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Mutational and Morphological Analysis - Jean-Pierre Aubin

Mutational and Morphological Analysis

Tools for Shape Evolution and Morphogenesis
Buch | Softcover
425 Seiten
2012 | Softcover reprint of the original 1st ed. 1999
Springer-Verlag New York Inc.
978-1-4612-7200-7 (ISBN)
CHF 149,75 inkl. MwSt
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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.

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.

Reihe/Serie Systems & Control: Foundations & Applications
Zusatzinfo XXXVII, 425 p.
Verlagsort New York
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Logik / Mengenlehre
Schlagworte Analysis
ISBN-10 1-4612-7200-9 / 1461272009
ISBN-13 978-1-4612-7200-7 / 9781461272007
Zustand Neuware
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