Edited by F.J.E. Dillen ,
L.C.A. Verstraelen , Katholieke Universiteit Leuven, Departement Wiskunde, Leuven, Belgium

Handbook of Differential Geometry, Volume 1

Description

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Contents
Preface.
Introduction (S.S. Chern).
List of Contributors.
Differential geometry of webs (M.A. Akivis, V.V. Goldberg).
Spaces of metrics and curvature functionals (D.E. Blair).
Riemannian Submanifolds (B.-Y. Chen).
Einstein metrics in dimension four (A. Derdzinski).
The Atiyah-Singer Index Theorem (P.B. Gilkey).
Survey of isospectral manifolds (C.S. Gordon).
Submanifolds with parallel fundamental form (?. Lumiste).
Sphere theorems (K. Shiohama).
Affine differential geometry (U. Simon).
A survey on isoparametric hypersurfaces and their generalizations (G. Thorbergsson).
Curves (T. Willmore).
Author Index.
Subject Index.

Hardbound

ISBN: 0-444-82240-2
1054 pages

W.A. de Graaf
School of Computational Science, North Haugh, St Andrews, Scotland

Lie Algebras: Theory and Algorithms

Included in series
North-Holland Mathematical Library, 56

Description
The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincar?-Birkhoff-Witt
theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Contents
Basic constructions.
On nilpotency and solvability.
Cartan subalgebras.
Lie algebras with non-degenerate Killing form.
The classification of the simple Lie algebras.
Universal enveloping algebras.
Finitely presented Lie algebras.
Representations of semisimple Lie algebras.
On associative algebras.
Bibliography.
Index of Symbols.
Index of Terminology.
Index of Algorithms.

2000
Hardbound
ISBN: 0-444-50116-9
406 pages

Edited by
Han-Fu Chen , /Dai-Zhan Cheng ,
Ji-Feng Zhang , Chinese Academy of Sciences, Beijing, PRC

Proceedings of the 14th World Congress of IFAC (18-Volume Set)
Proceedings of the 14th World Congress (International Federation of Automatic Control), Beijing, PRC, 5-9 July 1999

Description

As the last triennial World Congress of the International Federation of Automatic Control (IFAC) of this century, the 14th IFAC Congress was recognized as a preeminent event for the worldwide community of control systems science and engineering. Beijing, one of the oldest cities in the world, is fuelled by the rapid growth of the economy and the development of science and technology, including automation. Beijing is famous for the development of automatic machines over many centuries, including the armillary sphere for stimulating the Universe and the seismograph for detecting earthquakes, making the city one of great world centres
for automation. The International Program Committee (IPC) received 2169 submitted papers, 53 invited session proposals and eight panel discussion proposals from 68 countries and regions. The technical program for the Congress covers a broad range of topics, with sessions arranged into nine congress tracks and subdivided into 45 technical areas. Reviews were conducted by all of the IFAC Technical Committees,
with the help of hundreds of worldwide experts. Through this rigorous review procedure 1556 papers, one keynote speech, five plenary lectures, 47 invited session proposals and seven panel discussion proposals were accepted. There were five plenary lectures, one at the start of each of the five days of the Congress. The plenary speakers included some of the world's most outstanding authorities in various control fields. The topics of the plenary lectures covered surveys, prospects and introductions to advanced control theory and applications. Following the plenary addresses, the congress program was composed of more than 1500 papers, presented in 214 lecture-type sessions and 47 poster-type sessions. The paper sessions are supplemented by seven panel discussions. The Proceedings of the Congress are published in two forms, printed and CD-ROM. The Proceedings in its printed form consists of 18 volumes: 17 subject volumes, which contain all lecture and poster papers and a plenary volume. The plenary volume contains the keynote speech, plenary papers, panel discussions, and the table of contents, author index and subject index for the full set of subject volumes.
This Congress will be remembered as a showcase for the fruitful results on control theory and application achieved since the beginning of this century. In addition,we expect that several of the results and ideas demonstrated in this Congress will have lasting influence in the next century on the directions taken by the field of control systems engineering.

Audience
For researchers, engineers and participants from the Congress.


Volume A: Manufacturing, Social Effects, Scheduling
Volume B: Robotics Automation
Volume C: Control Design
Volume D: Linear System, Robust Control I
Volume E: Robust Control II
Volume F: Nonlinear System I
Volume G: Nonlinear System II, Optimal Control
Volume H: Modeling, Identification, Signal Processing I
Volume I: Modeling, Identification, Signal Processing II, Adaptive Control
Volume J: Discrete Event Systems, Stochastic Systems, Fuzzy and Neural Systems I
Volume K: Fuzzy and Neural Systems II, Control in Agricultural Processes
Volume L: Biomedical and Environmental Systems, Systems Engineering
Volume M: Management, Global and Educational Issues
Volume N: Chemical Process Control, Mineral and Metal Processing
Volume O: Power Systems, Biotechnological Processes, Fault Detection I
Volume P: Fault Detection II, Aerospace, Marine Systems
Volume Q: Transportation Systems, Computer Control
Plenary: Plenary Volume
18 Volume-Set

Yuri L. Ershov / Novosibirsk State University and Institute of Mathematics, Russia
Sergei S. Goncharov / Novosibirsk State Univeristy and Institute of Mathematics, Russia

Constructive Models

SIBERIAN SCHOOL OF ALGEBRA AND LOGIC

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers
and studying relations between algorithmic and structural properties of these models.

This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of
recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of
decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties.

Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time.

The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract
data types, and problems of synthesis and verification of programs. Therefore, the book will be useful for not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science.

The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science.

Contents
Preface. 1.Models, Computability, and Numberings 2.Constructive Models 3.Strongly Constructive and Decidable Models 4.Theories with a Countable Set of Countable Models 5.Algorithmic Dimensions and Computable Classes 6.Models of Finite Algorithmic Dimension and Autostability References.
Subject Index

Hardbound, ISBN 0-306-11066-0
March 2000, 306 pp.

A.L. Bughgeim

Volterra Equations and Inverse Problems

Inverse and Ill-Posed Problems Series

The main part of this new monograph in the Inverse and Ill-Posed Problems Series, deals with the theory of multidimensional Volterra equations and their applications to multidimensional inverse problems. The book opens with the basic concepts of the general ill-posed problem theory, followed by elements of the abstract operator Volterra theory. Subsequent chapters deal with: linear and nonlinear operator equations in scales of Banach spaces and applications to inverse problems; investigations by the method of the weight a priori estimates and the method based on the spectral von Neumann theorem; multidimensional integro-differential Volterra equations and problems of integral geometry; inverse problems of wave scattering and propagation.

This monograph will be of value and interest to researchers in applied mathematics, (mathematical) physics, and geophysics.

1999; x+204 pages
ISBN 90-6764-302-5

Contents
1. BASIC CONCEPTS OF ILL-POSED PROBLEM THEORY
2. LINEAR VOLTERRA OPERATORS AND THEIR PROPERTIES
3. LINEAR OPERATOR VOLTERRA EQUATIONS
4. NONLINEAR OPERATOR VOLTERRA EQUATIONS IN THE SCALES OF BANACH SPACES
5. ABSTRACT INTEGRO-DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS
6. MULTIDIMENSIONAL INVERSE PROBLEMS
7. MULTIDIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS OF VOLTERRA TYPE
8. INVERSE PROBLEMS OF WAVE PROPAGATION AND SCATTERING
Bibliography