Jon F. Carlson, Lisa Townsley, Luis Valero-Elizondo, Mucheng Zhang

Cohomology Rings of Finite Groups
with an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64

September 2003, ISBN 1-4020-1525-9, Hardbound

Book Series: ALGEBRAS AND APPLICATIONS : Volume 3

This text offers comprehensive coverage of group cohomology, from introductory material through the most recent developments in the field. The primary motivation for this book is the interaction of group cohomology with representation theory, especially the geometry of support varieties over cohomology rings. The appendices, comprising computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64, provide information useful for further developments in the field. A unique feature of this text is that it includes the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the computations. The programs for computing the cohomology rings were executed in the MAGMA computer algebra language. The text is a valuable resource for researchers in group cohomology and related disciplines. In addition, the book could be used as the text for an advanced graduate class or a graduate seminar.

David Kapanadze, B.-Wolfgang Schulze

Crack Theory and Edge Singularities

October 2003, ISBN 1-4020-1524-0, Hardbound

Book Series: MATHEMATICS AND ITS APPLICATIONS : Volume 561


The book studies boundary value problems connected with geometric singularities and models of the crack theory. New and interesting phenomena on the behaviour of solutions (regularity in weighted spaces, asymptotics) are analysed by means of parametrices obtained by inverting corresponding scalar and operator-valued symbols. Compared with other expositions in the field of crack theory and analysis on configurations with singularities the present book systematically develops for the first time an approach in terms of algebras of (pseudo-differential) boundary value problems. The calculus is decomposed into a number of simpler structures, namely boundary value problems (Chapter 1) and edge problems near the crack boundary (Chapter 4). Necessary tools on parameter-dependent cone operators (Chapter 2) and operators on spaces with conical exits to infinity (Chapter 3) are developed as theories of independent interest. The crack theory (Chapter 5) then appears as an application of the edge calculus.

The book is addressed to mathematicians and physicists interested in boundary value problems, geometric singularities, asymptotic analysis, as well as to specialists in the field of crack theory and other singular models.

B. J. Gardner; Richard Wiegandt

Radical Theory of Rings

Series Pure and Applied Mathematics, Volume: 261

Print Published: 11/01/2003
Print ISBN: 0-8247-5033-0

Description

Delving into the study of concrete radicals and structure theorems for rings, this reference explores the latest developments and research concerning the radical theory of rings?sketching the basic features of radical theories in varieties of nonassociative rings and rings with involution and near-rings.

Table of Contents

General Fundamentals
The General Theory of Radicals
Radical Theory for Associative Rings
Concrete Radicals and Structure Theorems
Special Features of the General Radical Theory
References
Author Index
Subject Index
List of Symbols

List of Standard Conditions.

Editors
M.G. Akritas, Penn State University, Department of Statistics, PA, USA
D.N. Politis, The University of California, Department of Mathematics, La Jolla, USA

Recent Advances and Trends in Nonparametric Statistics

Description

The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.

Key features:

algorithic approaches
wavelets and nonlinear smoothers
graphical methods and data mining
biostatistics and bioinformatics
bagging and boosting
support vector machines
resampling methods

Audience

Researchers in statistics; researchers in machine learning.

Contents

http://www.elsevier.nl/inca/publications/store/6/9/9/5/3/0/index.htt

Year 2003
Hardbound
ISBN: 0-444-51378-7
522 pages

Miloslav Feistauer, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, Jiri Felcman, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, and Ivan Straskraba, Mathematical Institute, Academy of Sciences of Czech Republic, Prague, Czech Republic

Mathematical and Computational Methods for Compressible Flow

0-19-850588-4
Publication date: 10 July 2003
550 pages, numerous figures and halftones, 234mm x 156mm

Useful as a textbook in universities
Excellent handbook for specialists
Contains recent developments in numerical treatment of compressible fluid flow
Good reference guide for solving applied problems
Informs a wide audience

Description

Numerical and computational methods play a major role in modelling compressible flow and are important tools in solving fluid dynamical problems faced in many areas of science and technology. This book thoroughly surveys and analyzes up-to-date methods, while reviewing the basic theoretical mathematical analysis.

Readership: Aimed at advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences, as well as specialists of pure and applied mathematics, aerodynamics, engineering, physics and natural science, working in research institutes and industrial companies.

Contents/contributors
Fundamental concepts and equations
1.1 Some mathematical concepts and notation
1.2 Governing equations and relations of gas dynamics
1.3 Some advanced mathematical concepts and results
1.4 Survey of concepts and results from functional analysis
Basic facts from the theory of the Euler and Navier-Stokes equations
2.1 Hyperbolic systems and the Euler equations
2.2 Existence of smooth solutions
2.3 Weak solutions
2.4 Nonstationary Navier-Stokes equations of compressible flow
2.5 Existence results for stationary compressible Navier-Stokes equations
Finite difference and finite volume methods for non-linear hyperbolic systems and the Euler equations
3.1 Further properties of the Euler equations
3.2 Numerical methods for hyperbolic systems with one space variable
3.3 The finite volume method for the multidimensional Euler equations
3.4 Osher-Solomon scheme
3.5 Higher order finite volume schemes
3.6 Adaptive methods
3.7 Examples of finite volume simulations
Finite element solution of compressible flow
4.1 Finite element method - elementary treatment
4.2 Finite element solution of viscous barotropic flow
4.3 Finite element solution of a heat conductive gas flow
4.4 Combined finite volume - finite element method for viscous compressible flow
4.5 Theory of the combined FV-FE method
4.6 Discontinuous Galerkin finite element method


Richard E. Neapolitan, Northeastern Illinois University

Learning Bayesian Networks

ISBN: 0-13-012534-2
Publisher: Prentice Hall
Copyright: 2004
Format: Cloth; 674 pp

Description
For courses in Bayesian Networks or Advanced Networking focusing on Bayesian networks found in departments of Computer Science, Computer Engineering and Electrical Engineering. Also appropriate as a supplementary text in courses on Expert Systems, Machine Learning, and Artificial Intelligence where the topic of Bayesian Networks is covered.

This book provides an accessible and unified discussion of Bayesian networks. It includes discussions of topics related to the areas of artificial intelligence, expert systems and decision analysis, the fields in which Bayesian networks are frequently applied. The author discusses both methods for doing inference in Bayesian networks and influence diagrams. The book also covers the Bayesian method for learning the values of discrete and continuous parameters. Both the Bayesian and constraint-based methods for learning structure are discussed in detail.

Table of Contents

Preface.

I. BASICS.
1. Introduction to Bayesian Networks.
2. More DAG/Probability Relationships.

II. INFERENCE.
3. Inference: Discrete Variables.
4. More Inference Algorithms.
5. Influence Diagrams.

III. LEARNING.
6. Parameter Learning: Binary Variables.
7. More Parameter Learning.
8. Bayesian Structure Learning.
9. Approximate Bayesian Structure Learning.
10. Constraint-Based Learning.
11. More Structure Learning.

IV. APPICATIONS.
12. Applications.
Bibliography.
Index.