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.


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 (UniversitEdi 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 systemsEclassical and quantum Eare considered.


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 PainlevEEquations Have the Painlev's
Property? (M Kruskal)
On Difference Analogs of PainlevEType 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.


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."


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

Readership: Researchers in applied mathematics, operations research, computer science,
genetics statistics and public health.

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.


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.


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)