July 2003, ISBN 1-4020-7540-5, Hardbound
Book Series: NETWORK THEORY AND APPLICATIONS
: Volume 10
This book considers a graph as a mathematical
structure on a set
of elements with a binary relation, and provides
the most
classical and important theory and application
of graphs. It
covers basic concepts, trees and graphic
spaces, plane graphs and
planar graphs, flows and connectivity, matchings
and independent
sets, coloring theory, graphs and groups.
These topics, both
theoretical and applied, are treated with
some depth and with
some suggestions for further reading. The
treatment of material
particularly lays stress on digraphs, the
mutual connections
among these topics and the equivalence of
some well-known
theorems. All theorems are stated clearly,
together with full and
concise proofs. A number of examples, more
than 350 figures and
more than 500 exercises are given to help
the reader understand
and examine the materials covered in the
book.
Audience: The book is particularly suitable
as a textbook of
graph theory for senior or beginning postgraduate
students who
are majoring in pure and applied mathematics,
operation research,
computer science, designing and analysis
of networks,
electronics, scientific management and others.
It is also
suitable as a reference book for those readers
who are engaged
and interested in graph theory and for all
researchers who use
graph theory as a mathematical tool.
July 2003, ISBN 1-4020-1414-7, Hardbound
Book Series: FUNDAMENTAL THEORIES OF PHYSICS
: Volume 130
This monograph deals with the geometrical
and topological aspects
related to quantum field theory with special
reference to the
electroweak theory and skyrmions. This book
is unique in its
emphasis on the topological aspects of a
fermion manifested
through chiral anomaly which is responsible
for the generation of
mass. This has its relevance in electroweak
theory where it is
observed that weak interaction gauge bosons
attain mass
topologically. These geometrical and topological
features help us
to consider a massive fermion as a skyrmion
and for a composite
state we can realise the internal symmetry
of hadrons from
reflection group. Also, an overview of noncommutative
geometry
has been presented and it is observed that
the manifold M 4 x Z2
has its relevance in the description of a
massive fermion as
skyrmion when the discrete space is considered
as the internal
space and the symmetry breaking gives rise
to chiral anomaly
leading to topological features.
Audience: This book will be of value to research
workers and
specialists in mathematical physics, quantum
field theory,
particle physics, differential geometry and
analysis of manifolds.
Contents
1: Theory of Spinors. 1.1. Spinors and Spin
Structure. 1.2.
Spinors in Different Dimensions. 1.3. Supersymmetry
and
Superspace.
2: Fermions and Topology. 2.1. Fermi Field
and Nonlinear Sigma
Model. 2.2. Quantization and Anomaly. 2.3.
Anomaly and Topology.
3: Electroweak Theory. 3.1. Weinberg-Salam
Theory. 3.2.
Topological Features in Field Theory. 3.3.
Topological Origin of
Mass.
4: Skyrme Model. 4.1. Nonlinear Sigma Model.
4.2. Skyrme Model
for Nucleons. 4.3. Baryons as Three Flavor
Solitons.
5: Geometrical Aspects of a Skyrmion. 5.1.
Microlocal Space Time
and Fermions. 5.2. Internal Symmetry of Hadrons.
5.3.
Supersymmetry and Internal Symmetry.
6: Noncommutative Geometry. 6.1. Quantum
Space Time. 6.2.
Noncommutative Geometry and Particle Physics.
6.3. Discrete Space
as the Internal Space.
July 2003, ISBN 1-4020-1402-3, Hardbound
Book Series: MATHEMATICAL MODELLING: THEORY
AND APPLICATIONS :
Volume 17
The already broad range of applications of
ring theory has been
enhanced in the eighties by the increasing
interest in algebraic
structures of considerable complexity, the
so-called class of
quantum groups. One of the fundamental properties
of quantum
groups is that they are modelled by associative
coordinate rings
possessing a canonical basis, which allows
for the use of
algorithmic structures based on Groebner
bases to study them.
This book develops these methods in a self-contained
way,
concentrating on an in-depth study of the
notion of a vast class
of non-commutative rings (encompassing most
quantum groups), the
so-called Poincare-Birkhoff-Witt rings. We
include algorithms
which treat essential aspects like ideals
and (bi)modules, the
calculation of homological dimension and
of the Gelfand-Kirillov
dimension, the Hilbert-Samuel polynomial,
primality tests for
prime ideals, etc. The text is mainly aimed
at postgraduate
students and researchers interested in ring
theory, the algebraic
theory of differential equations, symbolic
calculus and their
applications.
Contents
http://www.wkap.nl/prod/b/1-4020-1402-3?a=2
June 2003, ISBN 1-4020-7470-0, Hardbound
Book Series: NONCONVEX OPTIMIZATION AND ITS
APPLICATIONS : Volume
68
This volume, devoted to variational analysis
and its
applications, is made up of refereed contributions,
which provide
an outline of the field. New results, which
enlarge the field of
applications in variational analysis, are
presented; they deal
with vectorial analysis, time dependent variational
analysis,
exact penalization, high order derivatives,
geometric aspects,
distance functions and logquadratic proximal
methodology.
The new theoretical results make it possible
to improve, in a
remarkable way, the study of significant
problems arising from
the applied sciences, such as the continuum
model of
transportation, unilateral problems, multicriteria
spatial price
models, network equilibrium problems and
many others. Moreover,
the progress made in the field also makes
it possible to handle
problems whose equilibrium conditions are
not obtained by the
minimization of a functional. These problems
obey a more
realistic equilibrium condition expressed
by a generalized
orthogonality (complementarity) condition,
which enriches our
knowledge of the equilibrium behavior.
Audience: Graduate students and researchers.
July 2003, ISBN 1-4020-1407-4, Hardbound
The International Conference on Factorization,
Singular Operators
and Related Problems held from January 28
to February 1, 2002, at
the University of Madeira, Funchal, Portugal,
was dedicated to
mark Professor Georgii Litvinchuk's 70th
birthday.
Experts in various fields came to this conference
to pay tribute
to the great achievements of Professor Georgii
Litvinchuk in the
development of various topics of operator
theory. The main topics
of the conference were in the theory of singular
type operators
and in factorization problems, but other
topics such as potential
theory, fractional calculus and others were
also presented.
The 21 articles published in this book will
be of great interest
to researchers in Operator Theory, Real and
Complex Analysis,
Functional and Harmonic Analysis, Potential
Theory, Fractional
Calculus and others, as well as to graduate
students requiring
the most up-to-date results.