Shape Theory And Topological Sciences
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Shape Theory And Topological Sciences
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Author :
language : en
Publisher:
Release Date : 1981
Shape Theory And Topological Sciences written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Shape And Shape Theory
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Author : D. G. Kendall
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Shape And Shape Theory written by D. G. Kendall and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve practical problems concerning shape. This text presents an elegant account of the theory of shape that has evolved from Kendall's work. Features include: * A comprehensive account of Kendall's shape spaces * A variety of topological and geometric invariants of these spaces * Emphasis on the mathematical aspects of shape analysis * Coverage of the mathematical issues for a wide range of applications The early chapters provide all the necessary background information, including the history and applications of shape theory. The authors then go on to analyse the topic, in brilliant detail, in a variety of different shape spaces. Kendall's own procedures for visualising distributions of shapes and shape processes are covered at length. Implications from other branches of mathematics are explored, along with more advanced applications, incorporating statistics and stochastic analysis. Applied statisticians, applied mathematicians, engineers and computer scientists working and researching in the fields of archaeology, astronomy, biology, geography and physical chemistry will find this book of great benefit. The theories presented are used today in a wide range of subjects from archaeology through to physics, and will provide fascinating reading to anyone engaged in such research. Visit our web page! http://www.wiley.com/
Shape Theory
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Author : S. Mardešic
language : en
Publisher: Elsevier
Release Date : 1982-01-01
Shape Theory written by S. Mardešic and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
North-Holland Mathematical Library, Volume 26: Shape Theory: The Inverse System Approach presents a systematic introduction to shape theory by providing background materials, motivation, and examples, including shape theory and invariants, pro-groups, shape fibrations, and metric compacta. The publication first ponders on the foundations of shape theory and shape invariants. Discussions focus on the stability and movability of spaces, homotopy and homology pro-groups, shape dimension, inverse limits and shape of compacta, topological shape, and absolute neighborhood retracts. The text then takes a look at a survey of selected topics, including basic topological constructions and shape, shape dimension of metric compacta, complement theorems of shape theory, shape fibrations, and cell-like maps. The text ponders on polyhedra and Borsuk's approach to shape. Topics include shape category of metric compacta and metric pairs, homotopy type of polyhedra, and topology of simplicial complexes. The publication is a valuable source of data for researchers interested in the inverse system approach.
Shape Theory
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Author : J. M. Cordier
language : en
Publisher: Courier Corporation
Release Date : 2013-12-01
Shape Theory written by J. M. Cordier and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Science categories.
This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras. A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory—the concept that leads to movability and strong movability of systems—and illustrations of the equivalence of strong movability and stability in many contexts.
Shape Theory And Geometric Topology
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Author : S. Mardesic
language : en
Publisher:
Release Date : 2014-01-15
Shape Theory And Geometric Topology written by S. Mardesic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Topological Derivatives In Shape Optimization
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Author : Antonio André Novotny
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-14
Topological Derivatives In Shape Optimization written by Antonio André Novotny and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Technology & Engineering categories.
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.
Studies In Topology
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Author : Nick M. Stavrakas
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Studies In Topology written by Nick M. Stavrakas and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Studies in Topology is a compendium of papers dealing with a broad portion of the topological spectrum, such as in shape theory and in infinite dimensional topology. One paper discusses an approach to proper shape theory modeled on the "ANR-systems" of Mardesic-Segal, on the "mutations" of Fox, or on the "shapings" of Mardesic. Some papers discuss homotopy and cohomology groups in shape theory, the structure of superspace, on o-semimetrizable spaces, as well as connected sets that have one or more disconnection properties. One paper examines "weak" compactness, considered as either a strengthening of absolute closure or a weakening of relative compactness (subject to entire topological spaces or to subspaces of larger spaces). To construct spaces that have only weak properties, the investigator can use the various productivity theorems of Scarborough and Stone, Saks and Stephenson, Frolik, Booth, and Hechler. Another paper analyzes the relationship between "normal Moore space conjecture" and productivity of normality in Moore spaces. The compendium is suitable for mathematicians, physicists, engineers, and other professionals involved in topology, set theory, linear spaces, or cartography.
Geometric Topology And Shape Theory
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Author : Sibe Mardesic
language : en
Publisher:
Release Date : 2014-09-01
Geometric Topology And Shape Theory written by Sibe Mardesic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Shape Theory
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Author : Jerzy Dydak
language : en
Publisher: Springer Verlag
Release Date : 1978
Shape Theory written by Jerzy Dydak and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Theory Of Shape
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Author : Karol Borsuk
language : en
Publisher:
Release Date : 1975
Theory Of Shape written by Karol Borsuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Metric spaces categories.