgebra; Popular Science in Mathematics/Compu-ter Science/Natural Science/Technology; Mathe-matics Education


Product CategoryReference work

Due November 2011

2012. 370 p. Softcover7 $49.95ISBN 978-3-642-23791-1

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P. Deuflhard, Zuse-Institut Berlin (ZIB), Germany

Newton Methods for Nonlinear ProblemsAffine Invariance and Adaptive Algorithms

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term ‚affine invariance‘ means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, com-parison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.

Fields of interestsComputational Mathematics and Numerical Analysis; Computational Science and Engineering; Ordinary Differential Equations



Due October 2011

1st ed. 2004. Corr. 2nd printing 2004. XII, 428 p. 49 illus. (Springer Series in Computational Mathematics, Volume 35) Softcover7 $74.95ISBN 978-3-642-23898-7

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136

J. Deuschel, Technische Universität Berlin, Germany; B. Gentz, Bielefeld University, Germany; W. König, Weierstrass Institute Berlin, Germany; U. Schmock, Vienna University of Technology, Austria (Eds)

Probability in Complex Physical SystemsIn Honour of Erwin Bolthausen and Jürgen Gärtner

Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twen-ty articles on various topics in this field, including self-interacting random walks and polymer mo-dels in random and non-random environments, branching processes, Parisi formulas and metasta-bility in spin glasses, and hydrodynamic limits for gradient Gibbs models.

Features 7 With contributions by international ex-perts 7 Introduces new concepts 7 Includes a stimulating mixture of research articles and exclusive surveys on active research fields

Contents Laudatio - The Mathematical Work of Jürgen Gärtner – Hollander.- Part I The Parabolic Anderson Model.- Part II Self-interacting Ran-dom Walks and Polymers.- Part III Branching Processes.-Part IV Miscellaneous Topics in Statis-tical Mechanics.

Fields of interestsProbability Theory and Stochastic Processes; Statistics, general



Due December 2011

2011. X, 460 p. 46 illus., 14 in color. (Springer Proceedings in Mathematics, Volume 11) Hardcover7 $149.00ISBN 978-3-642-23810-9

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D. A. Di Pietro, IFP Energies nouvelles, Rueil-Malmaison, France; A. Ern, Université Paris Est, Marne-la-Vallée, France

Mathematical Aspects of Discontinuous Galerkin MethodsThis book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate stu-dents and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from ad-vection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs‘ systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation.

Features 7 Understanding the mathematical founda-tions helps the reader design methods for new applications 7 Bridging the gap between finite volumes, finite elements, and discontinuous Galer-kin methods provides new insight on numerical methods 7 The mathematical setting for the continuous model is a key to successful approxi-mation methods

Contents Basic concepts.- Steady advection-reaction.- Unsteady first-order PDEs.- PDEs with diffusion.- Additional topics on pure diffusi-on.- Incompressible flows.- Friedhrichs‘ Systems.- Implementation.

Fields of interestsNumerical Analysis; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Com-putational Methods of Engineering



Due October 2011

2011. X, 390 p. 21 illus., 3 in color. (Mathématiques et Applications, Volume 69) Softcover7 $124.00ISBN 978-3-642-22979-4

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S. S. Dragomir, Victoria University, Melbourne ,VIC, Australia

Operator Inequalities of the Jensen, Čebyšev and Grüss Type

Features 7 Presents recent results concerning inequalities of Jensen, Cebysev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces 7 Illustrates fundamen-tal facts concerning bounded selfadjoint operators on complex Hilbert spaces 7 Presents recent results obtained by the author that deal with diffe-rent aspects of this well research inequality than those recently reported

Contents -1. Functions of Selfadjoint Operators in Hilbert Spaces (Introduction, Bounded Selfadjoint Opera-tors, Continuous Functions of Selfadjoint Opera-tors, Step Functions of Selfadjoint Operators, The Spectral Decomposition of Selfadjoint Operators, References). -2. Inequalities of the Jensen Type ( Introduction, Reverses of the Jensen Inequality, Some Slater Type Inequalities, Other Inequali-ties for Convex Functions, Some Jensen Type Inequalities for Twice Differentiable Functions, Some Jensen’s Type Inequalities for Log-convex Functions, Hermite-Hadamard’s Type Inequalities, Hermite-Hadamard’s Type Inequalities for Opera-tor Convex Functions, References). -3. Inequali-ties of the Čebyšev and Grüss Type (Introduction, Čebyšev’s Inequality, Grüss Inequality, More Inequalities of Grüss Type, More Inequalities for the Čebyšev Functional, Bounds for the Čebyšev Functional of Lipschitzian Functions, Quasi Grüss Type Inequalities, Two Operator Grüss Type Inequalities, References).

Fields of interestsOperator Theory; Partial Differential Equations; Probability Theory and Stochastic Processes


Product Category

Due November 2011

2011. XI, 128 p. (SpringerBriefs in Mathematics) Softcover7 $49.95ISBN 978-1-4614-1520-6

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137

H. Dym, Weizmann Institute, Rehovot, Israel; M. A. Kaashoek, Vrije Universiteit, Amsterdam, The Netherlands; P. Lancaster, University of Calgary, AB, Canada; H. Langer, TU Wien, Austria; L. Lerer, Technion Israel Institute of Technology, Haifa, Israel (Eds)

A Panorama of Modern Operator Theory and Related TopicsThe Israel Gohberg Memorial Volume

This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathe-maticians of our time – who inspired innume-rable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests, with topics ranging from operator theory and linear algebra to integral and differential equations, complex analysis and engineering problems. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends.

Features 7 Written by top experts in operator theory and its applications reflecting the exceptionally wide range of Gohberg's mathematical achieve-ments 7 State of the art contributions to single and multivariable operator theory and its applica-tions 7 Not restricted to a specific issue. Rather it provides a wide picture of various directions, theoretical as well as applied ones 7 Deals with topics that are central for operator theory and its applications and have been initiated and/or deve-loped by Israel Gohberg

Fields of interestsOperator Theory; Functional Analysis; Several Complex Variables and Analytic Spaces


Product CategoryCommemorative publication

Due December 2011

2012. 600 p. (Operator Theory: Advances and Applications, Volume 218) Hardcover7 approx. $229.00ISBN 978-3-0348-0220-8

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W. Gautschi, Purdue University, West Lafayette, IN, USA

Numerical AnalysisRevised and updated, this second edition of Walter Gautschi‘s successful Numerical Analysis explo-res computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliogra-phic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth.

Features 7 Highly acclaimed style is simple and teacha-ble 7 Detailed bibliographic notes for further study 7 Integrated with mathematical soft-ware for advanced computations 7 Abundant exercises cover both theoretical and practical me-thods 7 Complete, 350-page solutions manual provides exceptional instructional value

Contents Preface to the Second Edition.- Preface.- Pro-logue.- Chapter 1. Machine Arithmetic and Related Matters.- Chapter 2. Approximation and Interpolation.- Chapter 3. Numerical Differentia-tion and Integration.- Chapter 4. Nonlinear Equa-tions.- Chapter 5. Initial Value Problems for ODEs --- One-Step Methods.- Chapter 6. Initial Value Problems for ODEs --- Multi-Step Methods.- Chapter 7. Two-Point Boundary Value Problems for ODEs.- References.- Subject Index.

Fields of interestsComputational Mathematics and Numerical Analysis; Computational Science and Engineering; Ordinary Differential Equations



Due December 2011

2nd Edition. 2012. XXVIII, 623 p. 37 illus. Hardcover7 $99.00ISBN 978-0-8176-8258-3

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D. Goldfeld, Columbia University, NY, USA; J. Jorgenson, The City College of New York, NY, USA; P. Jones, Yale University, New Haven, CT, USA; D. Ramakrishnan, California Institute of Technology, Pasadena, CA, USA; K. A. Ribet, University of California at Berkeley, CA, USA; J. Tate, Harvard University, Cambridge, MA, USA (Eds)

Number Theory, Analysis and GeometryIn Memory of Serge Lang

Contents -Preface.-Introduction (Tate).-Publications by Serge Lang.-Raynaud‘s Group-Scheme and Reduc-tion of Converings (Abramovich).-The Modular Degree, Congruence Primes, and Multiplicity One (Agashe, Ribet, Stein).-Le théorème de Siegel-Shidlovsky revisté (Bertrand).-Some Aspects of Harmonic Analysis on So3(Z[i])\So3(C)/SO(3), and SO(2,1)z\SO(2,1)/SO(2) (Brenner, Sinton).-Differential Characters on Curves (Buium).-Weyl Group Multpile Dirichlet Series of Type A_2 (Chinta, Gunnels).-Remarks on the Geomet-ry of the Diffeomorphism Group of the Circle (Constantin, Kolev).-Harmonic Representatives For Cuspidal Cohomology Classes (Dodziuk, McGowan, Perry).-About the ABC Conjecture and an Alternative (van Frenkenhuijsen).-Unifying Themes Suggested by Belyi‘s Theorem (Goldring).-On the Local Divisibility of Heegner Points (Gross, Parson).-Uniform Estimates for Primitive Divisors in Elliptic Divisibility Sequen-ces (Ingram, Silverman).-The Heat Kernel, Theta Inversion and Zetas on Gamma\G/K (Jorgenson, Lang).-Applications of Heat Kernels on Abelian Groups: zeta(2n), Quadratic Reciprocity, Bessel Integrals (Karlsson).-Report on the Irreducibility of L-Functions (Katz).-Remark on Fundamental Groups and Effective Diophantine Methods for Hyperbolic Curves (Kim). [...]

Fields of interestsNumber Theory; Analysis; Geometry



Due December 2011

2011. XII, 683 p. 4 illus. Hardcover7 $219.00ISBN 978-1-4614-1259-5

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138

G. E. Gorelik, Boston University, MA, USA; V. Y. Frenkel, A.E.Ioffe Physicotechnical Institute, St.Petersburg, Russia

Matvei Petrovich Bronsteinand Soviet Theoretical Physics in the Thirties Translated by Valentina M. LevinaTranslated by: V. M. Levina, Moscow, Russia

The short life and tragic death of Matvei Petrovich Bronstein (1906-1938) may be seen as a symbol of the man‘s time and his country. One of the most remarkable features of Soviet history was the impressive advance of its physical sciences against the brutal and violent background of totalitaria-nism. Soviet advances in nuclear and space tech-nology form an important part of world history. These achievements had their roots in the 1930s, when Bronstein‘s generation entered science. Among his friends were the famous physicists Lev Landau and George Gamow. Bronstein worked in the vast field of theoretical physics, ranging from nuclear physics to astrophysics and from relativis-tic quantum theory to cosmology.

Features 7 Well-documented and well-balanced biogra-phy 7 Gives insightful details on the politico-scientific context in this aera 7 Includes a sample of Bronstein’s works

Contents Foreword.- Chapter 1 Childhood and Youth. Road to Science.- Chapter 2 In the Leningrad University (1926-1932).- Chapter 3 At the Leningrad Physi-cotechnical Institute.- Chapter 4 Hard Times for the Laws of Conservation and for Theoreticians.- Chapter 5 cGh-Physics in Bronstein‘s Life.- Chap-ter 6 Creative Personality.- Afterword.- Chronolo-gy.- Notes.- Bibliography.- Appendix 1.- Appendix 2. Photographs.- Index.

Fields of interestMathematics, general



Due September 2011

Reprint of the 1994 Edition. 1994. X, 199 p. 3 illus. (Modern Birkhäuser Classics) Softcover7 $59.95ISBN 978-3-0348-0199-7

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V. Guedj, Université Paul Sabatier, Toulouse, France (Ed.)

Complex Monge–Ampère Equations and Geodesics in the Space of Kähler MetricsThe purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).

Features 7 The first self contained presentation of Krylov's stochastic analysis for the complex Monge-Am-pere equation 7 A comprehensive presentation of Yau's proof of the Calabi conjecture 7 A great part of the material (both classical results and more recent 4. 7 A pedagogical style, lectures accessible to non experts.developments) has not previously appeared in book form 7 Written in pedagogicalcal style, lectures accessible to non experts

Contents 1.Introduction.- I. The Local Homogenious Di-richlet Problem.-2. Dirichlet Problem in Domains of Cn.- 3. Geometric Maximality.- II. Stochastic Analysis for the Monge-Ampère Equation.- 4. Pro-babilistic Approach to Regularity.- III. Monge-Ampère Equations on Compact Manifolds.- 5.The Calabi-Yau Theorem.- IV Geodesics in the Space of Kähler Metrics.- 6. The Riemannian Space of Kähler Metrics.- 7. MA Equations on Manifolds with Boundary.- 8. Bergman Geodesics.

Fields of interestsSeveral Complex Variables and Analytic Spaces; Differential Geometry; Partial Differential Equa-tions



Due November 2011

2012. X, 310 p. 3 illus. (Lecture Notes in Mathematics, Volume 2038) Softcover7 $89.95ISBN 978-3-642-23668-6

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K. Gustafson, University of Colorado, Boulder, CO, USA

The Crossing of HeavenMemoirs of a MathematicianPreface by: I. Antoniou, Aristoteles University of Thessaloniki, Greece

Among the group of physics honors students huddled in 1957 on a Colorado mountain watching Sputnik bisect the heavens, one young scientist was destined, three short years later, to become a key player in America’s own top-secret spy satellite program. One of our era’s most prolific mathematicians, Karl Gustafson was given just two weeks to write the first US spy satellite’s software. The project would fundamentally alter America’s Cold War strategy, and this autobiogra-phical account of a remarkable academic life spent in the top flight tells this fascinating inside story for the first time.

Features 7 Previously untold story of early computing and the world’s first spy satellite 7 Unique accounts of personal interactions with Nobel laureates, Field’s Medal winners, and other sometimes stran-ge famous personalities in science 7 Tales and secrets of high finance, and dangers therein

Contents Preface.- 1 The Child in Iowa.- 2 The Boy in Boulder.- 3 The Student in Poverty.- 4 Compu-ters and Espionage.- 5 First Publication.- 6 Into Academia.- 7 The World Opens.- 8 Personas and Personalities.- 9 Wives, Lovers, Friends.- 10 Close Calls.- 11 Mathematics.- 12 High Finance.- 13 The Improbabilities.- 14 Realities.- 15 The Crossing of Heaven.- Appendix.

Fields of interestsMathematics, general; Applications of Mathema-tics; Quantitative Finance


Product CategoryBiography

Due November 2011

2012. X, 170 p. Hardcover7 $59.95ISBN 978-3-642-22557-4

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139

N. Herrmann, Leibniz Universität Hannover, Germany

The Beauty of Everyday MathematicsImagine that you’ve finally found a parking space after a long and harrowing search, but are now encountering some difficulty in trying to enter this space. Wouldn’t it be great if you knew a formu-la that allowed you to enter the space without difficulty? Are you annoyed because your soda can doesn’t remain upright during a picnic? Would you like to know why a mirror swaps right and left, but not top and bottom? Are you looking for a mathematical speech to toast your mother-in-law’s 85th birthday? Or do you want to give your heart away mathematically? Dr. Norbert Herrmann pro-vides amusing and entertaining solutions to these and many other problems that we encounter in everyday situations. “A book for teachers, students of mathematics, and anybody who likes unusual and amusing calculations.”

Features 7 Complicated mathematics presented in a gene-rally understandable way 7 Examples from eve-ryday life are mathematized 7 Many examples presented with a good sense of humor 7 Small riddles and conjuring tricks garantee an entertai-ning reading

Contents Preface.- The Soda Can Problem.- The Mirror Problem.- The Leg Problem.- The Sketch Prob-lem.- the Parallel Parking Problem.- The Parking Garage Problem.- the 85th Birthday Problem.- The Slippery-Ice of Bread-Slicing Problem.- the Snail-Racehorse Problem.- The Discus Thrower Pro-blem.- The Beer Coaster Problem.- the Toasting Problem.- The Heart Problem. Index.

Fields of interestsMathematics, general; Education (general); Phy-sics, general



Due September 2011

2011. VII, 150 p. 50 illus. Softcover7 approx. $29.95ISBN 978-3-642-22103-3

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B. Howard, Boston College, Chestnut Hill, MA, USA; T. Yang, University of Wisconsin, Madison, WI, USA

Intersections of Hirzebruch–Zagier Divisors and CM CyclesThis monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and uni-tary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert mo-dular surface, and the special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in defor-mation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.

Features 7 Develops new methods in explicit arithmetic intersection theory 7 Develops new techniques for the study of Shimura varieties and automor-phic forms, central objects in modern number theory 7 Proves new cases of conjectures of S. Kudla

Contents 1. Introduction.- 2. Linear Algebra.- 3. Moduli Spaces of Abelian Surfaces.- 4. Eisenstein Series.- 5. The Main Results.- 6. Local Calculations.

Fields of interestNumber Theory



Due November 2011

2012. VIII, 126 p. (Lecture Notes in Mathematics, Volume 2041) Softcover7 $49.95ISBN 978-3-642-23978-6

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I. Itenberg, IRMA, Université de Strasbourg, France; B. Jöricke, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France; M. Passare, Stockholm University, Sweden (Eds)

Perspectives in Analysis, Geometry, and TopologyOn the Occasion of the 60th Birthday of Oleg Viro

Contents Preface.- 1 Selman Akbulut, Exotic structures on smooth 4-manifolds.- 2 Kenneth Baker, John Etnyre, Rational linking and contact geometry.- 3 Robert Berman, Jean-Pierre Demailly, Regula-rity of plurisubharmonic upper envelopes in big cohomology classes.- 4 Alex Degtarev, Towards the generalized Shapiro and Shapiro conjecture.-5 Alex Degtarev, Ilia Itenberg, Viatcheslav Kharla-mov, On the number of components of a complete intersection of real quadrics.- 6 Tobias Ekholm, Rational Symplectic Field Theory and linearized Legendrian contact homology.- 7 Yakov Eliash-berg, N. Mishachev, Wrinkling IV: Mappings with prescribed singularities.- 8 Michael Entov, Leonid Polterovich, Pierre Py, On continuity of quasimorphisms for symplectic maps. With an appendix by Michael Khanevsky.- 9 David Gay, Andras Stipsicz, On symplectic caps.- 10 Gennadi Henkin, Cauchy-Pompeiu type formulas for a on affine algebraic Riemann surfaces and some applications.-11 Kiumars Kaveh, A. G. Khovanskii, Algebraic equations and convex bodies.- 12 Louis Kauffman, Graphical Bracket Invariants of Virtual Links.- 13 Ciprian Manolescu, Christopher Wood-ward, Floer homology on the extended moduli space.- 14 Ngaiming Mok, Projective-algebraicity of minimal compactifications of complex-hyper-bolic space forms of finite volume. [...]

Fields of interestsGeometry; Global Analysis and Analysis on Mani-folds; Topology



Due December 2011

2012. XXII, 437 p. 90 illus., 18 in color. (Progress in Mathematics, Volume 296) Hardcover7 $124.00ISBN 978-0-8176-8276-7

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140

J. Janno, J. Engelbrecht, Tallinn University of Technology, Estonia

Microstructured Materials: Inverse ProblemsComplex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materi-als. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to dispersion. The authors’ goal has been to construct algorithms that allow us to determine the parameters within which we are required to characterize microstructure.

Features 7 Mathematical modelling is based on physical principles 7 Physical models are interwoven with inverse problems 7 A novel concept of using solitary waves for NDE is proposed

Contents Introduction.- 1 Inverse problems and non-destructive evaluation.- 2 Mathematical models of microstructured solids.- 3 Linear waves.- 4 Inverse problems for linear waves.- 5 Solitary waves in nonlinear models.- 6 Inverse problems for solitary waves.- 7 Summary.- References.- Index

Fields of interestsPartial Differential Equations; Mechanics; Conti-nuum Mechanics and Mechanics of Materials



Due September 2011

2011. X, 162 p. 29 illus., 3 in color. (Springer Monographs in Mathematics) Hardcover7 $99.00ISBN 978-3-642-21583-4

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R. Khasminskii, Wayne State University, Detroit, MI, USA

Stochastic Stability of Differential EquationsWith contrib. by: G. N. Milstein, Ural State University, Ekaterinburg, Russia

Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and enginee-ring. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature.

Features 7 Completely revised and enlarged second edition 7 Important new results are contai-ned 7 Useful for researchers and for students in graduate courses

Contents Boundedness in Probability and Stability of Stochastic Processes Defined by Differential Equations.- 2.Stationary and Periodic Solutions of Differential Equations. 3.Markov Processes and Stochastic Differential Equations.- 4.Ergodic Properties of Solutions of Stochastic Equations.- 5.Stability of Stochastic Differential Equations.- 6.Systems of Linear Stochastic Equations.- 7.Some Special Problems in the Theory of Stability of SDE’s.- 8.Stabilization of Controlled Stochastic Systems.- A. Appendix to the First English Editi-on.- B. Appendix to the Second Edition. Moment Lyapunov Exponents and Stability Index.- Refe-rences.- Index.

Fields of interestsProbability Theory and Stochastic Processes; Mechanics



Due August 2011

2nd Edition 2011. XVIII, 330 p. 4 illus. (Stochastic Modelling and Applied Probability, Volume 66) Hardcover7 $129.00ISBN 978-3-642-23279-4

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H. Kielhöfer, University of Augsburg, Germany

Bifurcation TheoryAn Introduction with Applications to Partial Differential Equations

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurca-tions for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inc-lined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.

Features 7 Gives a unified presentation in an abstract setting 7 Two new sections along with many revisions 7 More references included

Contents Introduction.- Global Theory.- Applications.

Fields of interestsPartial Differential Equations; Dynamical Systems and Ergodic Theory; Applications of Mathematics



Due November 2011

2nd Edition. 2011. X, 404 p. (Applied Mathematical Sciences, Volume 156) Hardcover7 $74.95ISBN 978-1-4614-0501-6

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141

R. Krömer, Siegen, Germany; Y. Chin-Drian, Université Nancy 2/ LHSP-Archives Poincaré, Nancy, France (Eds)

New Essays on Leibniz ReceptionIn Science and Philosophy of Science 1800-2000

Contents Introduction Ralf Krömer and Yannick Chin-Drian.- The idea of number from Gauss to Cantor. The Leibnizian heritage and its surpassing Philippe Séguin.- The Reception of Leibniz’s Logic in 19th Century German Philosophy Volker Peck-haus.- Leibniz’s Metaphysics as an Epistemological Obstacle to the Mathematization of Nature: the View of a Late 19th Century Neo-Kantian, Kurd Lasswitz Françoise Willmann.- Peano and his School between Leibniz and Couturat: the influ-ence in mathematics and in international language Erika Luciano.- Couturat’s reception of Leibniz Anne-Françoise Schmid.- Russell and Leibniz on the classification of propositions Nicholas Griffin.- Cassirer, Reader, Publisher, and Interpreter of Leibniz’s Philosophy Jean Seidengart.- Leibniz on Relativity. The Debate between Hans Reichenbach and Dietrich Mahnke on Leibniz’s Theory of Moti-on and Time Vincenzo De Risi.- Interpretations of Leibniz’s Mathesis universalis at the beginning of the XXth Century David Rabouin.- Leibnizian tra-ces in H.Weyl’s Philosophie der Mathematik und Naturwissenschaft Erhard Scholz.- Gödel, Leibniz and “Russell’s mathematical logic” Gabriella Crocco.- Chaitin, Leibniz and complexity Herbert Breger.- Abbreviations. Index

Fields of interestsHistory of Mathematical Sciences; Philosophy of Science



Due December 2011

2011 2012. 200 p. (Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives / Science autour de / around 1900) Hardcover7 approx. $129.00ISBN 978-3-0346-0503-8

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G. Labinaz, M. Guay, Queen‘s University, Kingston, ON, Canada

Viability of Hybrid SystemsA Controllability Operator Approach

Contents 1 Introduction.- 1.1 Motivation and History.- 1.2 Summary and Organization.- 1.3 Summary.- 2 Literature Review.- 2.1 Nerode et al Approach to Viability of Hybrid Systems [50],[71].- 2.2 Aubin et al Approach to Viability of Hybrid Systems [15].- 2.3 Deshpande{Varaiya Ap-proach to Viability of Hybrid Systems [35].- 2.4 Related Literature.- 2.5 Conclusion.- 3 Hybrid Model.- 3.1 Hybrid Phenomena and Hybrid Model.- 3.2 Hybrid Trajectories and their Orde-ring.- 3.3 Continuity, Fixed Points, and Correct Finite Control Automaton.- 3.4 Uncertainty in Hybrid Systems.- 3.5 The Three-Tank Prob-lem.- 3.6 Nerode{Kohn Formalism for Hybrid Systems.- 3.7 Conclusion.- 4 Viability.- 4.1 Background.- 4.2 Time{Independent Viabili-ty Set.- 4.3 Fixed Point Approximation.- 4.4 Computation of TIC{COFPAA{I for Three Admissible Control Law Classes.- 4.4.1 Piecewi-se Constant Control.- 4.4.2 Piecewise Constant with Finite Switching.- 4.4.3 Piecewise Constant with Polynomial Control.- 4.5 Time{Dependent Viability Set.- 4.5.1 Piecewise Constant Con-trol.- 4.6 Examples.- 4.6.1 Time{Independent Constraints.- 4.6.2 Time{Dependent Cons-traints.- 4.7 Conclusion.- 5 Robust Viability.- 5.1 Uncertainty and Robustness.- 5.2 Ordering of the Controllability Operator under Uncertainty.- 5.3 The Uncertain Controllability Operator and the Uncertainty Operator.- 5.4 Robust Viability.- 5.5 Robust Viability Control Design.- 5.6 Examp-les.- 5.7 Conclusion.- 6 Viability in Practice.- 6.1 Reachable Set Computation of the Controllability Operator. [...]

Fields of interestsSystems Theory, Control; Robotics and Automati-on; Vibration, Dynamical Systems, Control



Due November 2011

2012. 250 p. (Intelligent Systems, Control and Automation: Science and Engineering, Volume 55) Hardcover7 approx. $139.00ISBN 978-94-007-2520-1

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T. Lery, European Science Foundation, Strasbourg, France; M. Primicerio, Universita degli Studi di Firenze, Italy; M. J. Esteban, Université Paris-Dauphine, France; M. Fontes, Centre for Mathematical Sciences, Lund, Sweden; Y. Maday, Université Pierre et Marie Curie, Paris, France; V. Mehrmann, TU Berlin, Germany; G. Quadros, Critical Software SA, Coimbra, Portugal; W. Schilders, TU Eindhoven, Netherlands; A. Schuppert, Bayer Technology Service GmbH, Leverkusen, Germany; H. Tewkesbury, KNT for Industrial Mathematics, Guildford, UK (Eds)

European Success Stories in Industrial Mathematics

Features 7 Contains valuable material and important lessons that can be applied in their own fields in each success story for researchers, students, entrepreneurs, policy makers and business leaders in a range of disciplines 7 A unique book and the first of its kind 7 Timely with respect to the importance of innovation in the political and scientific agendas at European level

Contents Foreword.- Preface.- Introduction.- Health Biolo-gy.- Energy & Environment.- Finance & Modelling.- Automotive Industry & Manu-facturing.- Aerospace & Electronics.- Servi-ces, Transport & Logistics.- Annex. Summary Report of the E.S.F. Forward Look .

Fields of interestsMathematics, general; Applications of Mathe-matics; Mathematical Modeling and Industrial Mathematics

Target groupsProfessional/practitioner


Due October 2011

2012. VIII, 140 p. 200 illus., 185 in color. Softcover7 $59.95ISBN 978-3-642-23847-5

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142

A. Logg, K. Mardal, Simula Research Laboratory, Lysaker, Norway; G. Wells, University of Cambridge, U.K. (Eds)

Automated Solution of Differential Equations by the Finite Element MethodThe FEniCS Book

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applica-tions. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS soft-ware. Chapters in Part III present the application of FEniCS to a wide range of applications, inclu-ding fluid flow, solid mechanics, electromagnetics and geophysics.

Features 7 Unique synthesis of theory and computer code 7 Takes readers from an introductory tuto-rial through to cutting-edge research in scientific computing 7 Demonstrates a modern software approach to solving problems spanning fluid flow, solid mechanics, electromagnetics and geophysics

Fields of interestsMathematical Software; Theoretical, Mathematical and Computational Physics; Numeric Computing



Due October 2011

2012. VI, 718 p. 358 illus., 311 in color. (Lecture Notes in Computational Science and Engineering, Volume 84) Hardcover7 $89.95ISBN 978-3-642-23098-1

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V. Mayer, Université Lille 1, Villeneuve d‘Ascq, France; M. Urbanski, University of North Texas, Denton, TX, USA; B. Skorulski, Universidad Catolica del Norte, Antofagasta, Chile

Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal GeometryThe theory of random dynamical systems origi-nated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynami-cal systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we intro-duce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the mul-tifractal formalism of the Gibbs states.

Features 7 Contains new results 7 Complete treatment of the topic 7 Originality of the topic

Contents 1 Introduction.- 2 Expanding Random Maps.- 3 The RPF–theorem.- 4 Measurability, Pressure and Gibbs Condition.- 5 Fractal Structure of Confor-mal Expanding Random Repellers.- 6 Multifractal Analysis.- 7 Expanding in the Mean.- 8 Classical Expanding Random Systems.- 9 Real Analyticity of Pressure.

Fields of interestDynamical Systems and Ergodic Theory



Due November 2011

2012. X, 110 p. 3 illus. in color. (Lecture Notes in Mathematics, Volume 2036) Softcover7 $49.95ISBN 978-3-642-23649-5

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M. Morishita, Kyushu University, Nishi-ku, Fukuoka, Japan

Knots and PrimesAn Introduction to Arithmetic Topology

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book.

Features 7 Starts at an elementary level and builds up to a more advanced theoretical discussion 7 Written by a world expert on arithmetic topology 7 A large number of illustrative examples are provided throughout

Contents Preliminaries - Fundamental Groups and Galois Groups.- Knots and Primes, 3-Manifolds and Number Rings.- Linking Numbers and Legendre Symbols.- Decompositions of Knots and Primes.- Homology Groups and Ideal Class Groups I - Genus Theory.- Link Groups and Galois Groups with Restricted Ramification.- Milnor Invariants and Multiple Power Residue Symbols.- Alexan-der Modules and Iwasawa Modules.- Homology Groups and Ideal Class Groups II - Higher Order Genus Theory.- Homology Groups and Ideal Class Groups III - Asymptotic Formulas.- Torsions and the Iwasawa Main Conjecture.- Moduli Spaces of Representations of Knot and Prime Groups.- De-formations of Hyperbolic Structures and of p-adic Ordinary Modular Forms.

Fields of interestsNumber Theory; Topology; Mathematics, general



Due November 2011

2012. XII, 212 p. 31 illus. (Universitext) Softcover7 $59.95ISBN 978-1-4471-2157-2

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143

A. Némethi, Á. Szilárd, Rényi Institute of Mathematics, Budapest, Hungary

Milnor Fiber Boundary of a Non-isolated Surface Singularity

Contents 1 Introduction.- 2 The topology of a hypersur-face germ f in three variables Milnor fiber.- 3 The topology of a pair (f ; g).- 4 Plumbing graphs and oriented plumbed 3-manifolds.- 5 Cyclic coverings of graphs.- 6 The graph GC of a pair (f ; g). The definition.- 7 The graph GC . Proper-ties.- 8 Examples. Homogeneous singularities.- 9 Examples. Families associated with plane curve singularities.- 10 The Main Algorithm.- 11 Proof of the Main Algorithm.- 12 The Collapsing Main Algorithm.- 13 Vertical/horizontal monodromies.- 14 The algebraic monodromy of H1(¶ F). Starting point.- 15 The ranks of H1(¶ F) and H1(¶ F nVg) via plumbing.- 16 The characteristic polynomial of ¶ F via P# and P#.- 18 The mixed Hodge structure of H1(¶ F).- 19 Homogeneous singularities.- 20 Cylinders of plane curve singularities: f = f 0(x;y).- 21 Germs f of type z f 0(x;y).- 22 The T¤;¤;¤–fami-ly.- 23 Germs f of type ˜ f (xayb; z). Suspensions.- 24 Peculiar structures on ¶ F. Topics for future research.- 25 List of examples.- 26 List of notations

Fields of interestsSeveral Complex Variables and Analytic Spaces; Algebraic Geometry; Algebraic Topology



Due November 2011

2012. XII, 236 p. (Lecture Notes in Mathematics, Volume 2037) Softcover7 $59.95ISBN 978-3-642-23646-4

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A. Nepomnyashchy, I. Simanovskii, Technion - Israel Institute of Technology, Haifa, Israel; J. C. Legros, Universite Libre de Bruxelles, Belgium

Interfacial Convection in Multilayer SystemsThis book gives a systematic investigation of con-vection in systems comprised of liquid layers with deformatable interfaces. This new edition includes completely updated and new material on flows in ultra thin films and brings up to date progress made in the technology on micro and nano scales. Also, this revised edition will reflect progress in the dynamics of complex fluids.

Contents Introduction.- Types of convective instabilities in systems with an interface.- Benard problem in multilayer systems with undeformable interfaces.- Benard problem in multilayer systems with defor-mable interfaces.- Stability of flows.- Outlook.

Fields of interestsPartial Differential Equations; Fluid- and Aerody-namics; Theoretical, Mathematical and Computa-tional Physics



Due December 2011

2nd ed. 2012. 400 p. (Applied Mathematical Sciences, Volume 179) Hardcover7 $99.00ISBN 978-0-387-87713-6

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R. Peikert, ETH Zürich, Switzerland; H. Hauser, University of Bergen, Norway; H. Carr, University of Leeds, UK; R. Fuchs, ETH Zürich, Switzerland (Eds)

Topological Methods in Data Analysis and Visualization IITheory, Algorithms, and Applications

When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-au-tomatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in sub-jects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland.

Features 7 Latest, peer-reviewed results in a growing research area 7 Topic with close interaction of mathematics and computer science 7 Many applications to science and engineering

Contents Part I: Discrete Morse Theory.- Part II: Hierar-chical Methods for Extracting and Visualizing Topological Structures.- Part III: Visualization of Dynamical Systems, Vector and Tensor Fields.- Part IV: Topological Visualization of Unsteady Flow.

Fields of interestsVisualization; Algorithms; Computing Methodo-logies



Due November 2011

2012. X, 260 p. 130 illus., 125 in color. (Mathematics and Visualization) Hardcover7 $124.00ISBN 978-3-642-23174-2

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144

C. Perna, M. Sibillo, University of Salerno, Italy (Eds)

Mathematical and Statistical Methods for Actuarial Sciences and FinanceThe book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to this aim.

Features 7 The book is the result of the Mathematical and Statistical interdisciplinary approach to the researches in the actuarial and financial to-pics 7 The book aims at providing state of the art research in development, implementation and real world applications of statistical and mathematical models in actuarial and finance sciences 7 The book offers the occasion for discussing problems of national and international interest

Contents On the estimation in continuous limit of GARCH processes by G. Albano, F. Giordano, and C. Perna. - Variable selection in forecasting models for default risk by A. Amendola, M. Restaino, and L. Sensini. - Capital structure with firm’s net cash payouts by F. Barsotti, M.E. Mancino, and M. Pon-tier. - Convex ordering of Esscher and minimal entropy martingale measures for discrete time models by F. Bellini and C. Sgarra. - On hyperbolic iterated distortions for the adjustment of survival functions by A. Bienvenue and D. Rullière. - Bey-ond Basel2: Modeling loss given default through survival analysis by S. Bonini and G. Caivano.

Fields of interestsQuantitative Finance; Statistics, general; Business/Management Science, general



Due September 2011

2011. XII, 408 p. 99 illus., 1 in color. Hardcover7 approx. $149.00ISBN 978-88-470-2341-3

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O. Post, Humboldt University, Berlin, Germany

Spectral Analysis on Graph-Like SpacesSmall-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures („graph-like spaces‘‘), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm con-vergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abs-tract definition of resonances via boundary triples.

Features 7 A thorough analysis of quantum graphs and their approximations (graph-like spaces) 7 A self-contained explanation of the tools needed (convergence of operators in different spaces, boundary triples) 7 The book is accessible for a graduate student with some knowledge in functio-nal analysis and operators on Hilbert spaces

Contents 1 Introduction.- 2 Graphs and associated Lapla-cians.- 3 Scales of Hilbert space and boundary triples.- 4 Two operators in different Hilbert spaces.- 5 Manifolds, tubular neighbourhoods and their perturbations.- 6 Plumber’s shop: Estima-tes for star graphs and related spaces.- 7 Global convergence results.

Fields of interestsAnalysis; Functional Analysis; Operator Theory



Due November 2011

2012. X, 416 p. 29 illus. (Lecture Notes in Mathematics, Volume 2039) Softcover7 $89.95ISBN 978-3-642-23839-0

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B. Prakasa Rao, University of Hyderabad, India

Associated Sequences, Demimartingales and Nonparametric InferenceThis book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demi-martingales and related processes. Probabilistic properties of associated sequences, demimartinga-les and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.

Features 7 Comprehensive survey of probabilistic properties of associated sequences 7 Extensive discussion on demimartingales and related proces-ses 7 First book to deal with inferential aspects of such processes

Contents Preface.- Associated Random Variables and Related Concepts.- Demimartingales.- N-De-mimartingales.- Conditional Demimartingales.- Multidimensionally Indexed Demimartingales and Continuous Parameter Demimartingales.- Limit Theorems for Associated Random Varia-bles.- Nonparametric Estimation for Associated Sequences.- Nonparametric Tests for Associated Sequences.- Nonparametric Tests for Change in Marginal Density Function for Associated Sequen-ces.- References.- Index.

Fields of interestProbability Theory and Stochastic Processes



Due December 2011

2012. 300 p. (Probability and its Applications, Volume) Hardcover7 approx. $124.00ISBN 978-3-0348-0239-0

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145

H. Riesel, The Royal Institute of Technology, Stockholm, Sweden

Prime Numbers and Computer Methods for FactorizationFrom the original hard cover edition: In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A ma-jor component of this system is the factorization of large numbers into their primes.

Features 7 Affordable reprint of the successful, expanded second edition of a unique monograph 7 Provi-des a unique perspective on the study of prime numbers and their importance in modern techno-logy 7 Applications remain relevant across the fields of modern computer science and informati-on transmission

Contents Preface.- The Number of Primes Below a Given Limit.- The Primes Viewed at Large.- Subtleties in the Distribution of Primes.- The Recognition of Primes.- Classical Methods of Factorization.- Modern Factorization Methods.- Prime Numbers and Cryptography.- Appendix 1. Basic Concepts in Higher Algebra.- Appendix 2. Basic concepts in Higher Arithmetic.- Appendix 3. Quadratic Resi-dues.- Appendix 4. The Arithmetic of Quadratic Fields.- Appendix 5. Higher Algebraic Number Fields.- Appendix 6. Algebraic Factors.- Appendix 7. Elliptic Curves.- Appendix 8. Continued Frac-tions.- Appendix 9. Multiple-Precision Arithme-tic.- Appendix 10. Fast Multiplication of Large Integers.- Appendix 11. The Stieltjes Integral.- Ta-bles.- List of Textbooks.- Index.

Fields of interestsNumber Theory; Data Encryption; Algorithms



Due December 2011

2nd Edition. 2012. XVI, 464 p. 8 illus. (Modern Birkhäuser Classics) Softcover7 $74.95ISBN 978-0-8176-8297-2

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R. Z. Ríos-Mercado, Y. A. Ríos-Solís, Universidad Autónoma de Nuevo León, San Nicolas de los Garza, NL, Mexico (Eds)

Just-in-Time SystemsContents Part I Just-in-Time Scheduling Systems. -1 Sche-duling to Maximize the Number of Just-in-Time Jobs: A Survey. Dvir Shabtay and George Steiner. -2 An Exact Algorithm for the Single-Machine Earliness-Tardiness Scheduling Problem. Shunji Tanaka. -3 Single-machine Scheduling Problems Simultaneous with Deteriorating and Learning Effects under a Deteriorating Maintenance Consideration. Suh-Jenq Yang and Dar-Li Yang. -4 Scheduling Unrelated Parallel Machines with Sequence Dependent Setup Times and Weighted Earliness-Tardiness Minimization. Eva Vallada and Rubén Ruiz. -5 Mixed-Integer Program-ming Models for Flowshop Scheduling Problems Minimizing the Total Earliness and Tardiness. Débora P. Ronconi and Ernesto G. Birgin. -6 Just-in-Time Scheduling with Equal-Size Jobs. Ameur Soukhal and Nguyen Huynh Toung. -7 No-Wait Scheduling Problems with Batching Machines. A. Oulamara. -Part II Just-in-Time Philosophy: Interaction with Other Areas. -8 Just-in-Time Scheduling in Modern Mass Production Envi-ronment. Joanna Józefowska. -9 Just-in-Time Planning and Lot-Sizing. Nabil Absi, Stéphane Dauzère-Pérès and Safia Kedad-Sidhoum. -10 Strategic Scheduling Games: Equilibria and Effici-ency. -Laurent Gourvès, Jérôme Monnot, and Orestis A. Telelis. -11 Artificial Neural Networks-Based Forecasting: An Attractive Option for Just-in-Time Systems. Mauricio Cabrera-R´ıos, Mar´ıa Angélica Salazar-Aguilar, Mar´ıa Guada-lupe Villarreal-Marroqu´ın, and A´ ngela Patricia Anaya Salazar. [...]

Fields of interestsOperations Research, Management Science; Ma-thematical Modeling and Industrial Mathematics; Optimization



Due December 2011

2011. XVI, 335 p. 78 illus., 26 in color. (Springer Optimization and Its Applications, Volume 60) Hardcover7 $149.00ISBN 978-1-4614-1122-2

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R. Rosen

Anticipatory SystemsPhilosophical, Mathematical, and Methodological Foundations: J. Rosen, New York, NY, USA; J. J. Kineman, Boulder, CO, USA; M. Nadin, University of Texas, Dallas, TX, USA

Robert Rosen was not only a biologist, he was also a brilliant mathematician whose extraordi-nary contributions to theoretical biology were tremendous. Founding, with this book, the area of Anticipatory Systems Theory is a remarkable outcome of his work in theoretical biology. This second edition of his book Anticipatory Sys-tems, has been carefully revised and edited, and includes an Introduction by Judith Rosen. It has also been expanded with a set of Prolegomena by Dr. Mihai Nadin, who offers an historical survey of this fast growing field since the original work was published. There is also some exciting new work, in the form of an additional chapter on the Ontology of Anticipation, by Dr. John Kineman.

Features 7 The only book on anticipatory sys-tems 7 Written by an expert 7 Carefully revised and edited second edition, including an introduction which places the work in perspective with the current status of the field

Contents Foreword.- Preface.- Introduction.- Preliminari-es.- Natural and Formal Systems.- The Modelling Relation.- The Encodings of Time.- Open Systems and the Modelling Relation.- Anticipatory Sys-tems.- Appendix.- Addendum: Autobiographical Reminiscences.- Index.

Fields of interestsMathematical and Computational Biology; Sys-tems Biology; Systems Theory, Control



Due December 2011

2nd ed. 2011. XIV, 530 p. 49 illus. (IFSR International Series on Systems Science and Engineering, Volume 28) Hardcover7 $124.00ISBN 978-1-4614-1268-7

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146

Z. Schuss, Tel Aviv University, Israel

Nonlinear Filtering and Optimal Phase TrackingThis book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory. The basis for this approach is the discrete numerical scheme used in Monte-Carlo simulations of stochastic differential equations and Wiener‘s associated path integral representation of the transition probability density. Furthermore, it presents analytical methods for constructing asymptotic approximations to their solution and for synthesizing asymptotically optimal filters. It also offers a new approach to the phase tracking problem, based on optimizing the mean time to loss of lock.

Features 7 Many exercises and examples included 7 Ba-lance between mathematical rigor and physical intuition 7 An analytical rather than measure-theoretical approach to the derivation and solution of the partial differential equations of nonlinear filltering theory

Contents Diffusion and Stochastic Differential Equa-tions.- Euler‘s Simulation Scheme and Wiener‘s Measure.- Nonlinear Filtering and Smoothing of Diffusions.- Small Noise Analysis of Zakai‘s Equation.- Loss of Lock in Phase Trackers.- Loss of Lock in RADAR and Synchronization.- Phase Tracking with Optimal Lock Time.- Bibliography.- Index

Fields of interestsProbability Theory and Stochastic Processes; Theoretical, Mathematical and Computational Physics; Partial Differential Equations



Due December 2011

2011. XVI, 259 p. 45 illus., 18 in color. (Applied Mathematical Sciences, Volume 180) Hardcover7 $74.95ISBN 978-1-4614-0486-6

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A. N. Sengupta, Louisiana State University, Baton Rouge, LA, USA

Representing Finite GroupsA Semisimple Introduction

This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Se-misimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules.

Features 7 Presents basics of representation theory of finite groups from the point of view of semisimple algebras and modules over them 7 Progres-ses systematically with a gentle and inviting pace 7 Exercises at the end of the chapter help reinforce the material

Contents Concepts and Constructs. -Basic Examples. - The Group Algebra. - More Group Algebra. - Simply Semisimple . -Representations of Sn. - Characters. - Induced Representations. - Commutant Duality. -Character Duality. -Representations of U(N). - PS: Algebra. -Bibliography.

Fields of interestsGroup Theory and Generalizations; Quantum Physics; Applications of Mathematics



Due December 2011

2012. XII, 366 p. 11 illus., 2 in color. Hardcover7 $74.95ISBN 978-1-4614-1230-4

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K. Tapp, Saint Joseph‘s University, Philadelphia, PA, USA

SymmetryA Mathematical Exploration

This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational num-bers, countable sets, permutations, and a proof of the Pythagorean Theorem.

Features 7 Symmetry is an ideal topic for a one semester math course for non-math majors 7 Includes many topics commonly found in sampler courses, but weaves these topics into a single compelling story about symmetry 7 Encourages effective analytical thinking and exposes non-math majors to elegant mathematical ideas 7 Contains excellent exercises for the intended audience; these exercises should help students attain good understanding of the main points 7 Hints of humor and easily accessible language coupled with a plethora of exercises provides the necessary motivation for a non-math major in a math-oriented class 7 Contains hundreds of beautiful illustrations

Contents Preface.- 1 Introduction to Symmetry.- 2 The Al-gebra of Symmetry.- 3 Isomorphism.- 4 The Clas-sification Theorems.- 5 Subgroups and Product Groups.- 6 Permutations.- 7 Symmetries of Solid Objects.- 8 The Five Platonic Solids.- 9 Symmetry and Optimization.- 10 What is a Number?.- 11 Cantor‘s Infinity.- 12 Euclidean Space.- 13 Sym-metry and Matrices.- Index

Fields of interestsMathematics, general; Geometry; Mathematics in the Humanities and Social Sciences

Target groupsLower undergraduate

Product CategoryUndergraduate textbook

Due December 2011

2012. XV, 199 p. 159 illus., 152 in color. Hardcover7 $49.95ISBN 978-1-4614-0298-5

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147

M. T. Thai, P. M. Pardalos, University of Florida, Gainesville, FL, USA (Eds)

Handbook of Optimization in Complex NetworksTheory and Applications

Contents Preface.- 1. Optimization in Designing Complex Communication Networks (F.S.H. Souza, G.R. Mateus, A.S. Cunha).- 2. Fitness-based Generative Models for Power-Law Networks (K. Nguyen, D.A. Tran).- 3. Double Pareto Lognormal Distributions in Complex Networks (Z. Fang, J. Wang, B. Liu, W. Gong).- 4. Laplacian Spectra and Synchronization Processes on Complex Networks (J. Chen, J. Lu, C. Zhan, G. Chen).- 5. Growing Networks driven by the Evolutionary Prisoner’s Dilemma Game (J. Poncela, J. Gomez-Gardenes, L.M. Floria, Y. Mo-reno).- 6. Defining and Discovering Communities in Social Networks (S. Kelley, M. Goldberg, M. Magdon-Ismail, K. Mertsalov, A. Wallace).- 7. Mo-dularity Maximization and Tree Clustering: Novel Ways to Determine Effective Geographic Borders (D. Grady, R. Brune, C. Thiemann, F. Theis, D. Brockmann).- 8. Emergence and Structure of Cy-bercommunities (M. Mitrovic, B. Tadic).- 9. k-core Organization in Complex Networks (G.J. Baxter, S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes).- 10. Hardness Complexity of Optimal Substructure Problems on Power-Law Graphs (Y. Shen, D.T. Nguyen, M. T. Thai).- 11. Path Problems in Com-plex Networks (P. Ghosh, A. Sen).- 12. Optimized Design of Large-scale Social Welfare Supporting Systems on Complex Networks (J. Janacek, L. Janosıkova, L. Buzna).- 13. Optimal Flows in Dy-namic Networks and Algorithms for Their Finding (M. Fonoberova).- 14. Some Distributed Approa-ches to the Service Facility Location Problem in Dynamic and Complex Networks (I. [...]

Fields of interestsOptimization; Computer Communication Net-works; Communications Engineering, Networks



Due November 2011

2011. XIV, 518 p. 214 illus., 141 in color. (Springer Optimization and Its Applications, Volume 57) Hardcover7 $179.00ISBN 978-1-4614-0753-9

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SpringerBriefs in OptimizationS. M. Robinson, P. M. Pardalos, M. T. Thai

SpringerBriefs present concise summaries of cutting-edge research and practical applica-tions across a wide spectrum of fields. Featuring compact volumes of 50 to 125 pages, the series covers a range of content from professional to academic. Briefs are characterized by fast, global electronic dissemination, standard publishing con-tracts, standardized manuscript preparation and formatting guidelines, and expedited production schedules.

Typical topics might include 7 A timely report of state-of-the art techniques 7 A bridge bet-ween new research results, as published in journal articles, and a contextual literature review 7 A snapshot of a hot or emerging topic 7 An in-depth case study 7 A presentation of core concepts that students must understand in order to make independent contributions

SpringerBriefs in Optimization show case algo-rithmic and theoretical techniques, case studies, and applications within the broad-based field of optimization. Manuscripts related to the ever-growing applications of optimization in applied mathematics, engineering, medicine, economics, and other applied sciences are encouraged.

M. T. Thai, University of Florida, Gainesville,FL, USA

Group Testing Theory in Network SecurityAn Advanced Solution

Features 7 Brand new solutions on several advanced net-works security problems, which may advance the research front on this area 7 New variants on the group testing theory, which enhance the research results in this field Great connection between mathematical approaches and practical applica-tions 7 Solutions are verified both in theoretical analysis and simulation results 7 Include a chap-ter discussing open problems and suggesting new solutions for various network security problems

Contents -1. Group Testing (Introduction, Basic Theory and Design, Applications in Network Security). -2.Size Constraint Group Testing and DoS Attacks (Overview, Network System Models, Size Con-straint Group Testing, Matrix Construction and Latency Analyses, Detection System Configurati-on, Experimental Analysis). -3. Interference Free Group Testing and Reactive Jamming Attacks (Overview, Problem Models and Preliminaries, Group Testing based Trigger Node Identification-Preprocessing, Identifying Trigger Nodes(ITN) Algorithm, Theoretical Analysis, Experimental Analysis). -4. Randomized Fault Tolerant Group Testing and Advanced Security (Advanced Attacker Model, Error-tolerant Randomized Non-Adaptive Group Testing, Clique-Independent Set, Advanced Trigger Node Identification, Advanced Solutions Toward Sophisticated Attack Models, Experimental Analysis). -5. Outlooks (General Detection Framework based on Group Testing, Size Constraint Group Testing, Jamming Attacks and Trigger Node Detection).-References. – Index.

Fields of interestsOptimization; Computer Communication Net-works; Industrial and Production Engineering


Product Category

Due October 2011

2011. VIII, 86 p. 23 illus., 15 in color. (SpringerBriefs in Optimization) Softcover7 $49.95ISBN 978-1-4614-0127-8

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148

R. Tobies

Iris RungeA Life at the Crossroads of Mathematics, Science and IndustryForeword by: H. Neunzert, Revised by: R. Tobies

Features 7 The book illuminates the beginnings of indus-trial mathematics and its international context, the history of the application of mathematical statistics, and the use of numerical and graphical methods in filament bulb and electron tube labo-ratories 7 Using many original sources, the book provides a comprehensive illustration of a woman scientist (the eldest daughter of the famous ma-thematician Carl Runge, and the sister-in-law of Richard Courant) who wrote her first publication as a student with the theoretical physicist Arnold Sommerfeld.

Contents Foreword.- Author’s Preface.- 1 Introduction.- 2 Formative Groups.- 3 Mathematics at The Osram and Telefunken Corporations.- 4 Interactions Bet-ween Science, Politics, And Society.- 5 Post-War Developments And Concluding Remarks.- Ap-pendix.- Bibliography.- Index of Names.

Fields of interestsHistory of Mathematical Sciences; History of Science



Due January 2012

2012. XVIII, 458 p. 16 illus. in color. (Science Networks. Historical Studies, Volume 43) Hardcover7 approx. $129.00ISBN 978-3-0348-0229-1

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G. F. Torres del Castillo, Ciudad Universitaria, Puebla de Zaragoza, Pue., México

Differentiable ManifoldsA Theoretical Physics Approach

This textbook explores the theory behind differen-tiable manifolds and investigates various physics applications along the way. Basic concepts, such as differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential forms, are briefly introduced in the first three chapters. Chapter 4 gives a concise introduction to differential geometry needed in subsequent chapters. Chapters 5 and 6 provide interesting applications to connections and Riemannian manifolds. Lie groups and Hamiltonian mecha-nics are closely examined in the last two chapters. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differen-tiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.

Features 7 Introduces differentiable manifolds using a theoretical physics approach; unique book in the literature 7 Provides a collection of exercises of varying degrees of difficulty 7 Includes applica-tions to differential geometry and general relativity

Contents Preface.-1 Manifolds.- 2 Lie Derivatives.- 3 Differential Forms.- 4 Integral Manifolds.- 5 Connections .- 6. Riemannian Manifolds.- 7 Lie Groups.- 8 Hamiltonian Classical Mechanics.- References.-Index.

Fields of interestsManifolds and Cell Complexes (incl. Diff.Topolo-gy); Mechanics; Mathematical Methods in Physics



Due December 2011

2012. VIII, 268 p. 20 illus. Hardcover7 $59.95ISBN 978-0-8176-8270-5

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K. Williams, Torino, Italy (Ed.)

Nexus Network Journal 13,1Architecture and Mathematics

Contents KIM WILLIAMS, JOÃO NUNO TAVARES and JOÃO PEDRO XAVIER. Nexus 2010: Relation-ships Between Architecture and Mathematics.- Letter from the Guest Editor.- LIONEL MARCH. Forty Years of Shape and Shape Grammars, 1971–2011 Shape and Shape Grammars.- GEOR-GE STINY. What Rule(s) Should I Use?.- SARA ELOY and JOSÉ PINTO DUARTE. A Transforma-tion Grammar for Housing Rehabilitation.- JOSÉ NUNO BEIRÃO, JOSÉ PINTO DUARTE and RUDI STOUFFS. Creating Specific Grammars with Generic Grammars: Towards Flexible Urban Design.- MINE ÖZKAR. Visual Schemas: Pragmatics of Design Learning in Foundations Studios.- M. PIEDADE FERREIRA, DUAR-TE CABRAL DE MELLO and JOSÉ PINTO DUARTE. The Grammar of Movement: A Step Towards a Corporeal Architecture.- ALEXAN-DRA PAIO and BENAMY TURKIENICZ. An Urban Grammar Study: A Geometric Method for Generating Planimetric Proportional and Symme-trical Systems.- MÁRIO KRÜGER, JOSÉ PINTO DUARTE and FILIPE COUTINHO. Decoding De re aedificatoria: Using Grammars to Trace Alberti’s Influence on Portuguese Classical Architecture.- ANDREW I-KANG LI. Computing Style.- DIRK HUYLEBROUCK, ANTONIA REDONDO BUI-TRAGO and ENCARNACIÓN REYES IGLESIAS. Octagonal Geometry of the Cimborio in Burgos Cathedral.- MARGARIDA TAVARES DA CON-CEIÇÃO. Translating Vitruvius and Measuring the Sky: On Pedro Nunes and Architecture.- ARTU-RO LYON and RODRIGO GARCIA. Interlocking, Ribbing and Folding: Explorations in Parametric Constructions. [...]

Fields of interestsMathematics, general; Architectural History and Theory



Available

2011. V, 150 p. (Nexus Network Journal, Volume 13,1) Softcover7 $109.00ISBN 978-3-0348-0159-1

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149

K. Williams (Ed.)

Nexus Network Journal 13,2Architecture and Mathematics

Contents KIM WILLIAMS. Letter from the Editor.- LINO CABEZAS. Ornamentation and Structure in the Representation of Renaissance Architecture in Spain.- CHRIS J. K. WILLIAMS. Patterns on a Surface: The Reconciliation of the Circle and the Square.- MARCO GIORGIO BEVILACQUA. Alexander Klein and the Existenzminimum : A ‘Scientific’ Approach to Design Techniques.- JOÃO PAULO CABELEIRA MARQUES COELHO. Inácio Vieira: Optics and Perspective as Instruments towards a Sensitive Space.- ELI-SEU GONÇALVES. The Octagon in the Houses of Orson Fowler.- TERESA MARAT-MENDES, MAFALDA TEIXEIRA DE SAMPAYO and DAVID M. S. RODRIGUES. Measuring Lisbon Patterns: Baixa from 1650 to 2010.- ANTÓNIO NUNES PEREIRA. Renaissance in Goa: Propor-tional Systems in Two Churches of the Sixteenth Century.- JONG-JIN PARK. Dynamics of Urban Centre and Concepts of Symmetry: Centroid and Weighted Mean.- VASCO ZARA. From Quantitative to Qualitative Architecture in the Sixteenth and Seventeenth Centuries: A New Musical Perspective.- LONE MOGENSEN. Ma-king a Difference.- MICHAEL J. OSTWALD. The Mathematics of Spatial Configuration: Revisiting, Revising and Critiquing Justified Plan Graph The-ory.- BERNARD PARZYSZ. From One Polygon to Another: A Distinctive Feature of Some Otto-man Minarets.- RACHEL FLETCHER. Thomas Jefferson’s Poplar Forest.- SYLVIE DUVERNOY. Review of The Mathematical Works of Leon Bat-tista Alberti by Kim Williams, Lionel March and Stephen R. Wassell (eds.).

Fields of interestsMathematics, general; Architectural History and Theory



Available

2011. IV, 150 p. 160 illus. (Nexus Network Journal, Volume 13,2) Softcover7 $109.00ISBN 978-3-0348-0170-6

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Static & Dynamic Game Theory: Foundations & ApplicationsT. Başar

Static & Dynamic Game Theory: Foundations & Applications aims to publish top quality state-of-the-art textbooks and research monographs at the graduate and post-graduate levels in game theory and its applications in a variety of fields, including biology, communications, computer and com-putational science, ecology, economics, environ-mental science, engineering, management science, networks, operations research, political science, security, and the social sciences. The scope of the series includes both cooperative and non-coope-rative games; static, repeated, and dynamic games, defined in discrete time as well as in continuous time (so-called differential games); determinis-tic as well as stochastic games (such as Markov games); and complete or incomplete information games. The series will also include titles that study learning, evolution, and asymptotics in high player population regimes such as mean-field analysis.

The series will appeal to a broad interdisciplinary readership of mathematically-oriented engineers, physical and social scientists, computer and com-putational scientists, and economists, as well as to mathematicians at the graduate and post-graduate levels. Students and researchers in these fields will benefit from the comprehensive treatment of topical areas, groundbreaking theoretical explora-tion and development of computational tools, and applications covering the entire interdisciplinary spectrum where multi-agent decision-making is at the forefront.

D. W. Yeung, Hong Kong Shue Yan University, China; L. A. Petrosyan, Saint Petersburg State University, Russia

Subgame Consistent Economic OptimizationAn Advanced Cooperative Dynamic Game Analysis

Features 7 The first title on the topic of subgame con-sistent economic optimization 7 Illustrates the potential of cooperative dynamic games to help formulate new policy on previously unsol-vable market problems 7 Valuable as both a re-search reference and as a textbook, with exercises included throughout the book 7 Suitable for an interdisciplinary audience of game theorists, economists, mathematicians, policy makers, and corporate planners

Contents Preface.- Introduction.- 1 Dynamic Strategic Interactions in Economic System.- 2 Dynamic Economic Optimization: Group Optimality and Individual Rationality.- 3 Time Consistency and Optimal-Trajectory-Subgame Consistent Econo-mic Optimization.- 4 Dynamically Stable Cost-sa-ving Joint Venture.- 5 Collaborative Environmen-tal Management.- 6 Dynamically Stable Dormant Firm Cartel.- 7 Subgame Consistent Economic Optimization Under Uncertainty.- 8 Cost-saving Joint Venture Under Uncertainty.- 9 Collaborative Environmental Management Under Uncertainty.- 10 Subgame Consistent Dormant Firm Cartel.- 11 Dynamic Consistency in Discrete-time Coopera-tive Games.- 12 Discrete-time Cooperative Games Under Uncertainty.- Technical Appendices.- Refe-rences.- Index.

Fields of interestsGame Theory, Economics, Social and Behav. Sciences; Game Theory/Mathematical Methods; Optimization



Due December 2011

2012. XIV, 370 p. 2 illus. (Static & Dynamic Game Theory: Foundations & Applications) Hardcover7 $74.95ISBN 978-0-8176-8261-3

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150

C. Woodford, C. Phillips, University of Newcastle upon Tyne, UK

Numerical Methods with Worked Examples: Matlab EditionThis book is for students following an introduc-tory course in numerical methods, numerical techniques or numerical analysis. It introduces MATLAB as a computing environment for experi-menting with numerical methods.

Features 7 In this book numerical methods are presen-ted in problem – solution – discussion order so that underlying theory is inferred naturally from experiment and experience 7 Teaching approach allows for learning the theory by using the methods 7 Accessible to a broad, non-specialist readership 7 Fully documented MATLAB code freely downloadable from extras springer.com 7 The book aims to encourage the reader to begin programming as quickly as possib-le. 7 Exercises with answers, complete programs and sample codes are provided throughout the book 7 As Matlab dependent material is separa-ted from the main text, the book may be used in conjunction with any programming system

Contents 1. Basic Matlab. - 2. Linear Equations.- 3. Non-linear Equations.- 4. Curve Fitting.- 5. Numerical Integration.- 6. Numerical Differentiation.- 7. Li-near Programming.- 8. Optimization.- 9. Ordi-nary Differential Equations.- 10. Eigenvalues and Eigenvectors.- 11. Statistics.

Fields of interestsApplications of Mathematics; Appl.Mathematics/Computational Methods of Engineering; Compu-ter Applications in Chemistry

Target groupsUpper undergraduate

Product CategoryUndergraduate textbook

Due October 2011

2nd Edition. 2012. VIII, 232 p. 32 illus. With online files/update. Hardcover7 $59.95ISBN 978-94-007-1365-9

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Z. Yosibash, Ben-Gurion University, Beer-Sheva, Israel

Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation

Features 7 Many solved example problems 7 Explicit mathematical expressions 7 Solutions to selected exercises in the book

Contents Preface.- Introduction.-An Introduction to the p- and hp-versions of the Finite Element Method.-Eigen-pairs Computation for Two-Dimensional Heat Conduction Singularities.-Computation of GFIFs for Two-Dimensional Heat Conduction Problems.-Eigen-pairs for two-dimensional elasticity.-Computing Generalized Stress Intensity Factors.-Thermal Generalized Stress Intensity Fac-tors in 2-D Domains.-Failure Criteria for Brittle Elastic Materials.-Thermo-Mechanical Failure Cri-terion at the Micron Scale in Electronic Devices.-Singular solutions of the heat conduction equation in polyhedra domains.-Computation of the Edge Flux Intensity Functions associated with polyhe-dra domains.-Vertex singularities associated with conical points for the 3-D Laplace equation.-Edge eigen-pairs and ESIFs of 3-D elastic problems.-Summary and Open Questions.

Fields of interestsComputational Mathematics and Numerical Analysis; Theoretical and Applied Mechanics; Appl.Mathematics/Computational Methods of Engineering



Due December 2011

2012. XX, 446 p. 202 illus., 79 in color. (Interdisciplinary Applied Mathematics, Volume 37) Hardcover7 $124.00ISBN 978-1-4614-1507-7

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F. Zhang, Nova Southeastern University, Fort Lauderdale, FL, USA

Matrix TheoryBasic Results and Techniques

The aim of this book is to concisely present fun-damental ideas, results, and techniques in linear algebra and mainly matrix theory. The book con-tains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and repre-sentative, followed by carefully selected problems.

Features 7 Updated and revised edition 7 Includes a new chapter on matrix inequalities, and a new chapter with updated material on numerical ranges and radii and matrix norms 7 Includes more than 1000 exercises 7 Aids the reader in mastering basic matrix results and techniques that are useful for applications in various fields such as mathematics, statistics, physics, computer science, and engineering

Contents Preface to the Second Edition.- Preface.- Fre-quently Used Notation and Terminology.- Fre-quently Used Terms.- 1 Elementary Linear Alge-bra Review.- 2 Partitioned Matrices, Rank, and Eigenvalues.- 3 Matrix Polynomials and Canonical Forms.- 4 Numerical Ranges, Matrix Norms, and Special Operations.- 5 Special Types of Matrices.- 6 Unitary Matrices and Contractions.- 7 Positive Semidefinite Matrices.- 8 Hermitian Matrices.- 9 Normal Matrices.- 10 Majorization and Matrix Inequalities.- References.- Notation.- Index.

Fields of interestsLinear and Multilinear Algebras, Matrix Theory; Operator Theory



Due October 2011

2nd Edition. 2011. XVII, 399 p. 8 illus., 1 in color. (Universitext) Softcover7 $74.95ISBN 978-1-4614-1098-0

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