Bøger af Jean-Pierre Aubin

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.   These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth.  However, shapes and images are basically sets, most often not smooth.  J.-P. Aubin thus constructs another vision, where shapes and images are just any compact set.  Hence their evolution -- which requires a kind of differential calculus -- must be studied in the metric space of compact subsets.  Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets.   "e;Mutational and Morphological Analysis"e; offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology.   Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields.

This authored monograph covers a viability to approach to traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;.

This book is intended to provide economists with mathematical tools necessary to handle the concepts of evolution under uncertainty and adaption arising in economics, pursuing the Arrow-Debreu-Hahn legacy.

Written by seven of the most prominent pioneers of the interval market model and game-theoretic approach to finance, this book provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics.

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.

The book presents a computation of the minimum endowment which restores economic viability and derives the dynamic laws that regulate both transactions and price fluctuations. The target audience primarily comprises open-minded and mathematically interested economists but the book may also be beneficial for graduate students.

The mathematical and algorithmic methods used by viability theory are relevant to an array of complex systems. This updated edition explains the applications of viability theory, explaining the central concepts and illustrating them with numerous examples.

"Gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject." --Mathematical Reviews

This book offers a self-contained, rigorous and concise review of the mathematical tools needed to study optima and equilibria, as solutions to problems in economics, management sciences, operations research, cooperative and non-cooperative games and more.