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.
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
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
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)
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
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
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