Totally Positive Matrices And Cyclic Polytopes

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Totally Positive Matrices And Cyclic Polytopes

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Author : University of Minnesota. Institute for Mathematics and Its Applications
language : en
Publisher:
Release Date : 1987

Totally Positive Matrices And Cyclic Polytopes written by University of Minnesota. Institute for Mathematics and Its Applications and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

Totality Positive Matrices And Cyclic Polytopes

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Author : B. Sturmfels
language : en
Publisher:
Release Date : 1987

Totality Positive Matrices And Cyclic Polytopes written by B. Sturmfels and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

Convex Polytopes

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Author : Branko Grünbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Convex Polytopes written by Branko Grünbaum 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 2013-12-01 with Mathematics categories.

"The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London

Combinatorial Aspects Of Scattering Amplitudes

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Author : Matteo Parisi
language : en
Publisher: Springer Nature
Release Date : 2023-12-11

Combinatorial Aspects Of Scattering Amplitudes written by Matteo Parisi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-11 with Science categories.

This book is a significant contribution within and across High Energy Physics and Algebraic Combinatorics. It is at the forefront of the recent paradigm shift according to which physical observables emerge from geometry and combinatorics. It is the first book on the amplituhedron, which encodes the scattering amplitudes of N=4 Yang-Mills theory, a cousin of the theory of strong interactions of quarks and gluons. Amplituhedra are generalizations of polytopes inside the Grassmannian, and they build on the theory of total positivity and oriented matroids. This book unveils many new combinatorial structures of the amplituhedron and introduces a new important related object, the momentum amplituhedron. Moreover, the work pioneers the connection between amplituhedra, cluster algebras and tropical geometry. Combining extensive introductions with proofs and examples, it is a valuable resource for researchers investigating geometrical structures emerging from physics for some time to come.

Oriented Matroids

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Author : Anders Björner
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18

Oriented Matroids written by Anders Björner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Handbook Of Convex Geometry

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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Handbook Of Convex Geometry written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

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.

Linear Programming Duality

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Author : Achim Bachem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Programming Duality written by Achim Bachem 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 2012-12-06 with Business & Economics categories.

This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are intro- duced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start withre- sults on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns of oriented ma- troids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for furt- herreading and the references provide an overview of the research in this field.

Aportaciones Matem Ticas

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Author : VV.AA.
language : en
Publisher: Ed. Universidad de Cantabria
Release Date : 1991

Aportaciones Matem Ticas written by VV.AA. and has been published by Ed. Universidad de Cantabria this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

Sum Of Squares Theory And Applications

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Author : Pablo A. Parrilo
language : en
Publisher: American Mathematical Soc.
Release Date :

Sum Of Squares Theory And Applications written by Pablo A. Parrilo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Education categories.

This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.

Lectures On Polytopes

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Author : Günter M. Ziegler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-03

Lectures On Polytopes written by Günter M. Ziegler 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 2012-05-03 with Mathematics categories.

Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.