Series: Texts in Theoretical Computer Science. An EATCS Series
2004, Approx. 330 p., Hardcover
ISBN: 3-540-21202-7
Due: July 5, 2004
About this textbook
This book is an introduction to finite model theory which
stresses the computer science origins of the area. In addition to
presenting the main techniques for analyzing logics over finite
models, the book deals extensively with applications in
databases, complexity theory, and formal languages, as well as
other branches of computer science. It covers Ehrenfeucht-Fraisse
games, locality-based techniques, complexity analysis of logics,
including the basics of descriptive complexity, second-order
logic and its fragments, connections with finite automata, fixed
point logics, finite variable logics, zero-one laws, and embedded
finite models, and gives a brief tour of recently discovered
applications of finite model theory. This book can be used both
as an introduction to the subject, suitable for a one- or two-semester
graduate course, or as reference for researchers who apply
techniques from logic in computer science.
Table of contents
1. Introduction; 2. Preliminaries; 3. Ehrenfeuch-Fraisse Games; 4.
Locality and Winning Games; 5. Ordered Structures; 6. Complexity
of First-Order Logic; 7. Monadic Second Order Logic and Automata;
8. Logics with Counting; 9. Turing Machines and Finite Models; 10.
Fixed Point Logics and Complexity Classes; 11. Finite Variable
Logics; 12. Zero-one Laws; 13. Embedded Finite Models; 14. Other
Applications of Finite Model Theory; References; List of
Notations; Index; Name Index
2004, Approx 300 p. 18 illus., Hardcover
ISBN: 3-540-21045-8
Due: September 2004
About this textbook
Complexity theory is the theory of determining the necessary
resources for the solution of algorithmic problems and,
therefore, the limits what is possible with the available
resources. The results prevent the search for non-existing
efficient algorithms. The theory of NP-completeness has
influenced the development of all areas of computer science. New
branches of complexity theory react to all new algorithmic
concepts. This textbook considers randomization as a key concept.
The chosen subjects have implications to concrete applications.
The significance of complexity theory for todays computer science
is stressed.
Table of contents
Introduction.- Algorithmic Problems and Their Complexity.-
Fundamental Complexity Classes.- Reductions - Algorithmic
Relations Between Problems.- The Theory of NP-Completeness.- NP-Complete
and NP-Equivalent Problems.- The Complexity Analysis´of Problems.-
The Complexity of Approximation Problems - Classical Results.-
The Complexity of Black-Box Problems.- Further Complexity Classes
and Relations between the Complexity Classes.- Interactive Proof
Systems.- The PCP-Theorem and the Complexity of Approximation
Problems.- Classical Subjects of Complexity Theory.- The
Complexity of Nonuniform Problems.- Communication Complexity.-
The Complexity of Boolean Function.- Conclusions.- Appendix: The
O-notation; Results from Probability Theory.- References.- Index.
Series: Graduate Texts in Mathematics, Vol. 225
2004, Approx. 410 p. 50 illus., Hardcover
ISBN: 0-387-21154-3
Due: September 2004
About this textbook
This book is intended for a one year graduate course on Lie
groups and Lie algebras. The author proceeds beyond the
representation theory of compact Lie groups (which is the basis
of many texts) and provides a carefully chosen range of material
to give the student the bigger picture. For compact Lie groups,
the Peter-Weyl theorem, conjugacy of maximal tori (two proofs),
Weyl character formula and more are covered. The book continues
with the study of complex analytic groups, then general
noncompact Lie groups, including the Coxeter presentation of the
Weyl group, the Iwasawa and Bruhat decompositions, Cartan
decomposition, symmetric spaces, Cayley transforms, relative root
systems, Satake diagrams, extended Dynkin diagrams and a survey
of the ways Lie groups may be embedded in one another. The book
culminates in a ``topics'' section giving depth to the student's
understanding of representation theory, taking the Frobenius-Schur
duality between the representation theory of the symmetric group
and the unitary groups as a unifying theme, with many
applications in diverse areas such as random matrix theory,
minors of Toeplitz matrices, symmetric algebra decompositions,
Gelfand pairs, Hecke algebras, representations of finite general
linear groups and the cohomology of Grassmannians and flag
varieties. Daniel Bump is Professor of Mathematics at Stanford
University. His research is in automorphic forms, representation
theory and number theory. He is a co-author of GNU Go, a computer
program that plays the game of Go. His previous books include
Automorphic Forms and Representations (Cambridge University Press
1997) and Algebraic Geometry (World Scientific 1998).
Table of contents
* Preface * Part I: Compact Groups: Haar Measure * Schur
Orthogonality * Compact Operators * The Peter-Weyl Theorem * Part
II: Lie Group Fundamentals: Lie Subgroups of GL(n, C) * Vector
Fields * Left Invariant Vector Fields * The Exponential Map *
Tensors and Universal Properties * The Universal Enveloping
Algebra * Extension of Scalars * Representations of sl(2, C) *
The Universal Cover * The Local Frobenius Theorem * Tori *
Geodesics and Maximal Tori * Topological proof of Cartan’s
Theorem * The Weyl Integration Formula * The Root System *
Examples of Root Systems * Abstract Weyl Groups * The Fundamental
Group * Semisimple Compact Groups * Highest Weight Vectors * The
Weyl Character Formula * Spin * Complexification * Coxeter Groups
* The Iwasawa Decomposition * The Bruhat Decomposition *
Symmetric Spaces * Relative Root Systems.* Embeddings of Lie
Groups * Part III: Frobenius-Schur Duality: Mackey Theory *
Characters of GL(n, C) * Duality between Sk and GL(n, C) * The
Jacobi-Trudi Identity * Schur Polynomials and GL(n, C) * Schur
Polynomials and Sk * Random Matrix Theory * Minors of Toeplitz
Matrices * Branching Formulae and Tableaux * The Cauchy Identity
* Unitary branching rules * The Involution Model for Sk * Some
Symmetric Algebras * Gelfand Pairs * Hecke Algebras * Cohomology
of Grassmannians * References
1. Edition - May 2004
49.90 Euro / 75.- SFR
2004. XI, 244 Pages, Softcover
ISBN 3-527-40438-4 - Wiley-VCH, Berlin
Short description
First textbook on the topic discusses theoretical
foundations as well as experimental realizations in detail. The
authors, both experienced teachers, didactically prepare the
basics of quantum communication and quantum information
processing, leading readers to modern technical implementations.
They also discuss errors and decoherence as well as methods of
avoiding and correcting them.
From the contents
1. Introduction and Survey
2. Physics of computation
3. Elements of classical computer science
4. Quantum Mechanics
5. Quantum bits and quantum gates
6. Feynman's contribution
7. Errors and decoherence
8. Tasks for Quantum Computers
9. How to build a quantum computer
10. Liquid state NMR quantum computer
11. Solid state quantum computers
12. Quantum communication
A. Two spins 1/2:Singlet and triplet states
This book provides the first-ever systematic introduction to
the theory of Riemannian submersions, which was initiated by
Barrett O'Neill and Alfred Gray less than four decades ago. The
authors focus their attention on classification theorems when the
total space and the fibres have nice geometric properties.
Particular emphasis is placed on the interrelation with almost
Hermitian, almost contact and quaternionic geometry. Examples
clarifying and motivating the theory are included in every
chapter. Recent results on semi-Riemannian submersions are also
explained. Finally, the authors point out the close connection of
the subject with some areas of physics.
Contents:
Riemannian Submersions
Submersions with Totally Geodesic Fibres
Almost Hermitian Submersions
Riemannian Submersions and Contact Metric Manifolds
Einstein Spaces and Riemannian Submersions
Riemannian Submersions and Submanifolds
Semi-Riemannian Submersions
Applications of Riemannian Submersions in Physics
Readership: Graduate students and researchers in differential
geometry, Riemannian geometry and related fields such as physics.
300pp (approx.) Pub. date: Scheduled Fall 2004
ISBN 981-238-896-6
*******************************************************************************************
This book captures the essence of the current state of
research in wavelet analysis and its applications, and identifies
the changes and opportunities ? both current and future ? in the
field. Distinguished researchers such as Prof John Daugman from
Cambridge University and Prof Victor Wickerhauser from Washington
University present their research papers.
Contents:
Volume 1:
Accelerating Convergence of Monte Carlo Simulations and Measuring
Weak Biosignals Using Wavelet Threshold Denoising (M V
Wickerhauser)
One of Image Compression Methods Based on Biorthogonal Wavelet
Transform and LBG Algorithm (J Lin et al.)
A Video Watermarking Algorithm Using Fast Wavelet (J Zhang et al.)
Structural and Geometric Characteristics of Sets of Convergence
and Divergence of Multiple Fourier Series of Functions which
Equal Zero on Some Set (I L Bloshanskii)
Sequence Images Data Fusion Based on Wavelet Transform Approach (H
Tao et al.)
Radar Detection of Minimum Altitude Flying Targets Based on
Wavelet Transforms (H Li et al.)
Precursors of Engine Failures Revealed by Wavelet Analysis (I M
Dremin)
Volume 2:
Demodulation by Complex-Valued Wavelets for Stochastic Pattern
Recognition: How Iris Recognition Works (J Daugman)
Wavelets and Image Compression (V A Nechitailo)
Fast Wavelet-Based Video Codec and its Application in an IP
Version 6-Ready Serverless Videoconferencing (H L Cycon et al.)
On a Class of Optimal Wavelets (N A Strelkov & V L Dol'nikov)
A Wavelet-Based Digital Watermarking Algorithm (H Q Sun et al.)
Research of the Gyro Signal De-Noising Method Based on Stationary
Wavelets Transform (J Guo et al.)
Adaptive De-Noising of Low SNR Signals (D Isar & A Isar)
Analysis of the DLA-Process with Gravitational Interaction of
Particles and Growing Cluster (A Loskutov et al.)
and other papers
Readership: Graduate students, academics and researchers in
computer science and engineering.
1056pp Pub. date: Apr 2003
ISBN 981-238-342-5(set)