edited by Yoshiaki Maeda, Nobuyuki Tose, Naoya Miyazaki (Keio University, Japan), Satoshi Watamura (Tohoku University, Japan) & Daniel Sternheimer (Bourgogne University, France)

NONCOMMUTATIVE GEOMETRY AND PHYSICS
Proceedings of the COE International Workshop Yokohama, Japan 26 - 28 February, 1 - 3 March 2004

Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety of mathematical areas related to noncommutative geometry and its interface with modern theoretical physics.

Contents:

Dynamics of Fuzzy Spaces (M Buri? & J Madore)
Induction of Representations in Deformation Quantization (H Bursztyn & S Waldmann)
Construction of Lagrangian Embeddings Using Hamiltonian Actions (R Chiang)
Deformation Quantization on a Hilbert Space (G Dito)
Noncommutative Solitons and Integrable Systems (M Hamanaka)
Witten's Deformed Laplacian and Its Classical Mechanics (A Inoue)
Higher Dimensional Spherical D-Branes and Matrix Model (Y Kimura)
A Short Note on Symplectic Floer Theory (K Ono)
Relation on Spin Bundle Gerbes and Mayer’s Dirac Operators (A Tomoda)
and other papers

Readership: Graduate students, academic researchers and professionals in mathematics and physics.

388pp Pub. date: Sept 2005
ISBN 981-256-492-6

by Shoshichi Kobayashi (University of California, Berkeley, USA)

HYPERBOLIC MANIFOLDS AND HOLOMORPHIC MAPPINGS
An Introduction (Second Edition)

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections "invariant metrics and pseudo-distances" and "hyperbolic complex manifolds" within the section "holomorphic mappings". The invariant distance introduced in the first edition is now called the "Kobayashi distance", and the hyperbolicity in the sense of this book is called the "Kobayashi hyperbolicity" to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.

Contents:

The Schwarz Lemma and Its Generalizations
Volume Elements and the Schwarz Lemma
Distance and the Schwarz Lemma
Invariant Distances on Complex Manifolds
Holomorphic Mappings into Hyperbolic Manifolds
The Big Picard Theorem and Extension of Holomorphic Mappings
Generalizations to Complex Spaces
Hyperbolic Manifolds and Minimal Models

Readership: Researchers and students interested in complex variables and complex differential geometry.

200pp (approx.) Pub. date: Scheduled Winter 2005
ISBN 981-256-496-9
ISBN 981-256-589-2(pbk)

edited by Linda J S Allen (Texas Tech University, USA), Bernd Aulbach (University of Augsburg, Germany), Saber Elaydi (Trinity University, USA) & Robert Sacker (University of Southern California, Los Angeles, USA)

DIFFERENCE EQUATIONS AND DISCRETE DYNAMICAL SYSTEMS
Proceedings of the 9th International Conference
University of Southern California, Los Angeles, California, USA 2 - 7 August 2004

Difference Equations or Discrete Dynamical Systems is a diverse field which impacts almost every branch of pure and applied mathematics. Not surprisingly, the techniques that are developed vary just as broadly. No more so is this variety reflected than at the prestigious annual International Conference on Difference Equations and Applications. Organized under the auspices of the International Society of Difference Equations, the Conferences have an international attendance and a wide coverage of topics.
The contributions from the conference collected in this volume invite the mathematical community to see a variety of problems and applications with one ingredient in common, the Discrete Dynamical System. Readers may also keep abreast of the many novel techniques and developments in the field.

The special emphasis of the meeting was on mathematical biology and accordingly about half of the articles are in the related areas of mathematical ecology and mathematical medicine.

Contents:

A Hybrid Approximation to Certain Delay Differential Equation with a Constant Delay (G Seifert)
Discrete Models of Differential Equations: The Roles of Dynamic Consistency and Positivity (R E Mickens)
Enveloping Implies Global Stability (P Cull)
Local Approximation of Invariant Fiber Bundles: An Algorithmic Approach (C Pötzsche & M Rasmussen)
On a Class of Generalized Autoregressive Processes (K C Chanda)
Regularity of Difference Equations (J Hietarinta)
Some Discrete Competition Models and the Principle of Competitive Exclusion (J M Cushing & S LeVarge)
Symbolic Dynamics in the Study of Bursting Electrical Activity (J Duarte et al.)
and other papers

Readership: Researchers in mathematics and dynamical systems.

336pp Pub. date: Oct 2005
ISBN 981-256-520-5

edited by Eric L Grinberg (University of New Hampshire, USA), Shougui Li (Wuhan University of Sciences and Technology, China), Gaoyong Zhang (Polytechnic University, USA) & Jiazu Zhou (Guizhou Normal University, China)

INTEGRAL GEOMETRY AND CONVEXITY
Proceedings of the International Conference Wuhan, China 18 - 23 October 2004

Integral geometry, known as geometric probability in the past, originated from Buffon’s needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.

Contents:

Floating Bodies and Illumination Bodies (E Werner)
Random Methods in Approximation of Convex Bodies (C Schuett)
Some Generalized Maximum Principles and Their Applications to Chern Type Problems (Y J Suh)
Volume Inequalities for Sets Associated with Convex Bodies (S Campi & P Gronchi)
On Integral Geometry in Projective Finsler Spaces (R Schneider)
The Geometry of Distance Functions in Riemannian Manifolds (R Howard)
The Radon Transform (E Grinberg)
Affinely Associate Bodies (M Ludwig)
Algebraic Integral Geometry (J Fu)
Applications of Information Theory to Convex Geometry (D Yang)
Directed Projection and Section Function (P Goodey)
Containment Measures in Integral Geometry (G Zhang & J Zhou)
Flag Curvatures in Finsler Geometry (X Chen)
and other papers

Readership: Graduate students and researchers in mathematics and physics.

400pp (approx.) Pub. date: Scheduled Winter 2005
ISBN 981-256-513-2

by Doug Hensley (Texas A&M University, USA)

CONTINUED FRACTIONS

The branch of continued fractions is one of the oldest in mathematics. While it has burgeoned over the course of the past decade and more, many of these results have not been brought together in book form. Continued fractions have been seen from the perspective of number theory, complex analysis, ergodic theory, dynamic processes, analysis of algorithms, and even theoretical physics, which has further complicated the situation.
This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for continued fractions. Extensive, attractive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.

Contents:

Generalizations of the gcd and the Euclidean Algorithm
Continued Fractions with Small Partial Quotients
Ergodic Theory
Complex Continued Fractions
Multi-Dimensional Diophantine Approximation
Powers of an Algebraic Integer
Marshall Hall’s Theorem
Functional- Analytic Techniques
The Generating Function Method
Conformal Iterated Function Systems
Convergence of Continued Fractions

Readership: Graduate students and researchers in pure and applied mathematics.

250pp (approx.) Pub. date: Scheduled Spring 2006
ISBN 981-256-477-2

edited by Takeyuki Hida (Meijo University, Nagoya, Japan)

STOCHASTIC ANALYSIS: CLASSICAL AND QUANTUM
Perspectives of White Noise Theory
Meijo University, Nagoya, Japan 1 - 5 November 2004

This volume includes papers by leading mathematicians in the fields of stochastic analysis, white noise theory and quantum information, together with their applications. The papers selected were presented at the International Conference on Stochastic Analysis: Classical and Quantum held at Meijo University, Nagoya, Japan from 1 to 5 November 2004. The large range of subjects covers the latest research in probability theory.

Contents:

Part 1:
White Noise Functional Approach to Polymer Entanglements (C C Bernido & M V Carpio-Bernido)
White Noise Analysis, Quantum Field Theory, and Topology (A Hahn)
A Topic on Noncanonical Representations of Gaussian Processes (Y Hibino)
Integral Representation of Hilbert?Schimdt Operators on Boson Fock Space (U C Ji)
The Dawn of White Noise Analysis (I Kubo)
White Noise Stochastic Integration (H-H Kuo)
Connes?Hida Calculus and Bismut?Quillen Superconnections (R Leandre & H Ouerdiane)
A Quantum Decomposition of Levy Processes (Y-J Lee & H-H Shih)
Generalized Entanglement and Its Classification (T Matsuoka)
A White Noise Approach to Fractional Brownian Motion (D Nualart)
Adaptive Dynamics in Quantum Information and Chaos (M Ohya)
Micro-Macro Duality in Quantum Physics (I Ojima)
White Noise Measures Associated to the Solutions of Stochastic Differential Equations (H Ouerdiane)
A Remark on Sets of Infinite Dimensional Spaces with Full or Zero Capacity (J Ren & M Rockner)
An Infinite Dimensional Laplacian in White Noise Theory (K Saito)
Invariance of Poisson Noise (Si Si et al.)
Nonequilibrium Steady States with Bose?Einstein Condensates (S Tasaki & T Matsui)
Multidimensional Skew Reflected Diffusions (G Trutnau)
On Quantum Mutual Type Entropies and Quantum Capacity (N Watanabe)
Part 2:
White Noise Calculus and Stochastic Calculus (L Accardi & A Boukas)

Readership: Academics and researchers in stochastic analysis, white noisy theory, and quantum information.

312pp Pub. date: Oct 2005
ISBN 981-256-526-4