edited by R E Mickens (Clark Atlanta University, USA)
The main purpose of this book is to provide a
concise introduction to the methods and philosophy of
constructing
nonstandard finite difference schemes and illustrate howsuch
techniques can be applied to several important problems.
Chapter 1 gives an overview of the subject and summarizes
previous work.
Chapters 2 and 3 consider in detail the construction and
numerical implementation of schemes for physical problems
involving convection謀iffusion睦eaction equations that arise in
groundwater pollution and scattering of electromagnetic
waves using Maxwell's equations.
Chapter 4 examines certain mathematical issues related to the
nonstandard discretization of competitive and cooperative models
for ecology. The application chapters illustrate well the power
of nonstandard methods. In particular, for the same accuracy as
obtained by standard techniques, larger step sizes can be used.
This volume will satisfy the needs of scientists, engineers, and
mathematicians who wish to know how to construct
nonstandard schemes and see how these are applied toobtain
numerical solutions of the differential equations which
arise in the study of nonlinear dynamical systems modeling
important physical phenomena.
Contents:
Nonstandard Finite Difference Methods (R E Mickens)
Nonstandard Eulerian Lagrangian Methods for Convection Diffusion乏eaction
Equations (B Chen)
Nonstandard Finite Differences and Physical Applications (J B
Cole)
Nonstandard Discretization of Competitive and Cooperative Models
(S Elaydi)
General Methods for Obtaining Unconventional and Nonstandard
Finite Difference Schemes (R Meyer-Spasche)
Readership: Researchers in applied mathematics and in the natural
and engineering sciences who wish to apply nonstandard finite
difference methods.
160pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4133-X
edited by V Scheffer & J Taylor (Rutgers University)
Q-Valued Functions Minimizing Dirichlet's
Integral and the Regularity of Area-Minimizing Rectifiable
Currents up to Codimension 2
Fred Almgren created the excess method for proving regularity
theorems in the calculus of variations.
His techniques yielded Hder continuity except for a small
closed singular set. In the sixties and seventies
Almgren refined and generalized his methods. Between 1974 and
1984 he wrote a 1,700-page proof that
was his most ambitious exposition of his ground-breaking ideas.
Originally, this monograph was available
only as a three-volume work of limited circulation. The entire
text is faithfully reproduced here.
This book gives a complete proof of the interior regularity of an
area-minimizing rectifiable current up to
Hausdorff codimension 2. The argument uses the theory of Q-valued
functions, which is developed in detail.
For example, this work shows how first variation estimates from
squash and squeeze deformations yield
a monotonicity theorem for the normalized frequency of
oscillation of a Q-valued function that minimizes
a generalized Dirichlet integral. The principal features of the
book include an extension theorem analogous to Kirszbraun's
theorem and theorems on the approximation in mass of nearly flat
mass-minimizing rectifiable
currents by graphs and images of Lipschitz Q-valued functions.
Contents:
Basic Properties of Q and Q-Valued Functions
Properties of Dir-Minimizing Q-Valued Functions and Tangent Cone
Stratification of Mass-Minimizing
Rectifiable Currents Approximation in Mass of Nearly Flat
Rectifiable Currents which are Mass-Minimizing
in Manifolds by Graphs of Lipschitz Q-Valued Functions Which Can
Be Weakly Nearly Dir-Minimizing
Approximation in Mass of a Nearly Flat Rectifiable Current Which
Is Mass-Minimizing in a Manifold by
the Image of a Lipschitz Q(Rm+n)-Valued Function Defined on a
Center Manifold
Bounds on the Frequency Functions and the Main Interior
Regularity Theorem
Readership: Students and researchers dealing with the calculus of
variations.
960pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4108-9
by Tan Wai-Yuan (University of Memphis)
This book discusses systematically treatment on
the development of stochastic, statistical and state space
models of the HIV epidemic and of HIV pathogenesis in
HIV-infected individuals, and presents the applications
of these models. The book is unique in several ways: (1) it uses
stochastic difference and differential equations
to present the stochastic models of the HIV epidemic and HIV
pathogenesis; in this sense, the deterministic
models are considered as special cases when the numbers of
different type of people or cells are very large;
(2) it provides a critical analysis of deterministic and
statistical models in the literature; (3) it develops state
space models by combining stochastic models and statistical
models; and (4) it provides a detailed discussion
on the pros and cons of the different modeling approaches.
This book is the first to introduce state space models for the
HIV epidemic. It is also the first to develop
stochastic models and state space models for the HIV pathogenesis
in HIV-infected individuals.
Contents:
Introduction
Basic Concepts and Some Useful Stochastic Models for Modeling the
HIV Epidemic and HIV Pathogenesis
Modeling the HIV Epidemic ・Some Stochastic Population
Transmission Models Statistical Modeling of the HIV
Epidemic The Backcalculation Method for the HIV Epidemic State
Space Models (Kalman Filter Models) of the
HIV Epidemic Stochastic Models of HIV Pathogenesis in
HIV-Infected Individuals in the Absence of Anti-Viral Treatment
Stochastic Models of HIV Pathogenesis in HIV-Infected Individuals
Under Treatment by Anti-Viral
Drugs and Development of Drug Resistance Some State Space Models
of HIV Pathogenesis in HIV-Infected
Individuals
Readership: Graduate students in probability and statistics.
300pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4122-4
edited by
L M Tomilchik (B I Stepanov Institute of Physics, Belarus), I D Feranchuk (Belarussian State University, Belarus),
S A Maksimenko & A S Lobko (Institute for Nuclear Problems,
Belarus)
Proceedings of the 3rd International Workshop
Minsk, Belarus 9 - 13 June 1999
This book is a collection of recent results
obtained by participants in QS '99. It presents local and global
geometrical and topological phenomena in quantum systems and new
methods of their research. Electromagnetic effects and transport
phenomena in nanoscale low-dimensional structures are also
considered. The book will be
interesting to experienced researchers and useful for students
studying modern theoretical physics and the
physics of nanostructures.
Contents:
Non-Perturbative Methods for Many-Dimensional Quantum Systems (I
Feranchuk et al.)
Coherent States for Non-Quadratic Quantum Systems (V Bagrov &
B Samsonov)
Semiclassical Quantization of the Relative Equilibria for the
Helium-Like Atoms (V Belov et al.)
Non-Euclidean Geometry and Description of Strongly Coupled
Systems (L Tomilchik et al.)
Ultrametric Effects in Quantum Dynamics (G Djordjevic & B
Dragovich)
On the Problem of Unitary Evolution in a Quantum Cosmology (A
Margolin & V Strazhev)
Two-Body Problem on a Sphere (Yu Kurochkin & V Otchik)
Multidimensional Oscillator with Topologically Nontrivial
Constraints and Generalized Kepler Problem
(M Pletyukhov & E Tolkachev)
Anomaly Free String Inspired Model (A Bogush et al.)
Classical and Quantum Chaos in the Three-Body Multichannel
Scattering System (A Bogdanov & A Gevorkyan)
Electrodynamics of Spatially Nonhomogeneous Nanostructures (S
Maksimenko & G Slepyan)
High-Harmonic Generation in CN-Based Arrays (V Kalosha et al.)
Negative Differential Conductivity in Carbon Nanotubes (Ant
Maksimenko & G Slepyan)
Surface Polyaritons in Carbon Nanotubes (A Gusakov et al.) and
other papers
Readership: Researchers and students in physics.
300pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4144-5
by Minoru Wakimoto (Kyushu University, Japan)
The representation theory of affine Lie
algebras has been developed in close connection with various
areas
of mathematics and mathematical physics in the last two decades.
There are three excellent books on it,
written by Victor G Kac. This book begins with a survey and
review of the material treated in Kac's books.
In particular, modular invariance and conformal invariance are
explained in more detail. The book then goes
further, dealing with some of the recent topics involving the
representation theory of affine Lie algebras.
Since these topics are important not only in themselves but also
in their application to some areas of mathematics
and mathematical physics, the book expounds them with examples
and detailed calculations.
Contents:
Modular and Conformal Invariance and Branching Functions
Admissible Representations of Affine Lie Algebras
Representation of W-Algebras via Quantized Drinfeld亡okolov
Reduction and Their Fusion Algebras
Orbifold Theory and Fusion Algebras
Vertex Representations of Affine Lie Algebras and Associated
Hierarchy of Soliton Equations
Readership: Graduate students and researchers interested in
representation theory, combinatorics,
vertex algebras, modular forms, soliton equations, particle
physics and solvable models.
250pp (approx.)
Pub. date: Spring 2000
ISBN 981-02-4128-3
ISBN 981-02-4129-1(pbk)