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Author : B. Grunbaum
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.3/5 (91 download)
Download or read book Partitions of Mass-distributions and of Convex Bodies by Hyperplanes written by B. Grunbaum and published by . This book was released on 1960 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Gabor Toth
Publisher : Springer
ISBN 13 : 3319237330
Total Pages : 278 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 278 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 : Gerard Meurant
Publisher : Elsevier
ISBN 13 : 0080934390
Total Pages : 801 pages
Book Rating : 4.0/5 (89 download)
Download or read book Handbook of Convex Geometry written by Gerard Meurant and published by Elsevier. This book was released on 2014-06-28 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Victor Klee
Publisher : American Mathematical Soc.
ISBN 13 : 0821814079
Total Pages : 516 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 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacob E. Goodman
Publisher : Cambridge University Press
ISBN 13 : 9780521848626
Total Pages : 640 pages
Book Rating : 4.8/5 (486 download)
Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman and published by Cambridge University Press. This book was released on 2005-08-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Author : Peter Gritzmann
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870839
Total Pages : 660 pages
Book Rating : 4.8/5 (78 download)
Download or read book Applied Geometry and Discrete Mathematics written by Peter Gritzmann and published by American Mathematical Soc.. This book was released on 1991 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.
Author :
Publisher :
ISBN 13 :
Total Pages : 138 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 1960 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alberto Del Pia
Publisher : Springer Nature
ISBN 13 : 3031327268
Total Pages : 494 pages
Book Rating : 4.0/5 (313 download)
Download or read book Integer Programming and Combinatorial Optimization written by Alberto Del Pia and published by Springer Nature. This book was released on 2023-05-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Author : Yurii Nesterov
Publisher : SIAM
ISBN 13 : 9781611970791
Total Pages : 414 pages
Book Rating : 4.9/5 (77 download)
Download or read book Interior-point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Author : Edgar A. Ramos
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (31 download)
Download or read book Equipartition of Mass Distributions by Hyperplanes written by Edgar A. Ramos and published by . This book was released on 1993 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: As an intermediate result we prove a Borsuk-Ulam type theorem on a product of balls. The motivation for this work was to resolve the case (4,1,4) the only case open for k=d and j=1. Unfortunately the approach fails to give an answer in this case."
Author : Alexander Koldobsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110775387
Total Pages : 480 pages
Book Rating : 4.1/5 (17 download)
Download or read book Harmonic Analysis and Convexity written by Alexander Koldobsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Author : Quentin Louveaux
Publisher : Springer
ISBN 13 : 3319334611
Total Pages : 412 pages
Book Rating : 4.3/5 (193 download)
Download or read book Integer Programming and Combinatorial Optimization written by Quentin Louveaux and published by Springer. This book was released on 2016-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2016, held in Liège, Belgium, in June 2016. The 33 full papers presented were carefully reviewed and selected from 125 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 1461300398
Total Pages : 491 pages
Book Rating : 4.4/5 (613 download)
Download or read book Lectures on Discrete Geometry written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Author : N.Z. Shor
Publisher : Springer Science & Business Media
ISBN 13 : 1475760159
Total Pages : 407 pages
Book Rating : 4.4/5 (757 download)
Download or read book Nondifferentiable Optimization and Polynomial Problems written by N.Z. Shor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef'; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x Nondifferentiable optimization and polynomial problems where A(P) is the set of monomials contained in polynomial P.
Author : Silouanos Brazitikos
Publisher : American Mathematical Soc.
ISBN 13 : 1470414562
Total Pages : 594 pages
Book Rating : 4.4/5 (74 download)
Download or read book Geometry of Isotropic Convex Bodies written by Silouanos Brazitikos and published by American Mathematical Soc.. This book was released on 2014-04-24 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.
Author : Oscar H. Ibarra
Publisher : Springer
ISBN 13 : 3540456554
Total Pages : 614 pages
Book Rating : 4.5/5 (44 download)
Download or read book Computing and Combinatorics written by Oscar H. Ibarra and published by Springer. This book was released on 2003-08-02 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th Annual International Computing and Combinatorics Conference, COCOON 2002, held in Singapore in August 2002. The 60 revised full papers presented together with three invited contributions were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on complexity theory, discrete algorithms, computational biology and learning theory, radio networks, automata and formal languages, Internet networks, computational geometry, combinatorial optimization, and quantum computing.
