Description: Mutational and Morphological Analysis by 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Author Biography Aubin, University of Paris-Dauphine, France. Table of Contents I Mutational Analysis in Metric Spaces.- 1 Mutational Equations.- 2 Mutational Analysis.- II Morphological and Set-Valued Analysis.- 3 Morphological Spaces.- 4 Morphological Dynamics.- 5 Set-Valued Analysis.- III Geometrical and Algebraic Morphology.- 6 Morphological Geometry.- 7 Morphological Algebra.- IV Appendix.- 8 Differential Inclusions: A Tool-Box.- Biblographical Comments. Review "This monograph collects various tools needed for the analysis of shape evolution, viability problems, image processing, visual control, biological morphogenesis, wave-front propagation, etc. It consists of four parts:1 -- mutational analysis (a sort of calculus in metric spaces); 2 -- morphological and set-valued analysis; 3 -- geometrical and algebraic morphology; 4 -- differential inclusions (an outline only). The large list of references contains 472 items, moreover, exhaustive bibliographical comments are provided. The concept of mutational space explored in the first two chapters is a framework for developing a sort of differential calculus for maps between general metric spaces. The third chapter contains a description of mutational structures in hyperspaces, especially in the space of nonvoid compact subsets of Euclidean spaces... The present monograph offers a structure that embraces and integrates various approaches to shape evolution and may be useful for...scientists working with images arising in engineering, interval analysis, physics, biological morphogenesis, population dynamics and dynamic economic theory." —Zentralblatt Math Promotional Springer Book Archives Long Description 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. Review Quote "This monograph collects various tools needed for the analysis of shape evolution, viability problems, image processing, visual control, biological morphogenesis, wave-front propagation, etc. It consists of four parts:1 -- mutational analysis (a sort of calculus in metric spaces); 2 -- morphological and set-valued analysis; 3 -- geometrical and algebraic morphology; 4 -- differential inclusions (an outline only). The large list of references contains 472 items, moreover, exhaustive bibliographical comments are provided. The concept of mutational space explored in the first two chapters is a framework for developing a sort of differential calculus for maps between general metric spaces. The third chapter contains a description of mutational structures in hyperspaces, especially in the space of nonvoid compact subsets of Euclidean spaces... The present monograph offers a structure that embraces and integrates various approaches to shape evolution and may be useful for...scientists working with images arising in engineering, interval analysis, physics, biological morphogenesis, population dynamics and dynamic economic theory." Details ISBN1461272009 Author Jean-Pierre Aubin Language English Subtitle Tools for Shape Evolution and Morphogenesis Edition 98199th ISBN-10 1461272009 ISBN-13 9781461272007 Short Title MUTATIONAL & MORPHOLOGICAL ANA Series Systems & Control: Foundations & Applications Media Book Residence Paris, US Affiliation Univ. of Paris-Dauphine Universit?? de Paris IX (Paris-Dauphine) Univ. Year 2012 Publication Date 2012-10-10 Imprint Springer-Verlag New York Inc. Place of Publication New York Country of Publication United States DEWEY 511.3 Illustrations XXXVII, 425 p. AU Release Date 2012-10-10 NZ Release Date 2012-10-10 US Release Date 2012-10-10 UK Release Date 2012-10-10 Pages 425 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 1999 Format Paperback Alternative 9780817639358 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96392885;
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ISBN-13: 9781461272007
Book Title: Mutational and Morphological Analysis
Number of Pages: 425 Pages
Language: English
Publication Name: Mutational and Morphological Analysis: Tools for Shape Evolution and Morphogenesis
Publisher: Springer-Verlag New York Inc.
Publication Year: 2012
Subject: Mathematics
Item Height: 235 mm
Item Weight: 718 g
Type: Textbook
Author: Jean-Pierre Aubin
Item Width: 155 mm
Format: Paperback
