Introduction To Circle Packing
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Introduction To Circle Packing
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Author : Kenneth Stephenson
language : en
Publisher: Cambridge University Press
Release Date : 2005-04-18
Introduction To Circle Packing written by Kenneth Stephenson 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 2005-04-18 with Mathematics categories.
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Planar Maps Random Walks And Circle Packing
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Author : Asaf Nachmias
language : en
Publisher: Springer Nature
Release Date : 2019-10-04
Planar Maps Random Walks And Circle Packing written by Asaf Nachmias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-04 with Mathematics categories.
This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
New Approaches To Circle Packing In A Square
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Author : Péter Gábor Szabó
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-31
New Approaches To Circle Packing In A Square written by Péter Gábor Szabó 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 2007-05-31 with Mathematics categories.
This book presents an overview of recent results achieved in solving the circle packing problem. It provides the reader with a comprehensive view of both theoretical and computational achievements. Illustrations of problem solutions are shown, elegantly displaying the results obtained.
Uniformizing Dessins And Belyimaps Via Circle Packing
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Author : Philip L. Bowers
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Uniformizing Dessins And Belyimaps Via Circle Packing written by Philip L. Bowers 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 2004 with Mathematics categories.
Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.
Introduction To Cutting And Packing Optimization
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Author : Guntram Scheithauer
language : en
Publisher: Springer
Release Date : 2017-10-20
Introduction To Cutting And Packing Optimization written by Guntram Scheithauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Business & Economics categories.
This book provides a comprehensive overview of the most important and frequently considered optimization problems concerning cutting and packing. Based on appropriate modeling approaches for the problems considered, it offers an introduction to the related solution methods. It also addresses aspects like performance results for heuristic algorithms and bounds of the optimal value, as well as the packability of a given set of objects within a predefined container. The problems discussed arise in a wide variety of different fields of application and research, and as such, the fundamental knowledge presented in this book make it a valuable resource for students, practitioners, and researchers who are interested in dealing with such tasks.
Selected Works Of Oded Schramm
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Author : Itai Benjamini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-12
Selected Works Of Oded Schramm written by Itai Benjamini 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 2011-08-12 with Mathematics categories.
This volume is dedicated to the memory of the late Oded Schramm (1961-2008), distinguished mathematician. Throughout his career, Schramm made profound and beautiful contributions to mathematics that will have a lasting influence. In these two volumes, Editors Itai Benjamini and Olle Häggström have collected some of his papers, supplemented with three survey papers by Steffen Rohde, Häggström and Cristophe Garban that further elucidate his work. The papers within are a representative collection that shows the breadth, depth, enthusiasm and clarity of his work, with sections on Geometry, Noise Sensitivity, Random Walks and Graph Limits, Percolation, and finally Schramm-Loewner Evolution. An introduction by the Editors and a comprehensive bibliography of Schramm's publications complete the volume. The book will be of especial interest to researchers in probability and geometry, and in the history of these subjects.
A Discrete Hilbert Transform With Circle Packings
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Author : Dominik Volland
language : en
Publisher: Springer
Release Date : 2017-12-01
A Discrete Hilbert Transform With Circle Packings written by Dominik Volland and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-01 with Mathematics categories.
Dominik Volland studies the construction of a discrete counterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a conjecture on discrete problems formulated by Wegert. Moreover, he illustrates its properties by carefully chosen numerical examples.
Sphere Packings Lattices And Groups
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Author : J.H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Sphere Packings Lattices And Groups written by J.H. Conway 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 2013-03-09 with Mathematics categories.
The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.
Low Dimensional Geometry
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Author : Francis Bonahon
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-07-14
Low Dimensional Geometry written by Francis Bonahon 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 2009-07-14 with Mathematics categories.
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
Open Problems In Optimization And Data Analysis
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Author : Panos M. Pardalos
language : en
Publisher: Springer
Release Date : 2018-12-04
Open Problems In Optimization And Data Analysis written by Panos M. Pardalos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-04 with Mathematics categories.
Computational and theoretical open problems in optimization, computational geometry, data science, logistics, statistics, supply chain modeling, and data analysis are examined in this book. Each contribution provides the fundamentals needed to fully comprehend the impact of individual problems. Current theoretical, algorithmic, and practical methods used to circumvent each problem are provided to stimulate a new effort towards innovative and efficient solutions. Aimed towards graduate students and researchers in mathematics, optimization, operations research, quantitative logistics, data analysis, and statistics, this book provides a broad comprehensive approach to understanding the significance of specific challenging or open problems within each discipline. The contributions contained in this book are based on lectures focused on “Challenges and Open Problems in Optimization and Data Science” presented at the Deucalion Summer Institute for Advanced Studies in Optimization, Mathematics, and Data Science in August 2016.