Jean-Francois Pommaret
CERMA, ENPC, Marne-la-Vallee, France

Partial Differential Control Theory
Volume I: Mathematical Tools, Volume II: Control Systems

MATHEMATICS AND ITS APPLICATIONS Volume 530

Algebraic analysis, that is the algebraic study of systems of partial differential equations by means of module theory and homological algebra, was pioneered around 1970 by M. Kashiwara, B. Malgrange, and V.P. Palamodov. The theory of differential modules, namely modules over a noncommutative ring of differential operators, is a fashionable subject of research today. However, despite its fundamental importance in mathematics, it can only be found in specialist books and papers, and has only been applied in control theory since 1990.

This book provides a self-contained and exhaustive account of algebraic analysis and its application to control systems defined by partial differential equations. The first volume presents the mathematical tools needed from both commutative algebra, homological algebra, differential geometry and differential algebra. The second volume applies these new methods in order to study the structural and input/output properties of both linear and nonlinear control systems. Hundreds of explicit examples allow the reader to gain insight and experience in these topics.

The book is written at a graduate level and is intended for researchers in mathematics, mathematical physics, computer algebra, control theory, and theoretical mechanics

Contents
Foreword. Introduction. Volume I: Mathematical Tools. I. Commutative Algebra. II. Homological Algebra. III. Differential Geometry. IV. Differential Algebra. Volume II: Control Systems. V. Linear Control Systems. VI. Nonlinear Control Systems. Bibliography. Index.

Kluwer Academic Publishers, Dordrecht
Hardbound Set only of 2 volumes, ISBN 0-7923-7037-6
June 2001, 976 pp.

John L. Fan
Stanford University and Iospan Wireless, CA, USA

Constrained Coding and Soft Iterative Decoding

THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE Volume 627

Constrained Coding and Soft Iterative Decoding is the first work to combine the issues of constrained coding and soft iterative decoding (e.g., turbo and LDPC codes) from a unified point of view. Since constrained coding is widely used in magnetic and optical storage, it is necessary to use some special techniques (modified concatenation scheme or bit insertion) in order to apply soft iterative decoding.

Recent breakthroughs in the design and decoding of error-control codes (ECCs) show significant potential for improving the performance of many communications systems. ECCs such as turbo codes and low-density parity check (LDPC) codes can be represented by graphs and decoded by passing probabilistic (a.k.a. `soft') messages along the edges of the graph. This message-passing algorithm yields powerful decoders whose performance can approach the theoretical limits on capacity. This exposition uses `normal graphs,' introduced by Forney, which extend in a natural manner to block diagram representations of the system and provide a simple unified framework for the decoding of ECCs, constrained codes, and channels with memory. Soft iterative decoding is illustrated by the application of turbo codes and LDPC codes to magnetic recording channels.

For magnetic and optical storage, an issue arises in the use of constrained coding, which places restrictions on the sequences that can be transmitted through the channel; the use of constrained coding in combination with soft ECC decoders is addressed by the modified concatenation scheme also known as `reverse concatenation.' Moreover, a soft constraint decoder yields additional coding gain from the redundancy in the constraint, which may be of practical interest in the case of optical storage. In addition, this monograph presents several other research results (including the design of sliding-block lossless compression codes, and the decoding of array codes as LDPC codes).

Constrained Coding and Soft Iterative Decoding will prove useful to students, researchers and professional engineers who are interested in understanding this new soft iterative decoding paradigm and applying it in communications and storage systems.


`This monograph is a most welcome addition to the coding theory literature. It contains a masterfully written and easily accessible tutorial treatment of new and exciting error-correction codes, such as turbo codes and low-density parity-check (LDPC) codes. In addition, it introduces novel and promising approaches to integration of error correction codes with constrained codes as well as hybrid constructions of algebraic codes and LDPC. While these codes can be applied to any communications channel, special focus is given to the magnetic recording channel. Students as well as professionals in the information sciences will benefit greatly from having this monograph on their desks. I highly recommend it'

B.Marcus, IBM Almaden Research Center
Kluwer Academic Publishers, Boston
Hardbound, ISBN 0-7923-7455-X
July 2001, 280 pp.

Pascal Chossat/Institut Non Lineaire de Nice, CNRS - Universite de Nice, Sophia-Antipolis,
Dieter Armbruster/Dept. of Mathematics, Arizona State University, Tempe, USA
Iuliana Oprea/Faculty of Mathematics, University of Bucharest, Romania

Dynamo and Dynamics, a Mathematical Challenge
Proceedings of the NATO Advanced Research Workshop, Cargese, France, 21-26 August 2000

NATO SCIENCE SERIES: II: Mathematics, Physics and Chemistry Volume 26

The dynamo effect has been one of the most challenging in modern physics. It has also been one of the most important, since it is believed that the Earth's magnetic field, that of the Sun and astrophysical magnetic fields in general are produced by dynamos resulting from the motion of electrically conducting fluids. Although predicted by theory, the existence, and more specifically, the dynamics of the dynamo have been controversial for many years. Problems have centred around the difficulty of producing a dynamo in the laboratory, and difficulty in solving the equations.

Working laboratory dynamos have now been reported. New ideas have emerged to explain the Earth's and Solar dynamos and their 'strange' evolution. Significant progress has been reported in understanding dynamo action in a variety of astrophysical and laboratory fluid flows. The variety and originality of the presentations here make the book an invaluable source for scientists and students interested in the dynamo problem: physicists, astrophysicists, geophysicists, mathematicians and others.

Contents and Contributors

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7069-4
July 2001, 416 pp.
Paperback, ISBN 0-7923-7070-8
July 2001, 416 pp.

Laurent Baulieu/CNRS and Universite Pierre et Marie Curie (Paris VI), France
Michael Green/DAMTP, University of Cambridge, UK
Marco Picco/CNRS and Universite Pierre et Marie Curie (Paris VI), France
Paul Windey/Universite Pierre et Marie Curie (Paris VI), France

Progress in String Theory and M-Theory
Proceedings of the NATO Advanced Study Institute, Cargese, France, May 24-June 5, 1999

NATO SCIENCE SERIES: C: Mathematical and Physical Sciences (continued within NATO SCIENCE SERIES II: Mathematics, Physics and Chemistry)
Volume 564

Recent developments in supersymmetric field theory, string theory, and brane theory have been revolutionary. The main focus of the present volume is developments of M-theory and its applications to superstring theory, quantum gravity, and the theory of elementary particles. Topics included are D-branes, boundary states, and world volume solitons. Anti-De-Sitter quantum field theory is explained, emphasising the way it can enforce the holography principle, together with the relation to black hole physics and the way Branes provide the microscopic interpretation for the entropy of black holes. Developments in D-branes within type-I superstring and related theories are described. There are also possible phenomenological implications of superstring theory that would lie within the range of quantum gravity effects in the future generation of accelerators, around 1 TeV.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7033-3
July 2001, 432 pp.
Paperback, ISBN 0-7923-7034-1
July 2001, 432 pp.

H. Fujita, Tokai University/ N. Saito, Toyama University/T. Suzuki, Osaka University

Operator Theory and Numerical Methods

Studies in Mathematics and its Applications, 30

Description

In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.

Year 2001
Hardbound
ISBN: 0-444-50474-5
320 pages