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
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.
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
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
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.