Series: Lecture Notes in Mathematics , Vol.
1826
2003, VIII, 113 p., Softcover
ISBN: 3-540-20025-8
About this book
This introduction to the recent theory of
abstract tubes
describes the framework for establishing
improved inclusion-exclusion
identities and Bonferroni inequalities, which
are provably at
least as sharp as their classical counterparts
while involving
fewer terms. All necessary definitions from
graph theory, lattice
theory and topology are provided. The role
of closure and kernel
operators is emphasized, and examples are
provided throughout to
demonstrate the applicability of this new
theory. Applications
are given to system and network reliability,
reliability covering
problems and chromatic graph theory. Topics
also covered include
Zeilberger's abstract lace expansion, matroid
polynomials and
Mobius functions.
Table of contents
1. Introduction and Overview.- 2. Preliminaries.-
3.Bonferroni
Inequalities via Abstract Tubes.- 4. Abstract
Tubes via Closure
and Kernel Operators.- 5. Recursive Schemes.-
6. Reliability
Applications.- 7. Combinatorial Applications
and Related Topics.-
Bibliography.- Index.
Series: Universitext
2004, 172 p., Softcover
ISBN: 3-540-40502-X
Written for:
Undergraduate students in finance
Keywords:
Mathematical finance
options
stochastic analysis
Monte Carlo methods
Table of contents
Introduction.- Statistical Analysis of Data
from the Stock Market.-
An Introduction to Stochastic Analysis.-
Pricing and Hedging of
Contingent Claims.- Numerical Pricing and
Hedging of Contingent
Claims.- Appendix, Solutions to Selected
Exercises.
Series: Monographs in Theoretical Computer
Science. An EATCS
Series
2004, X, 247 p. 20 illus., Hardcover
ISBN: 3-540-40823-1
About this book
Duration calculus constitutes a formal approach
to the
development of real-time systems; as an interval
logic with
special features for expressing and analyzing
time durations of
states in real-time systems, it allows for
representing and
formally reasoning about requirements and
designs at an
appropriate level of abstraction. This book
presents the logical
foundations of duration calculus in a coherent
and thorough
manner. Through selective case studies it
explains how duration
calculus can be applied to the formal specification
and
verification of real-time systems. The book
also contains an
extensive survey of the current research
in this field. The
material included in this book has been used
for graduate and
postgraduate courses, while it is also suitable
for experienced
researchers and professionals.
Table of contents
Introduction.- Interval Logic.- Duration
Calculus.- Deadline
Driven Scheduler.- Relative Completeness.-
Decidability.-
Undecidability.- Model-Checking: Linear Duration
Invariants.-
State Transitions and Events.- Super-dense
Transitions.-
Neighbourhood Logic.- Probabilistic Duration
Calculus.-
References.- Abbrevitions.- Symbol Index.-
Index.
Series: Texts in Theoretical Computer Science.
An EATCS Series
2004, Approx. 110 p., Hardcover
ISBN: 3-540-40344-2
About this textbook
This book treats algorithms for the venerable
"primality
problem": Given a natural number n,
decide whether it is
prime or composite. The problem is basic
in number theory;
efficient algorithms that solve it, i.e.,
algorithms that run in
a number of computational steps which is
polynomial in the number
of decimal digits needed to write n, are
important for
theoretical computer science and for applications
in algorithmics
and cryptology. This book gives a self-contained
account of
theoretically and practically important efficient
algorithms for
the primality problem, covering the randomized
algorithms by
Solovay-Strassen and Miller-Rabin from the
late 1970s as well as
the recent deterministic algorithm of Agrawal,
Kayal, and Saxena.
The volume is written for students of computer
science, in
particular those with a special interest
in cryptology, and
students of mathematics, and it may be used
as a supplement for
courses or for self-study.
Written for:
Graduate and undergraduate students, lecturers,
researchers
Keywords:
Primality Testing
Efficient Algorithms
Number Theoretical Algorithms
Randomized Algorithms
Polynomia Time Algorithms
Efficient Primality Testing
Deterministic Primality Testing
Factorization
Computational Number Thoery
Series: Monographs in Theoretical Computer
Science. An EATCS
Series
2004, Approx. 120 pp., Hardcover
ISBN: 3-540-66815-2
About this book
Restricted-orientation convexity is the study
of geometric
objects whose intersections with lines from
some fixed set are
connected. This notion generalizes standard
convexity and several
types of nontraditional convexity. The authors
explore the
properties of this generalized convexity
in multidimensional
Euclidean space, and describ restricted-orientation
analogs of
lines, hyperplanes, flats, halfspaces, and
identify major
properties of standard convex sets that also
hold for restricted-orientation
convexity. They then introduce the notion
of strong restricted-orientation
convexity, which is an alternative generalization
of convexity,
and show that its properties are also similar
to that of standard
convexity.
Written for:
Scientists, Researchers, Graduates, Libraries
Keywords:
Generalized convexity
Visibility
Euclidean geometry
Higher dimensions
Theory
Algorithms
Series: Universitext
2004, Approx. 410 p., Hardcover
ISBN: 0-387-40510-0
About this textbook
From reviews of the German edition: "This
is an exciting
text and a refreshing contribution to an
area in which challenges
continue to flourish and to captivate the
viewer. Even though
representation theory and constructions of
simple groups have
been omitted, the text serves as a springboard
for deeper study
in many directions. One who completes this
text not only gains an
appreciation of both the depth and the breadth
of the theory of
finite groups, but also witnesses the evolutionary
development of
concepts that form a basis for current investigations.
This is
accomplished by providing a thread that permits
a natural flow
from one concept to another rather than compartmentalizing.
Operators on sets and groups are introduced
early and used
effectively throughout. The bibliography
provides excellent
supplemental support...The text is tight;
there is no fluff. The
format builds on concepts essential for later
expansion and
associated reading. On occasion, results
are stated without
proof; continuity is maintained. Several
proofs are provided free
of representation theory on which the originals
were based. More
generally the proofs are direct, perhaps
at times brief. The
focus is on the underlying structural components,
with selected
details left to the reader. As a result the
reader develops the
maturity required for approaching the literature
with confidence.
The first eight chapters have an abundance
of exercises, not
prorated, and some of the more challenging
are addressed later in
the text. Due to the nature of the material,
fewer exercises
appear in the remaining chapters." (H.
Bechtell,
Mathematical Reviews)
Table of contents
Preface.- List of Symbols.- Basic Concepts.-
Abelian Groups.-
Action and Conjugation.- Permutation Groups.-
p-Groups and
Nilpotent Groups.- Normal and Subnormal Structure.-
Transfer and
p-Adic Factor Groups.- Groups Acting on Groups.-
Quadratic Action.-
The Embedding of p-Local Subgroups.- Signalizer
Functors.- N-Groups.-
Appendix.- Bibliography.
Series: Springer Monographs in Mathematics
2004, X, 290 p. 52 illus., Hardcover
ISBN: 1-85233-767-2
About this book
This volume contains a wealth of results
and methodologies
applicable to a wide range of problems arising
in reaction-diffusion
theory. The first part is concerned with
obtaining the complete
structure of the large-time solution of scalar
reaction diffusion
equations, and systems of reaction-diffusion
equations. The
second part is concerned with the analysis
of a class of singular
reaction-diffusion equations. In this detailed
analysis, use is
made of the method of matched asymptotic
expansions, dynamical
systems theory, and comparison theorems,
which provide a powerful
combination of techniques for the detailed
analysis of this broad
class of reaction-diffusion equations. The
monograph can be
viewed both as a handbook, and as a detailed
description of the
methodology. Researchers in reaction-diffusion
theory, and
scientists applying reaction-diffusion theory
to such areas as
chemical kinetics, biological systems, epidemiology
and
population dynamics, will find it a popular
addition to the
literature.
Table of contents