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.
hard cover
soft cover

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.