WOLFGANG WOESS
Imperial College
Description: The main theme of this book is the interplay between
the behaviour of a class of stochastic processes (random walks)
and
discrete structure theory. The author considers Markov chains
whose state space is equipped with the structure of an infinite,
locally-finite
graph, or as a particular case, of a finitely generated group.
The transition probabilities are assumed to be adapted to the
underlying
structure in some way that must be specified precisely in each
case.
From the probabilistic viewpoint, the question is what impact the
particular type of structure has on various aspects of the
behaviour of
the random walk. Vice-versa, random walks may also be seen as
useful tools for classifying, or at least describing the
structure of graphs
and groups. Links with spectral theory and discrete potential
theory are also discussed.
This book will be essential reading for all researchers working
in stochastic process and related topics.
Contents:Part I. The Type Problem: 1. Basic facts; 2. Recurrence
and transience of infinite networks; 3. Applications to random
walks; 4.
Isoperimetric inequalities; 5. Transient subtrees, and the
classification of the recurrent quasi transitive graphs; 6. More
on recurrence; Part
II. The Spectral Radius: 7. Superharmonic functions and
r-recurrence; 8. The spectral radius; 9. Computing the Green
function; 10. Spectral
radius and strong isoperimetric inequality; 11. A lower bound for
simple random walk; 12. Spectral radius and amenability; Part
III. The
Asymptotic Behaviour of Transition Probabilities: 13. The local
central limit theorem on the grid; 14. Growth, isoperimteric
inequalities,
and the asymptotic type of random walk; 15. The asymptotic type
of random walk on amenable groups; 16. Simple random walk on the
Sierpinski graphs; 17. Local limit theorems on free products; 18.
Intermezzo; 19. Free groups and homogenous trees; Part IV. An
Introduction to Topological Boundary Theory: 20. Probabilistic
approach to the Dirichlet problem, and a class of
compactifications; 21.
Ends of graphs and the Dirichlet problem; 22. Hyperbolic groups
and graphs; 23. The Dirichlet problem for circle packing graphs;
24. The
construction of the Martin boundary; 25. Generalized lattices,
Abelian and nilpotent groups, and graphs with polynomial growth;
27. the
Martin boundary of hyperbolic graphs; 28. Cartesian products.
ISBN, Binding, Price:0521552923 Hardback c.
Approximate Publication date:16 November 1999
Main Subject Category:Mathematics - analysis, probability
Series:Cambridge Tracts in Mathematics, 138
1999 228 x 152 mm 336pp 12 line diagrams
KEN-ITI SATO
Imperial College
Description: Levy processes are rich mathematical objects and
constitute perhaps the most basic class of stochastic processes
with a
continuous time parameter. This book is intended to provide the
reader with comprehensive basic knowledge of Levy processes, and
at
the same time serve as an introduction to stochastic processes in
general. No specialist knowledge is assumed and proofs are given
in
detail. Systematic study is made of stable and semi-stable
processes, and the author gives special emphasis to the
correspondence between
Levy processes and infinitely divisible distributions. All
serious students of random phenomena will find that this book has
much to offer.
Contents:1. Basic examples; 2. Infinitely divisible distributions
and characterization; 3. Stable processes and their extensions;
4. Levy-It・
decomposition of sample functions; 5. Distributional properties
of Levy processes; 6. Subordination and density transformation;
7.
Recurrence and transcience; 8. Potential theory for Levy
processes; 9. Wiener-Hopf factorizations; 10. More distributional
properties on the
line.
ISBN, Binding,0521553024 Hardback
Approximate Publication date:2 November 1999
Series:Cambridge Studies in Advanced Mathematics, 68
1999 228 x 152 mm 480pp
Comparable titles:BERTOIN/Levy Processes/1996/0521 646324
JUN GU
University of Calgary, Alberta, Canada
PAUL W. PURDOM
Indiana University, Bloomington
JOHN FRANCO
University of Cincinnati, Ohio
AND BENJAMIN W. WAH
University of Illinois, Urbana
Description: The satisfiability (SAT) problem is central in
mathematical logic and computing theory, representing a core of
computationally intractable NP-complete problems. It is a
fundamental hurdle in solving many problems in automated
reasoning,
computer-aided design, computer-aided manufacturing, machine
vision, database construction and maintenance, robotics,
scheduling,
integrated circuit design, computer architecture design, and
computer networking. Efficient methods for solving the SAT
problem play an
important role in the development of practical computing systems.
Traditional methods treat SAT as a discrete, constrained decision
problem. In recent years, many optimization methods, parallel
algorithms, and other practical new techniques have been
developed for
solving the SAT problem. This book describes these
state-of-the-art methods, both sequential and parallel, and
discusses tradeoffs and
limitations in the rapidly growing field of satisfiability
testing. It will be useful for computer theorists, algorithmists,
and practitioners
working in all areas in computer science, computer engineering,
operations research, and applied logic.
ISBN, Binding, :0521640415 Hardback
Approximate Publication date:7 November 1999
1999 228 x 152 mm 250pp
EDITED BY E. BRIAN DAVIES
King's College London
AND YURI SAFAROV
King's College London
Description: This volume brings together lectures from an
instructional meeting on spectral theory and geometry held under
the auspices
of the International Centre for Mathematical Sciences in
Edinburgh. The contributions here come from world experts and
many are much
expanded versions of the lectures they gave. Together they survey
the core material and go beyond to reach deeper results. For
graduate
students and experts alike, this book will be a highly useful
resource.
Contents:1. Basic Riemannian geometry F. E. Burstall; 2. The
Laplacian on Riemannian manifolds I. Chavel; 3. Computational
spectral
theory E. B. Davies; 4. Isoperimetric and universal inequalities
for eigenvalues M. Ashbaugh; 5. Estimates of heat kernels on
Riemannian
manifolds A. Grigoryan; 6. Spectral theory of the Schringer
operators on non-compact manifolds: qualitative results M.
Shubin; 7.
Lectures on wave invariants S. Zelditch.
ISBN, Binding, 0521777496 Paperback
Approximate Publication date:10 September 1999
Series:London Mathematical Society Lecture Note Series
1999 228 x 152 mm 344pp
Comparable titles:DAVIES/Spectral Theory and Differential
Operators/1995/0521 587107
EDITED BY P. VASSILIOU
University of Canberra
AND I. LISLE
University of Canberra
Description: This book provides a concise and accessible
exposition of a wide range of topics in geometric approaches to
differential
equations. The aim of the book is to present an overview of this
developing subject and a brief introduction to a number of
related topics,
including twistor theory, vortex filament dynamics, calculus of
variations, exterior differential systems and B臘klund
transformations.
Written by leading experts, this book is an ideal starting point
for graduate students embarking on research. It will also be of
use to
researchers and anybody wishing to learn more about this
burgeoning field of mathematical endeavour.
Contents:Preface; 1. Geometric approaches to differential
equations: an introduction Peter J. Vassiliou; 2. B臘klund and
his works:
applications in soliton theory Colin Rogers, Wolfgang K. Schief
and Mark E. Johnston; 3. Recent developments in integrable curve
dynamics Annalisa Calini; 4. An elementary introduction to
exterior differential systems Niky Kamran; Cartan structure of
infinite Lie
pseudogroups Ian G. Lisle and Gregory J. Reid; 5. Cartan's method
of equivalence David Hartley; 6. The inverse problem in the
calculus of
variations and its ramifications Geoff E. Prince; 7. Twistor
theory Michael K. Murray.
ISBN, Binding,:0521775981 Paperback
Approximate Publication date:9 December 1999
Series:Australian Mathematical Society Lecture Series
Contributors:Peter J. Vassiliou, Colin Rogers, Wolfgang K.
Schief, Mark E. Johnston, Niky Kamran, Ian G. Lisle, Gregory J.
Reid, David
Hartley, Geoff E. Prince, Michael K. Murray
1999 228 x 152 mm 232pp 21 line diagrams 1 half-tone 2 tables
RICHARD P. STANLEY
Massachusetts Institute of Technology
Description: This book is the first of a two-volume basic
introduction to enumerative combinatorics at a level suitable for
graduate
students and research mathematicians. It concentrates on the
theory and application of generating functions, a fundamental
tool in
enumerative combinatorics. The book covers those parts of
enumerative combinatorics of greatest applicability to other
areas of
mathematics. The four chapters are devoted to an introduction to
enumeration (suitable for advanced undergraduates), sieve methods
(including the Principle of Inclusion-Exclusion), partially
ordered sets, and rational generating functions. There are a
large number of
exercises, almost all with solutions, which greatly augment the
text and provide entry into many areas not covered directly.
Graduate
students and research mathematicians who wish to apply
combinatorics to their work will find this an authoritative
reference.
Contents:1. What is enumerative combinatorics?; 2. Sieve methods;
3. Partially ordered sets; 4. Rational generating functions.
ISBN, Binding,:0521663512 Paperback
Approximate Publication date:23 December 1999
1999 228 x 152 mm 352pp
Learning Functional Programming Through Multimedia
PAUL HUDAK
Yale University
Description: Functional programming is a style of programming
that emphasizes the use of functions (in contrast to
object-oriented
programming, which emphasizes the use of objects). It has become
popular in recent years because of its simplicity, conciseness,
and
clarity. This book teaches functional programming as a way of
thinking and problem solving, using Haskell, the most popular
purely
functional language. Rather than using the conventional (boring)
mathematical examples commonly found in other programming
language textbooks, the author uses examples drawn from
multimedia applications, including graphics, animation, and
computer music,
thus rewarding the reader with working programs for inherently
more interesting applications. Aimed at both beginning and
advanced
programmers, this tutorial begins with a gentle introduction to
functional programming and moves rapidly on to more advanced
topics.
Details about progamming in Haskell are presented in boxes
throughout the text so they can be easily found and referred to.
Contents:1. Problem solving, programming, and calculation; 2. A
module of shapes: part I; 3. Simple graphics; 4. Shapes II:
drawing
shapes; 5. Polymorphic and higher-order functions; 6. Shapes III:
perimeters of shapes; 7. Trees; 8. A module of regions; 9. More
about
higher-order functions; 10. Drawing regions; 11. Proof by
induction; 12. Qualified types; 13. A module of simple
animations; 14.
Programming with streams; 15. A module of reactive animations;
16. Communicating with the outside world; 17. Rendering reactive
animations; 18. Higher-order types; 19. An imperative robot
language; 20. Functional music composition; 21. Algebraic
properties of
multimedia; 22. Interpreting functional music; 23. A tour of the
prelude list module; 24. A Tour of Haskell's standard type
classes.
Essential Information
First Author:Hudak
Title:The Haskell School of Expression
ISBN, Binding, 0521643384 Hardback
ISBN, Binding, 0521644089 Paperback
Approximate Publication date:1 September 1999
1999 234 x 177 mm 300pp 15 line diagrams 75 exercises
STEVEN KRANTZ
Description: Tracing a path from the earliest beginnings of
Fourier series through to the latest research A Panorama of
Harmonic Analysis
discusses Fourier series of one and several variables, the
Fourier transform, spherical harmonics, fractional integrals, and
singular
integrals on Euclidean space. The climax is a consideration of
ideas from the point of view of spaces of homogeneous type, which
culminates in a discussion of wavelets. This book is intended for
graduate students and advanced undergraduates, and mathematicians
of
whatever background who want a clear and concise overview of the
subject of commutative harmonic analysis.
Contents:0. An overview of measure theory and functional
analysis; 1. Fourier series basics; 2. The Fourier transform; 3.
Multiple Fourier
series; 4. Spherical harmonics; 5. Fractional integrals, singular
integrals and Hardy spaces; 6. Modern theories of integral
operators; 7.
Wavelets; 8. A retrospective; Appendices.
ISBN, Binding, :0883850311 Hardback
Approximate Publication date:2 September 1999
Series:Carus Mathematical Monographs, 27
1999 136 x 206 mm 374pp
SHERMAN STEIN
Description: Many people have heard two things about Archimedes:
he was the greatest mathematician of antiquity, and he ran naked
from his bath crying 'Eureka!'. However, few people are familiar
with the actual accomplishments upon which his enduring
reputation
rests, and it is the aim of this book to shed light upon this
matter. Archimedes' ability to achieve so much with the few
mathematical tools
at his disposal was astonishing. He made fundamental advances in
the fields of geometry, mechanics, and hydrostatics. No great
mathematical expertise is required of the reader, and the book is
well illustrated with over 100 diagrams. It should prove
fascinating to
students and professional mathematicians alike.
Contents:1. The life of Archimedes; 2. The lever; 3. The centre
of gravity; 4. Big literary find in Constantinople; 5. The
mechanical method;
6. Two sums; 7. The parabola; 8. Floating bodies; 9. The spiral;
10. The ball; 11. Archimedes traps p.
ISBN, Binding, :0883857189 Paperback
Approximate Publication date:2 September 1999
1999 128 x 229 mm 166pp