Mutational and Morphological Analysis: Tools for Shape Evolution and Morphogenesis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1999
|
| Schriftenreihe: | Systems & Control: Foundations & Applications
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XXXVII, 425 p) |
| ISBN: | 9781461215769 9781461272007 |
| ISSN: | 2324-9749 |
| DOI: | 10.1007/978-1-4612-1576-9 |
Internformat
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Datensatz im Suchindex
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| author | Aubin, Jean-Pierre |
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| building | Verbundindex |
| bvnumber | BV042419868 |
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| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1576-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461215769 9781461272007 |
| issn | 2324-9749 |
| language | English |
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| physical | 1 Online-Ressource (XXXVII, 425 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
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| publisher | Birkhäuser Boston |
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| series2 | Systems & Control: Foundations & Applications |
| spelling | Aubin, Jean-Pierre Verfasser aut Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis by Jean-Pierre Aubin Boston, MA Birkhäuser Boston 1999 1 Online-Ressource (XXXVII, 425 p) txt rdacontent c rdamedia cr rdacarrier Systems & Control: Foundations & Applications 2324-9749 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 Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Applications of Mathematics Mathematik Mathematische Morphologie (DE-588)4505783-7 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 s 1\p DE-604 Mathematische Morphologie (DE-588)4505783-7 s 2\p DE-604 Shape-Theorie (DE-588)4193842-2 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-1576-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aubin, Jean-Pierre Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Applications of Mathematics Mathematik Mathematische Morphologie (DE-588)4505783-7 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Shape-Theorie (DE-588)4193842-2 gnd |
| subject_GND | (DE-588)4505783-7 (DE-588)4270772-9 (DE-588)4193842-2 |
| title | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis |
| title_auth | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis |
| title_exact_search | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis |
| title_full | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis by Jean-Pierre Aubin |
| title_fullStr | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis by Jean-Pierre Aubin |
| title_full_unstemmed | Mutational and Morphological Analysis Tools for Shape Evolution and Morphogenesis by Jean-Pierre Aubin |
| title_short | Mutational and Morphological Analysis |
| title_sort | mutational and morphological analysis tools for shape evolution and morphogenesis |
| title_sub | Tools for Shape Evolution and Morphogenesis |
| topic | Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Applications of Mathematics Mathematik Mathematische Morphologie (DE-588)4505783-7 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Shape-Theorie (DE-588)4193842-2 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Logic, Symbolic and mathematical Analysis Mathematical Logic and Foundations Applications of Mathematics Mathematik Mathematische Morphologie Mengenwertige Abbildung Shape-Theorie |
| url | https://doi.org/10.1007/978-1-4612-1576-9 |
| work_keys_str_mv | AT aubinjeanpierre mutationalandmorphologicalanalysistoolsforshapeevolutionandmorphogenesis |