springer.de/buchhandel Springer News 11/12/2007 Mathematik 39
R. P. Agarwal, Florida Institute of Technology, L. Ambrosio, L. Caffarelli, M. G. Crandall, L. C. Evans, C. Bardos, Université Denis Diderot, Paris, France; Melbourne, FL, USA; D. O‘Regan, National University N. FuscoB. Dacorogna, P. Marcellini (Eds.) A. Fursikov, Moscow State University, Institute of of Ireland, Galway, Ireland Numerical Mathematics RAS (Eds.) Calculus of Variations and An Introduction to Ordinary Non-Linear Partial Differential Instability in Models Differential Equations Equations Connected with Fluid Flows I Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005 Ordinary differential equations serve as mathemat- The notions of stability and instability play a very ical models for many exciting real world problems. With contributions by: E. Mascolo important role in mathematical physics and, in Rapid growth in the theory and applications of particular, in mathematical models of fluids flows. differential equations has resulted in a continued Currently, one of the most important roblems in interest in their study by students in many disci- This volume provides the texts of lectures given by this area is to describe different kinds of instability, plines. L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, to understand their nature, and also to work out Key Features of this textbook: Organizes material N. Fusco at the Summer course held in Cetraro methods for recognizing whether a mathematical around theorems and proofs; Comprises of 42 (Italy) in 2005. These are introductory reports on model is stable or instable. In the current volume, class-tested lectures that effectively convey the current research by world leaders in the fields of Claude Bardos and Andrei Fursikov, have drawn subject in easily manageable sections; presentation calculus of variations and partial differential equa- together an impressive array of international is driven by detailed examples that illustrate how tions. The topics discussed are transport equations contributors to present important recent results the subject works; includes numerous exercise for non smooth vector fields, homogenization, and perspectives in this area. The main topics sets, with an “answers and hints” section; provides viscosity methods for the infinite Laplacian, weak covered are devoted to mathematical aspects of the a background and history of the subject through KAM theory and geometrical aspects of symmetri- theory but some novel schemes used in applied interesting preliminary lectures; the rich array zation. Besides there is also an historical overview mathematics are also presented. of topics allows for flexibility in developing the of all CIME courses on the calculus of variations subject beyond the basics. and partial differential equations contributed by Features Elvira Mascolo. 7 A unique collection of papers of leading From the contents specialists presenting the very recent results and Solvable Differential Equations.- Second Order Contents advantages in the main directions of stability Differential Equations.- Preliminaries to Series Preface by Bernard Dacorogna and Paolo theory in connection with fluid flows Solutions.- Solution at an Ordinary Point.- Solu- Marcellini.- Luigi Ambrosio: Transport Equation tion at a Singular Point.- Solution at a Singular and Cauchy Problem for Non-Smooth Vector Contents Point (Contd.).- Legendre Polynomials and Fields.- Luis Caffarelli and Luis Silvestre: Issues in Preface, Claude Bardos and Andrei Fursikov.- Functions.- Chebyshev, Hermite and Laguerre Homogenization for Problems with non Diver- Solid Controllability in Fluid Dynamics, Andrey Polynomials.- Bessel Functions.- Hypergeometric gence Structure.- Michael G. Crandall: A Visit with Agrachev and Andrey Sarychev.- Analyticity of Functions.- Piecewise Continuous and Periodic the 8-Laplace Equation.- Lawrence C. Evans: Weak Periodic Solutions of the 2D Boussinesq System, Functions.- Orthogonal Functions and Polyno- KAM Theory and Partial Differential Equations.- Maxim Arnold.- Nonlinear Dynamics of a System mials.- Orthogonal Functions and Polynomials Nicola Fusco: Geometrical Aspects of Symmetriza- of Particle-Like Wavepackets, Anatoli Babin and (contd.).- Boundary Value Problems.- Boundary tion.- Elvira Mascolo: CIME Courses on Partial Aleksander Figotin.- Attractors for Nonautono- Value Problems (contd.).- Green’s Functions.- Differential Equations and Calculus of Variations. mous Navier–Stokes System and Other Partial Regular Perturbations.- Singular Perturba- Differential Equations, Vladimir Chepyzhov and tions.- Sturm-Liouville Problems.- Eigenfunction Fields of interest Mark Vishik.- Recent Results in Large Amplitude Expansions.- Eigenfunction Expansions (contd.).- Calculus of Variations and Optimal Control; Opti- Monophase Nonlinear Geometric Optics, Chris- Convergence of the Fourier Series.- Convergence mization; Partial Differential Equations tophe Cheverry. of the Fourier Series (contd.).- Fourier Series Solutions of Ordinary Differential Equations.- Target groups Fields of interest Partial Differential Equations.- First Order Partial Researchers and graduate students Analysis; Calculus of Variations and Optimal Differential Equations. Control; Optimization; Computational Math- Type of publication ematics and Numerical Analysis Fields of interest Collection of essays Ordinary Differential Equations; Partial Differen- Target groups tial Equations; Appl. Mathematics/Computational Researches, specialists in calculus, mathematical Methods of Engineering analysis, theory of PDEs, optimal control, fluid mechanics, theoretical physics, computational Target groups mathematics, and also related disciplines Senior undergraduates, graduate students, math- ematicians Type of publication Contributed volume Type of publication Graduate/Advanced undergraduate textbook Due December 2007 Due February 2008 Due January 2008 2008. XII, 202 p. (Lecture Notes in Mathematics / 2008. Approx. 400 p. (International Mathematical Series, 2008. Approx. 335 p. 8 illus. (Universitext) Softcover Fondazione C.I.M.E., Firenze, Volume 1927) Softcover Volume 6) Hardcover 7 approx. * € (D) 49,43 | € (A) 50,82 | sFr 80,50 7 approx. * € (D) 42,75 | € (A) 43,95 | sFr 70,00 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 9
C. Bardos, Université Denis Diderot, Paris, France; C. Bardos, Université Denis Diderot, Paris, France; S. Benzoni-Gavage, Université Claude Bernard Lyon A. Fursikov, Moscow State University, Institute of A. Fursikov, Moscow State University, Institute of I, France; D. Serre, Ecole Normale Supérieure, Lyon, Numerical Mathematics RAS (Eds.) Numerical Mathematics RAS (Eds.) France (Eds.) Instability in Models Instability in Models Hyperbolic Problems: Theory, Connected with Fluid Flows II Connected with Fluid Flows Numerics, Applications Set Proceedings of the XIth International Conference on Hyperbolic Problems held Stability is a very important property of math- in Ecole Normale Supérieure, Lyon, ematical models simulating physical processes The advantages of the study of the stability and July 17-21, 2006 which provides an adequate description of the instability of models in fluid mechanics are process. Starting from the classical notion of the presented by world-recognized specialists in math- well-posedness in the Hadamard sense, this notion ematical analysis, PDEs, optimal control, etc. was adapted to different areas of research and at The two volumes are available separately, or This volume contains papers that were presented at present is understood, depending on the physical together at a reduced price for the two-volume HYP2006, the eleventh international Conference problem under consideration, as the Lyapunov set. See the entries for the individual volumes for on Hyperbolic Problems: Theory, Numerics and stability of stationary solutions, stability of speci- details of the coverage of each volume. Applications held at the Ecole Normale Supérieure fied initial data, stability of averaged models, etc. de Lyon, France, July 17-21, 2006. This biennial The stability property is of great interest for Features series of conferences has become one of the most researchers in many fields such as mathematical 7 A unique collection of papers of leading important international events in Applied Math- analysis, theory of partial differential equa- specialists presenting the very recent results and ematics. As computers became more and more tions, optimal control, numerical analysis, fluid advantages in the main directions of stability powerful, the interplay between theory, model- mechanics, etc. theory in connection with fluid flows ling, and numerical algorithms gained consider- able impact, and the scope of HYP conferences Features From the contents expanded accordingly. The field is currently in 7 A unique collection of papers of leading Key chapters from Vol I and II (see the entries for interaction with a variety of scientific domains, specialists presenting the very recent results and each volume for the full contents lists): On Aspects including fluid dynamics, physics, electromagne- advantages in the main directions of stability of Control Theory and Instability, A. Agrachev.- tism, chemistry, biology, road and network traffic, theory in connection with fluid flows On Hamiltonian Systems, S. B. Kuksin.- Well- and engineering. Many of these papers present new posedness of Mathematical Models of Mechanics effective numerical methods and their application From the contents and Thermodynamics, E. Radkevich.- Dynamical in various contexts. Justifying Asymptotics for 3D Water–Waves, David Approach for Elliptic Systems, S. Zelik.- Dynamic Lannes.- Generalized Solutions of the Cauchy and Control Systems, Armen Shirikyan.- Linear- Fields of interest Problem for a Transport Equation with Discon- ization method in Hydrodynamical Stability Computational Mathematics and Numerical tinuous Coefficients, Evgenii Panov.- Irreducible Theory, V. Yudovich.- Fluid flow in a very Analysis; Numerical Analysis; Partial Differential Chapman–Enskog Projections and Navier–Stokes Non-Homogeneous Porous Medium, Aleksandr Equations Approximations, Evgenii Radkevich.- Exponen- Shnirelman.- An Eulerian-Lagrangian Approach tial Mixing for Randomly Forced Partial Differ- for Incompressible Fluids, P. Constantin.- On Target groups ential Equations: Method of Coupling, Armen new models in thermodynamics, S.K.Godunov.- Researchers and graduate students Shirikyan.- On Problem of Stability of Equilibrium Global steady-state controllability, Jean-Michel Figures of Uniformly Rotating Viscous Incom- Coron.- Models for Spin Glasses, Michel Talga- Type of publication pressible Liquid, Vsevolod Solonnikov. rand.- Wavelets and turbulence, Vale’rie Perrier.- Proceedings Some methods for solving evolution problems in Fields of interest mathematical physics, A. Zlotnik. Analysis; Calculus of Variations and Optimal Control; Optimization; Computational Math- Fields of interest ematics and Numerical Analysis Analysis; Calculus of Variations and Optimal Control; Optimization; Computational Math- Target groups ematics and Numerical Analysis Researches, specialists in calculus, mathematical analysis, theory of PDEs, optimal control, fluid Target groups mechanics, theoretical physics, computational Researches, specialists in calculus, mathematical mathematics, and also related disciplines analysis, theory of PDEs, optimal control, fluid mechanics, theoretical physics, computational Type of publication mathematics, and also related disciplines Contributed volume Type of publication Contributed volume
Due February 2008 Due February 2008 Due December 2007 2008. Approx. 400 p. (International Mathematical Series, 2008. Approx. 800 p. (International Mathematical Series, Volume 7) Hardcover Volume 6&7) 2008. Approx. 1010 p. Hardcover 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 7 * € (D) 123,00 | € (A) 126,45 | sFr 200,50 7 * € (D) 106,95 | € (A) 109,95 | sFr 174,00 9
F. Biagini, Y. Hu, B. Øksendal, T. Zhang E. Buzano, L. Rodino, Università di Torino, Italia Stochastic Calculus for New Series Global Pseudo-diff erential Fractional Brownian Motion Calculus on Euclidean Spaces and Applications Pseudo-diff erential Operators Th e book presents a global pseudo-diff erential Fractional Brownian motion (fBm) has been Series editor : M. Wong calculus in Euclidean spaces, which includes widely used to model a number of phenomena in SG as well as Shubin classes and their natural diverse fi elds from biology to fi nance. Th is huge generalizations containing Schroedinger operators range of potential applications makes fBm an Pseudo-Diff erential Operators: Th eory, Applica- with non-polynomial potentials. Th is calculus is interesting object of study. Several approaches have tions and Related Areas is a series of moderately applied to study global hypoellipticity for several been used to develop the concept of stochastic priced graduate-level textbooks and monographs pseudo-diff erential operators, spectral properties calculus for fBm. Th e purpose of this book is to appealing to students and experts alike. Pseudo- and complex powers of hypoelliptic operators, present a comprehensive account of the diff erent diff erential operators are understood in a very Schatten-von Neumann classes, the Connes- defi nitions of stochastic integration for fBm, broad sense and include such topics as harmonic Wodzicki residue in Euclidean spaces, exponential and to give applications of the resulting theory. analysis, PDE, geometry, mathematical physics, decay of eigenfunctions, regularity and decay of Particular emphasis is placed on studying the rela- microlocal analysis, time-frequency analysis, homoclinics for semilinear equations, travelling tions between the diff erent approaches. Readers imaging and computations. Modern trends waves. are assumed to be familiar with probability theory and novel applications in mathematics, natural Th e book is completely self-contained and acces- and stochastic analysis, although the mathematical sciences, medicine, scientifi c computing, and sible to graduate students. techniques used in the book are thoroughly engineering are highlighted. exposed and some of the necessary prerequisites, Features such as classical white noise theory and fractional 7 Addresses global pseudo-diff erential calculus calculus, are recalled in the appendices. Th is book and hypoellipticity 7 Includes classic calculus will be a valuable reference for graduate students as a special case 7 Gives several applications to and researchers in mathematics, biology, meteo- global problems in Euclidean spaces, including rology, physics, engineering and fi nance. non-linear PDEs
Features Contents 7 Th e fi rst book to compare the diff erent Background Material.- Global Pseudo-diff erential frameworks and methods of stochastic integration Calculus.- Globally Hypoelliptic PDEs.- Spectral for fBm. It also discusses the applications of the Properties of Pseudo-diff erential Operators.- Other resulting theory. 7 Written by leading contribu- Applications.- Appendix.- Bibliography.- Index. tors to the fi eld. Fields of interest From the contents Partial Diff erential Equations; Global Analysis and Part I: Fractional Brownian Motion.- Intrinsic Analysis on Manifolds; Fourier Analysis properties of the fractional Brownian motion. Part II: Stochastic Calculus.- Wiener and divergence- Target groups type integrals for fractional Brownian motion.- Graduates, postgraduates, and researchers in PDEs Fractional Wick-Itô-Skorohod (fWIS-) integrals and mathematical physics for fractional Brownian motion of Hurst Index H > ½.- Wick-Itô-Skorohod integrals for fractional Type of publication Brownian motion.- Pathwise integrals for frac- Monograph tional Brownian motion.- A useful summary.
Fields of interest Probability Th eory and Stochastic Processes; Statistics for Business/Economics/Mathematical Finance/Insurance; Applications of Mathematics
Target groups Researchers and graduate students; probabilists working on Brownian motion
Type of publication Monograph
Due December 2007 Due May 2008
2008. Approx. 350 p. (Probability and its Applications) 2008. Approx. 350 p. (Pseudo-diff erential Operators, Hardcover Volume 1) Softcover 7 * € (D) 82,34 | € (A) 84,65 | sFr 134,00 7 approx. * € (D) 53,39 | € (A) 54,89 | sFr 89,90 ISBN 978-1-85233-996-8 ISBN 978-3-7643-8511-8 9
J. Brylinski, Pennsylvania State University M. Chang, U.S. Army Research Offi ce, Durham, NC, P. Chow, B. S. Mordukhovich, G. Yin (Eds.) USA Loop Spaces, Characteristic Topics in Stochastic Analysis Classes and Geometric Stochastic Control of and Nonparametric Quantization Hereditary Systems and Estimation Applications
Th is book deals with the diff erential geometry To assess the past achievement and to provide of manifolds, loop spaces, line bundles and Th is research monograph develops the Hamilton- a road map for future research, an IMA partici- groupoids, and the relations of this geometry to Jacobi-Bellman theory via dynamic programming pating institution conference entitled “Conference mathematical physics. principle for a class of optimal control problems on Asymptotic Analysis in Stochastic Processes, Various developments in mathematical physics for stochastic hereditary diff erential equations Nonparametric Estimation, and Related Problems” (e.g., in knot theory, gauge theory, and topological (SHDEs) driven by a standard Brownian motion was held at Wayne State University, September quantum fi eld theory) have led mathemati- and with a bounded or an infi nite but fading 15-17, 2006. Th is conference was also held to cians and physicists to search for new geometric memory. Th ese equations represent a class of honor Professor Rafail Z. Khasminskii for his structures on manifolds and to seek a synthesis stochastic infi nite-dimensional systems that fundamental contributions to many aspects of of ideas from geometry, topology and category become increasingly important and have wide stochastic processes and nonparametric estima- theory. In this spirit, this book develops the diff er- range of applications in physics, chemistry, biology, tion theory on the occasion of his seventy-fi ft h ential geometry associated to the topology and engineering and economics/fi nance. birthday. It assembled an impressive list of invited obstruction theory of certain fi ber bundles (more Th is monograph can be used as a research refer- speakers, who are renowned leaders in the fi elds of precisely, associated to grebes). Th e theory is a ence for researchers and advanced graduate probability theory, stochastic processes, stochastic 3-dimensional analog of the familiar Kostant-Weil students who have special interest in optimal diff erential equations, as well as in the nonpara- theory of line bundles. In particular the curvature control theory and applications of stochastic metric estimation theory, and related fi elds. now becomes a 3-form. hereditary systems. Contents Features Features Some recent results on averaging principle.- 7 Discusses open problems and further research 7 Very active research area 7 Chang bridges Cramer‘s theorem for nonnegative multivariate extensions 7 Written by a distinguished and well- area of stochastic control and stochastic delay point processes with independent increments.- published researcher in the fi eld 7 Includes many equations On bounded solutions of the balanced general- examples and fi gures ized pantograph equation.- Numerical methods Contents for non-zero-sum stochastic diff erential games: Contents Preface.- Introduction and Summary.- Chapter Convergance of the Markov chain approxima- Introduction.- Complexes of Sheaves and Th eir 1. Stochastic Hereditary Diff erential Equa- tion method.- On the estimation of an analytic Cohomology.- Line Bundles and Geometric tions.- Chapter 2. Stochastic Calculus.- Chapter 3. spectral density outside of the observation band.- Quantization.- Kähler Geometry of the Space Optimal Classical Control.- Chapter 4. Optimal On oracle inequalities related to high dimen- of Knots.- Degree 3 Cohomology: Th e Dixmier- Stopping.- Chapter 5. Discrete Approximations.- sional linear models.- Hypothesis testing under Douady Th eory.- Degree 3 Cohomology: Sheave of Chapter 6. Option Pricing.- Chapter 7. Hereditary composite functions alternative.- On parabolic Groupoids.- Line Bundles over Loop Spaces.- Th e Portfolio Optimization.- References.- List of pdes and spdes in Sobolov spaces W2/p without Dirac Monopole.- Bibliography.- List of Nota- Symbols.- Index. and with weights.- Stochastic parabolic equations tions.- Index. of full second order. Fields of interest Fields of interest Probability Th eory and Stochastic Processes; Fields of interest Diff erential Geometry; Topology; Category Th eory, Partial Diff erential Equations; Control Engineering Probability Th eory and Stochastic Processes; Homological Algebra Applications of Mathematics Target groups Target groups Graduate students, researchers Target groups Graduate students and researchers with an interest Researchers in topology, geometry, Lie algebra, and math- Type of publication ematical physics Monograph Type of publication Professional book Type of publication Graduate/Advanced undergraduate textbook
Due November 2007
Originally published as volume 107 in the series: Progress in Mathematics Due January 2008 Due November 2007
1st ed. 1993. 3rd printing 2008. XVIII, 300 p. 6 illus. 2008. Approx. 415 p. (Stochastic Modelling and Applied 2008. Approx. 210 p. (The IMA Volumes in Mathematics (Modern Birkhäuser Classics) Softcover Probability, Volume 59) Hardcover and its Applications, Volume 145) Hardcover 7 * € (D) 37,34 | € (A) 38,39 | sFr 59,90 7 * € (D) 67,36 | € (A) 69,25 | sFr 110,00 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 9
springer.de/buchhandel Springer News 11/12/2007 Mathematik 43
A. Dickenstein, F. Schreyer, A. J. Sommese (Eds.) Y. Dodge, Université Neuchâtel, Suisse S. Gabelli, Università „Roma Tre“, Roma, Italia Algorithms in Algebraic Mathématiques de base pour Teoria delle Equazioni e Teoria Geometry économistes di Galois
In the last decade, there has been a burgeoning Ce livre contient des éléments fondamentaux de L‘algebra è nata come lo studio della risolubilità of activity in the design and implementation of mathématiques comme les notions de logique, delle equazioni polinomiali e tale è essenzialmente algorithms for algebraic geometric compuation. les représentations graphiques des fonctions, les rimasta fino a quando, dopo secoli di tentativi Some of these algorithms were originally designed suites, les applications économiques des dérivées, falliti e successi parziali, nel 1830 Evariste Galois, for abstract algebraic geometry, but now are of les intégrales, les séries mathématiques, les fonc- matematico geniale dalla vita breve e avventurosa, interest for use in applications and some of these tions de plusieurs variables, l‘algèbre linéaire ainsi ha definitivamente risolto questo problema ed algorithms were originally designed for applica- qu‘un bref aperçu du logiciel Mathematica®. ha posto allo stesso tempo le basi per la nascita tions, but now are of interest for use in abstract Il est composé de trois parties, elles-mêmes divi- dell‘algebra moderna intesa come lo studio delle algebraic geometry. sées en douze chapitres. De nombreux exemples strutture algebriche. La Teoria di Galois clas- The workshop on Algorithms in Algebraic Geom- économiques sont présentés chaque fois que cela sica viene oggi insegnata a vari livelli nell‘ambito etry that was held in the framework of the IMA était possible. dei Corsi di Laurea in Matematica. Questo libro Annual Program Year in Applications of Algebraic Il est destiné aux étudiants de première année di testo è stato scritto per essere usato in modo Geometry by the Institute for Mathematics and en sciences économiques et sociales. Il peut être flessibile. La prima parte contiene le nozioni di Its Applications on September 18-22, 2006 at the considéré à la fois comme un point reliant les base della Teoria dei Campi e potrà essere utile University of Minnesota is one tangible indication différents types de diplômes d‘études secondaires anche a tutti gli studenti di Algebra, Geometria e of the interest. One hundred ten participants from supérieures mais aussi comme un lien entre les Teoria dei Numeri. Molto spazio è dedicato allo eleven countries and twenty states came to listen to cours élémentaires d‘économie et de statistique. studio delle equazioni polinomiali di grado basso the many talks; discuss mathematics; and pursue Il est accessible pour tous ceux qui ont peu de e alle equazioni ciclotomiche ed al problema collaborative work on the many faceted problems connaissances en mathématiques. della costruibilità con riga compasso delle figure and the algorithms, both symbolic and numberic, geometriche. that illuminate them. Contents Analyse: Prologue. Représentation graphique Fields of interest Contents des fonctions. Suites, limites et première dérivée. Algebra; Geometria; Teoria dei numeri Application of a numerical version of Terracini’s Applications des dérivées. Intégrales. Les séries. lemma for secants and joins.- On the sharpness of Fonctions de plusieurs variables.- Algèbre linéaire: Target groups fewnomial bounds and the number of components Calcul matriciel. Systèmes d‘équations linéaires. L‘opera è rivolta agli studenti del triennio dei corsi of fewnomial hypersurfaces.- Intersections of Vecteurs et espaces vectoriels. Approche matrici- di laurea in Matematica Schubert varieties and other permutation array elle du calcul différentiel.- Mathematica: Introduc- schemes.- Efficient inversion of rational maps over tion à Mathematica. Epilogue. Quelques corrigés Type of publication finite fields.- Higher-order deflation for polyno- d‘exercices. Libro di testo introduttivo mial systems with isolated singular solutions.- Polars of real singular plane curves.- Semidefinite Fields of interest representation of the k-ellipse.- Solving polyno- Mathématiques appliquées; Economie générale; mial systems equation by equation. Statistiques pour le commerce/Economie/Mathé- matiques Fields of interest Algebraic Geometry; Algorithms; Applications of Target groups Mathematics Étudiants de première année en sciences économiques; étudiants de première année en Target groups sciences sociales Researchers Type of publication Type of publication Monographie Professional book
Pubblicazione prevista per il mese di Due December 2007 dicembre 2007 A paraître novembre 2007 2008. XII, 164 p. (The IMA Volumes in Mathematics and 2008. XX, 200 pagg. (UNITEXT / La Matematica per il 3+2) its Applications, Volume 146) Hardcover 2008. Approx. 590 p. Broché Brossura 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 7 * € (D) 55,78 | € (A) 57,34 | sFr 91,00 7 approx. * € (D) 29,79 | € (A) 30,62 | sFr 48,50 9
S. G. Gal, University of Oradea, Romania B. Gustafsson, Uppsala University, Uppsala, Sweden R. J. Hosking, University Brunei Darussalam, Gadong, Brunei; E. Venturino, Università di Torino, Italia (Eds.) Shape-Preserving High Order Diff erence Approximation by Real and Methods for Time Dependent Aspects of Mathematical Complex Polynomials PDE Modelling Applications in Science, Medicine, Economics Consulting editor: G. A. Anastassiou and Management Th e subject of this book is high order fi nite diff er- ence methods for time dependent PDE. Th e idea Th is monograph presents the fi rst comprehen- is to give an overview of the basic theory and Th e construction of mathematical models is an sive treatment in book form of shape-preserving construction principles by using model examples. essential scientifi c activity. Mathematics has long approximation by real or complex polynomials Th e book also contains a general presentation of been associated with developments in the exact in one or several variables. Such approximation the techniques and results for well-posedness and sciences and engineering, but more recently math- methods are useful in many problems arising in stability, with inclusion of the three fundamental ematical modelling has been used to investigate science and engineering requiring an optimal methods of analysis both for PDE in its original complex systems that arise in many other fi elds. mathematical representation of physical reality. and discretized form: the Fourier transform, Th e contributors to this book demonstrate the Th ree diff erent constructive methods are applicable the eneregy method and the Laplace transform. application of mathematics to modern research to all four categories of shape-preserving approxi- Various types of wave propagation problems are topics in ecology and environmental science, mation by polynomials and thus serve as ‘red lines’ treated in specifi c detail since high order methods health and medicine, phylogenetics and neural for the book: Bernstein-type, Shisha-type, and are particularly eff ective for these problems. networks, theoretical chemistry, economics and convolution-type. management. Containing many open problems at the end of Fields of interest each chapter to spur future research as well as Computational Mathematics and Numerical Features a rich and updated bibliography surveying the Analysis; Partial Diff erential Equations 7 Provides examples of modern modelling appli- vast literature, the text will be useful to graduate cations 7 Unusual collection of contributions students and researchers interested in approxima- Target groups from less traditional fi elds tion theory, mathematical analysis, numerical Researchers and graduate students analysis, Computer Aided Geometric Design, From the contents robotics, data fi tting, chemistry, fl uid mechanics, Type of publication Mathematical Models of Pattern Formation and engineering. Monograph in Planktonic Predation-Diff usion Systems: A Review.- Toward a General Th eory of Ecosystem Features Stability: Plankton-Nutrient Interaction as a 7 First comprehensive treatment in book form Paradigm.- Nutrient, Non-Toxic Phytoplankton, of shape-preserving approximation by real or Toxic Phytoplankton and Zooplankton Interaction complex polynomials in one or several variables in an Open Marine System.- Stability and Optimal 7 Of interest to grad students and researchers Harvesting in a Stage Structure Predator-Prey in approximation theory, mathematical analysis, Switching Strategy.- Reducing the Emission of numerical analysis, Computer Aided Geometric Pollutants in Industrial Wastewater through the Design, robotics, data fi tting, chemistry, fl uid Use of Membrane Bioreactors.- Insecticidal Bt mechanics, and engineering 7 Contains many Crops under Massive Bt-resistant Pest Invasion: open problems to spur future research Mathematical Simulation.- Mathematical Model- ling and Simulation of Coronary Blood Flow.- Fields of interest Modelling Vaccine Protocols. Approximations and Expansions; Real Functions; Functions of a Complex Variable Fields of interest Mathematical Biology in General Target groups Graduate students and researchers in Approxima- Target groups tion Th eory, Mathematical Analysis, Numerical Researchers and postgraduate students interested Analysis, Computer Aided Geometric Design, in biomathematics Robotics, Data Fitting, Chemistry, Fluid Mechanics, and Engineering Type of publication Monograph Type of publication Monograph
Due December 2007 Due December 2007 Due April 2008 2008. Approx. 350 p. (Springer Series in Computational 2008. Approx. 325 p. 77 illus. (Mathematics and Biosci- 2008. Approx. 340 p. Hardcover Mathematics, Volume 38) Hardcover ences in Interaction) Hardcover 7 approx. * € (D) 81,59 | € (A) 83,88 | sFr 133,00 7 * € (D) 85,55 | € (A) 87,95 | sFr 139,50 7 * € (D) 138,03 | € (A) 141,90 | sFr 229,00 9
J. Jonsson, KTH Royal Institute of Technology, Stock- G. Kersting, A. Wakolbinger, Universität Frankfurt, D. Konaté, Virginia Tech, Blacksburg, VA, USA (Ed.) holm, Sweden Germany Mathematical Modeling, Simplicial Complexes of Stochastik Simulation, Visualization and Graphs Band 1: Eine Einführung e-Learning Proceedings of an International Workshop held at Rockefeller Foundation‘ s Bellagio A graph complex is a fi nite family of graphs closed In der modernen Stochastik werden Wahr- Conference Center, Milan, Italy, 2006 under deletion of edges. Graph complexes show up scheinlichkeiten immer im Zusammenhang mit naturally in many diff erent areas of mathematics, Zufallsvariablen gedacht. Damit macht dieses including commutative algebra, geometry, and Lehrbuch Ernst, schon die Welt uniform verteilter knot theory. Identifying each graph with its edge Zufallsgrößen wird dann farbig und reichhaltig. Th is book is a collection of articles written by some set, one may view a graph complex as a simplicial Das Konzept der Zufallsgrößen prägt den Aufb au of the most prominent leading applied mathemati- complex and hence interpret it as a geometric des auf zwei Bänden ausgelegten Textes. Der erste cians, as well as articles from young and prom- object. Th is volume examines topological proper- Band stellt diskrete Zufallsvariable in den Vorder- ising scientists from Africa, Asia and Europe. Th e ties of graph complexes, focusing on homotopy grund, bis zu zufälligen Pfaden und den Anfängen common objective of these articles is to present type and homology. der Markovketten. Kontinuierliche Zufallsvariable an important issue which is currently widely Many of the proofs are based on Robin Forman’s mit ihren Dichten werden in wichtigen Beispielen discussed in scientifi c investigation with major discrete version of Morse theory. As a byproduct, diskutiert. Je ein Kapitel ist Ideen der Statistik und human, economic or ecological implications. One this volume also provides a loosely defi ned toolbox der Informationstheorie gewidmet. Der zweite main feature of the series, which the current book for attacking problems in topological combi- Band vertieft zentrale Th emen in allgemeinerem exemplifi es, is that each article is as deep as an natorics via discrete Morse theory. In terms of Rahmen. Damit liefert das Buch Orientierung und expert lecture but is also self-contained, so that simplicity and power, arguably the most effi cient Material für verschiedene Varianten einfüh- even isolated scientists with limited resources can tool is Forman’s divide and conquer approach via render Lehrveranstaltungen, 2-stündig, oder in profi t greatly from it. Another feature of this book decision trees; it is successfully applied to a large Verbindung mit Band 2 auch 4-stündig. is that each article is meant to present a collection number of graph and digraph complexes. of open questions which can fuel undergraduate Pluspunkte or graduate research activities even in smaller or From the contents 7 Vermittelt solide mathematische Kenntnisse more isolated scientifi c communities. Part I Introduction and Basic Concepts: 1. Intro- und Fertigkeiten im Bereich der Stochastik duction and Overview.- 2. Abstract Graphs and 7 Anwendungsorientierte Herangehensweise Fields of interest Set Systems.- 3. Simplicial Topology.- Part II Tools: mit anschaulichem Material für Studenten und Computational Mathematics and Numerical 4. Discrete Morse Th eory.- 5. Decision Trees.- 6. Dozenten 7 Einsatz begleitend zur Vorlesung Analysis; Mathematical Modeling and Industrial Miscellaneous Results.- Part III Overview of Graph oder zusätzlich möglich Mathematics; Visualization Complexes: 7. Graph Properties.- 8. Dihedral Graph Properties.- 9. Digraph Properties.- 10. Inhalt Target groups Main Goals and Proof Techniques.- Part IV Vertex I. Zufallsvariable und Verteilungen.- II. Abhängige Research scientists, undergraduate and graduate Degree: 11. Matchings.- 12. Graphs of Bounded Zufallsvariable und bedingte Verteilungen.- III. students Degree.- Part V Cycles and Crossings: 13. Forests Ideen aus der Statistik.- IV. Ideen aus der Informa- and Matroids.- 14. Bipartite Graphs.- 15. Directed tionstheorie. Type of publication Variants of Forests and Bipartite Graphs.- 16. Proceedings Noncrossing Graphs.- 17. Non-Hamiltonian Fachgebiete Graphs.- Part VI Connectivity: 18. Disconnected Wahrscheinlichkeitstheorie und Stochastische Graphs.- 19. Not 2-connected Graphs.- 20. Not Prozesse 3-connected Graphs and Beyond. Zielgruppen Fields of interest Studenten und Dozenten der Bachelor- oder Combinatorics; Algebraic Topology; Order, Masterstudiengänge im Bereich Mathematik und Lattices, Ordered Algebraic Structures angrenzender Fachgebiete
Target groups Kategorie Researchers and graduate students Lehrbuch
Type of publication Monograph
Due November 2007 Erscheint April 2008 Due December 2007 2008. XIV, 378 p. (Lecture Notes in Mathematics, Volume 1928) Softcover 2008. Etwa 150 S. (Mathematik kompakt) Brosch. 2008. XVI, 380 p. Hardcover 7 * € (D) 53,45 | € (A) 54,95 | sFr 87,00 7 € (D) 18,90 | € (A) 19,43 | *sFr 29,90 7 * € (D) 74,85 | € (A) 76,95 | sFr 122,00 9
46 Mathematik Springer News 11/12/2007 springer.de/buchhandel
S. G. Krantz, Washington University, St. Louis, MO, U. Langer, M. Discacciati, D. Keyes, O. Widlund, H. P. Langtangen, Simula Research Laboratory, USA; H. Parks, Oregon State University, Corvallis, OR, W. Zulehner (Eds.) Lysaker, and University of Oslo, Norway USA Domain Decomposition Python Scripting for Geometric Integration Theory Methods in Science and Computational Science Engineering XVII
Th is textbook introduces geometric measure Th e goal of this book is to teach computational theory through the notion of currents. Currents, Th is volume contains a selection of papers scientists how to develop tailored, fl exible, and continuous linear functionals on spaces of diff er- presented at the 17th International Conference on human-effi cient working environments built from ential forms, are a natural language in which to Domain Decomposition Methods in Science and small programs (scripts) written in the easy-to- formulate types of extremal problems arising in Engineering held at St. Wolfgang / Strobl, Austria, learn, high-level language Python. Th e focus is on geometry, and can be used to study generalized July 3 - 7, 2006. Domain decomposition is an examples and applications of relevance to compu- versions of the Plateau problem and related ques- active, interdisciplinary research fi eld concerned tational scientists: gluing existing applications tions in geometric analysis. with the development, analysis, and implemen- and tools, e.g. for automating simulation, data Th e text provides considerable background for tation of coupling and decoupling strategies in analysis, and visualization; steering simulations the student and discusses techniques that are mathematical and computational models. Domain and computational experiments; equipping old applicable to complex geometry, partial diff er- decomposition methods provide effi cient tools for programs with graphical user interfaces; making ential equations, harmonic analysis, diff erential treating problems in all computational sciences. computational Web applications; and creating geometry, and many other parts of mathematics. Th e reader will become familiar with the newest interactive interfaces with a Maple/Matlab-like Topics include the deformation theorem, the area domain decomposition techniques and their use in syntax to numerical applications in C/C++ or and coareas formulas, the compactness theorem, the modelling and simulation of complex problems Fortran. In short, scripting with Python makes you the slicing theorem and applications to minimal from diff erent fi elds of application. much more productive, increases the reliability of surfaces. your scientifi c work and lets you have more fun Fields of interest - on Unix, Windows and Macintosh. All the tools Features Computational Mathematics and Numerical and examples in this book are open source codes. 7 Self-contained, inclusive, and accessible for Analysis; Scientifi c Computing; Numerical and both the graduate students and researchers Computational Methods Features 7 Motivates the key ideas with examples and 7 Shows how to develop tailored, fl exible, and fi gures 7 Includes considerable background Target groups human-effi cient working environments using material and complete proofs Computational scientists the easy-to-learn, high-level Python language 7 Focuses on examples and applications of Contents Type of publication practical use to computational scientists 7 Th e Preface.- Basics.- Carathéodory’s Construction and Proceedings third edition is compatible with the new NumPy Lower-Dimensional Measures.- Invariant Meaures implementation and features updated informa- and the Construction of Haar Meaure.- Covering tion, correction of errors, and improved associated Th eorems and the Diff erentiation of Integrals.- soft ware tools Analytical Tools: the Area Formula, the Coarea Formula, and Poincaré Inequalities.- Th e Calculus Fields of interest of Diff erential Forms and Stokes’s Th eorem.- Intro- Scientifi c Computing; Numerical and Computa- duction to Currents.- Currents and the Calculus tional Methods; Soft ware Engineering/Program- of Variations.- Regularity of Mass-Minimizing ming and Operating Systems Currents.- Appendix.- Bibliography.- Index of Notation.- Index. Target groups Undergraduate students in computer science, Fields of interest computational science and engineering; Measure and Integration; Integral Equations; Inte- researchers gral Transforms, Operational Calculus Type of publication Target groups Graduate/Advanced undergraduate textbook Graduate students and researchers interested in geometric measure theory
Type of publication Graduate/Advanced undergraduate textbook
Due December 2007 Due December 2007 Due April 2008 2008. Approx. 660 p. (Lecture Notes in Computational 3rd ed. 2008. Approx. 770 p. (Texts in Computational 2008. Approx. 380 p. 10 illus. (Cornerstones) Hardcover Science and Engineering, Volume 60) Softcover Science and Engineering, Volume 3) Hardcover 7 approx. * € (D) 57,67 | € (A) 59,29 | sFr 94,00 7 * € (D) 106,95 | € (A) 109,95 | sFr 174,00 7 * € (D) 53,45 | € (A) 54,95 | sFr 87,00 9
springer.de/buchhandel Springer News 11/12/2007 Mathematik 47
F. Lorenz, University of Muenster, Germany M. Manetti, Università La Sapienza, Roma, Italia Y. Manin, Max-Planck-Institut für Mathematik, Bonn, Germany; A. A. Panchishkin, Université Joseph Algebra Topologia Fourier, Saint Martin d‘Hères, France Volume II: Fields with Structure, Algebras and Introduction to Modern Advanced Topics Nato dall’esperienza dell’autore nell’insegnamento Number Theory Translated from the German by: S. Levy della topologia agli studenti del corso di Laurea Fundamental Problems, Ideas and Theories in Matematica, questo libro contiene le nozioni fondamentali di topologia generale ed una From Math Reviews: This is Volume II of a two- introduzione alla topologia algebrica. La scelta “Introduction to Modern Number Theory“ surveys volume introductory text in classical algebra. The degli argomenti, il loro ordine di presentazione e, from a unified point of view both the modern text moves carefully with many details so that soprattutto, il tipo di esposizione tiene conto delle state and the trends of continuing development of readers with some basic knowledge of algebra can tendenze attuali nell’insegnamento della topologia various branches of number theory. Motivated by read it without difficulty. The book can be recom- e delle novita’ nella struttura dei corsi di Laurea elementary problems, the central ideas of modern mended either as a textbook for some particular scientifici conseguenti all’introduzione del sistema theories are exposed. Some topics covered include algebraic topic or as a reference book for consulta- 3+2. Il libro contiene circa 400 esercizi, in parte non-Abelian generalizations of class field theory, tions in a selected fundamental branch of algebra. risolti. recursive computability and Diophantine equa- The book contains a wealth of material. Amongst tions, zeta- and L-functions. the topics covered in Volume II the reader can Fields of interest This substantially revised and expanded new find: the theory of ordered fields (e.g., with refor- Matematica, generale; Topologia; Topologia edition contains several new sections, such as mulation of the fundamental theorem of algebra algebrica Wiles’ proof of Fermat’s Last Theorem, and in terms of ordered fields, with Sylvester’s theorem relevant techniques coming from a synthesis of on the number of real roots), Nullstellen-theo- Target groups various theories. Moreover, the authors have added rems (e.g., with Artin’s solution of Hilbert’s 17th Studenti dei corsi di laurea in ingegneria, a part dedicated to arithmetical cohomology and problem and Dubois’ theorem), fundamentals of matematica, statistica noncommutative geometry, a report on point the theory of quadratic forms, of valuations, local counts on varieties with many rational points, the fields and modules. Type of publication recent polynomial time algorithm for primality Libro di testo introduttivo testing, and some others subjects Features 7 Nicely written comprehensive survey of clas- From the reviews of the 2nd edition 7 … For my sical algebra 7 Includes unique collection of part, I come to praise this fine volume. This book is topics 7 Author provides enough detail that the a highly instructive read … the quality, knowledge, only prerequisite is basic knowledge of algebra and expertise of the authors shines through. … The present volume is almost startlingly up-to-date ... Contents 7 A. van der Poorten, Gazette, Australian Math. Foreword.- Ordered fields and real fields.- Hilbert’s Soc. 34 (1), 2007 seventeenth problem and the real nullstellensatz.- Orders and quadratic forms.- Absolute values Features on fields.- Residue class degree and ramification 7 Covers the most recent results around Fermat’s index.- Local fields.- Witt vectors.- The tsen rank Theorem (Andrew Wiles) and the Langlands of a field.- Fundamentals of modules.- Wedder- Conjecture (Lafforgue) burn theory.- Crossed products.- The brauer group of a local field.- Local class field theory.- Fields of interest Semisimple representations of finite groups.- The Number Theory; Algebraic Geometry; Mathemat- schur group of a field.- Appendix: problems and ical Logic and Foundations remarks.- Index. Target groups Fields of interest Researchers and graduate students in number Algebra; Commutative Rings and Algebras; Field theory, algebra, logic and algebraic geometry Theory and Polynomials Type of publication Target groups Monograph Advanced undergraduates, graduate students
Type of publication Graduate/Advanced undergraduate textbook Available
Original Russian version of the first edition was Due January 2008 Pubblicazione prevista per il mese di published by VINITI, Moscow in 1990 dicembre 2007 Original German edition published by Spektrum 2nd ed. 2005. Corr. 2nd printing 2007. XVI, 514 p. 17 illus. 2008. Ca. 270 pagg. (UNITEXT / La Matematica per il 3+2) (Encyclopaedia of Mathematical Sciences, Volume 49) 2008. Approx. 345 p. (Universitext) Softcover Brossura Hardcover 7 * € (D) 42,75 | € (A) 43,95 | sFr 70,00 7 approx. * € (D) 28,76 | € (A) 29,57 | sFr 47,00 7 * € (D) 112,30 | € (A) 115,45 | sFr 183,00 9
J. Matousek, Charles University, Prague, Czech Y. Mishura, Kiev National Taras Shevchenko Univer- S. Okada, W. J. Ricker, E. A. Sánchez Pérez Republic. sity, Kiev, Ukraine Optimal Domain and Integral Using the Borsuk-Ulam Stochastic Calculus for Extension of Operators Theorem Fractional Brownian Motion Acting in Function Spaces Lectures on Topological Methods in and Related Processes Combinatorics and Geometry Th is book deals with the analysis of linear opera- Assisted by: A. Björner, G. Ziegler Th e theory of fractional Brownian motion and tors from a quasi-Banach function space into a other long-memory processes are addressed in this Banach space. Th e central theme is to extend the volume. Interesting topics for PhD students and operator to as large a (function) space as possible, A number of important results in combinatorics, specialists in probability theory, stochastic analysis its optimal domain, and to take advantage of this discrete geometry, and theoretical computer and fi nancial mathematics demonstrate the in analyzing the original operator. Applications are science have been proved using algebraic topology. modern level of this fi eld. Among these are results given to Maurey-Rosenthal factorization of opera- While the results are quite famous, their proofs about Levy characterization of fractional Brownian tors and to classical operators arising in commuta- are not so widely understood. Th ey are scattered motion, maximal moment inequalities for Wiener tive harmonic analysis. Th e main tool is the vector in research papers or outlined in surveys, and integrals including the values 0 Type of publication Monograph Available Previously announced in Springer News 03/2003 Due December 2007 Due May 2008 1st ed. 2003. Corr. 2nd printing 2008. XII, 210 p. 2008. Approx. 410 p. (Lecture Notes in Mathematics, 2008. Approx. 400 p. Hardcover (Operator Theory : (Universitext) Softcover Volume 1929) Softcover Advances and Applications, Volume 180) 7 * € (D) 42,75 | € (A) 43,95 | sFr 70,00 7 approx. * € (D) 53,45 | € (A) 54,95 | sFr 87,00 7 * € (D) 105,93 | € (A) 108,90 | sFr 175,00 9 springer.de/buchhandel Springer News 11/12/2007 Mathematik 49 L. Perko, Northern Arizona University, Flagstaff , AZ, S. Pigola, Università dell‘Insubria, Como, Italia; G. D. Prato, Scuola Normale Superiore, Pisa, Italy USA M. Rigoli, Università di Milano, Italia; A. G. Setti, Università dell‘Insubria, Como, Italia Introduction to stochastic Diff erential Equations and analysis and Malliavin Dynamical Systems Vanishing and Finiteness Results in Geometric Analysis calculus A Generalization of the Bochner Technique Th is textbook presents a systematic study of the Th is volume collects lecture notes from courses qualitative and geometric theory of nonlinear delivered in the past years at the Scuola Normale diff erential equations and dynamical systems. Th e aim of the book is to describe very recent Superiore in Pisa, and also at the Trento and Although the main topic of the book is the local results involving an extensive use of analytical Funchal Universities. It presents an introductory and global behavior of nonlinear systems and tools in the study of geometrical and topological course on diff erential stochastic equations and their bifurcations, a thorough treatment of linear properties of complete Riemannian manifolds. Malliavin calculus. Th e lectures are addressed to systems is given at the beginning of the text. All An extension of the Bochner technique to readers familiar with basic notions of measure the material necessary for a clear understanding the non compact setting is analyzed in detail, theory and functional analysis. Th e fi rst part of the qualitative behavior of dynamical systems is yielding conditions which ensure that solutions is devoted to the Gaussian measure in a sepa- contained in this textbook, including an outline of of geometrically signifi cant diff erential equations rable Hilbert space, the Malliavin derivative, the the proof and examples illustrating the proof of the either are trivial (vanishing results) or give rise construction of the Brownian motion and Itô‘s Hartman-Grobman theorem, the use of the Poin- to fi nite dimensional vector spaces (fi niteness formula. Th e second part deals with the diff er- caré map in the theory of limit cycles, the theory of results). To make up for the lack of compactness, ential stochastic equations and their connection rotated vector fi elds and its use in the study of limit a range of methods, from spectral theory and with parabolic problems. Several applications are cycles and homoclinic loops, and a description of qualitative properties of solutions of PDEs, to given, notably the Feynman-Kac, Girsanov and the behavior and termination of one-parameter comparison theorems in Riemannian geometry Clark-Ocone formulae, the Krylov-Bogoliubov and families of limit cycles. and potential theory, are developed. All needed Von-Neumann theorems. tools are described in detail, oft en with an original Contents approach. Some of the applications presented Features Series Preface.- Preface to the Th ird Edition.- concern the topology at infi nity of submanifolds, 7 Graduate text originating from a lot of teaching Linear Systems.- Nonlinear Systems: Local Lp cohomology, metric rigidity of manifolds with experiences 7 Deals in particular with stochastic Th eory.- Nonlinear Systems: Global Th eory.- positive spectrum, and structure theorems for diff erential equations Nonlinear Systems: Bifurcation Th eory.- Refer- Kaelher manifolds. ences.- Additional References.- Index. Contents Features 1. Gaussian measures in Hilbert spaces.- 2. L2 Fields of interest 7 Comprehensive account of very recent results and Sobolev spaces w.r.t. a Gaussian measure.- Analysis; Fluids; Mechanics in geometric analysis 7 Essentially self- 3. Brownian Motion.- 4. Markov property of the contained, supplying the necessary background Brownian motion.- 5. Th e Itô integral.- 6. Th e Itô Target groups material which is not easily available in book form formula.- 7. Stochastic diff erential equations.- Lecturers, undergraduates and presenting much of it in a new, original form 8. Transition evolution operators.- 9. Formulae of Feynman–Kac and Girsanov.- 10. One dimensional Type of publication From the contents Malliavin calculus.- 11. Malliavin calculus in more Graduate/Advanced undergraduate textbook 1. Harmonic Maps, (1,1)-Geodesic Maps and Basic dimensions.- 12. Asymptotic behaviour of the Hermitian and Kählerian Geometry.- 2. Compar- transition semigroup. ison Results.- 3. Review of Spectral Th eory.- 4. Vanishing Results.- 5. A Finite Dimensionality Fields of interest Result.- 6. Applications to Harmonic Maps. Partial Diff erential Equations; Mathematical Methods in Physics; Probability Th eory and Fields of interest Stochastic Processes Analysis; Global Analysis and Analysis on Mani- folds Target groups Graduate students Target groups Researchers and advanced graduate students in Type of publication geometric analysis and related areas Graduate/Advanced undergraduate textbook Type of publication Monograph Due December 2007 Available Due April 2008 2008. Approx. 150 p. (Publications of the Scuola Normale 3rd ed. 2001. Corr. 3rd printing 2007. XIV, 553 p. 229 illus. 2008. Approx. 300 p. (Progress in Mathematics, Superiore / Lecture Notes (Scuola Normale Superiore), (Texts in Applied Mathematics, Volume 7) Hardcover Volume 266) Hardcover Volume 6) Softcover 7 * € (D) 69,50 | € (A) 71,45 | sFr 113,50 7 * € (D) 53,39 | € (A) 54,89 | sFr 89,90 7 * € (D) 25,68 | € (A) 26,40 | sFr 39,00 9 50 Mathematik Springer News 11/12/2007 springer.de/buchhandel R. Remmert, Westfälische Wilhelms-Universität G. Rempala, University of Louisville, KY, USA; S. I. Resnick, Cornell University, Ithaca, NY, USA Münster; P. Ullrich, Universität Koblenz-Landau J. Wesolowski, Politechnika Warszawska, Waarszawa, Poland Extreme Values, Regular Elementare Zahlentheorie Symmetric Functionals Variation, and Point Processes Um die Fragestellungen in der elementaren on Random Matrices and Zahlentheorie zu verstehen, reicht die Fähigkeit Random Matching Problems Extremes Values, Regular Variation and Point zu zählen aus; um sie zu beantworten, bedarf es Processes is a readable and effi cient account of aber oft scharfsinniger Überlegungen und der the fundamental mathematical and stochastic Entwicklung fundamentaler Prinzipien. So beginnt Th is book presents the current state of the art of process techniques needed to study the behavior of dieses Buch mit der Primfaktorzerlegung und dem the mathematical theory of symmetric func- extreme values of phenomena based on indepen- grössten gemeinsamen Teiler, zwei Begriff en, die tionals on random matrices with emphasis on its dent and identically distributed random variables aus dem Schulunterricht bekannt sind, die bei connection with the statistical non-parametric and vectors. It presents a coherent treatment of genauerer Betrachtung aber viel von ihrer Selbst- estimation theory. Th e book provides a thorough, the distributional and sample path fundamental verständlichkeit verlieren. Auch der theoretische detailed description of the approach of symmetric properties of extremes and records. It emphasizes Hintergrund des aus dem Alltag wohlvertrauten function decompositions to the asymptotic theory the core primacy of three topics necessary for Dezimalsystems wird erörtert. Weitere behandelte of symmetric functionals, including the classical understanding extremes: the analytical theory Th emen sind Kongruenzenrechnung, primitive theory of U-statistics. It also presents applications of regularly varying functions; the probabilistic Wurzeln und, zu guter Letzt, das Reziprozitätsge- of the theory to investigating complex biological theory of point processes and random measures; setz für quadratische Reste. Das vorliegende Buch systems like sequence alignment, sequencing, and the link to asymptotic distribution approxima- richtet sich an Dozenten und Studenten der Mathe- SNP (single nucleotide polymorphism) detection, tions provided by the theory of weak convergence matik, Lehrer an Realschulen und Gymnasien, and DNA microarrays, as well as some stochastic of probability measures in metric spaces. jeden, der sich für ein weit über dreitausend Jahre networks models. An initial overview of the fi eld altes Teilgebiet der Mathematik interessiert. Es of symmetric random functions makes this book a Features setzt dabei keine Kenntnisse ausser elementarem useful introduction for newcomers to the fi eld. 7 Presents a readable and effi cient account of Schulstoff voraus. the fundamental mathematical and stochastic Features process techniques needed to study the behavior Pluspunkte 7 Th orough, detailed description of the approach of extreme values of phenomena 7 Presents 7 Setzt keine Kenntnisse ausser elementarem of symmetric function decompositions to the a coherent treatment of the distributional and Schulstoff voraus 7 Aufgrund seiner Ausführ- asymptotic theory of symmetric functionals, sample path fundamental properties of extremes lichkeit nicht nur vorlesungsbegleitend zu including the classical theory of U-statistics and records 7 Emphasizes the core primacy of verwenden, sondern auch zum Selbststudium 7 Organized by lectures 7 Hot topic three topics necessary for understanding extremes geeignet 7 Aufgaben am Ende eines jeden Paragraphen üben den behandelten Stoff ein Contents Contents und vertiefen ihn Basic Concepts.- Properties of P-statistics.- Preface.- Preliminaries.- Domains of Attraction Asymptotics for Random Permanents.- Weak and Norming Constants.- Quality of Conver- Aus dem Inhalt Convergence of Permanent Processes.- Weak gence.- Point Processes.- Records and Extremal 1. Primzerlegung in Z und Q.- 2. Th eorie des Convergence of P-statistics.- Permanent Designs Processes.- Multivariate Extremes.- References.- grössten gemeinsamen Teilers in Z.- 3. Zahlen- and Related Topics.- Products of Partial Sums and Index. theorie in allgemeinen Integritätsringen.- 4. Der Wishart Determinants. g-adische Algorithmus.- 5. Kongruenzen und Fields of interest Restklassenringe.- 6. Prime Restklassengruppen.- Fields of interest Probability Th eory and Stochastic Processes; Math- 7. Th eorie der quadratischen Reste. Applications of Mathematics; Statistical Th eory ematical Modeling and Industrial Mathematics; and Methods; Communications Engineering, Approximations and Expansions Fachgebiete Networks Mathematik, allgemein Target groups Target groups Researchers, mathematicians, engineers, and Zielgruppen Graduate students, researchers and practitioners graduate students Dozenten und Studenten der Mathematik, Lehrer working with problems revolving around statistical an Realschulen und Gymnasien sowie jeder, der testing and estimation in complex environments Type of publication sich für ein weit über dreitausend Jahre altes Teil- Monograph gebiet der Mathematik interessiert Type of publication Monograph Kategorie Einführendes Lehrbuch Due December 2007 Originally published as volume 4 in the series: Applied Erscheint März 2008 Due December 2007 Probability 3. Aufl . 2008. Etwa 280 S. (Grundstudium Mathematik) 2008. Approx. 220 p. (The IMA Volumes in Mathematics 2008. XIV, 320 p. (Springer Series in Operations Research Brosch. and its Applications, Volume 147) Hardcover and Financial Engineering) Softcover 7 € (D) 24,90 | € (A) 25,60 | *sFr 39,90 7 * € (D) 67,36 | € (A) 69,25 | sFr 110,00 7 approx. * € (D) 41,20 | € (A) 42,35 | sFr 67,50 9 springer.de/buchhandel Springer News 11/12/2007 Mathematik 51 S. Salsa, Politecnico di Milano, Italia F. Santambrogio, Université Paris Dauphine, Paris, V. Srinivas, Tata Institute, India France Partial Diff erential Equations Algebraic K-Theory Perspectives and Applications Variational problems in transport theory with mass concentration Algebraic K-Th eory has become an increasingly Th e main purpose is on the one hand to train the active area of research. With its connections to students to appreciate the interplay between theory algebra, algebraic geometry, topology, and number and modelling in problems arising in the applied Th e book mainly deals with variational problems theory, it has implications for a wide variety of sciences; on the other hand to give them a solid involving optimal transportation of probability researchers and graduate students in mathematics. theoretical background for numerical methods, measures, in competition with concentration Th e book is based on lectures given at the author’s such as fi nite elements. Accordingly, this textbook eff ects. First, some problems are presented where home institution, the Tata Institute in Bombay, and is divided into two parts. Th e fi rst one has a rather measures have to be selected minimizing transport elsewhere. A detailed appendix on topology was elementary character with the goal of developing costs between them but satisfying some concentra- provided in the fi rst edition to make the treatment and studying basic problems from the macro-areas tion criteria, with possible applications mainly to accessible to readers with a limited background of diff usion, propagation and transport, waves and urban planning (where the concentrated measures in topology. Th is new edition also includes an vibrations. Ideas and connections with concrete stand for services in the city and the diff use ones appendix on algebraic geometry that contains the aspects are emphasized whenever possible, in for population). Th e second part of the book required defi nitions and results needed to under- order to provide intuition and feeling for the is devoted to optimization problems where the stand the core of the book; this makes the book subject. For this part, a knowledge of advanced concentration or diff usion phenomena occurs accessible to a wider audience. calculus and ordinary diff erential equations is directly at the level of the transportation structure: required. Also, the repeated use of the method for instance in most communication networks, Features of separation of variables assumes some basic as well as in river basins and blood vessels joint 7 Appendices on topology and algebraic geom- results from the theory of Fourier series, which are transportation is favoured, while some models for etry provide requisite background material for the summarized in an appendix. traffi c congestion or compressible fl uid mechanics subject 7 Provides many examples to solidify give raise to problems where spread confi gurations understanding in the reader 7 Discusses funda- Fields of interest are preferred. mentals and new research extensions Partial Diff erential Equations Features Contents Target groups 7 Deals in a unifi ed manner with several Preface to the First Edition.- Preface to the Advanced undergraduates, fi rst-year graduates; problems where diff erent concentration eff ects Second Edition.- “Classical” K-Th eory.- Th e courses for students from various disciplines like are considered 7 Key points of the book are Plus Construction.- Th e Classifying Space of a applied mathematics, physics, engineering modelling issues 7 For variational problems both Small Category.- Exact Categories and Quillen’s existence results and necessary optimality condi- Q-Construction.- Th e K-Th eory of Rings and Type of publication tions are considered, arriving at the identifi cation Schemes.- Proofs of the Th eorems of Chapter Monograph of explicit solutions when possible 4.- Comparison of the Plus and Q-Constructions.- Th e Merkurjev-Suslin Th eorem.- Localization for Fields of interest Singular Varieties.- Appendix A. Results from Calculus of Variations and Optimal Control; Topology.- Appendix B. Results from Category Optimization Th eory.- Appendix C. Exact Couples.- Appendix D. Results from Algebraic Geometry.- Bibliography. Target groups Researchers Fields of interest K-Th eory; Algebraic Geometry; Algebraic Type of publication Topology Monograph Target groups Graduate students and researchers interested in k-theory Type of publication Graduate/Advanced undergraduate textbook Due November 2007 Due November 2007 Due November 2007 Only available in print Originally published as volume 90 in the series: Progress in Mathematics Original Italian edition published in the Series: UNITEXT 2008. Approx. 225 p. (Publications of the Scuola Normale Superiore / Theses (Scuola Normale Superiore), 2nd ed. 1996. 3rd printing 2008. XX, 342 p. (Modern 2008. Approx. 470 p. (Universitext) Softcover Volume 4) Softcover Birkhäuser Classics) Softcover 7 * € (D) 42,75 | € (A) 43,95 | sFr 70,00 7 * € (D) 19,26 | € (A) 19,80 | sFr 30,00 7 * € (D) 37,34 | € (A) 38,39 | sFr 59,90 9 52 Mathematik Springer News 11/12/2007 springer.de/buchhandel S. M. Srivastava, Indian Statistical Institute, Kolkata, R. F. Tichy, Technical University Vienna, Graz, Austria; Z. Yao, Tsinghua University, Beijing, China; M. Yuan, India H. P. Schlickewei, Phillipps-University, Marburg, Peking University, Beijing, China (Eds.) Germany; K. Schmidt, University of Vienna, Austria A Course on Mathematical (Eds.) Computational Mechanics Logic Diophantine Approximation Proceedings of the 2007 International Symposium on Computational Mechanics in Festschrift for Wolfgang Schmidt Beijing This textbook is written for advanced undegradu- ates or first year graduate students of mathematics and computer science. It is also intended for the This volume contains 21 research and survey Computational Mechanics is the Proceedings of working mathematician who wants to gain an papers on recent developments in the field of the 2007 International Symposium on Computa- appreciation of Mathematical Logic. There are no diophantine approximation. This includes contri- tional Mechanics (ISCM) held July 30-August 1, prerequisites for this book; however, some math- butions to Wolfgang Schmidt’s subspace theorem 2007 in Beijing. The book includes 22 full papers of ematical maturity is required. The book is written and its applications to diophantine equations and plenary and semi-plenary lectures, and approxi- in a totally mathematical style, and any mathema- to the study of linear recurring sequences. The mately 150 one-page summaries; the CD-ROM tician should feel at home reading this. The book articles are either in the spirit of more classical contains all full papers presented at the conference. starts with the definition of first order languages, diophantine analysis or of geometric or combina- This conference is the first of a series that is created proceeds through propositional logic, complete- torial flavour. Several articles deal with estimates by a group of prominent scholars from the Main- ness theorems, and finally the two Incompleteness for the number of solutions of diophantine equa- land of China, Hong Kong, Taiwan, and overseas Theorems of Godel. In the process, the reader is tions as well as with congruences and polynomials. Chinese, who are very active in the field. This also introduced to model theory and recursion Furthermore, the volume contains transcendence conference series will be held alternately in the Theory. After reading this book, the reader will results for special functions and contributions to Mainland of China, Hong Kong, Macao, Taiwan, be ready to branch into model Theory, recursion metric diophantine approximation and discrep- and overseas countries. Theory, axiomatic set theory or even theoretical ancy theory. The articles are based on lectures computer science. given at a conference at the Erwin Schrödinger- Features Institute (Vienna, 2003), where many leading 7 Some recent progress in the field of computa- Features experts in the field of diophantine approxiamtion tional mechanics 7 Full-length manuscripts of 7 Written in a clear, concise style 7 Contains participated. plenary and semi-plenary lectures of high level numerous exercises and examples 7 Employs only 7 One-page detailed abstracts of other Godels completeness and incompleteness theorems Features papers to provide more information to motivate the entire text 7 Modern language 7 Current information on important branches of and notation will appeal to undergrads as well as diophantine approximation from leading experts System requirements graduate students in the field 7 Diverse methods are presented For PC. For the complete system requirements see: 7 The influence of diophantine approximation springer.com Contents in other fields, e.g. combinatorial geometry, game Introduction.- First-order languages.- Semantics of theory Fields of interest first-order languages.- Propositional logic.- First- Computational Mathematics and Numerical order theories.- Completeness theorem and model Fields of interest Analysis; Mechanics; Appl.Mathematics/Computa- theory.- Recursive functions and arithmetization Algebra; Computational Mathematics and tional Methods of Engineering of theories.- Incompleteness theorems and recur- Numerical Analysis; Number Theory sion theory.- References.- Index. Target groups Target groups Researchers in the field of computational Fields of interest Researchers and graduate students mechanics, computational engineering, and Mathematical Logic and Foundations sciences Type of publication Target groups Proceedings Type of publication Advanced undergraduate/graduate math students Proceedings Type of publication Graduate/Advanced undergraduate textbook Due January 2008 Due February 2008 Distribution rights in China: Tsinghua University Press. Only available in print Jointly published with Tsinghua University Press Due March 2008 2008. Approx. 430 p. (Developments in Mathematics, Volume 16) Hardcover 2008. Approx. 300 p. 100 illus. With CD-ROM. Hardcover 2008. Approx. 160 p. 2 illus. (Universitext) Softcover 7 approx. * € (D) 106,95 | € (A) 109,95 | 7 approx. * € (D) 211,86 | € (A) 217,80 | 7 approx. * € (D) 41,20 | € (A) 42,35 | sFr 67,00 sFr 174,00 sFr 345,00 9 J. Zabczyk, Polish Academy of Sciences, Warsaw, Poland Mathematical Control Theory An Introduction Mathematical Control Th eory: An Introduction presents, in a mathematically precise manner, a unifi ed introduction to deterministic control theory. With the exception of a few more advanced concepts required for the fi nal part of the book, this presentation requires only a knowledge of basic facts from linear algebra, diff erential equa- tions, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infi nite dimensional systems, and the solution of minimum energy problems. Th e book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. Features 7 Covers a remarkable number of topics in a concise manner 7 Includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems - subjects not usually covered in an ‘intro- ductory’ book 7 Excellent book for introducing a mathematician to control theory 7 Can be used in a novel one-semester course covering both linear and nonlinear systems Fields of interest Systems Th eory, Control; Applications of Math- ematics; Calculus of Variations and Optimal Control; Optimization Target groups Graduate students in systems and control, math- ematicians needing a good introduction to control theory Type of publication Graduate/Advanced undergraduate textbook Due November 2007 Originally published as a hardcover edition in the series: Systems & Control: Foundations & Applications 1st ed. 1992., 3rd printing 2008. XII, 260 p. (Modern Birkhäuser Classics) Softcover 7 * € (D) 37,34 | € (A) 38,39 | sFr 59,90 9