Description: This is the second volume
of a two-volume set that provides a modern
account of basic Banach algebra theory including
all known results on general Banach *-algebras.
The author emphasizes the roles of *-algebra
structure and explores the algebraic results
which underlie the theory of Banach algebras
and *-algebras. Proofs are presented in complete
detail at a level accessible to graduate
students. The books will become the standard
reference for the general theory of *-algebras.
This second volume deals with *-algebras.
Chapter 9 develops the theory of *-algebras
without additional restrictions. Chapter
10 proves nearly all the results previously
known for Banach *-algebras and hermitian
Banach *-algebras for *-algebras with various
essentially algebraic restrictions. Chapter
11 restates the previous results in terms
of Banach *-algebras and uses them to prove
results explicitly involving the complete
norm. Chapter 12 is devoted to locally compact
groups and the *-algebras related to
them.
Contents: 9. *-algebras; 10. Special
*-algebras; 11. Banach *-algebras; 12. Locally
compact groups and their *-algebras.
ISBN, Binding, : 0521366380 Hardback
Approximate Publication date: 1 May
2000
Main Subject Category: Mathematics
- analysis, probability
Series: Encyclopedia of Mathematics
and its Applications
Description: Symmetry is the key to
solving differential equations. There are
many well-known techniques for obtaining
exact Solutions, but most of them are special
cases of a few powerful symmetry methods.
Furthermore, these methods can be applied
to differential equations of an unfamiliar
type; they do not rely on special 'tricks'.
Instead, a given differential equation is
forced to reveal its symmetries, which are
then used to construct exact solutions. This
book is a straightforward introduction to
the subject, and is aimed at applied mathematicians,
physicists, and engineers. The presentation
is informal, using many worked examples to
illustrate the main symmetry methods. It
is written at a level suitable for postgraduates
and advanced undergraduates, and is designed
to enable the reader to master the main techniques
quickly and easily. The book contains methods
that have not previously appeared in a text.
These include methods for obtaining discrete
symmetries and integrating factors.
Contents: 1. Introduction to symmetries;
1.1. Symmetries of planar objects; 1.2. Symmetries
of the simplest ODE; 1.3. The symmetry condition
for first-order ODEs; 1.4. Lie symmetries
solve first-order ODEs; 2. Lie symmetries
of first order ODEs; 2.1. The action of Lie
symmetries on the plane; 2.2. Canonical coordinates;
2.3. How to solve ODEs with Lie symmetries;
2.4. The linearized symmetry condition; 2.5.
Symmetries and standard methods; 2.6. The
infinitesimal generator; 3. How to find Lie
point symmetries of ODEs; 3.1 The symmetry
condition. 3.2. The determining equations
for Lie point symmetries; 3.3. Linear ODEs;
3.4. Justification of the symmetry condition;
4. How to use a one-parameter Lie group;
4.1. Reduction of order using canonical coordinates;
4.2. Variational symmetries; 4.3. Invariant
solutions; 5. Lie symmetries with several
parameters; 5.1. Differential invariants
and reduction of order; 5.2. The Lie algebra
of point symmetry generators; 5.3. Stepwise
integration of ODEs; 6. Solution of
ODEs with multi-parameter Lie groups; 6.1
The basic method: exploiting solvability;
6.2. New symmetries obtained during reduction;
6.3. Integration of third-order ODEs with
sl(2); 7. Techniques based on first integrals;
7.1. First integrals derived from symmetries;
7.2. Contact symmetries and dynamical symmetries;
7.3. Integrating factors; 7.4. Systems of
ODEs; 8. How to obtain Lie point symmetries
of PDEs; 8.1. Scalar PDEs with two dependent
variables; 8.2. The linearized symmetry condition
for general PDEs; 8.3. Finding symmetries
by computer algebra; 9. Methods for obtaining
exact solutions of PDEs; 9.1. Group-invariant
solutions; 9.2. New solutions from known
ones; 9.3. Nonclassical symmetries; 10. Classification
of invariant solutions; 10.1. Equivalence
of invariant solutions; 10.2. How to classify
symmetry generators; 10.3. Optimal systems
of invariant solutions; 11. Discrete symmetries;
11.1. Some uses of discrete symmetries; 11.2.
How to obtain discrete symmetries from
Lie symmetries; 11.3. Classification of discrete
symmetries; 11.4. Examples.
ISBN, Binding, : 0521497035 Hardback
ISBN, Binding, : 0521497868 Paperback 5
Approximate Publication date: 20 March
2000
Main Subject Category: Applied mathematics,
mathematical physics
Series: Cambridge Texts in Applied
Mathematics, 22
Description: In 1928 the physicist
Paul Dirac predicted the existence of antimatter
in a mirror world, where the electrical charges
on particles would be opposite to those of
ordinary matter. This mirror world is found,
fleetingly, at the quantum level, with positrons
the counterpart of electrons, and antiprotons
the opposite of protons. This book introduces
the Lewis Carroll world of antimatter without
using technical language or equations. The
author shows how the quest for symmetry in
physics slowly revealed the properties of
antimatter. When large particle accelerators
came on line, the antimatter debris of collisions
provided new clues on its properties. This
is a fast-paced and lucid account of how
science fiction became fact.
Contents: 1. Science fiction becomes
science fact; 2. Mirror worlds; 3. An imbalanced
kit of electrical parts; 4. The quantum master;
5. Positive proof; 6. The back passage of
time; 7. The quark and the antiquark; 8.
Broken mirrors; 9. The cosmic corkscrew;
10. Antiparticle collision course; 11. Setting
a trap for antimatter; 12. Glue versus antichemistry;
13. Antimatter in action; 14. Antimatter
of the utmost gravity.
ISBN, Binding, : 0521652529 Hardback
Approximate Publication date: 2 May
2000
Main Subject Category: Physics (general)
Description: This text provides a comprehensive
introduction to the physical principles and
design of particle detectors, covering all
major detector types in use today. The book
begins with a reprise of the size and energy
scales involved in different physical processes.
It then considers non-destructive methods,
including the photoelectric effect, photomultipliers,
scintillators, Cerenkov and transition radiation,
scattering and ionisation and the use of
magnetic fields in drift and wire chambers.
A complete chapter is devoted to silicon
detectors. In the final part of the book,
the author discusses destructive measurement
techniques including Thompson and Compton
scattering, Bremsstrahlung and calorimetry.
Throughout the book, emphasis is placed on
explaining the physical principles on which
detection is based, and showing, by considering
appropriate examples, how those principles
are best utilised in real detectors. This
approach also reveals the limitations that
are intrinsic to different devices.
Exercises and detailed further reading lists
are included.
Contents: Part I. Introduction: 1.
Size, energy, cross section; Part II. Non-Destructive
Measurements: Part II. A. Time and Velocity:
2. The photoelectric effect, photomultipliers,
scintillators; 3. Cerenkov radiation; 4.
Transition radiation; Part II. B. Scattering
and Ionization: 5. Elastic EM scattering;
6. Ionization; Part II. C. Position and Momentum:
7. Magnetic fields; 8. Drift and diffusion
in materials, wire chambers; 9. SI detectors;
Part III. Destructive Measurements: Part
III. A. Radiation: 10. Radiation and photon
scattering; Part III. B. Energy Measurements:
11. EM Calorimetry; 12. Hadronic calorimetry;
Part IV. The Complete Set of Measurements:
13. Summary; Appendices.
ISBN, Binding, : 0521662265 Hardback
Approximate Publication date: 6 June
2000
Main Subject Category: Nuclear physics,
cosmology
Series: Cambridge Monographs on Particle
Physics, Nuclear Physics and Cosmology, 12
Description: This book provides a comprehensive
account of a key (and perhaps the most important)
theory upon which the Taylor-Wiles proof
of Fermat's last theorem is based. The book
begins with an overview of the theory of
automorphic forms on linear algebraic groups
and then covers the basic theory and recent
results on elliptic modular forms, including
a substantial simplification of the Taylor-Wiles
proof by Fujiwara and Diamond. It contains
a detailed exposition of the representation
theory of profinite groups (including deformation
theory), as well as the Euler characteristic
formulas of Galois cohomology groups. The
final chapter presents a proof of a non-abelian
class number formula and includes several
new results from the author. The book will
be of interest to graduate students and researchers
in number theory (including algebraic and
analytic number theorists) and arithmetic
algebraic geometry.
Contents: Preface; 1. Overview of modular
forms; 2. Representations of a group; 3.
Representations and modular forms; 4. Galois
cohomology; 5. Modular L-values and Selmer
groups; Bibliography; Subject index; List
of statements; List of symbols.
ISBN, Binding, : 052177036X Hardback
Approximate Publication date: 24 May
2000
Main Subject Category: Number theory
Series: Cambridge Studies in Advanced
Mathematics, 69
Comparable titles: LAUMON/Cohomology
of Drinfeld Modular Varieties v1/1995/0521
470609
LAUMON/Cohomology of Drinfeld Modular
Varieties v2/1997/0521 470617
KLINGEN/Lectures on Siegel Modular
Forms/1990/0521 350522
HIDA/Elementary Theory of L-functions
and Eisenstein Series/1993/0521 434114
Randomness and Complexity
Description: The discrepancy method
is the glue that binds randomness and complexity.
It is the link between discrepancy theory,
an area of mathematics concerned with irregularities
in distributions, and the seemingly unrelated
subject of randomized algorithms. The discrepancy
method has been the most fruitful line of
attack on a pivotal computer science question:
what is the computational power of random
bits? It has also played a major role in
recent developments in complexity theory.
This books tells the story of the discrepancy
method in a few short independent vignettes.
The itinerary includes such topics as communication
complexity, rapidly mixing Markov chains,
points on a sphere, derandomization, geometric
sampling and VC-dimension theory, circuit
complexity, and multidimensional searching.
The mathematical treatment is thorough and
self-contained, with minimal prerequisites.
Thus the book should appeal to students as
well as researchers in computer science,
operations research, pure and applied
mathematics, and engineering.
Contents: 1. Combinatorial discrepancy;
2. Upper bounds in geometric discrepancy;
3. Lower bounds in geometric discrepancy;
4. Sampling; 5. Geometric searching; 6. Complexity
lower bounds; 7. Convex hulls and Voronoi
diagrams; 8. Linear programming and extensions;
9. Pseudo-randomness; 10. Communication complexity;
11. Minimum spanning trees; Appendix A. Probability
theory; Appendix B. Harmonic analysis; Appendix
C. Convex geometry.
ISBN, Binding, : 0521770939 Hardback
Approximate Publication date: 11 July
2000
Main Subject Category: Theory of computation,
data
Comparable titles: MOTWANI and RAGHAVAN/Randomized
Algorithms/1995/0521 474655
Description: This collection of articles
by well-known experts is intended for researchers
in computer science, practitioners of formal
methods, and computer programmers working
in safety-critical applications or in the
technology of component-based systems. The
work brings together, for the first time,
several elements of this area that are fast
becoming the focus of much current research
and practice in computing. The introduction
by Clemens Szyperski gives a snapshot of
current research in the field. About half
the articles deal with theoretical frameworks,
models, and systems of notation; the rest
of the book concentrates on case studies
by researchers who have built prototype systems
and present findings on architectures verification.
The emphasis is on advances in the technological
infrastructure of component-based systems;
how to design and specify reusable components;
and how to reason about, verify, and validate
systems from components. Thus the book shows
how theory might move into practice.
Contents: Introduction: component software
- a snapshot and future directions Clemens
Szyperski; Part I. Frameworks and Architectures:
1. Key concepts in architecture definition
languages David C. Luckham, James Vera and
Sigurd Meldal; 2. Acme: a basis for architectural
integration David Garlan, Robert Monroe and
David Wile; 3. An extensible language for
composition Markus Lumpe, Franz Achermann,
and Oscar Nierstrasz; 4. A framework for
a formal and automated approach to component-based
reuse Betty H. C. Cheng and Yonghao Chen;
Part II. Object-Based Specification and Verification:
5. Behavioral subtyping Gary T. Leavens and
Krishna Kishore Dhara; 6. Modular specification
and verification techniques for object-oriented
software components Peter Mueller and Arnd
Poetzsch-Heffter; 7. Respectful type converters
for objects Jeannette M. Wing and John Ockerbloom;
Part III. Formal Models and Semantics: 8.
A formal model of componentware Klaus Bergner,
Manfred Broy, Andreas Rausch, Marc Sihling
and Alexander Vilbig; 9. General semantic
spaces for specifications and templates David
S. Gibson, Bruce W. Weide, Steven H. Edwards
and Scott Pike; 10. An implementation-oriented
semantics for module composition Joseph Goguen
and Will Tracz; Part IV. Reactive and Distributed
Systems: 11. Composition of reactive system
components K. Lano, J. Bicarregui, T. Maibaum
and J. Fiadeiro; 12. The IOA language and
toolset: support for mathematics-based distributed
programming Stephen J. Garland and Nancy
A. Lynch.
ISBN, Binding, : 0521771641 Hardback
Approximate Publication date: 17 March
2000
Main Subject Category: Computer software
And Other Kernel-based Learning Methods
Description: This is the first comprehensive
introduction to Support Vector Machines (SVMs),
a new generation learning system based on
recent advances in statistical learning theory.
SVMs deliver state-of-the-art performance
in real-world applications such as text categorisation,
hand-written character recognition, image
classification, biosequences analysis, etc.,
and are now established as one of the standard
tools for machine learning and data mining.
Students will find the book both stimulating
and accessible, while practitioners will
be guided smoothly through the material required
for a good grasp of the theory and its applications.
The concepts are introduced gradually in
accessible and self-contained stages, while
the presentation is rigorous and thorough.
Pointers to relevant literature and web sites
containing software ensure that it forms
an ideal starting point for further study.
Equally, the book and its associated web
site will guide practitioners to updated
literature, new applications, and on-line
software.
Contents: Preface; 1. The learning
methodology; 2. Linear learning machines;
3. Kernel-induced feature spaces; 4. Generalisation
theory; 5. Optimisation theory; 6. Support
vector machines; 7. Implementation techniques;
8. Applications of support vector machines;
Appendix 1. Pseudocode for the SMO algorithm;
Appendix 2. Background mathematics; Appendix
3. Glossary; Appendix 4. Notation; Bibliography;
Index.
ISBN, Binding, 0521780195 Hardback
Approximate Publication date: 4 February
2000
Main Subject Category: Computer applications
Description: In The Quantum Theory
of Fields, Nobel Laureate Steven Weinberg
combines his exceptional physical insight
with his gift for clear exposition to provide
a self-contained, comprehensive, and up-to-date
introduction to quantum field theory. The
first volume introduces the foundations of
quantum field theory, the second volume examines
modern applications, and finally the third
volume presents supersymmetry, an area of
theoretical physics likely to be at the centre
of progress in the physics of elementary
particles and gravitation. The development
is fresh and logical, with each step carefully
motivated by what has gone before. The presentation
of modern mathematical methods is throughout
interwoven with accounts of applications
in both elementary particle and condensed
matter physics. The three volumes contain
much original material, and are peppered
with examples and insights drawn from the
author's experience as a leader of elementary
particle research. Problems are included
at the end of each chapter.
Contents: Volume I: 1. Historical introduction;
2. Relativistic quantum mechanics; 3. Scattering
theory; 4. The cluster decomposition principle;
5. Quantum fields and antiparticles; 6. The
Feynman rules; 7. The canonical formalism;
8. Massless particles: electrodynamics; 9.
Path integral methods; 10. Nonperturbative
methods; 11. One-loop radiative corrections
in quantum electrodynamics; 12. General renormalization
theory; 13. Infrared effects; 14. Bound states
in external fields.
Volume II: 15. Non-Abelian gauge theories;
16. External field methods; 17. Renormalization
of gauge theories; 18. Renormalization group
methods; 19. Spontaneously broken global
symmetries; 20. Operator product expansions;
21. Spontaneous breaking of gauge symmetries;
22. Anomalies; 23. Topological complications;
Subject index; Author index.
Volume III: 24. Historical introduction;
25. Supersymmetry algebras; 26. Supersymmetric
field theories; 27. Supersymmetric gauge
theories; 28. Supersymmetric versions of
the standard model; 29. Beyond perturbation
theory; 30. Supergraphs; 31. Supergravity;
32. Supersymmetry in higher dimensions; Author
index; Subject index.
ISBN, Binding, : 0521780829 3 volume
set
Approximate Publication date: 1 February
2000
Description: This book provides a lucid
and comprehensive introduction to the differential
geometric study of partial differential equations.
It is the first book to present substantial
results on local solvability of general and,
in particular, nonlinear PDE systems without
using power series techniques. The book describes
a general approach to systems of partial
differential equations based on ideas developed
by Lie, Cartan and Vessiot. The most basic
question is that of local solvability, but
the methods used also yield classifications
of various families of PDE systems. The central
idea is the exploitation of singular vector
field systems and their first integrals.
These considerations naturally lead to local
Lie groups, Lie pseudogroups and the equivalence
problem, all of which are covered in detail.
This book will be a valuable resource for
graduate students and researchers in partial
differential equations, Lie groups and related
fields.
Contents: Preface; 1. Introduction
and summary; 2. PDE systems, pfaffian systems
and vector field systems; 3. Cartan's local
existence theorem; 4. Involutivity and the
prolongation theorem; 5. Drach's classification,
second order PDEs in one dependent variable
and Monge characteristics; 6. Integration
of vector field systems n satisfying dim
n' = dim n + 1; 7. Higher order contact transformations;
8. Local Lie groups; 9. Structural classification
of 3-dimensional Lie algebras over the complex
numbers; 10. Lie equations and Lie vector
field systems; 11. Second order PDEs in one
dependent and two independent variables;
12. Hyperbolic PDEs with Monge systems admitting
2 or 3 first integrals; 13. Classification
of hyperbolic Goursat equations; 14. Cartan's
theory of Lie pseudogroups; 15. The equivalence
problem; 16. Parabolic PDEs for which the
Monge system admits at least two first integrals;
17. The equivalence problem for general 3-dimensional
pfaffian systems in five variables; 18. Involutive
second order PDE systems in one dependent
and three independent variables, solved by
the method of Monge; Bibliography; Index.
ISBN, Binding, : 0521780888 Hardback
Approximate Publication date: 1 May
2000
Main Subject Category: Dynamics, Control,
Differential & Integral Equations
Series: Encyclopedia of Mathematics
and its Applications, 80