Avner Friedman

Differential Games


ISBN: 0486449955
Page Count: 368
Dimensions: 5 3/8 x 8 1/2

This volume lays the mathematical foundations for the theory of differential games, developing a rigorous mathematical framework with existence theorems. Topics include games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, and games with restricted phase coordinates. 1971 ed.










Jacques Tilouine - Henri Carayol - Michael Harris - Marie-France Vigneras (Ed.)

Formes Automorphes (II) - - Le cas du groupe

Asterisque 302 (2005), xiv+436 pages

Acheter l'ouvrage

Gerard Laumon
Fonctions zetas des varietes de Siegel de dimension trois

Rainer Weissauer
Four dimensional Galois Representations

Eric Urban
Sur les representations p-adiques associees aux representations cuspidales de

Alain Genestier - Jacques Tilouine
Systemes de Taylor-Wiles pour

David Whitehouse
The twisted weighted fundamental lemma for the transfer of automorphic forms from to

ISBN : 2-85629-184-8

Pettini, Marco

Riemannian Geometry, Hamiltonian Dynamics and Applications

Cloth. Springer-Verlag,N.Y., New York, NY, UK, 2006 (ISBN 038730892X).

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Reimannian formulations of dynamics using either the Jacobi metric or the Eisenhart metric in extended configuration space; and topological aspects of phase transitions. Other items such as quantum systems are also discussed in this framework. This book deals wih exciting applications of dynamical systems to statistical mechanics. Mathematicians and physicists working in this area will find this book of interest. TOC:Background in Physics.- Geometrization of Hamiltonian Dynamics.- Integrability.- geometry and Chaos.- Topological aspects of phase transitions.- Quantum systems.- Appendices: A. Elements of Riemannian geometry B. Kaehler manifolds C. Elementary Morse theory D. de Rham's cohomology theory

Contents

Background in Physics * Geometrization of Hamiltonian Dynamics * Integrability * geometry and Chaos * Topological aspects of phase transitions * Quantum systems * Appendices: A. Elements of Riemannian geometry B. Kaehler manifolds C. Elementary Morse theory D. de Rham's cohomology theory

Edited by William G. Faris

Diffusion, Quantum Theory, and Radically Elementary Mathematics.

Paper | Oct.2006 | ISBN: 0-691-12545-7
254 pp. | 6 x 9 | 32 line illus.

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians.

The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

William G. Faris is Professor of Mathematics at the University of Arizona.

Series:

Mathematical Notes(MN-47)

A. Ya. Helemskii, Moscow State University, Russia

Lectures and Exercises on Functional Analysis

Translations of Mathematical Monographs Volume: 233
2006; 468 pp; hardcover
ISBN-10: 0-8218-4098-3
ISBN-13: 978-0-8218-4098-6
Expected publication date is September 17, 2006.

The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus.

The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.

Readership

Graduate students and research mathematicians interested in functional analysis and operator theory.

Table of Contents

Foundations: Categories and the like
Normed spaces and bounded operators ("Waiting for completeness")
Banach spaces and their advantages
From compact spaces to Fredholm operators
Polynormed spaces, weak topologies, and generalized functions
At the gates of spectral theory
Hilbert adjoint operators and the spectral theorem
Fourier transform
Bibliography
Index


Edited by: Habib Ammari, Ecole Polytechnique, Palaiseau, France,
and Hyeonbae Kang, Seoul National University, Korea

Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory

Contemporary Mathematics Volume: 408
2006; approx. 251 pp; softcover
ISBN-10: 0-8218-3968-3
ISBN-13: 978-0-8218-3968-3
Expected publication date is September 10, 2006.

Recent developments in inverse problems, multi-scale analysis and effective medium theory reveal that these fields share several fundamental concepts. This book is the proceedings of the research conference, "Workshop in Seoul: Inverse Problems, Multi-Scale Analysis and Homogenization," held at Seoul National University, June 22-24, 2005. It highlights the benefits of sharing ideas among these areas, of merging the expertise of scientists working there, and of directing interest towards challenging issues such as imaging nanoscience and biological imaging. Contributions are written by prominent experts and are of interest to researchers and graduate students interested in partial differential equations and applications.

Readership

Graduate students and research mathematicians interested in partial differential equations and applications to inverse problems, multi-scale analysis and homogenization.

Table of Contents

H. Ammari and H. Kang -- Generalized polarization tensors, inverse conductivity problems, and dilute composite materials: A review
Y. Capdeboscq and H. Kang -- Improved bounds on the polarization tensor for thick domains
H. Kang and G. W. Milton -- On conjectures of Polya-Szego and Eshelby
K. Houzaki, N. Nishimura, and Y. Otani -- An FMM for periodic rigid-inclusion problems and its application to homogenisation
H. Cheng, W. Crutchfield, Z. Gimbutas, L. Greengard, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao -- Remarks on the implementation of the wideband FMM for the Helmholtz equation in two dimensions
T. Hou, D. Yang, and H. Ran -- Multiscale computation of isotropic homogeneous turbulent flow
N. Albin and A. Cherkaev -- Optimality conditions on fields in microstructures and controllable differential schemes
M. Fink -- Time-reversal acoustics
G. Dassios -- What is recoverable in the inverse magnetoencephalography problem?
J. J. Liu, H. C. Pyo, J. K. Seo, and E. J. Woo -- Convergence properties and stability issues in MREIT algorithm
G. Nakamura, G. Uhlmann, and J.-N. Wang -- Oscillating-decaying solutions for elliptic systems
M. Ikehata -- Stroh eigenvalues and identification of discontinuity in an anisotropic elastic material
G. Nakamura, R. Potthast, and M. Sini -- A comparative study between some non-iterative methods for the inverse scattering

Anne L. Young, Loyola College in Maryland, Baltimore, MD

Mathematical Ciphers: From Caesar to RSA

Mathematical World Volume: 25
2006; approx. 176 pp; softcover
ISBN-10: 0-8218-3730-3
ISBN-13: 978-0-8218-3730-6
Expected publication date is October 1, 2006.

A cipher is a scheme for creating coded messages for the secure exchange of information. Throughout history, many different coding schemes have been devised. One of the oldest and simplest mathematical systems was used by Julius Caesar. This is where Mathematical Ciphers begins. Building on that simple system, Young moves on to more complicated schemes, ultimately ending with the RSA cipher, which is used to provide security for the internet.

This book is structured differently from most mathematics texts. It does not begin with a mathematical topic, but rather with a cipher. The mathematics is developed as it is needed; the applications motivate the mathematics. As is typical in mathematics textbooks, most chapters end with exercises. Many of these problems are similar to solved examples and are designed to assist the reader in mastering the basic material. A few of the exercises are one-of-a-kind, intended to challenge the interested reader.

Implementing encryption schemes is considerably easier with the use of the computer. For all the ciphers introduced in this book, JavaScript programs are available from the web.

In addition to developing various encryption schemes, this book also introduces the reader to number theory. Here, the study of integers and their properties is placed in the exciting and modern context of cryptology. Mathematical Ciphers can be used as a textbook for an introductory course in mathematics for all majors. The only prerequisite is high school mathematics.

Readership

Undergraduate students interested in number theory, cryptology, and discrete mathematics.

Table of Contents

Introduction
Caesar cipher
Terminology and results from number theory
Modular arithmetic
Describing the Caesar cipher mathematically
Cryptanalysis for the Caesar cipher
Multiplication cipher
Cryptanalysis for the multiplication cipher
Multiplication-shift cipher
Cryptanalysis for the multiplication-shift cipher
Non-mathematical substitution ciphers
Preparing to generalize
Finding inverses modulo $n$
General multiplication-shift cipher
Security of the general multiplication-shift cipher
Introduction to the exponential cipher
Deciphering the exponential cipher
Cryptanalysis for the exponential cipher
Mathematical basis for the exponential cipher
Public key ciphers
RSA cipher
Signatures
Security and implementation of the RSA cipher
Computer programs
Further reading
Answers to selected exercises
Index