Author | Aubin, Jean-Pierre. author |
---|---|

Title | Mutational and Morphological Analysis [electronic resource] : Tools for Shape Evolution and Morphogenesis / by Jean-Pierre Aubin |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1999 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-1576-9 |

Descript | XXXVII, 425 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Applied mathematics
Engineering mathematics
Mathematical logic
Mathematics
Analysis
Mathematical Logic and Foundations
Applications of Mathematics