Publication is planned for May 2004 | Hardback
| 220 pages |
ISBN: 0-521-83653-0
The theory of Levy processes in Lie groups
is not merely an
extension of the theory of Levy processes
in Euclidean spaces.
Because of the unique structures possessed
by non-commutative Lie
groups, these processes exhibit certain interesting
limiting
properties which are not present for their
counterparts in
Euclidean spaces. These properties reveal
a deep connection
between the behaviour of the stochastic processes
and the
underlying algebraic and geometric structures
of the Lie groups
themselves. The purpose of this work is to
provide an
introduction to Levy processes in general
Lie groups, the
limiting properties of Levy processes in
semi-simple Lie groups
of non-compact type and the dynamical behavior
of such processes
as stochastic flows on certain homogeneous
spaces. The reader is
assumed to be familiar with Lie groups and
stochastic analysis,
but no prior knowledge of semi-simple Lie
groups is required.
Contents
1. Levy processes in Lie groups; 2. Generator
and stochastic
integral equation of a Levy process; 3. Semi-simple
Lie gropus of
non-compact type; 4. Limiting propersties
of Levy processes; 5.
Rate of convergence; 6. Levy processes as
stochastic flows.
Publication is planned for June 2004 | Hardback
| 150 pages |
ISBN: 0-521-83821-5
This book provides a unified approach to
much of the theories of
equivalence and duality between categories
of modules that has
transpired over the last 45 years. In particular,
during the past
dozen or so years many authors (including
the authors of this
book) have investigated relationships between
categories of
modules over a pair rings that are induced
by both covariant and
contravariant representable functors, in
particular by tilting
and cotilting theories. By here collecting
and unifying the basic
results of these investigations with innovative
and easily
understandable proofs, the authors’ aim
is to provide an aid to
further research in this central topic in
abstract algebra, and a
reference for all whose research lies in
this field.
Contents
0. Preface; 1. Some module theoretic observations;
2.
Representable equivalences; 3. Tilting modules;
4. Representable
dualities; 5. Cotilting; A. Adjoints and
category equivalnece; B.
Noetherian serial rings.
Description
In this volume, the author formulates and
proves a duality
theorem for the equivariant stable homotopy
category, using the
language of Verdier duality from sheaf theory.
He works with the
category of $G$-equivariant spectra (for
a compact Lie group $G$)
parametrized over a $G$-space $X$ and considers
a smooth
equivariant family $f: X \rightarrow Y$,
which is a $G$-equivariant
bundle whose fiber is a smooth compact manifold,
and with actions
of subgroups of $G$ varying smoothly over
$Y$. Then the main
theorem is a natural equivalence between
a certain direct image
functor $f_*$ and a "direct image with
proper support
functor" $f_!$, in the stable equivariant
homotopy category
over $Y$. In particular, the Wirthmuller
and Adams isomorphisms
in equivariant stable homotopy theory turn
out to be special
cases of this duality theorem.
Contents
Introduction
Motivation
Spaces and spectra over a base space
Closed model structure on spectra over a
base
The equivariant duality theorem
Proof of the main theorem
The Wirthmuller and Adams isomorphisms
Proof of results on the model structure over
a base
Bibliography
Details:
Series: Asterisque, Number: 285
Publication Year: 2003
ISBN: 2-85629-136-8
Paging: 108 pp.
Binding: Softcover
ISBN: 0-471-43307-1
Paperback
320 pages
February 2003, Wiley-IEEE Press
Description
Everything you need to know?basic essential
concepts?about
calculus
For anyone looking for a readable alternative
to the usual
unwieldy calculus text, here’s a concise,
no-nonsense approach
to learning calculus. Following up on the
highly popular first
edition of Understanding Calculus, Professor
H. S. Bear offers an
expanded, improved edition that will serve
the needs of every
mathematics and engineering student, or provide
an easy-to-use
refresher text for engineers.
Understanding Calculus, Second Edition provides
in a condensed
format all the material covered in the standard
two-year calculus
course. In addition to the first edition’s
comprehensive
treatment of one-variable calculus, it covers
vectors, lines, and
planes in space; partial derivatives; line
integrals; Green’s
theorem; and much more. More importantly,
it teaches the material
in a unique, easy-to-read style that makes
calculus fun to learn.
By explaining calculus concepts through simple
geometric and
physical examples rather than formal proofs,
Understanding
Calculus, Second Edition, makes it easy for
anyone to master the
essentials of calculus.
If the dry "theorem-and-proof"
approach just doesn’t
work, and the traditional twenty pound calculus
textbook is just
too much, this book is for you.
ISBN: 0-471-26610-8
Hardcover
633 pages
April 2003
Description
The electronic component of the book is based
on the widely used
and highly praised Mathematica software package.
Each chapter of the bookis a Mathematica
notebook with links to
web-based material.
The methods are applied to a range of problems
taken from physics
and engineering.
The book covers elementary and advaned numerical
methods used in
modern scientific computing.
Table of Contents
Preface.
Ordinary Differential Equations in the Physical
Sciences.
Fourier Series and Transforms.
Introduction to Linear Partial Differential
Equations.
Eigenmode Analysis.
Partial Differential Equations in Infinite
Domains.
Numerical Solution of Linear Partial Differential
Equations.
Nonlinear Partial Differential Equations.
Introduction to Random Processes.
An Introduction to Mathematica (Electronic
Version Only).
Appendix: Finite-Differenced Derivatives.
Index.