Roger Temam, Indiana University, Bloomington, IN
Navier-Stokes Equations: Theory and Numerical
Analysis
Expected publication date is April 18, 2001
From a review for the First Edition:
"This book, in many ways remarkable,
gives a detailed
account of a number of results concerned
with the theory and
numerical analysis of the Navier-Stokes
equations of viscous incompressible fluids."
-- Zentralblatt fur Mathematik
Description
This book was originally published in 1977
and has since been
reprinted four times (the last reprint was
in 1985). The current
volume is reprinted and fully retypeset
by the AMS. It is very close in content to
the 1985 edition. The
book presents a systematic treatment of results
on the theory and
numerical analysis of the
Navier-Stokes equations for viscous incompressible
fluids.
Considered are the linearized stationary
case, the nonlinear
stationary case, and the full nonlinear
time-dependent case. The relevant mathematical
tools are
introduced at each stage.
The new material in this book is Appendix
III, reproducing a
survey article written in 1998. This appendix
contains a few
aspects not addressed in the earlier
editions, in particular a short derivation
of the Navier-Stokes
equations from the basic conservation principles
in continuum
mechanics, further historical perspectives,
and indications on new developments in the
area. The appendix
also surveys some aspects of the related
Euler equations and the
compressible Navier-Stokes
equations. Readers are advised to peruse
this appendix before
reading the core of the book.
This book presents basic results on the theory
of Navier-Stokes
equations and, as such, continues to serve
as a comprehensive
reference source on the topic.
Contents
The steady-state Stokes equations
Steady-state Navier-Stokes equations
The evolution Navier-Stokes equation
Appendix I: Properties of the curl operator
and application to
the steady-state Navier-Stokes equations
Appendix II (by F. Thomasset): Implementation
of non-conforming
linear finite elements (Approximation APX5--Two-dimensional
case)
Appendix III: Some developments on Navier-Stokes
equations in the
second half of the 20th century
Bibliography to Appendix III
Comments
Additional comments to the revised edition
Bibliography
Index
Details:
Publisher: American Mathematical Society
Series: AMS Chelsea Publishing
Publication Year: 2001
ISBN: 0-8218-2737-5
Paging: approximately 424 pp.
Binding: Hardcover
Aminov, Y.
Differential Geometry and Topology of Curves
Differential geometry is an actively developing
area of modern
mathematics and this volume presents a classical
approach to
the general topics of the geometry of curves
including the
theory of curves in n-dimensional Euclidean
space. The author
investigates problems for special classes
of curves and gives
the working method to obtain the conditions
for closed
polygonal curves. The proof of the Bakel-Werner
theorem in
conditions of boundedness for curves with
periodic curvature
and torsion is presented. The volume also
highlights the
contributions made by great geometers, past
and present, to
differential geometry and topology of curves.
Contents: Definition of a Curve ・Vector-Valued
Functions
Depending on Numerical Arguments ・The Regular
Curve and
Its Representations ・Straight Line Tangent
to a Curve ・
Osculating Plane of a Curve ・The Arc Length
of a Curve ・The
Curvature and Torsion of a Curve ・Osculating
Circle of a Plane
Curve ・Singular Points of Plane Curves ・Peano's
Curve ・
Envelope of the Family of Curves ・Frenet
Formulas ・
Determination of a Curve with Given Curvature
and Torsion ・
Analogies of Curvature and Torsion for Polygonal
Lines ・Curves
with a Constant Ratio of Curvature and Torsion
・Osculating
Sphere ・Special Planar Curves ・Curves in
Mechanics ・Curve
Filling a Surface ・Curves with Locally Convex
Projection ・
Integral Inequalities for Closed Curves ・Reconstruction
of a
Closed Curve with Given Spherical Indicatrix
of Tangents ・
Conditions for a Curve to be Closed ・Isoperimetric
Property of
a Circle ・One Equality for a Closed Curve
・Necessary and
Sufficient Condition of the Boundedness of
a Curve with
Periodic Curvature and Torsion ・Delaunay's
Problem ・Jordan's
Theorem on Closed Plane Curves ・Gauss's
Integral for Two
Linked Curves ・Knots ・Alexander's Polynomial
・Curves in
n-Dimensional Euclidean Space ・Curves with
Constant
Curvatures in n-Dimensional Euclidean Space
・Generalization
of the Fenchel Inequality ・Knots and Links
in Biology and One
Mystery ・Jones・Polynomial, Its Generalization
and Some
Applications
Readership: Graduates and researchers in
mathematics and
geometry.
September, 2000 / 216 pp / Cloth / 90-5699-091-8
edited by Antonis Botinis
University of Skorde, Sweden, and University
of Athens, Greece
Intonation
Analysis, Modelling and Technology
TEXT, SPEECH AND LANGUAGE TECHNOLOGY Volume
15
The volume Intonation: Analysis, Modelling
and Technology covers
the
main aspects of intonation, written by international
researchers
in the field.
Following the Introduction, fourteen chapters
are organised into
five
thematic sections: Overview of Intonation,
Prominence and Focus,
Boundaries and Discourse, Intonation Modelling
and Intonation
Technology.
Each chapter is basically autonomous within
a thematic section,
but the
subject of several chapters extends over
more than one thematic
section.
The combination of a wide range of research
areas, as well as
interdisciplinary approaches in the study
of intonation, makes
this volume a
unique contribution to the international
scientific community.
Basic knowledge of Intonation and Prosody
is assumed in the
context of
linguistic and computational backgrounds.
Readers may range from
students
of advanced undergraduate to postgraduate
and research levels as
well as
individual researchers within a variety of
disciplines such as
Experimental
Phonetics, General and Computational Linguistics,
Computer
Science, and
Speech-anguage Engineering.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6605-0
October 2000, 408 pp.
Paperback, ISBN 0-7923-6723-5
October 2000, 408 pp.
edited by Harry Bunt Tilburg University, The Netherlands
Anton Nijholt University of Twente, Enschede,
The Netherlands
Advances in Probabilistic and Other Parsing
Technologies
TEXT, SPEECH AND LANGUAGE TECHNOLOGY Volume
16
Parsing technology is concerned with finding
syntactic structure
in language.
In parsing we have to deal with incomplete
and not necessarily
accurate
formal descriptions of natural languages.
Robustness and
efficiency are
among the main issuesin parsing. Corpora
can be used to obtain
frequency
information about language use. This allows
probabilistic
parsing, an
approach that aims at both robustness and
efficiency increase.
Approximation techniques, to be applied at
the level of language
description, parsing strategy, and syntactic
representation, have
the same
objective. Approximation at the level of
syntactic representation
is also
known as underspecification, a traditional
technique to deal with
syntactic
ambiguity.
In this book new parsing technologies are
collected that aim at
attacking the
problems of robustness and efficiency by
exactly these
techniques: the
design of probabilistic grammars and efficient
probabilistic
parsing
algorithms, approximation techniques applied
to grammars and
parsers to
increase parsing efficiency, and techniques
for
underspecification and the
integration of semantic information in the
syntactic analysis to
deal with
massive ambiguity.
The book gives a state-of-the-art overview
of current research
and
development in parsing technologies. In its
chapters we see how
probabilistic methods have entered the toolbox
of computational
linguistics
in order to be applied in both parsing theory
and parsing
practice. The
book is both a unique reference for researchers
and an
introduction to the
field for interested graduate students.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6616-6
October 2000, 288 pp.
Gerard J. Chang Dept. of Applied Mathematics, National Chiao Tung University, Taiwan,
R.O.C. Lirong Cui Reliability and Safety Research Center, China
Aerospace Corp., PR of China
Frank K. Hwang Dept. of Applied Mathematics, National
Chiao Tung University, Taiwan, R.O.C.
Reliabilities of Consecutive-k Systems
NETWORK THEORY AND APPLICATIONS Volume 4
Since its start in 1980 the study of the
consecutive-k system has
resulted in
the accumulation of hundreds of research
papers. Its popularity
is due to its
close ties with many mathematical topics
such that the system has
become a
prototype of how mathematical analysis can
help in the study of
system
reliability. This is the first book to put
together all the
material on the
subject. However, it is not just a collection
of results. The
authors have built
a framework to fit the results into and then
sort them and
compare them, so
that the reader has a good idea what is currently
the best
methodology. The
authors also cover important extensions such
as window systems,
network
systems, graph systems, and 2-dimensional
systems. The
consecutive-k
system is known for its wide applicability
and the authors have
included a
chapter on applications.
Audience: All systems engineering researchers,
not just those
specializing in
the consecutive-k system. The book could
also be used for a
graduate
course to demonstrate how mathematics is
actually applied to
systems
engineering.
Contents
List of Figures. Preface. 1. Introduction.
2. Computation of
Reliability. 3.
Design of Optimal Consecutive Systems. 4.
The Lifetime
Distribution. 5.
Asymptotic Analysis. 6. Window Systems. 7.
The Network Model. 8.
Consecutive-2 Graphs. 9. Some Related Systems.
10. Applications.
References. Index.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6661-1
November 2000, 210 pp.