by M. Abate ... [et al (2004)
The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.'s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.
P.G. Lemarié (éd
This book surveys the recent theory of wavelet transforms and its applications in various fields both within mathematics (singular integrals, localization of singularities) and beyond it, in computer vision, the physics of fractals, time-frequency analysis.
Susanne C. Brenner, L. Ridgway Scott
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. The initial chapter provides an introduction to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to multigrid methods and other iterative solution techniques, mixed methods with applications to elasticity and fluid flow models, variational "crimes" including nonconforming and isoparametric methods and numerical integration, error estimates in the maximum norm with applications to nonlinear problems, and Banach-space operator-interpolation techniques. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject.
Jukka Saranen, Gennadi Vainikko
Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general theory of periodic pseudodifferential equations and methods of solving are developed, including trigonometric Galerkin and collocation methods, their fully discrete versions with fast solvers, quadrature and spline based methods. The theory of periodic pseudodifferential operators is presented in details, with preliminaries (Fredholm operators, periodic distributions, periodic Sobolev spaces) and full proofs. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
Guoqing Chen, Mingsheng Ying, Kai-Yuan Cai
Fuzzy Logic and Soft Computing contains contributions from world-leading experts from both the academic and industrial communities. The first part of the volume consists of invited papers by international authors describing possibilistic logic in decision analysis, fuzzy dynamic programming in optimization, linguistic modifiers for word computation, and theoretical treatments and applications of fuzzy reasoning. The second part is composed of eleven contributions from Chinese authors focusing on some of the key issues in the fields: stable adaptive fuzzy control systems, partial evaluations and fuzzy reasoning, fuzzy wavelet neural networks, analysis and applications of genetic algorithms, partial repeatability, rough set reduction for data enriching, limits of agents in process calculus, medium logic and its evolution, and factor spaces canes. These contributions are not only theoretically sound and well-formulated, but are also coupled with applicability implications and/or implementation treatments. The domains of applications realized or implied are: decision analysis, word computation, databases and knowledge discovery, power systems, control systems, and multi-destinational routing. Furthermore, the articles contain materials that are an outgrowth of recently conducted research, addressing fundamental and important issues of fuzzy logic and soft computing.