The book presents a systematic and unified
study of geometric nonlinear functional analysis.
This area has its classical roots in the
beginning of the twentieth century
and is now a very active research area, having
close connections to geometric measure theory,
probability, classical analysis, combinatorics,
and Banach space theory.
The main theme of the book is the study of
uniformly continuous and Lipschitz functions
between Banach spaces
(e.g., differentiability, stability, approximation,
existence of extensions, fixed points, etc.).
This study leads naturally also to the classification
of Banach space
and of their important subsets (mainly spheres)
in the uniform and Lipschitz categories.
Nov. 1999 313 pp.
0-8218-0835-4
A. M. S.
The past two decades have brought explosive
growth in 4-manifold theory.
Many books are currently appearing that approach
the topic from viewpoints such as
gauge theory or algebraic geometry.
This volume, however, offers an exposition
from a topological point of view.
It bridges the gap to other disciplines and
presents classical
but important topological techniques that
have not previously appeared in the literature.
Part I of the text presents the basics of
the theory at the second-year graduate level
a offers an overview of current research.
Part II is devoted to an exposition of Kirby
calculus, or handlebody theory on 4-manifolds.
It is both elementary and comprehensive.
Part III offers in depth a broad range of
topics from current 4-manifold research.
Oct 1999 576 pp.
0-8218-0994-6
A. M. S.
Volume 1 in this series laid the mathematical
foundations of sampling theory;
Volume 2 surveys the many applications of
the theory both within mathematics and in
other areas of science.
Topics range over a wide variety of areas,
and each application is given a modern treatment.
Contents
* 1 Applications of sampling theory to combintorial
analysis,
Stirling numbers, special functions and the
Riemann zeta function.
* 2 Sampling theory and the arithmetic Fourier
transform
* 3 Derivative sampling - a pardigm example
of multi-channel methods
* 4 Computational methods in linear prediction
for band-limited signals based on past samples
* 5 Interpolation and sampling theories,
and linear ordinary boundary value problems
* 6 Sampling by generalized kernels
* 7 Sampling theory and wavelets
* 8 Approximation by translates of a radial
function
* 9 Almost sure sampling restoration of band-limited
stochastic signals
* 10 Abstract harmonic analysis & the
sampling theorem
July 1999 304 pp.
0-19-853496-5 .
Oxford University Press
Astronomy and celestial mechanics alwoys
initated great
breakthroughs in the development of science
and mathematics.
The authors of the film describe these developments
starting with Ptolemy
and ending with contemporary sotellite-streering
techniques.
The explanations come via conversations,
illustrations,
famous scentific publication and animation.
The film is of interest to everyone with
an interest
in mathematics and science, from school students
to researshers.
July 1999 30 minutes
3-540-92638-2
Springer
The authors of this film explain the topic
of
symmetry in mathematics with examples from
Islamic art.
The mathemtiical background - plane crystallographic
groups -
is spectacularly illustrated by examples
at the Alhambra in Granada, Spain.
This film will be enjoyed by everyone interested
in
mathematics, from school students to researchers.
July 1999 20 minutes
3-540-92639-9
Springer
A man with no home and nojob, Poul Erdos
was the most prolific mathematician who ever
lived.
A wondering genius, Erdos, who died in 1996
at the age of 83,
spent his life engaged in a cosmic struggle
to uncovr truths hidden by a stubborn adversary-God.
In N is a Number he describes this metaphysical
duel with
the same wry humor he applied to politics,
relationship and death.
The documentary follows him through four
countries to discover what makes mathematicians
tick.
N is a Number presents Erdos’ mathematical
quest, its personal and philosophical dimensions,
and the tragic historical events that molded
his life.
Two animated sequences illustrate kinds ff
problems Erdos pursued throughout his life.
July 1999 60 minutes
3-540-92641-0 6,790.
Springer
The authors' aim is to provide the reader
with the very basic knowledge necessary
to begin research on differential equations
with professional ability.
The Selection of topics should provide the
reader with methods and results
which are applicable in a variety of different
fields.
The book is divided into four parts.
The first covers fundamental existence, uniqueness,
smoothness with respect to data, and nonuniqueness.
The second part describes the basic results
concerning linear differential equations,
the third deals with nonlinear equations.
In the last Part the authors write about
the basic results concerning power series
solutions.
Aug. 1999 454 pp.
3-540-6594l-2
Springer
Integrating both classical and modern treatments
of difference
equations, this book contains the most updated
and comprehensive
material on stability, Z-transform, discrete
control theory,
asymptotic theory, continued fractions and
orthogonal polynomials.
Sep. 1999 470 pp.
0-387-98830-0
Springer
Originally published by Prentice-Hall 1967
Maxilmum Principles are central fo the theory
and applications of
second-order partial differen tiai equations
and systems.
This self-contained text establishes the
fundamental prlnciples and provides a variety
of applitations.
July 1999 2nd rev. and exp. ed. 501 pp.June
1999 261 pp.
3-540-96068-6
Springer
Contents:
Linear Algebra: Random Vectors:
Gamma, Dirichlet and F Distributions.- Invariance.-
Multivariate Normal.-
Multivariate Sampling.- Wishart Distributions.-
Tests on Mean and Variance.-
Multivariate Regression.- Principal Components.-
Canonical Correlations.-
Asymptotic Expansions.- Robustness.- Bootstrap
Confidence Regions and Tests.
Intended as a textbook for students taking
a first graduate course in the subject,
as well as for the general reference of interested
research workers, this text discusses,
in a readable form, developments from recently
published work on
certain brood topics not otherwise easily
accessible,
such as robust inference and the use of the
bootstrap in a multivariate setting.
A minimum background expected of the reader
would include at least two courses in mathematical
statistics,
and certainly some exposure to the calculus
of several variables together
with the descriptive geometry of linear algebra.
Sep. 1999 315 pp.
0-387-98739-8
Springer
Designed for a Master's level course in stochastic
processes,
this text features the introduction and use
of martingales,
allowing much more to be done with Brownian
motion,
e.g., option pricing, and queueing theory
are integrated into
the Continuous Time Markov Chain and Renewal
Theory chapters.
Sep. 1999 305 pp.
0-387-98836-X
Springer
Originally published by BI Wissenschafts-Verlag
1991
The topic of this book is finite group actions
and their use in order to
approach finite unlabeled structures by defining
them as orbits offinite groups of sets.
Well-known examples are graph, linear codes,
chemical isomers, spin configurations,
isomorphism classes of combinatorial designs
etc.
Aug.1999 454 pp.
3-540-6594l-2
Springer
Revised by D. Alevras
This book offers a comprehensive treatment
ofinear programming as well as
of the optimization of linear functions over
polyhedra in finite dimensional Euclidean
vector spaces.
An introduction surveying fiffty years oflinear
optimization is given.
The book can serve both as a graduate textbook
for linearprogramming and as
a text for advanced topics classes or semilnars.
Exercises as well as several case studies
are included.
The book is based on the author’s long term
experience in teaching and research.
July 1999 2nd rev. and exp. ed. 501 pp.
3-540165833-5
Springer