Series:

Systems & Control: Foundations and Applications

3 total works

Cover of Viability Theory

Viability Theory

by Jean-Pierre Aubin

Published 1 November 1991
"The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis!The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." --Bulletin of the AMS "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research!It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." --Mededelingen van het Wiskundig Genootschap

Cover of Mutational and Morphological Analysis

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.

"Mutational and Morphological Analysis" 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.

v. 2

Cover of Set-valued Analysis
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible--it has made a subject which is generally inhospitable to nonspecialists because of its 'family jargon' appear nonintimidating even to a beginning graduate student." --The Journal of the Indian Institute of Science "The book under review 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!The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." --Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject...'Set-Valued Analysis' goes a long way toward providing a much needed basic resource on the subject."
--Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps!The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." --Zentralblatt Math