by Ryotaro Kamimura (Tokai University, Japan)

STRUCTURAL AND ALPHA-INFORMATION FOR COMPLEX SYSTEMS

In order to develop new types of information media and technology, it is essential to model complex and flexible information processing in living systems. This book presents a new approach to modeling complex information processing in living systems. Traditional information-theoretic methods in neural networks are unified in one framework, i.e. a-entropy. This new approach will enable information systems such as computers to imitate and simulate human complex behavior and to uncover the deepest secrets of the human mind.


Readership: Students and researchers in artificial intelligence and neural networks.

300pp (approx.) Pub. date: Scheduled Summer 2001
ISBN 981-02-4075-9

edited by Maurizio Falcone (Universit・di Roma "La Sapienza", Italy)
& Charalampos Makridakis (University of Crete, Greece)

NUMERICAL METHODS FOR VISCOSITY SOLUTIONS AND APPLICATIONS

Series on Advances in Mathematics for Applied Sciences - Vol. 59

The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.

Contents:

Geometrical Optics and Viscosity Solutions (A-P Blanc et al.)
Computation of Vorticity Evolution for a Cylindrical Type-II Superconductor Subject to Parallel and Transverse Applied Magnetic Fields (A Briggs et al.)
A Characterization of the Value Function for a Class of Degenerate Control Problems (F Camilli)
Some Microstructures in Three Dimensions (M Chipot & V Lecuyer)
Convergence of Numerical Schemes for the Approximation of Level Set Solutions to Mean Curvature Flow (K Deckelnick & G Dziuk)
Optimal Discretization Steps in Semi-Lagrangian Approximation of First Order PDEs (M Falcone et al.)
Convergence Past Singularities to the Forced Mean Curvature Flow for a Modified Reaction-Diffusion Approach (F Fierro)
The Viscosity/Duality Solutions Approach to Geometric Optics for the Helmholtz Equation (L Gosse & F James)
Adaptive Grid Generation for Evolutive Hamilton-Jacobi-Bellman Equations (L Gr・e)
Solution and Application of Anisotropic Curvature Driven Evolution of Curves (and Surfaces) (K Mikula)
An Adaptive Scheme on Unstructured Grids for the Shape-from-Shading Problem (M Sagona & A Seghini)
On a Posteriori Error Estimation for Constant Obstacle Problems (A Veeser)

Readership: Graduate students, researchers, academics and lecturers in numerical & computational mathematics, analysis & differential equations and mathematical modeling.

200pp (approx.) Pub. date: Scheduled Fall 2001
ISBN 981-02-4717-6

edited by K Fukaya (Kyoto University, Japan), Y-G Oh (University of Wisconsin-Madison, USA &Korea Institute for Advanced Study, South Korea), K Ono (Hokkaido University, Japan) & G Tian (Massachusetts Institute of Technology, USA)

SYMPLECTIC GEOMETRY AND MIRROR SYMMETRY
Proceedings of the 4th KIAS Annual International Conference
Seoul, South Korea 14 - 18 August 2000

In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry, which had originally been discovered by physicists in string theory as a duality between families of three-dimensional Calabi?Yau manifolds. The proposal uses Fukaya's construction of the A\-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was enhanced by physicists in the language of D-branes and by Strominger?Yau?Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope from geometry and topological algebra to physics.
In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry. Floer theory, Lagrangian torus fibrations, D-branes, Virasoro conjecture and Lefschetz fribration. Kontsevich?Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of the A-infinity category, and Ohta describes the rigorous construction of the A\-category by Fukaya?Oh?Ohta?Ono. There follow a number of contributions on the homological mirror conjecture, Lagrangian torus fibrations, D-branes and the Virasoro conjecture. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.

Contents:

Estimated Transversality in Symplectic Geometry and Projective Maps (D Auroux)
Local Mirror Summetry and Five-Dimensional Gauge Theory (T Eguchi)
Examples of Special Lagrangian Fibrations (M Gross)
Linear Models of Supersymmetric D-Branes (K Hori)
The Connectedness of the Moduli Space of Maps to Homogeneous Spaces (B Kim & R Pandharipande)
Homological Mirror Symmetry and Torus Fibrations (M Kontsevich & Y Soibelman)
Genus 1-Virasoro Conjecture on the Small Phase Space (X-B Liu)
Obstruction to and Deformation of Lagrangian Intersection Floer Cohomology (H Ohta)
Topological Open p-Branes (J-S Park)
Lagrangian Torus Fibration and Mirror Symmetry of Calabi?Yau Manifold (W-D Ruan)
More About Vanishing Cycles and Mutation (P Seidel)
Moment Maps, Monodromy and Mirror Manifolds (R Thomas)

Readership: Researchers and graduate students in differential geometry, topology and theoretical physics.

400pp (approx.) Pub. date: Scheduled Fall 2001
ISBN 981-02-4714-1

edited by J P Hsu (University of Massachusetts Dartmouth, USA)
& Y Z Zhang (Academia Sinica, China)

LORENTZ AND POINCARE INVARIANCE
100 Years of Relativity

This book provides a broad view of the developments of Lorentz and Poincar・invariance as well as space釦ime symmetry in the past 100 years. It includes: (1) formulations of the relativity theories which do not assume universal constancy of the speed of light but, nevertheless, can be consistent with the four-dimensional symmetry of the Lorentz and Poincar・groups and with previous experiments; (2) logical analyses of simultaneity and physical time from the philosophy of science, by Reichenbach; (3) mathematical analyses of profound implications of the Poincar・group, originated by Wigner; (4) far-reaching results of the union of the relativity and quantum theories through Dirac's landmark papers which mark the beginnings of quantum electrodynamics and relativistic quantum mechanics; and (5) interesting discussions on the "aether" (or vacuum) based on quantum field theory, by Dirac, T D Lee and Bjorken. Item (1) includes papers by Edwards, L Hsu, Sherry and others. It also presents the top ten experiments and argues that previous experiments actually support a broad Lorentz and Poincar・invariance (and space釦ime) rather than just the special theory of relativity. In retrospect, interesting developments of Lorentz and Poincareinvariance in the past 50 years lie in (i) the broadening of the views on simultaneity, physical time and the nature of the speed of light within the four-dimensional symmetry framework, and (ii) the recognition that the ultimate simplicity of the four-dimensional theory of relativity can be constructed based solely on one postulate ・the principle of relativity for physical laws.


Readership: Upper-level undergraduates, graduate students, researchers and academics in mathematical physics and theoretical physics.

350pp (approx.) Pub. date: Scheduled Spring 2002
ISBN 981-02-4721-4

by Masami Ito (Kyoto Sangyo University, Japan)

ALGEBRAIC THEORY OF AUTOMATA AND LANGUAGES

There are a few books dealing with algebraic theory of automata but their contents consist mainly of Krohn-Rhodes theory and related topics. The topics in the present book are rather different. For example, endomorphism monoids and automorphism groups of automata are systematically discussed. Moreover, some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with. The book is self-contained and hence does not require any knowledge of automata or formal languages.
This important book deals with the following topics: Endomorphism Monoids and Automorphism Groups of Automata, Classes of Automata as Partially Ordered Sets, Insertion and Shuffle Operations on Languages, Deterministic and Nondeterministic Directable Automata and Related Languages, and so on.

Readership: Researchers, lecturers, senior undergraduates and graduate students in theoretical computer science.

200pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 981-02-4727-3

Wu Zhuoqun, Yin Jingxue, Li Huilai (Jilin University, China)
& Zhao Junning (Xiamen University, China)

NONLINEAR DIFFUSION EQUATIONS

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.
This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.

Contents:

Newtonian Filtration Equations: Existence and Uniqueness of Solutions
Regularity of Solutions
Properties of Free Boundary
Initial Trace of Solutions
Other Problems
Non-Newtonian Filtration Equations: Existence of Solutions
Harnack Inequality and Initial Trace of Solutions
Regularity of Solutions
Uniqueness of Solutions
Properties of Free Boundary
Other Problems
General Quasilinear Degenerate Parabolic Equations of Second Order: Weakly Degenerate Equations
Strongly Degenerate Equations in One Dimension
Strongly Degenerate Equations in Higher Dimension Without Terms of Lower Order
General Strongly Degenerate Equations in Higher Dimension
Classes BV and BVx
Nonlinear Diffusion Equations of Higher Order: Similarity Solutions of a Fourth Order Equation
Equations with Double Degeneracy
Cahn-Hilliard Equations with Constant Mobility
　Cahn-Hilliard Equations with Positive Concentration Dependent Mobility
　Thin-Film Equation
　Cahn-Hilliard Equation with Degenerate Mobility

Readership: Researchers, lecturers and graduate students in the fields of analysis and differential equations, mathematical physics and fluid mechanics.

500pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 981-02-4718-4