Runde, V., University of Alberta, Edmonton, AB, Canada
Lectures on Amenability
2002. XIII, 296 pp. Softcover
3-540-42852-6
The notion of amenability has its origins
in the beginnings of
modern measure theory: Does a finitely additive
set function
exist which is invariant under a certain
group action? Since the
1940s, amenability has become an important
concept in abstract
harmonic analysis (or rather, more generally,
in the theory of
semitopological semigroups). In 1972, B.E.
Johnson showed that
the amenability of a locally compact group
G can be characterized
in terms of the Hochschild cohomology of
its group algebra L^1(G):
this initiated the theory of amenable Banach
algebras. Since
then, amenability has penetrated other branches
of mathematics,
such as von Neumann algebras, operator spaces,
and even
differential geometry. Lectures on Amenability
introduces second
year graduate students to this fascinating
area of modern
mathematics and leads them to a level from
where they can go on
to read original papers on the subject. Numerous
exercises are
interspersed in the text.
Contents:
0 Paradoxical decompositions
1 Amenable, locally comact groups
2 Amenable Banach algebras
3 Exemples of amenable Banach algebras
4 Amenability-like properties
5 Banach homology
6 C* and W*-algebras
7 Bounded approximate identities for Fourier
algebras
8 Geometry of spaces of homomorphisms
Open problems
A Abstract harmonic analysis
B The algebraic tensor products
C Banach space properties
D Operator spaces
List of symbols
References
Index
Series: Lecture Notes in Mathematics. VOL.
1774
Nekorkin, V.I., University of Nizhny Novgorod, Russia;
Velarde, M.G., Universidad Complutense de
Madrid, Spain
Synergetic Phenomena in Active Lattices
Patterns, Waves, Solitons, Chaos
2002. XVI, 340 pp. 207 figs. Hardcover
3-540-42715-5
Within nonlinear spatio-temporal dynamics,
active lattice systems
are of relevance to the study of multi-dimensional
dynamical
systems and the theory of nonlinear waves
and dis- sipative
structures of extended systems. In this book,
the authors deal
with basic concepts and models, with methodolo-
gies for studying
the existence and stability of motions, understanding
the
mechanisms of formation of patterns and waves,
their propagation
and interactions in active lattice systems,
and about how much
cooperation or competition bet- ween order
and chaos is crucial
for synergetic behavior and evolution. The
results described in
the book have both in- ter- and trans-disciplinary
features and a
fundamental cha- racter. It is a textbook
for graduate courses in
nonlinear sciences, including physics, biophysics,
biomathematics, bioengineering, neurodynamics,
electrical and
electronic engineering, mathematical economics,
and computer
sciences.
Keywords: Lattice Dynamics, Soliton, Self-Organization,
Waves,
Chua ' s Circuit, Chaotic Attractors, Stability
.
Contents: From the contents: Introduction.-
Solitary Waves, Bound
Soliton States, and Chaotic Soliton Trains
in a Dissipative
Boussinesq-Korteweg-de Vries Equation.- Self-Organization
in a
Long Josephson Junction.- Spatial Structures,
Wave Fronts,
Periodic Waves, Pulses and Solitary Waves
in a One-Dimensional
Array of Chua's Circuits.- Patterns, Spatial
Disorder and Waves
in a Dynamical Lattice of Bistable Units.-
Mutual
Synchronization, Control and Replication
of Patterns and Waves in
Coupled Lattices Composed of Bistable Units.-
Spatio-Temporal
Chaos in Bistable Coupled Map Lattices.-
Conclusions and
Perspective.- Appendices.- Bibliography.-
Subject Index.
Series: Springer Series in Synergetics.
Rosanov, N.N., Research Centre "Vavilov State Optical Institute",
St. Petersburg, Russia
Spatial Hysteresis and Optical Patterns
2002. XII, 296 pp. 149 figs. 2 tabs. Hardcover
3-540-42793-7
The book is devoted to the study of optical
patterns and to
optical bistability and hysteresis. In its
methodology it is at
the intersection of investigations in synergetics
and modern
nonlinear optics. This first monograph on
optical patterns
addresses researchers as well as students.
The author studies the
rich class of spatially distributed bistable
optical systems, and
especially dissipative optical solitons which
resemble molecules,
crystals or biological objects when combined.
The author studies
further the inhomogeneities of bistable systems
and gives a
consistent description of spatial hysteresis.
Further topics
include diffractive mechanisms for coupling,
three-dimensional
optical solitons, quantum aspects and optical
information
processing, lasers with a saturable absorber,
non-linear
waveguides and fibers with nonlinear gain
or losses.
Keywords: Hysteresis, Optical Patterns, Complex
Systems,
Nonlinear Optics, Optical Solitons, Optical
Information
Processing .
Contents: Introduction to Physics of Distributed
Bistable Systems.-
Increasing Absorption Bistability.- Hybrid
Bistable Devices.-
Driven Nonlinear Interferometers.- Nonlinear
Radiation Reflection.-
Bistable Laser Schemes.- Conclusion: Comparing
Different Types of
Optical Patterns.- Paraxial and Nonparaxial
Radiation Propagation.-
Constitutive Equations for Medium Nonlinear
Polarization.-
Transverse Structures and Digital Optical
Computing.- Bistability
of Quantum Anharmonic Oscillator.- Transverse
Effects for
Squeezed States of Light.- References.- Index.
Series: Springer Series in Synergetics.
Davis, C.S., Elan Pharmaceuticals, San Diego, CA, USA
Statistical Methods for the Analysis of Repeated
Measurements
2002. Approx. 425 pp. Hardcover
0-387-95370-1
This book provides a comprehensive summary
of a wide variety of
statistical methods for the analysis of repeated
measurements. It
is designed to be both a useful reference
for practitioners and a
textbook for a graduate-level course focused
on methods for the
analysis of repeated measurements.
The important features of this book include
a comprehensive
coverage of classical and recent methods
for continuous and
categorical outcome variables; numerous homework
problems at the
end of each chapter; and the extensive use
of real data sets in
examples and homework problems.
The 80 data sets used in the examples and
homework problems can
be downloaded from www.springer-ny.com at
the list of author
websites. Since many of the data sets can
be used to demonstrate
multiple methods of analysis, instructors
can easily develop
additional homework problems and exam questions
based on the data
sets provided. In addition, overhead transparencies
produced
using TeX and solutions to homework problems.
Contents: Introduction.- Univariate Methods.-
Normal-Theory
Methods: Unstructured Multivariate Approach.-
Normal Theory
Methods: Multivariate Analysis of Variance.-
Normal-Theory
Methods: Repeated Measures ANOVA.- Normal
Theory Methods: Linear
Mixed Models.- Weighted Least Squares Analysis
of Repeated
Categorical Outcomes.- Randomization Model
Methods for One-Sample
Repeated Measurements.- Methods Based on
Extensions of
Generalized Linear Models.- Nonparametric
Methods.
Series: Springer Texts in Statistics.
Honerkamp, J., University of Freiburg, Germany
Statistical Physics
An Advanced Approach with Applications. Web-enhanced
with
Problems and Solutions
2nd ed. 2002. X, 510 pp. 82 figs., 7 tabs.,
with 60 problems and solutions. Hardcover
3-540-43020-2
The application of statistical methods to
physics is essential.
This unique book on statistical physics offers
an advanced
approach with numerous applications to the
modern problems
students are confronted with. Therefore the
text contains more
concepts and methods in statistics than the
student would need
for statistical mechanics alone. Methods
from mathematical
statistics and stochastics for the analysis
of data are discussed
as well. The book is divided into two parts,
focusing first on
the modeling of statistical systems and then
on the analysis of
these systems. Problems with hints for solution
help the students
to deepen their knowledge. The second edition
has been updated
and enlarged with new material on estimators
based on a
probability distribution for the parameters,
identification of
stochastic models from observations, and
statistical tests and
classification methods (Chaps. 10-12). Moreover,
a customized set
of problems with solutions is accessible
on the Web. The author
teaches and conducts research on stochastic
dynamical systems at
the University of Freiburg, Germany.
Keywords: Statistical physics, probability
theory, stochastic
processes, stochastic models, statistical
tests, random variables
.
Contents: Statistical Physics is more than
Statistical Mechanics.-
Part I. Modeling of Statistical Systems:
Random Variables:
Fundamentals of Probability Theory and Statistics.-
Random
Variables in State Space: Classical Statistical
Mechanics of
Fluids.- Random Fields: Textures and Classical
Statistical
Mechanics of Spin Systems.- Time-Dependent
Random Variables:
Classical Stochastic Processes.- Quantum
Random Systems.- Changes
of External Conditions.- Part II. Analysis
of Statistical Systems:
Estimation of Parameters.- Signal Analysis:
Estimation of Spectra.-
Estimators Based on a Probability Distribution
for the Parameters.-
Identification of Stochastic Models from
Observations.-
Statistical Tests and Classification Methods.-
Problems + Hints
and Solutions.- References.- Index.
Series: Advanced Texts in Physics.
JEFFREY R. WEEKS
THE SHAPE OF SPACE, SECOND EDITION
【J R ウイークス 「空間の形: 局面と３次元多様体を視る」待望の
第２版】
SERIES: Pure and Applied Mathematics - Vol.249
December 2001 328 pages, illustrated
ISBN: 0-8247-0709-5 (Adoption Price: $20.00 Available for orders
of five or more copies, for classroom use
only)
J R ウイークス「空間の形」の第２版。真の宇宙の形を決定する実験に関する新章を加えた新版では，２次元・３次元空間の幾何学を分かりやすく概観し，われわれの住む宇宙の形についての新たな可能性を視覚化している。数多くのイラストや章末問題を収録した本書は，数学に興味を持つ広範な読者を対象に，幾何学と観測的宇宙論の最新をわかり易く解説している。位相数学の入門書としても高校から大学まで学生・教育図書室必備の書といえる。
the Second Edition of The Shape of Space:
* offers three new chapters that apply topology
to cosmology
* illustrates the connection between geometry
and the behavior of the physical universe
* seeks patterns in the arrangement of galaxies
* explains how radiation remaining from the
big bang may reveal the actual shape of the
universe
【Reviews】
Abundant praise for the previous edition...
"This is a wonderful book, loaded with
interesting puzzles and new information."
-Rudy Rucker, author of Fourth Dimension
and Infinity and the Mind
"...stimulating and mind-bending experience."
-Mathematical Spectrum
"...fascinating....
"The book is well supplied with clearly
drawn diagrams and contains an instructive
collection of exercises."
-Proceedings of the Edinburgh Mathematical
Society
【CONTENTS】SURFACES AND THREE-MANIFOLDS:
Flatland; Gluing; Vocabulary; Orientability;
Connected Sums; Products; Flat Manifolds;
Orientability vs. Two-Sidedness. GEOMETRIES
ON SURFACES: The Sphere; The Hyperbolic Plane;
Geometries on Surfaces; The Gauss?Bonnet
Formula and the; Euler Number. GEOMETRIES
ON THREE-MANIFOLDS: Four-Dimensional Space;
The Hypersphere; Hyperbolic Space; Geometries
on Three-Manifolds I; Bundle;s Geometries
on Three-Manifolds II. THE UNIVERSE: The
Universe; The History of Space; Cosmic Crystallography;
Circles in the Sky. APPENDIX A Answers; B
Bibliography; C Conway’s ZIP Proof; Index.