2003 Approx. 400 p. Softcover
3-540-00744-X
These ten detailed and authoritative survey
articles on numerical
methods for direct and inverse wave propagation
problems are
written by leading experts. Researchers and
practitioners in
computational wave propagation, from postgraduate
level onwards,
will find the breadth and depth of coverage
of recent
developments a valuable resource. The articles
describe a wide
range of topics on the application and analysis
of methods for
time and frequency domain PDE and boundary
integral formulations
of wave propagation problems. Electromagnetic,
seismic and
acoustic equations are considered. Recent
developments in methods
and analysis ranging from finite differences
to hp-adaptive
finite elements, including high-accuracy
and fast methods are
described with extensive references.
Keywords: wave propagation, numerical approximation,
computational electromagnetics, scattering,
inverse problems
Contents:
Thomas Hagstrom: New results on absorbing
layers and radiation
boundary conditions.- Oscar Bruno: Fast,
high-order, high-frequency
integral methods for computational acoustics
and electromagnetics.-
Analisa Buffa and Ralf Hiptmair: Galerkin
boundary element
methods for electromagnetic scattering.-
Martin Costabel and
Monique Dauge: Computation of resonance frequencies
for Maxwell
equations in non-smooth domains.- Leszek
Demkowicz: hp-adaptive
finite elements for time-harmonic Maxwell
equations.- Patrick
Joly: Variational methods for time-dependent
wave propagation
problems.- Bengt Fornberg: Some numerical
techniques for
Maxwell's equations in different types of
geometries.- Tuong Ha
Duong: On retarded potential boundary integral
equations and
their discretisation.- Andreas Kirsch: Inverse
scattering theory
for time-harmonic waves.- David Colton and
Peter Monk: Herglotz
wave functions in inverse electromagnetic
scattering theory.
Series: Universitext.
2003 Approx. 370 p. Softcover
3-540-44319-3
This book contains detailed lecture notes
on six topics at the
forefront of current research in numerical
analysis and applied
mathematics. Each set of notes presents a
self-contained guide to
a current research area and has an extensive
bibliography. In
addition, most of the notes contain detailed
proofs of the key
results. The notes start from a level suitable
for first year
graduate students in applied mathematics,
mathematical analysis
or numerical analysis and proceed to current
research topics. The
reader should therefore be able to gain quickly
an insight into
the important results and techniques in each
area without
recourse to the large research literature.
Current (unsolved)
problems are also described and directions
for future research
are given. This book is also suitable for
professional
mathematicians who require a succint and
accurate account of
recent research in areas parallel to their
own and graduates in
mathematical sciences.
Keywords: finite element approximation, mean
curvature flow,
multiscale solutions, symplectic integration,
eigenvalue
problems, control problems, optimization
Contents:
Franco Brezzi and Donatella Marini: Subgrid
Phenomena and
Numerical Schemes.- Franco Brezzi: Stability
of Saddle-points in
Finite Dimensions. Klaus Deckelnick and Gerhard
Dziuk: Mean
Curvature Flow.- Nicholas I.M. Gould and
Sven Leyffer: An
Introduction to Algorithms for Nonlinear
Optimization.- Ernst
Hairer and Martin Hairer: Matlab Programs
for Geometric Numerical
Integration.- Thomas Y. Hou: Numerical Approximations
to
Multiscale Solutions in Partial Differential
Equations.- Volker
Mehrmann: Numerical Methods for Eigenvalue
and Control Problems.
Series: Universitext.
2003 IX, 354 p. 23 illus. Hardcover
0-387-95554-2
This text describes how fractal phenomena,
both deterministic and
random, change over time, using the fractional
calculus. The
intent is to identify those characteristics
of complex physical
phenomena that require fractional derivatives
or fractional
integrals to describe how the process changes
over time. The
discussion emphasizes the properties of physical
phenomena whose
evolution is best described using the fractional
calculus, such
as systems with long-range spatial interactions
or long-time
memory.
In many cases, classic analytic function
theory cannot serve for
modeling complex phenomena; "Fractal
Operators" shows
how classes of less familiar functions, such
as fractals, can
serve as useful models in such cases. Because
fractal functions,
such as the Weierstrass function (long known
not to have a
derivative), do in fact have fractional derivatives,
they can be
cast as solutions to fractional differential
equations. The
traditional techniques for solving differential
equations,
including Fourier and Laplace transforms
as well as Green's
functions, can be generalized to fractional
derivatives.
Fractal Operators addresses a general strategy
for understanding
wave propagation through random media, the
nonlinear response of
complex materials, and the fluctuations of
various forms of
transport in heterogeneous materials. This
strategy builds on
traditional approaches and explains why the
historical techniques
fail as phenomena become more and more complicated.
Series: Institute for Nonlinear Science.
2003 X, 266 p. Softcover
3-540-00395-9
Error-correcting codes have been incorporated
in numerous working
communication and memory systems. This book
covers the
mathematical aspects of the theory of block
error-correcting
codes together, in mutual reinforcement,
with computational
discussions, implementations and examples
of all relevant
concepts, functions and algorithms. This
combined approach
facilitates the reading and understanding
of the subject.
The digital companion of the book is a non-printable
.pdf
document with hyperlinks. The examples included
in the book can
be run with just a mouse click and modified
and saved by users
for their own purpose.
Keywords: Error-Correcting Codes
Series: Universitext.
Graduate Students in Mathematics, Computer
Science ane Electrical
Engineering
Book category: Graduate/Advanced undergraduate
textbook
Publication language: English
2nd ed. 2003 Approx. 440 p. 1 illus. Hardcover
0-387-00293-6
Written for: Graduate mathematics students,
advanced
undergraduates, research mathematicians
Book category: Graduate/Advanced undergraduate
textbook
Publication language: English
The field of generalized inverses has grown
much since the
appearance of the first edition in 1974,
and is still growing.
This book accounts for these developments
while maintaining the
informal and leisurely style of the first
edition. New material
has been added, including a chapter on applications,
an appendix
on the work of E.H. Moore, new exercises
and applications.
Contents:
Glossary of Notation.- Introduction.- Preliminaries.-
Existence
and Construction of Generalized Inverses.-
Linear Systems and
Characterization of Generalized Inverses.-
Minimal Properties of
Generalized Inverses.- Spectral Generalized
Inverses.-
Generalized Inverses of Partitioned Matrices.-
A Spectral Theory
for Rectangular Matrices.- Computational
Aspects of Generalized
Inverses.- Miscellaneous Applications.- Generalized
Inverses of
Linear Operators between Hilbert Spaces.-
Appendix A: The Moore
of the Moore-Penrose Inverse.- Bibliography.-
Subject Index.-
Author Index.
Series: CMS Books in Mathematics.
2nd ed. 2003 Approx. 450 p. 46 illus. Hardcover
0-387-00211-1
This book serves as an introduction to queuing
theory and
provides a thorough treatment of tools like
Markov processes,
renewal theory, random walks, Levy processes,
matrix-analytic
methods and change of measure. It also treats
in detail basic
structures like GI/G/1 and GI/G/s queues,
Markov-modulated models
and queuing networks, and gives an introduction
to areas such as
storage, inventory, and insurance risk. Exercises
are included
and a survey of mathematical prerequisites
is given in an
appendix This much updated and expanded second
edition of the
1987 original contains an extended treatment
of queuing networks
and matrix-analytic methods as well as additional
topics like
Poisson's equation, the fundamental matrix,
insensitivity, rare
events and extreme values for regenerative
processes, Palm
theory, rate conservation, Levy processes,
reflection, Skorokhod
problems, Loynes' lemma, Siegmund duality,
light traffic, heavy
tails, the Ross conjecture and ordering,
and finite buffer
problems. Students and researchers in statistics,
probability
theory, operations research, and industrial
engineering will find
this book useful.
Keywords: applied probability, queueing theory,
Markov processes
Contents:
Simple Markovian Models.- Markov Chains.-
Markov Jump Processes.-
Queueing Theory at the Markovian Level.-
Basic Mathematical Tools.-
Basic Renewal Theory.- Regenerative Processes.-
Further Topics in
Renewal Theory and Regenerative Processes.-
Random Walks.-
Special Models and Methods.- Steady-State
Properties of GI/G/1.-
Explicit Examples in the Theory of Random
Walks and Single Server
Queues.- Multidimensional Methods.- Many-server
Queues.-
Conjugate Processes.- Insurance Risk, DAM
and Storage Models.-
Appendices.
Series: Applications of Mathematics. Volume.
51
2003 IX, 414 p. 75 illus. Hardcover
3-540-00615-X
This volume gathers together 26 selected
papers from the
International Congress of Mathematicians'
1st Satellite
Conference on Game Theory and its Applications
(2002). It
contains four sections: Foundations, Concepts,
and Structure;
Equilibrium Properties; Applications to the
Natural and Social
Sciences; Computational Aspects of Games.
The first section
explores fundamental ideas, leading to new
and analytically
interesting analysis of current problems,
new games and new
modeling approaches. Papers in the second
section discuss issues
in the solution of games, and present a number
of potentially
fruitful ideas regarding game equilibrium.
The third and fourth
sections are devoted to applications to the
natural and social
sciences and to computation. The articles
on market structure and
game-based computations would be of particular
interest to
researchers and practitioners.
Keywords: Game theory, Differential games,
Cooperative games,
Bargaining, Non-cooperative games
Contents:
From the contents: Foundations, Concepts,
and Structure.-
Equilibrium Properties.- Applications to
the Natural and Social
Sciences.- Computational Aspects of Games.