edited by F Cucker & R Wong (City University of Hong Kong)

THE COLLECTED PAPERS OF STEPHEN SMALE
(In 3 Volumes)

Stephen Smale is one of the great mathematicians of the 20th century. His work encompasses a wide variety of subjects: differential topology, dynamical systems, calculus of variations, theory of computation, mechanics and mathematical economy. In all these subjects he has left the imprint of a collection of fundamental results. He has obtained several distinctions, including the Fields Medal, the Veblen Prize, the Chauvenet Prize, the von Neumann Award and the National Medal of Science.

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article
by Smale with his own retrospective views.

Contents:

Volume I: Topology
Economics
Miscellaneous
Volume II: Calculus of Variations (Global Analysis) and PDE's
Dynamics
Mechanics
Biology, Electric Circuits, Mathematical Programming
Volume III: Theory of Computation

1740pp
Pub. date: Jul 2000
ISBN 981-02-4307-3(set)

E N Chukwu (North Carolina State University)

DIFFERENTIAL MODELS AND NEUTRAL SYSTEMS FOR CONTROLLING
THE WEALTH OF NATIONS

Series on Advances in Mathematics for Applied Sciences - Vol. 54

This monograph derives from familiar economic principles the dynamics of national income, the interest rate, employment, the value of capital stock, prices, and the cumulative balance of payments. This is a Volterra neutral integrodifferential game of pursuit. The quarry control is government intervention in the form of taxation, control of money supply, tariffs, foreign credit, interest equalization tax, preferential trade
agreements (which reduce trade barriers and enhance trade flows between nations), transportation and distance between trading partners. The pursuer controls include wages and productivity. The book provides conditions for controllability and then deduces how big government intervention (compared with private firms' contributions) should be to ensure the possibility of growth.

The reader is assumed to be familiar with advanced calculus and to have a working knowledge of ordinary differential equations. The required theory of hereditary systems can be obtained from the book itself.

Contents:

Continuous Delay Models: Motivation
Economic Dynamic Model
Main Results
Economic Interpretation and Fundamental Economic Principles
Economic Hereditary Models of Canada
Soft Landing of Key Economic Indicators with Private and Government Controls Under Scarcity
Stability of Hereditary Economic Systems
Economic Systems with Delay in Control
The Nonlinear Theory of Controllability of Volterra Neutral Integrodifferential Dynamics
Economic Models of USA, Canada, UK, Germany, and India
Models, Programs, and Graphs
Optimal Control of Volterra Integral Neutral Equations and of Linear Neutral Equations
The Time-Optimal Control Theory of Nonlinear Systems of Neutral Type
Controllable Nonlinear Neutral Systems
Function Space Control of Nonlinear Interconnected Economic Systems of Neutral Type
Nonlinear Mathematical Controllability Theory of the Growth of Wealth of Nations with Delays
Oscillation
Reform of Global Economic Systems Structure and Design of Econometric Meter: General Remarks

Readership: Senior undergraduates and graduate students in applied mathematics, control theory, mathematical economics and engineering.

500pp (approx.)
Pub. date: Scheduled Fall 2000
ISBN 981-02-4381-2

edited by Charles Dunkl, Monrad Ismail & Roderick Wong (City University of Hong Kong)

SPECIAL FUNCTIONS
Proceedings of the International Workshop Hong Kong 21 - 25 June 1999

Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.


Readership: Researchers and graduate students in asymptotics, harmonic analysis and mathematical physics.

340pp (approx.)
Pub. date: Scheduled Fall 2000
ISBN 981-02-4393-6

edited by Cameron Gordon (University of Texas, USA), Vaughan F R Jones (University of California, Berkeley, USA), Louis Kauffman (University of Illinois, Chicago, USA), Sofia Lambropoulou
(University of Gottingen, Germany) & Jozef H Przytycki (George Washington University, USA)

KNOTS IN HELLAS '98
Proceedings of the International Conference on Knot Theory and Its Ramifications

Series on Knots and Everything - Vol. 24


There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon-Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected
by the following path: hyperbolic structures, PSL(2,C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.


Readership: Researchers and graduate students in topology, theoretical physics, molecular biology and polymer chemistry.

600pp (approx.)
Pub. date: Scheduled Summer 2000
ISBN 981-02-4340-5

edited by Wu Yue-Liang (Chinese Academy of Sciences)
& Hsu Jong-Ping (University of Massachusetts, Dartmouth)

THE FRONTIERS OF PHYSICS AT THE MILLENNIUM
Proceedings of the Symposium Beijing, China 8 - 11 October 1999

This volume covers high energy physics and particle physics, astrophysics and cosmology, nuclear physics, plasma physics, condensed matter and solid state physics, high temperature superconductivity, semiconductors, optics, laser physics, biophysics, mathematical physics and quantum mechanics.

Contents:

The Structure and the Physical Properties of Carbon Nanotubes (S-S Xie)
Recent Development and the Future of Bose-Einstein Condensation (Z G Zhao)
Fabrication and Application of One-Dimensional Nano-Materials (S-S Fan)
Band Suppression, Fractional Wannie-Stark Ladders and Rabi Oscillations (X-G Zhao)
Dark Matter and Its Energy in the Universe (X-P Wu)
Quantum Mechanics in Action (C-P Sun)
Boundary Potential Effect on Kondo Problem in Luttiger Liquid (Y-P Wang)
Fundamental Problems in Astrophysics and Physics (T-B Li)
Recent Progress in the Research on High Temperature Superconductivity (X Tao)
Review of and Progress in the Research on Low Dimensional Magnetism (X-F Jin)
Progress in Superstring Theory (Z-J Zhu)
and other papers

Readership: Physicists.

450pp (approx.)
Pub. date: Scheduled Fall 2000
ISBN 981-02-4332-4