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Author: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 1461215765 Category : Mathematics Languages : en Pages : 460
Book 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: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 1461215765 Category : Mathematics Languages : en Pages : 460
Book 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: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 9780817639358 Category : Mathematics Languages : en Pages : 472
Book 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: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 0817648488 Category : Science Languages : en Pages : 474
Book Description
"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. ...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "This book provides a thorough introduction to multivalued or set-valued analysis... 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
Author: Degif Petros Banksira Publisher: John Benjamins Publishing ISBN: 9027298475 Category : Language Arts & Disciplines Languages : en Pages : 366
Book Description
This monograph, which evolved from the first linguistic dissertation to be written on Chaha (an Ethiopian Semitic language), is also the first book to deal exclusively with the phonology and morphology of the language. It is an exhaustive description and analysis, by a native speaker, of the sound patterns of this often misdescribed language and deserves to be the standard reference on the phonology of Chaha. The book presents a vast amount of new data and it unearths some fascinating new generalizations about double linking, geminate devoicing, nasalization of liquid consonants, phonotactic constraints within morphemes, and palatalization and labialization triggered by decomposition of a single back high round vowel. The book also challenges the categorization of Semitic subject affixes into prefix and suffix sets, instead proposing a novel classification in which all prefixes and some suffixes form a set that excludes the remaining suffixes. The generalizations and analyses are significant not only for the study of Chaha and Semitic languages, but also for phonological theory in general.
Author: Thomas Lorenz Publisher: Springer Science & Business Media ISBN: 3642124704 Category : Language Arts & Disciplines Languages : en Pages : 526
Book Description
Ordinary differential equations have been extended to evolution equations in Banach spaces. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals.
Author: Paul Bourgine Publisher: Springer Science & Business Media ISBN: 3642131743 Category : Technology & Engineering Languages : en Pages : 353
Book Description
What are the relations between the shape of a system of cities and that of fish school? Which events should happen in a cell in order that it participates to one of the finger of our hands? How to interpret the shape of a sand dune? This collective book written for the non-specialist addresses these questions and more generally, the fundamental issue of the emergence of forms and patterns in physical and living systems. It is a single book gathering the different aspects of morphogenesis and approaches developed in different disciplines on shape and pattern formation. Relying on the seminal works of D’Arcy Thompson, Alan Turing and René Thom, it confronts major examples like plant growth and shape, intra-cellular organization, evolution of living forms or motifs generated by crystals. A book essential to understand universal principles at work in the shapes and patterns surrounding us but also to avoid spurious analogies.
Author: Jean Serra Publisher: Springer Science & Business Media ISBN: 9401110409 Category : Computers Languages : en Pages : 391
Book Description
Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc. MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.
Author: Claudine Elmerich Publisher: Springer Science & Business Media ISBN: 9401151598 Category : Science Languages : en Pages : 709
Book Description
Nitrogen availability is one of the most critical factors that limits plant productivity. The largest reservoir of nitrogen is the atmosphere, but this gaseous molecular nitrogen only becomes available to plants through the biological nitrogen fixation process, which only prokaryotic cells have developed. The discovery that microbes were providing fixed nitrogen to legumes and the isolation of the first nitrogen-fixing bacteria occured at the end the 19th Century, in Louis Pasteur's time. We are now building on more than 100 years of research in this field and looking towards the 21st Century. The International Nitrogen Fixation Congress series Started more than 20 years ago. The format of this Congress is designed to gather scientists from very diverse origins, backgrounds, interests and scientific approaches and is a forum where fundamental knowledge is discussed alongside applied research. This confluence of perspectives is, we believe, extremely beneficial in raising new ideas, questions and concepts.
Author: Jean-Pierre Aubin
Author: Jean-Pierre Aubin
Author: Jean-Pierre Aubin
Author: Jean-Pierre Aubin
Author: Degif Petros Banksira
Author: Thomas Lorenz
Author: Paul Bourgine
Author: Jean Serra
Author: National Institutes of Health (U.S.). Division of Research Grants
Author: Aixin Liang
Author: Claudine Elmerich