by Marek A Abramowicz &
Sebastiano Sonego
(Geborg 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訪lein
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 (Universit・di Lecce, Italy)
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・classical
and quantum ・are 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忙akarevich
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 L駮n 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・Equations Have the Painlev's
Property? (M Kruskal)
On Difference Analogs of Painlev・Type 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)
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)
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鳳aley 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 ｮ 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-Universit舩 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)
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
・algorithms 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)
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坊acuum Expectation
and the Quantum Group SL(2)q
Yang烹axter models for Specializations of the Homfly Polynomial
Knot Crystals ・Classical 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 ・Knotted Strings?
DNA and Quantum Field Theory
Knots in Dynamical Systems ・The 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)