Kategoria BISAC: Mathematics >> Mathematical Analysis

An Introduction to Nonlinear Analysis: Applications offers an exposition of the main applications of Nonlinear Analysis. Its starting point is a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics.

This book is an excellent springboard for anyone wishing to conduct advanced research or work on a postgraduate text. Many...

Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which...

Convex functions play an important role in almost all branches of mathematics as well as other areas of science and engineering. This book is a thorough introduction to contemporary convex function theory addressed to all people whose research or teaching interests intersect with the field of convexity. It covers a large variety of subjects, from the one real variable case (with all its mathematical gems) to some of the most advanced topics such as Choquet's theory, the Prekopa-Leindler type inequalities and their ramifications, as well as the variational approach of partial differential...

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises....

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.

The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the...

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them.

Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision...