EMS Series of Lectures in Mathematics
ISBN 978-3-03719-061-6
December 2009, 239 pages, softcover, 17 x 24 cm.
This text provides an introduction to noncommutative geometry and some
of its applications. The book can be used either as a textbook for a graduate
course on the subject or for self-study. It will be useful for graduate
students and researchers in
mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature
of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background
material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis,
algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful.
Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing
conjectures in topology and geometry and has recently made headways in
theoretical physics and number theory. The book starts with a detailed
description of some of the most pertinent algebra-geometry correspondences
by casting geometric notions in algebraic terms, then proceeds in the second
chapter to the idea of a noncommutative space and how it is constructed.
The last two chapters deal with homological tools: cyclic cohomology and
Connes?Chern characters in K-theory and K-homology, culminating in one
commutative diagram expressing the equality of topological and analytic
index in a noncommutative setting. Applications to integrality of noncommutative
topological invariants are given as well.
xiv+520 pages, hard cover, ISBN 978-3-88538-407-6,
This book has been written as an introductory and advanced course in applied linear algebra for mathematicians, computer
scientists, engineers, and other scientists. The intention is to provide a gentle and sympathic introduction to many of the
problems of scientific computing, and the wide variety of methods used for their solutions. The presentation of each
numerical method is based on the successful teaching methodology of first
providing examples and geometric motivation for a method, and a concise
statement of the steps to carry out the computation. Only then a mathematical
derivation of the process is presented, followed by a discussion of the
more theoretical issues that are relevant to the use and understanding
of the method. To provide maximum teaching flexibility, each chapter and
each section begins with the basic, elementary material, and gradually
builds up to the more advanced material. Many applications of linear systems
and eigenvalue problems are also discussed. It exposes students to theoretical,
applied, and numerical mathematics and has applications in a diverse range
of disciplines.
The practical justification of the methods is presented through computer examples through the use of MATLAB. This book
explains everything one needs to know to begin using MATLAB to do all these
things and more intermediate and advanced users will find useful information
here, especially if they are making the switch to MATLAB 7.4 from the earlier
versions. The book is written in such a way that it will be very helpful
for juniors and seniors in mathematics, computer science, engineering,
and physics.
xiv+166 pages, soft cover, ISBN 978-3-88538-231-7,
The class of compact topological groups is perhaps the most understood
part of topological groups. This monograph deals with larger classes defined
by properties shared by compact groups. For instance, if G is a compact
topological group, then for every group H, the image of every closed subgroup
of G × H under the second projection is closed in H. Topological groups
with this property are called c-compact.
Is every c-compact topological group compact?
Chapter 1 is an elementary introduction to topological groups.
Chapter 2 presents cardinal invariants, a more specialized aspect of topological group theory.
Chapter 3 focuses on two compactness-like properties, namely, precompactness and minimality.
Chapter 4 relates to the main question by proving compactness theorems (that is, results of the type: if G is c-compact and
has an additional property, then G is compact), open mapping theorems,
and reduction theorems (reducing the general question to smaller classes
of groups).
Preface v
Introduction vii
Acknowledgments xi
Chapter 1: Preliminaries
1.1 Neighborhoods of the identity 2
1.2 Locally compact groups 15
1.3 Completeness 22
1.4 Notes 28
Chapter 2: Cardinal invariants of topological groups
2.1 The Gτ-topology and τ-representable groups 32
2.2 τ-balanced groups 36
2.3 τ-precompact groups 42
2.4 Closed subgroups of products 47
2.5 Notes 58
Chapter 3: Minimal and totally minimal groups
3.1 Precompactness 61
3.2 Minimality and total minimality 67
3.3 Extensions and products 77
3.4 Notes 84
Chapter 4: From c-compactness to sequential h-completeness
4.1 Basics 90
4.2 Characterizations using special filters 99
4.3 Open mapping and structure theorems 113
4.4 Compactness theorems 121
4.5 Special cases: Locally compact and discrete groups 131
4.6 Notes and open problems 135
Appendix: History of the problem of c-compactness 139
List of symbols 147
Bibliography 149
ISBN: 978-0-470-24877-5
Hardcover
640 pages
February 2010
Random Data provides first-rate, practical tools for dynamic data and statistical methods for engineering problems. This
revised bestseller presents the latest developed procedures and a complete rewrite of the Fast Fourier Transforms of applied
fields. Plus, this resource includes a new chapter on frequency domain
techniques. The updated book explores novel techniques on modern digital
data storage, oversampling, and temporal moments. With new problem sets
and examples, this guide is the ideal text and reference for students studying
random data analysis theory and applications.
ISBN: 978-0-470-51641-6
Hardcover
456 pages
May 2010
Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering,
medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample
size and many variables, especially in observational studies.
The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and
multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current
thinking.
Examines the most up-to-date methodologies of univariate and multivariate permutation testing.
Includes extensive software codes in MATLAB, R and SAS, featuring worked
examples, and uses real case studies from both experimental and observational
studies.
Includes a standalone free software NPC Test Release 10 with a graphical
interface which allows practitioners from every scientific field to easily
implement almost all complex testing procedures included in the book.
Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses.
A supplementary website containing all of the data sets examined in the book along with ready to use software codes.
Together with a wide set of application cases, the Authors present a thorough
theory of permutation testing both with formal description and proofs,
and analysing real case studies. Practitioners and researchers, working
in different scientific fields such as engineering, biostatistics, psychology
or medicine will benefit from this book.
Advanced Studies in Pure Mathematics Vol.56
This volume constitutes the Proceedings of the Fourth Franco-Japanese Symposium on Singularities held at Toyama in August
2007 and also the Workshop on Singularities held at Niigata prior to this Symposium. Recently the research on singularities
is widely expanding and is now applied in various areas in Mathematics and other sciences. Experts of singularities from many
different fields are contributing their articles, mostly on original results and some surveys. The reader will benefit of
knowing the vividly developing domains and will be inspired by many different approaches to singularities.