Azzouz Awane
Universit・Hassan II-Mohammedia, Facult・Sciences, Casablanca, Maroco
Michel Goze
Dept. of Mathematics, Universit・de Haute Alsace, Mulhouse-Colmar, France

Pfaffian Systems, k-Symplectic Systems

The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan.

We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics.

Audience: This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras.

Contents
Introduction. 1. Exterior Forms. 2. Exterior Systems. 3. k-Symplectic Exterior Systems. 4. Pfaffian Systems. 5. Classification of Pfaffian Systems. 6. k-Symplectic Manifolds. 7. k-Symplectic Affine Manifolds. 8. Homogeneous k-Symplectic G-Spaces. 9. Geometric Pre-Quantization.

Kluwer Academic Publishers, Dordrecht

Hardbound, ISBN 0-7923-6373-6
June 2000, 260 pp.

Fuchs, D.B., University of California, Davis, CA, USA
Viro, O.Y., Uppsala University, Sweden

Topology II
Homotopy and Homology. Classical Manifolds

2000. Approx. 295 pp. 38 figs.
3-540-51996-3

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

Keywords: homotopy, homology, cohomology, manifolds, Lie groups

Contents: Part I. Introduction to Homotopy Theory by O.Ya.Viro and D.B.Fuchs: 1. Basic
Concepts.- 2. Bundle Techniques.- 3. Cellular Techniques.- 4. The Simplest Calculations.- Part II.
Homology and Cohomology by O.Ya. Viro and D.B.Fuchs: 1. Additive Theory.- 2. Multiplicative
Theory.- 3. Obstructions, Characteristic Classes and Cohomology Operations.- References.- Part
III. Classical Manifolds by D.B.Fuchs: Introduction.- 1. Spheres.- 2. Lie Groups and Stiefel
Manifolds.- 3. Grassman Manifolds and Spaces.- 4. Some Other Important Homogeneous Spaces.-
5. Some Manifolds of Low Dimension.- References.

Series: Encyclopaedia of Mathematical Sciences.VOL. 24

Edited by: Ling Hsiao,
Institute of Mathematics, Academia Sinica, Beijing, People's Republic of China,
and Zhouping Xin,
New York University, Courant Institute, NY

Some Current Topics on Nonlinear Conservation Laws:
Lectures at the Morningside Center of Mathematics, 1

Description

This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading
experts who have made fundamental contributions to this field of research. A. Bressan's theory of $L^1$-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results i the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave--a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics.

This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis.


Contents

A. Bressan -- Stability of entropy solutions to n x n conservation laws
G.-Q. Chen -- Compactness methods and nonlinear hyperbolic conservation laws
P. Degond -- Mathematical modelling of microelectronics semiconductor devices
B. Perthame -- Lecture notes on kinetic formulation of conservation laws
Z. Xin -- Theory of viscous conservation laws
Y. Zheng -- Some problems of incompressible fluid dynamics

Details:

Series: AMS/IP Studies in Advanced Mathematics, Volume: 15
Publication Year: 2000
ISBN: 0-8218-1965-8
Paging: 226 pp.
Binding: Softcover

Aggarwala, R., University of Calgary, Alberta, Canada /
Balakrishnan, N., McMaster University, Ontario, Canada

Progressive Censoring
Theory, Methods and Applications

2000. Approx. 256 pages. Hardcover
ISBN 3-7643-4001-0
Due in May 2000

This new book offers a thorough guide to the theory and methods of progressive censoring for practitioners and professionals in applied statistics, quality control, life testing and reliability testing.

In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early due to a variety of circumstances. Samples that arise from such experiments are called censored
samples, and a new, efficient alternative method is referred to as "progressive censoring " (where the removal of live units at time of failure is employed).

Progressive Censoring first introduces progressive sampling foundations, then discusses various properties of progressive samples. It also describes how to make exact or approximate inferences for the different
statistical models with samples based on progressive censoring schemes. With many concrete examples, the book points out the greater efficiency gained by using this scheme instead of classical right-censoring
methods.

With its accessible style and examples, the book is an essential resource for progressive censoring methodology. Advanced students, practitioners, and professionals in applied statistics, reliability and life-testing research will find it a useful guide to understanding and using this new methodology in their work.

Contents:

Preface
List of Tables
Ch. 1, Introduction
Ch. 2, Mathematical Properties of
Progressively Type-II Right Censored
Order Statistics
Ch. 3, Simulational Algorithms
Ch. 4, Recursive Computation and
Algorithms
Ch. 5, Alternative Computational
Methods
Ch. 6, Linear Inference
Ch. 7, Likelihood Inference: Type-I
and Type-II Censoring
Ch. 8, Linear Prediction
Ch. 9, Conditional Inference
Ch. 10, Optimal Censoring Schemes
Ch. 11, Acceptance Sampling Plans
Bibliography
Author Index
Subject Index

Topics and Features:
Lucid formulations of all foundation topics and analysis for progressive censoring Tables of optimal progressive censoring schemes Coverage of simulation algorithms Alternative computational methods
Practical, concrete examples used to show how methods work efficiently and reliably Discussion of prediction of failures

edited by T Hida & K Saito (Meijo University, Japan)

QUANTUM INFORMATION
Proceedings of the First International Conference Meijo University, Japan 4 - 8 November 1997

Contents:

How We, Human Being, Have Evolved to Such Complexity from Nothing? (M Oda)
Why and How Physicists are Interested in Brain and Mind? (M Oda)
A Method for Information Analysis of Sequences by Two-Dimensional Pattern Formation with Coloration (N Obata et al.)
Teleportation of General Quantum States (L Accardi & M Ohya)
On a Certain Integral Formula in Stochastic Analysis (I D�ku)
Comments on Nelson's Quantum Stochastic Process ・Tunneling Time and Domain Structure (T Hashimoto)
Some of Future Directions in White Noise Analysis (T Hida)
Quantum Computer ・An Overview (A Hosoya)
On the Computational Power of Bounded Error Quantum Turing Machines (T Nishino)
Mutual Entropy in Quantum Information and Information Genetics (M Ohya)
The Levy Laplacian as a Self-Adjoint Operator (K Saito & A H Tsoi)
On Variation Theory of Structures and Kiho's Problem (Y Shikata & M Tsukamoto)
Topics on Random Fields (Si Si), Extracting Order from Chaotic World through Perceptual Grouping Processes in Human Sensory System
(N Sugie)
Models of Quantum Computers and Decoherence Problem (I V Volovich)
Analysis and Control of Decoherence in Spin System (M Yamanoi)


Readership: Classical and quantum probabilists, functional analysts and mathematical physicists.

240pp
Pub. date: Aug 1999
ISBN 981-02-3934-3

Iliya I Blekhman (Russian Academy of Sciences, St. Petersburg)

VIBRATIONAL MECHANICS
Nonlinear Dynamic Effects, General Approach, Applications

This important book deals with vibrational mechanics ・the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.

The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrational maintenance or deceleration (retardation) of the rotation of unbalanced rotors, resonances in the motions of celestial bodies, vibrational displacement and shift, vibrational excitation of streams and the transportation of bodies in the fluid. The book considers the use of these effects in creating new vibrational machines, technologies, and also principally new materials ("dynamical materials").

Vibrational Mechanics contains many results published only in Russian and therefore unknown to the specialists in the West, and also a review of the new results obtained by researchers after the book was first published in Russia.


Contents:

Fundamentals of Theory of Vibrational Mechanics: Introduction. Subject-matter of Vibrational Mechanics
On the Mechanics of Systems with Hidden Motions
Basic Statements and Mathematical Apparatus of Vibrational Mechanics
Potential on the Average Dynamic Systems and Extremal Signs of Stability of Certain Motions
Vibrational Mechanics of Machines, Mechanisms and Pendulum Devices: Devices of Pendulum Type
Rotor Mechanisms. Machine Aggregates
Self-synchronization of Mechanical Vibro-exciters
Generalized Principle of Auto-balancing
Vibrational Mechanics of Processes (Vibrational Displacement and Shift): The Main Models and General Regularities of Processes of
Vibrational Displacement from the Position of Vibrational Mechanics
Effects of Vibrational Displacement in Technique, Technology and in Nature
Vibrational Shift (Drift)
Vibrorheology: On Rheology and Vibrorheology
Effective Rheological Characteristics Under the Action of Vibration
Vibrorheological Transformation of Nonlinear Mechanical Systems with Discontinuous Characteristics into Systems with Viscous Friction
Vibrational Control of Properties of Mechanical Systems, Creating New Materials ("Dynamical Materials")
Vibrorheology of Granular Materials
Penetration of Vibration into Certain Media
Microvibrorheology: The Behavior of Suspension Under Vibration, Effective Viscosity and Effective Density of Suspension
The Problem of the Control of Vibrorheological Properties of Mechanical Systems. The Idea of Creating Dynamic Materials
Supplements
Some Other Problems: The Motion of the Particle in a Fast Oscillating Nonuniform Field
Resonance (Synchronization) in Orbital Motions of Celestial Bodies



Readership: Researchers in theoretical and applied mechanics, nonlinear dynamics and nonlinear oscillation theory; engineers,researchers and inventors dealing with the application of usefulvibration and the elimination of harmful vibration; mathematicians whoare specialists in differential equations.