2003. 96 pages. Softcover
ISBN 3-7643-2170-9
English
The book contains a clear exposition of two
contemporary topics
in modern differential geometry:
distance geometric analysis on manifolds,
in particular,
comparison theory for distance functions
in spaces which have
well defined bounds on their curvature is
applied to study the
Laplace operator on minimal submanifolds
the application of the Lichnerowicz formula
for Dirac operators
to the study of Gromov's invariants to measure
the K-theoretic
size of a Riemannian manifold.
It is intended for both graduate students
and researchers who
want to get a quick and modern introduction
to these topics.
Table of contents
Distance Geometric Analysis on Manifolds
(Steen Markvorsen) (.-)
The Dirac Operator in Geometry and Physics
(Maung Min-Oo)
2003. 1092 pages. Hardcover
Progress in Mathematics, vol.219
ISBN 3-7643-6995-7
English
The book explores the theory of discrete
integrable systems, with
an emphasis on the following general problem:
how to discretize
one or several of independent variables in
a given integrable
system of differential equations, maintaining
the integrability
property? This question (related in spirit
to such a modern
branch of numerical analysis as geometric
integration) is treated
in the book as an immanent part of the theory
of integrable
systems, also commonly termed as the theory
of solitons.
Among several possible approaches to this
theory, the Hamiltonian
one is chosen as the guiding principle. A
self-contained
exposition of the Hamiltonian (r-matrix,
or "Leningrad")
approach to integrable systems is given,
culminating in the
formulation of a general recipe for integrable
discretization of
r-matrix hierarchies. After that, a detailed
systematic study is
carried out for the majority of known discrete
integrable systems
which can be considered as discretizations
of integrable ordinary
differential or differential-difference (lattice)
equations. This
study includes, in all cases, a unified treatment
of the
correspondent continuous integrable systems
as well. The list of
systems treated in the book includes, among
others: Toda and
Volterra lattices along with their numerous
generalizations (relativistic,
multi-field, Lie-algebraic, etc.), Ablowitz-Ladik
hierarchy,
peakons of the Camassa-Holm equation, Garnier
and Neumann systems
with their various relatives, many-body systems
of the Calogero-Moser
and Ruijsenaars-Schneider type, various integrable
cases of the
rigid body dynamics. Most of the results
are only available from
recent journal publications, many of them
are new.
Thus, the book is a kind of encyclopedia
on discrete integrable
systems. It unifies the features of a research
monograph and a
handbook. It is supplied with an extensive
bibliography and
detailed bibliographic remarks at the end
of each chapter.
Largely self-contained, it will be accessible
to graduate and
post-graduate students as well as to researchers
in the area of
integrable dynamical systems. Also those
involved in real
numerical calculations or modelling with
integrable systems will
find it very helpful.
Table of contents
I. General Theory (.-) Hamiltonian Mechanics
(-) R-matrix
Hierarchies (-) II. Lattice Systems (.-)
Toda Lattice (-)
Volterra Lattice (-) Newtonian Equations
of the Toda Type (-)
Relativistic Toda Lattice (-) Relativistic
Volterra Lattice (-)
Newtonian Equations of the Relativistic Toda
Type (-) Explicit
Discretizations for Toda Systems (-) Explicit
Discretizations of
Newtonian Toda Systems (-) Bruschi-Ragnisco
Lattice (-) Multi-field
Toda-like Systems (-) Multi-field Relativistic
Toda Systems (-)
Belov-Chaltikian Lattices (-) Multi-field
Volterra-like Systems
(-) Multi-field Relativistic Volterra Systems
(-) Bogoyavlensky
Lattices (-) Ablowitz-Ladik Hierarchy (-)
III. Systems of
Classical Mechanics (.-) Peakons System (-)
Standard-like
Discretizations (-) Lie-algebraic Toda Systems
(-) Garnier System
(-) Henon-Heiles System (-) Neumann System
(-) Lie-algebraic
Generalizations of the Garnier Systems (-)
Integrable Cases of
Rigid Body Dynamics (-) Systems of Calogero-Moser
Type (-)
Bibliography (.-) Notation (.-) Index
224 pages , 6 1/8 x 9 , 40 illus., paperback
ISBN:3-7643-4288-9, published 2003
expected release date: 10/12/2003
ABOUT THIS BOOK
A Path to Combinatorics for Undergraduates'
is unique in its
creative approach and presentation of material:
unconventional,
essay-type, non-routine combinatorial examples
followed by a
number of carefully selected challenging
problems and extensive
discussions of their solutions. New mathematical
tools and
methods are acquired, thanks to the interplay
between well-organized
combinatorial concepts and practical problems
that bridge
ordinary high school permutation/combination
examples and
exercises.
A good foundation in combinatorics is provided
in the early
chapters that cover ideas in combinatorial
geometry, e.g,
Sylvester's problem, convexity, covering,
dissections, and
Euclidean Ramsey theorems. Later chapters
deal with concepts in
set theory, number theory and group theory---
for example,
cardinality, the Chinese Remainder Theorem,
modulo operations,
affine projections, all of which are innovatively
implemented in
combinatorial type problems. Lastly, problems
in the language of
combinatorics are translated into the language
of graph theory.
This book is intended for anyone who wants
to broaden his or her
mathematical horizons. It serves as a solid
stepping stone for
more advanced combinatorics studies in related
mathematical
science fields or in computer science. Amateur
mathematicians
seeking new brain teasers, instructors desiring
to teach advanced
problem-solving classes and students from
high school juniors to
college seniors will find inspiration and
an intellectual delight
in this text.
TABLE OF CONTENTS
1. Let's Count; 2. What is a proof?; 3. Combinatorial
Models; 4.
Combinatorial Arguments; 5. Combinatorial
Number Theory; 6. What?
Is this graph theory? 7. Hints and solutions;
Index
Series: Progress in Mathematics
384 pages , 6 1/8 x 9 , hardcover
ISBN: 3-7643-3207-7, published 2003
expected release date: 06/30/2003
ABOUT THIS BOOK
This volume is devoted to the theme of Noncommutative
Harmonic
Analysis and consists of articles in honor
of Jacques Carmona,
whose scientific interests range through
all aspects of Lie group
representations. Thus, the topics encompass
the theory of
representations of reductive Lie groups,
and especially the
determination of the unitary dual, the problem
of geometric
realizations of representations, harmonic
analysis on reductive
symmetric spaces, the study of automorphic
forms, and results in
harmonic analysis that apply to the Langlands
program.
General Lie groups is also discussed, particularly
from the orbit
method perspective, which has been a constant
source of
inspiration for both the theory of reductive
Lie groups and for
general Lie groups. Also covered is Kontsevich
quantization,
which has appeared in the recent years as
a powerful tool.
Contributors to this volume include: Baldoni,
Barbasch, Barchini,
Bieliavsky, Bouaziz, Delorme, Van Den Ban,
Harinck, Hersant,
Khalgui, Knapp, Kostant, Libine, Mantini,
Pevzner, Rossmann,
Rubenthaler, Schmid, Torasso, Vergne.
TABLE OF CONTENTS
Baldoni/Vergne: Morris identities for a system
of type An *
Barbasch: A reduction theorem for the unitary
spectrum of U(p,q)
* Barchini: Zeta distributions and Boundary
values of poisson
Transforms * Bouaziz: Quelques remarques
sur les distributions
invariantes dans les algebres de Lie reductives
* Delorme * Van
Den Ban * Pascale Harinck: Transfert d'orbitales
integrales *
Hersant: Sur certains espaces d'homologie
relative d'algebres de
Lie- Le cas des polarisations positives *
Khalgui/Torasso:
Formule de Plancherel pour les groupes algebriques
* Knapp: Some
tiny unitary representations of indefinite
orthogonal groups *
Kostant: A Branching law for subgroups fixed
by an involution and
a non compact analogue of the Borel-Weil
theorem * Libine: A
Localization Argument for Characters of Reductive
Lie Groups: An
Introduction and Examples * Mantini * Bieliavsky/Pevzner:
Symmetric Spaces and star representations.
The Poincare disk *
Rossmann: McKay correspondence and characters
of finite subgroups
of SU(2) * Rubenthaler * Schmid
350 pages , 6 1/8 x 9 , 20 illus., hardcover
ISBN: 3-7643-4173-4, published 2004
expected release date: 04/02/2004
ABOUT THIS BOOK
This work will serve as an excellent first
course in modern
analysis. Key topics in nonlinear pde's as
well as several
fundamental tools and methods are presented;
few prerequisites
are required of the reader. Challenging exercises,
examples, and
illustrations help explain the rigorous analytic
basis for the
Navier--Stokes equations, mean curvature
flow equations, and
other important equations describing real
phenomena.
The main focus of the text is on showing
how self-similar
solutions are useful in studying the behavior
of solutions of
nonlinear partial differential equations,
especially those of
parabolic type. The exposition moves systematically
from the
basic to more sophisticated concepts, and
in the final chapters
recent developments and several open problems
are presented. An
extensive index is provided.
Written for graduate students and researachers
by one of Japan's
leading analysts, this will be an excellent
resource for self-study
or classroom use.
TABLE OF CONTENTS
Introduction * Part I: Asymptotic Behavior
of Solutions of
Partial Differential Equations * Behavior
Near Time Infinity of
Solution of the Heat Equation * Behavior
Near Time Infinity of
Solutions of the Vorticity Equation * Self-Similar
Solutions of
Various Equations * Part II: Useful Analytic
Tools * Various
Properties of Solutions of the Heat Equation
* Compactness
Theorems * Calculus Inequalities * Convergence
Theorems in the
Theory of Integrations * Solutions to Exercises
* Bibliography *
Index