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Author : E. Asplund
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.3/5 (91 download)
Download or read book On a Measure of Asymmetry of Convex Bodies written by E. Asplund and published by . This book was released on 1960 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. Asplund
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Measure of Asymmetry for Convex Surfaces written by E. Asplund and published by . This book was released on 1960 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gabor Toth
Publisher : Springer
ISBN 13 : 3319237330
Total Pages : 289 pages
Book Rating : 4.3/5 (192 download)
Download or read book Measures of Symmetry for Convex Sets and Stability written by Gabor Toth and published by Springer. This book was released on 2015-11-26 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats two important and related matters in convex geometry: the quantification of symmetry of a convex set—measures of symmetry—and the degree to which convex sets that nearly minimize such measures of symmetry are themselves nearly symmetric—the phenomenon of stability. By gathering the subject’s core ideas and highlights around Grünbaum’s general notion of measure of symmetry, it paints a coherent picture of the subject, and guides the reader from the basics to the state-of-the-art. The exposition takes various paths to results in order to develop the reader’s grasp of the unity of ideas, while interspersed remarks enrich the material with a behind-the-scenes view of corollaries and logical connections, alternative proofs, and allied results from the literature. Numerous illustrations elucidate definitions and key constructions, and over 70 exercises—with hints and references for the more difficult ones—test and sharpen the reader’s comprehension. The presentation includes: a basic course covering foundational notions in convex geometry, the three pillars of the combinatorial theory (the theorems of Carathéodory, Radon, and Helly), critical sets and Minkowski measure, the Minkowski–Radon inequality, and, to illustrate the general theory, a study of convex bodies of constant width; two proofs of F. John’s ellipsoid theorem; a treatment of the stability of Minkowski measure, the Banach–Mazur metric, and Groemer’s stability estimate for the Brunn–Minkowski inequality; important specializations of Grünbaum’s abstract measure of symmetry, such as Winternitz measure, the Rogers–Shepard volume ratio, and Guo’s Lp -Minkowski measure; a construction by the author of a new sequence of measures of symmetry, the kth mean Minkowski measure; and lastly, an intriguing application to the moduli space of certain distinguished maps from a Riemannian homogeneous space to spheres—illustrating the broad mathematical relevance of the book’s subject.
Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 1107601010
Total Pages : 759 pages
Book Rating : 4.1/5 (76 download)
Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author :
Publisher :
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.3/5 (91 download)
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1963 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : United States. Air Force. Office of Scientific Research
Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.3/5 (243 download)
Download or read book AFOSR. written by United States. Air Force. Office of Scientific Research and published by . This book was released on 1960 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Horst Martini
Publisher : Springer
ISBN 13 : 3030038688
Total Pages : 486 pages
Book Rating : 4.0/5 (3 download)
Download or read book Bodies of Constant Width written by Horst Martini and published by Springer. This book was released on 2019-03-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.
Author : Vitor Balestro
Publisher : Springer Nature
ISBN 13 : 3031505077
Total Pages : 1195 pages
Book Rating : 4.0/5 (315 download)
Download or read book Convexity from the Geometric Point of View written by Vitor Balestro and published by Springer Nature. This book was released on with total page 1195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 0521352207
Total Pages : 506 pages
Book Rating : 4.5/5 (213 download)
Download or read book Convex Bodies written by Rolf Schneider and published by Cambridge University Press. This book was released on 1993-02-25 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.
Author :
Publisher :
ISBN 13 :
Total Pages : 788 pages
Book Rating : 4.F/5 ( download)
Download or read book OAR Cumulative Index of Research Results written by and published by . This book was released on with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : United States. Air Force. Office of Aerospace Research
Publisher :
ISBN 13 :
Total Pages : 800 pages
Book Rating : 4.E/5 ( download)
Download or read book OAR Quarterly Index of Current Research Results written by United States. Air Force. Office of Aerospace Research and published by . This book was released on 1959 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. Groemer
Publisher : Cambridge University Press
ISBN 13 : 0521473187
Total Pages : 343 pages
Book Rating : 4.5/5 (214 download)
Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by Cambridge University Press. This book was released on 1996-09-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
Author : Victor Klee
Publisher : American Mathematical Soc.
ISBN 13 : 0821814079
Total Pages : 534 pages
Book Rating : 4.8/5 (218 download)
Download or read book Convexity written by Victor Klee and published by American Mathematical Soc.. This book was released on 1963 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 968 pages
Book Rating : 4.3/5 (91 download)
Download or read book Air Force Scientific Research Bibliography written by and published by . This book was released on 1962 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : GRUBER
Publisher : Birkhäuser
ISBN 13 : 3034858582
Total Pages : 419 pages
Book Rating : 4.0/5 (348 download)
Download or read book Convexity and Its Applications written by GRUBER and published by Birkhäuser. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
Author : Eric Carlen
Publisher : Springer
ISBN 13 : 1493970054
Total Pages : 620 pages
Book Rating : 4.4/5 (939 download)
Download or read book Convexity and Concentration written by Eric Carlen and published by Springer. This book was released on 2017-04-20 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.
Author : Steven R. Finch
Publisher : Cambridge University Press
ISBN 13 : 9780521818056
Total Pages : 634 pages
Book Rating : 4.8/5 (18 download)
Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
