Handbook Of Convex Geometry

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Handbook of Convex Geometry

Bozzano G Luisa
Handbook of Convex Geometry Book PDF

Author : Bozzano G Luisa
Publisher : Elsevier
Page : 803 pages
File Size : 47,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080934396

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Handbook of Convex Geometry by Bozzano G Luisa Pdf

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

Handbook of Convex Geometry

Peter M. Gruber,Jörg M. Wills
Handbook of Convex Geometry Book PDF

Author : Peter M. Gruber,Jörg M. Wills
Publisher : North Holland
Page : 774 pages
File Size : 49,6 Mb
Release : 1993-08-24
Category : Mathematics
ISBN : UOM:39015059097884

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Handbook of Convex Geometry by Peter M. Gruber,Jörg M. Wills Pdf

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Handbook of Convex Geometry

P. M. Gruber,J. M. Wills
Handbook of Convex Geometry Book PDF

Author : P. M. Gruber,J. M. Wills
Publisher : Unknown
Page : 0 pages
File Size : 47,8 Mb
Release : 1993
Category : Convex geometry
ISBN : 1493305719

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Handbook of Convex Geometry by P. M. Gruber,J. M. Wills Pdf

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions.The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. T

Handbook of Convex Geometry

Anonim
Handbook of Convex Geometry Book PDF

Author : Anonim
Publisher : North Holland
Page : 801 pages
File Size : 48,8 Mb
Release : 1993-09-07
Category : Mathematics
ISBN : 0444895965

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Handbook of Convex Geometry by Anonim Pdf

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

Handbook of Convex Geometry

Bozzano G Luisa
Handbook of Convex Geometry Book PDF

Author : Bozzano G Luisa
Publisher : Elsevier
Page : 769 pages
File Size : 45,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080934402

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Handbook of Convex Geometry by Bozzano G Luisa Pdf

Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.

Handbook of the Geometry of Banach Spaces

Anonim
Handbook of the Geometry of Banach Spaces Book PDF

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 50,7 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Handbook of Discrete and Computational Geometry

Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Handbook of Discrete and Computational Geometry Book PDF

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 51,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Foundations of Convex Geometry

W. A. Coppel
Foundations of Convex Geometry Book PDF

Author : W. A. Coppel
Publisher : Cambridge University Press
Page : 236 pages
File Size : 51,7 Mb
Release : 1998-03-05
Category : Mathematics
ISBN : 0521639700

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Foundations of Convex Geometry by W. A. Coppel Pdf

This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

Convex and Discrete Geometry

Peter M. Gruber
Convex and Discrete Geometry Book PDF

Author : Peter M. Gruber
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 46,9 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9783540711339

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Convex and Discrete Geometry by Peter M. Gruber Pdf

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.

Selected Topics in Convex Geometry

Maria Moszynska
Selected Topics in Convex Geometry Book PDF

Author : Maria Moszynska
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 51,9 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780817644512

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Selected Topics in Convex Geometry by Maria Moszynska Pdf

Examines in detail those topics in convex geometry that are concerned with Euclidean space Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

Bodies of Constant Width

Horst Martini,Luis Montejano,Déborah Oliveros
Bodies of Constant Width Book PDF

Author : Horst Martini,Luis Montejano,Déborah Oliveros
Publisher : Springer
Page : 486 pages
File Size : 54,9 Mb
Release : 2019-03-16
Category : Mathematics
ISBN : 9783030038687

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Bodies of Constant Width by Horst Martini,Luis Montejano,Déborah Oliveros Pdf

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.

Handbook of Differential Geometry

Franki J.E. Dillen,Leopold C.A. Verstraelen
Handbook of Differential Geometry Book PDF

Author : Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher : Elsevier
Page : 574 pages
File Size : 46,5 Mb
Release : 2005-11-29
Category : Mathematics
ISBN : 0080461204

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Handbook of Differential Geometry by Franki J.E. Dillen,Leopold C.A. Verstraelen Pdf

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Measures of Symmetry for Convex Sets and Stability

Gabor Toth
Measures of Symmetry for Convex Sets and Stability Book PDF

Author : Gabor Toth
Publisher : Springer
Page : 278 pages
File Size : 55,9 Mb
Release : 2015-11-26
Category : Mathematics
ISBN : 9783319237336

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Measures of Symmetry for Convex Sets and Stability by Gabor Toth Pdf

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.

Handbook of Computational Geometry

J.R. Sack,J. Urrutia
Handbook of Computational Geometry Book PDF

Author : J.R. Sack,J. Urrutia
Publisher : Elsevier
Page : 1087 pages
File Size : 42,8 Mb
Release : 1999-12-13
Category : Mathematics
ISBN : 9780080529684

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Handbook of Computational Geometry by J.R. Sack,J. Urrutia Pdf

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Handbook of Discrete and Computational Geometry, Second Edition

Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Handbook of Discrete and Computational Geometry Second Edition Book PDF

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1557 pages
File Size : 51,5 Mb
Release : 2004-04-13
Category : Mathematics
ISBN : 9781420035315

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Handbook of Discrete and Computational Geometry, Second Edition by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies