Alan Jeffrey University of Newcastle upon Tyne, UK

Complex Analysis and Applications, Second Edition

ISBN: 158488553X
Publication Date: 10/26/2005
Number of Pages: 576

Explains complex analysis for students of applied mathematics and engineering
Contains large exercise sets at the end of each chapter, with answers included for odd-numbered exercises
Illustrates each newly introduced topic with examples that reinforce key points
Encourages the use of readily accessible computer algebra packages, aiding the understanding of various aspects of the subject
Incorporates new material on the Laplace inversion integral and asymptotic methods
Offers a solutions manual with qualifying course adoptions

Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems.

A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed.

In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.

Table of Contents

Karim F Hirji Statistical Consultant, Los Angeles, California, USA

Exact Analysis of Discrete Data

ISBN: 1584880708
Publication Date: 11/21/2005
Number of Pages: 544

Provides an accessible treatment of an important and increasingly popular area of statistics
Covers the concepts, statistical methods, and computational techniques for exact analysis of a wide range of discrete data problems.
Combines the exposition of basic theory with detailed worked examples and real applications
Includes an extensive set of problems and a guide to the relevant literature in each chapter
Uses an elementary approach to explain computational algorithms, and gives a step by step scheme and implementation details, not available elsewhere, for them

Despite the growing appeal of exact statistical methods, a beginner level and integrated exposition of the subject is hard to come by. This book provides the statistical theory, analytic methods, and computational techniques for exact analysis of discrete data. Using elementary ideas and data examples, it brings material thus far buried in specialists' journals to a broader audience. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case - control studies, paired binary and trinomial response models, and Markov chain data. Related large sample methods and the generalizations to complex settings are also indicated. An important feature is the use of a simple polynomial formulation for distributions and algorithms to provide a unified view of the subject. The mid-p value, confidence interval curves and exact power are employed as the main tools for data analysis. To comprehend the material, readers require only a first course covering the basic ideas of probability distributions and statistical inference.

Table of Contents

Foreword. Discrete Distributions. One-Sided Univariate Analysis. Two-Sided Univariate Analysis. Computing Fundamentals. Elements of Conditional Analysis. Two 2 x 2 Tables. Assessing Inference. Several 2 x 2 Tables: I. Several 2 x 2 Tables: II. The 2 x K Table. Polynomial Algorithms: I. Polynomial Algorithms: II. Multinomial Models. Matched and Dependent Data. Reflections on Exactness. References.


Hung T Nguyen New Mexico State University, Las Cruces, New Mexico, USA
Elbert A Walker New Mexico State University, Las Cruces, New Mexico, USA

A First Course in Fuzzy Logic, Third Edition

Publication Date: 10/5/2005
Number of Pages: 440

Introduces the theory and applications of fuzzy logic in an extensively classroom-tested presentation ideal for course work or self-study
Builds the foundation for applying fuzzy logic in intelligent systems design, particularly in control engineering
Covers new topics, such as type-2 fuzzy sets
Includes extensive exercise set at the end of each chapter

A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications.

New in the Third Edition:

· A section on type-2 fuzzy sets - a topic that has received much attention in the past few years
· Additional material on copulas and t-norms
· More discussions on generalized modus ponens and the compositional rule of inference
· Complete revision to the chapter on possibility theory
· Significant expansion of the chapter on fuzzy integrals
· Many new exercises

With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.

Table of Contents


Daniel Beltita Romanian Academy, Bucharest, Romania

Smooth Homogeneous Structures in Operator Theory

Series: Monographs & Surveys in Pure & Applied Math Volume: 137

ISBN: 158488617X
Publication Date: 11/9/2005
Number of Pages: 320

Provides an introduction to infinite-dimensional Lie groups and infinite-dimensional complex manifolds
Examines applications of differential geometry to operator theory
Contains an extensive list of references
Presents open problems throughout the text to stimulate further research

Smooth Homogeneous Structures in Operator Theory addresses the role geometric ideas and techniques play in operator theory and the theory of operator algebras. The book provides an introduction to infinite-dimensional Lie groups as well as infinite-dimensional complex manifolds. The author examines various applications to operator theory, presenting open problems in order to stimulate further research. He also investigates symmetry properties of abstract reproducing kernels and applies results to Kahler homogeneous spaces. With extensive references, the text is ideal for graduate students and researchers working in functional analysis, Lie groups, representation theory, and complex geometry.

Table of Contents

TOPOLOGICAL LIE ALGEBRAS
Fundamentals
Universal enveloping algebras
The Baker-Campbell-Hausdor series
Convergence of the Baker-Campbell-Hausdor series
Notes
LIE GROUPS AND THEIR LIE ALGEBRAS
Definition of Lie groups
The Lie algebra of a Lie group
Logarithmic derivatives
The exponential map
Special features of Banach-Lie groups
Notes
ENLARGIBILITY
Integrating Lie algebra homomorphisms
Topological properties of certain Lie groups
Enlargible Lie algebras
Notes
Smooth Homogeneous Spaces
Basic facts on smooth homogeneous spaces
Symplectic homogeneous spaces
Some homogeneous spaces related to operator algebras
Notes
QUASIMULTIPLICATIVE MAPS
Supports, convolution, and quasimultiplicativity
Separate parts of supports
Hermitian maps
Notes
COMPLEX STRUCTURES ON HOMOGENEOUS SPACES
General results
Pseudo-Koler manifolds
Flag manifolds in Banach algebras
Notes
EQUIVARIANT MONOTONE OPERATORS
Definition of equivariant monotone operators
H*-algebras and L*-algebras
Equivariant monotone operators as reproducing kernels
H*-ideals of H*-algebras
Elementary properties of H*-ideals
Notes
L*-IDEALS AND EQUIVARIANT MONOTONE OPERATORS
From ideals to operators
From operators to ideals
Parameterizing L*-ideals
Representations of automorphism groups
Applications to enlargibility
Notes
HOMOGENEOUS SPACES OF PSEUDO-RESTRICTED GROUPS
Pseudo-restricted algebras and groups
Complex polarizations
Kler polarizations
Admissible pairs of operator ideals
Some Koler homogeneous spaces
Notes
APPENDICES
Differential Calculus and Smooth Manifolds
Basic Differential Equations of Lie Theory
Topological Groups

References
Index

Antonio Giambruno Universita Di Palermo, Italy
Cesar Polcino Milies Universidade de Sao Paulo, Sao Paulo, Brazil
S.K. Sehgal University of Alberta, Edmonton, AB, Canada

Groups, Rings and Group Rings

Series: Lecture Notes in Pure and Applied Mathematics Volume: 247

ISBN: 1584885815
Publication Date: 1/12/2006
Number of Pages: 344

Presents research papers and surveys from the Conference on Groups, Rings, and Group rings held in Brazil
Familiarizes researchers with the latest topic, techniques, and methologies
Examines broad themes from group theory and ring theory, exploring their relations with other branches of algebra
Features contributions from international experts

This book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.