by Marek A Abramowicz &
Sebastiano Sonego

(Göteborg University & Chalmers University of Technology,
Sweden)

This book presents the physics of black holes
from an entirely new perspective. It is based on a conformal

rescaling of the geometry of space, called optical geometry,
which allows one to give a simple, unified and

intuitively appealing description of black hole physics. Among
the topics covered are dynamics of particles,

fluids and gyroscopes, electrodynamics, gravitational waves,
thermodynamics, and Hawking radiation.

Optical geometry is also discussed in the wider context of Kaluza–Klein
theories and quantum gravity.

The first chapter of the book describes the subject in
non-technical terms; the rest of it provides all the

mathematical details in a systematic, self-contained way.

Contents:

Introduction and Overview

Geometry and Dynamics in Newton's Theory

Geometry and Dynamics in Einstein's Theory

Exact Stationary and Axially Symmetric Solutions

Conformal Transformations

Optical Geometry for Static Spacetimes

Optical Geometry for Stationary Spacetimes

Optical Geometry for Non-Stationary Spacetime

Quantum Effects

Unsolved Problems

Readership: Graduate students and researchers in black hole
physics, astrophysics, general relativity,

string theory and quantum theory.

400pp (approx.)

Pub. date: Spring 2000

ISBN 981-02-4116-X

edited by M Boiti, L Martina, F Pempinelli, B Prinari & G Soliani (UniversitEdi Lecce, Italy)

Twenty Years After NEEDS '79

Proceedings of the Workshop Le Sirenuse,
Gallipoli, Lecce, Italy 1 - 10 July 1999

This book discusses achievements in the last 20 years, recent
developments and future perspectives

in nonlinear science. Both continuous and discrete systemsEclassical
and quantum Eare considered.

Contents:

Integrability: On Time Evolutions Associated with the
Non-Stationary Schrodinger Equation (A Pogrebkov)

A Generalization of Liouville Integrability (G Marmo)

Random Matrices and Integrable Systems (P Van Moerbeke)

Hamiltonian Structures: Separation of Variables for Gelfand–Zakarevich
Systems (F Magri)

Geometrical Aspects: Surfaces in 4D and Their Integrable Dynamics
(B Konopelchenko et al.)

Symmetries:Symmetry Classification of 2nd Order Difference
Equations (P Winternitz)

Applications To: Nonlinear Optics: Dispersion Managed Solitons (A
Hasegawa)

Molecular Dynamics: Nonlinear Dynamics in Hydrogen Bounded
Molecules (J Léon et al.)

Solid State Physics: Momentum Conservation Implies Anomalous
Conductivity in 1D Lattices (D Campbell)

String Theory and Gravity: Monodromy Transform Approach to
Solution of Some Field Equations in General

Relativity and String Theory (G Alekseev)

New Mathematical Methods and Applications: How Do You Know the
Six PainlevEEquations Have the Painlev's

Property? (M Kruskal)

On Difference Analogs of PainlevEType Equations (M Ablowitz)

Dressing Chains and Lattices (A Shabat)

and 63 more lectures given by some of the major experts in
nonlinear science

Readership: Physicists and mathematicians.

600pp (approx.)

Pub. date: Summer 2000

ISBN 981-02-4147-X

World Scientific Series in 20th Century Physics

edited by Laurie M Brown (Northwestern University, USA)

(With Commentary)

These scientific papers of Richard Feynman are
renowned for their brilliant content and the author's striking

original style. They are grouped by topic: path integral approach
to the foundations of quantum mechanics and

quantum field theory, renormalized quantum electrodynamics,
theory of superfluid liquid helium, theory of the

Fermi interaction, polarons, gravitation, partons, etc. Feynman's
Princeton PhD thesis appears in print for the

first time. Comments are provided by the editor, together with
biographical notes and an annotated bibliography of Feynman and
his work.

Readership: Physicists and historians of science.

600pp (approx.)

Pub. date: Spring 2000

ISBN 981-02-4130-5

ISBN 981-02-4131-3(pbk)

edited by R Coifman (Yale University)

Selected Theses

This book contains five theses in analysis, by
A C Gilbert, N Saito, W Schlag, T Tao and C M Thiele.

It covers a broad spectrum of modern harmonic analysis, from
Littlewood–Paley theory (wavelets) to subtle

interactions of geometry and Fourier oscillations. The common
theme of the theses involves intricate local

Fourier (or multiscale) decompositions of functions and operators
to account for cumulative properties

involving size or structure.

Contents:

Lp ® Lq Estimates for the Circular Maximal Function (W Schlag)

Three Regularity Results in Harmonic Analysis (T Tao)

Time-Frequency Analysis in the Discrete Phase Plane (C M Thiele)

Multiresolution Homogenization Schemes for Differential Equations
and Applications (A C Gilbert)

Local Feature Extraction and Its Applications Using a Library of
Bases (N Saito)

Readership: Researchers in the fields of analysis &
differential equations, signal processing and

applied mathematics.

470pp (approx.)

Pub. date: Spring 2000

ISBN 981-02-4093-7

ISBN 981-02-4094-5(pbk)

Series on Applied Mathematics - Vol. 3

by D-Z Du (Univ Minnesota) & F K Hwang
(AT&T Bell Labs.)

Group testing was first proposed for blood
tests, but soon found its way to many industrial applications.

Combinatorial group testing studies the combinatorial aspect of
the problem and is particularly related to

many topics in combinatorics, computer science and operations
research. Recently, the idea of combinatorial

group testing has been applied to experimental designs, coding,
multiaccess computer communication, clone

library screening and other fields. This book is the first
attempt to cover the theory and applications of

combinatorial group testing in one place.

"The book under review for the first time collects all
theory and applications about combinatorial group testing

in one place. The presentation of the material is well organized,
the material is illustrated by many examples.

This book may not only serve as a source and reference book, but
is also attractive to students since it treats

interesting 'real life' problems."

Contents:

Introduction

General Algorithms

Algorithms for Special Cases

Nonadaptive Algorithms and Binary Superimposed Codes

Multiaccess Channels and Extensions

Some Other Group Testing Models

Competitive Group Testing

Unreliable Tests, Optimal Search in One Variable

Unbounded Search

Group Testing on Graphs

Membership Problems

Complexity Issues

Index

Readership: Researchers in applied mathematics, operations
research, computer science,

genetics statistics and public health.

264pp

Pub. date: Nov 1993

ISBN 981-02-1293-3

by Alexander Fel'shtyn (E-M-Arndt-Universität Greifswald, Germany)

This book deals with the study of new dynamical
zeta functions connected with Nielsen fixed point theory.

The study of dynamical zeta functions is part of the theory of
dynamical systems, but it is also intimately

related to algebraic geometry, number theory, topology and
statistical mechanics. The book consists of four parts.

Part I presents a brief account of Nielsen fixed point theory.

Part II deals with dynamical zeta functions connected with
Nielsen fixed point theory.

Part III is concerned with an analog of Dold congruences for the
Reidemeister and Nielsen numbers.

Part IV explains how dynamical zeta functions give rise to
Reidemeister torsion, a very important topological invariant
which has useful applications in knots theory, quantum field
theory and dynamical systems.

Contents:

Nielsen Fixed Point Theory

The Reidemeister Zeta Function

The Nielsen Zeta Function

Reidemeister and Nielsen Zeta Functions Modulo Normal Subgroup,
Minimal Dynamical Zeta Functions

Congruences for Reidemeister and Nielsen Numbers

The Reidemeister Torsion

Readership: Graduate students and researchers in dynamical
systems, topology, group theory

and number theory.

200pp (approx.)

Pub. date: Autumn 2000

ISBN 981-02-4150-X

Advanced Series in Nonlinear
Dynamics

by Andreas Galka (Christian-Albrechts-University of Kiel,
Germany)

With Implications for EEG Analysis

This book provides a thorough review of a class
of powerful algorithms for the numerical analysis

of complex time series data which were obtained from dynamical
systems. These algorithms are based

on the concept of state space representations of the underlying
dynamics, as introduced by nonlinear

dynamics. In particular, current algorithms for state space
reconstruction, correlation dimension estimation,

testing for determinism and surrogate data testing are presented
Ealgorithms which have been playing

a central role in the investigation of deterministic chaos and
related phenomena since 1980. Special emphasis

is given to the much-disputed issue whether these algorithms can
be successfully employed for the analysis

of the human electroencephalogram.

Readership: Graduates and scientists in physics, applied
mathematics and neurology.

360pp (approx.)

Pub. date: Spring 2000

ISBN 981-02-4148-8

Series on Knots and Everything -
Vol. 1

by Louis H Kauffman (University of Illinois,
Chicago)

(3rd Edition)

This invaluable book is an introduction to knot
and link invariants as generalised amplitudes for a
quasi-physical process. The demands of knot theory, coupled with
a quantum-statistical framework, create a context that

naturally and powerfully includes an extraordinary range of
interrelated topics in topology and mathematical

physics. The author takes a primarily combinatorial stance toward
knot theory and its relations with these

subjects. This stance has the advantage of providing direct
access to the algebra and to the combinatorial

topology, as well as physical ideas.

The book is divided into two parts: Part I is a systematic course
on knots and physics starting from the ground up,

and Part II is a set of lectures on various topics related to
Part I. Part II includes topics such as frictional properties

of knots, relations with combinatorics, and knots in dynamical
systems.

In this third edition, a paper by the author entitled
"Functional Integration and Vassiliev Invariants" has
been added. This paper shows how the Kontsevich integral approach
to the Vassiliev invariants is directly related to the
perturbative expansion of Witten's functional integral. While the
book supplies the background, this paper can

be read independently as an introduction to quantum field theory
and knot invariants and their relation to quantum gravity. As in
the second edition, there is a selection of papers by the author
at the end of the book. Numerous clarifying remarks have been
added to the text.

Contents:

Physical Knots

States and the Bracket Polynomial

The Jones Polynomial and Its Generalisations

Braids and the Jones Polynomial

Formal Feynman Diagrams, Bracket as a Vacuum–Vacuum Expectation
and the Quantum Group SL(2)q

Yang–Baxter models for Specializations of the Homfly Polynomial

Knot Crystals EClassical Knot Theory in Modern Guise

The Kauffman Polynomial

Three Manifold Invariants from the Jones Polynomial

Integral Heuristics and Witten's Invariants

The Chromatic Polynomial

The Potts Model and the Dichromatic Polynomial

The Penrose Theory of Spin Networks

Knots and Strings EKnotted Strings?

DNA and Quantum Field Theory

Knots in Dynamical Systems EThe Lorenz Attractor

and selected papers

Readership: Physicists and mathematicians.

750pp (approx.)

Pub. date: Spring 2000

ISBN 981-02-4111-9

ISBN 981-02-4112-7(pbk)