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Author : Kenneth Stephenson
Publisher : Cambridge University Press
Page : 380 pages
File Size : 41,9 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 0521823560
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Author : Asaf Nachmias
Publisher : Springer Nature
Page : 120 pages
File Size : 45,5 Mb
Release : 2019-10-04
Category : Mathematics
ISBN : 9783030279684
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.
Author : Péter Gábor Szabó,Mihaly Csaba Markót,Tibor Csendes,Eckard Specht,Leocadio G. Casado,Inmaculada García
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 49,7 Mb
Release : 2007-05-31
Category : Mathematics
ISBN : 9780387456768
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.
Author : Guntram Scheithauer
Publisher : Springer
Page : 410 pages
File Size : 46,8 Mb
Release : 2017-10-20
Category : Business & Economics
ISBN : 9783319644035
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.
Author : Dominik Volland
Publisher : Springer
Page : 102 pages
File Size : 54,9 Mb
Release : 2017-12-01
Category : Mathematics
ISBN : 9783658204570
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.
Author : Philip L. Bowers,Kenneth Stephenson
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 42,6 Mb
Release : 2004
Category : Circle packing
ISBN : 9780821835234
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.
Author : Itai Benjamini,Olle Häggström
Publisher : Springer Science & Business Media
Page : 1199 pages
File Size : 53,8 Mb
Release : 2011-08-12
Category : Mathematics
ISBN : 9781441996756
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.
Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 54,7 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9780821848166
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.
Author : Panos M. Pardalos,Athanasios Migdalas
Publisher : Springer
Page : 330 pages
File Size : 48,5 Mb
Release : 2018-12-04
Category : Mathematics
ISBN : 9783319991429
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.
Author : John Bryant,Chris Sangwin
Publisher : Princeton University Press
Page : 320 pages
File Size : 51,7 Mb
Release : 2011-02-28
Category : Mathematics
ISBN : 9781400837953
How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.
Author : Haeng Kon Kim,Sio-Iong Ao,Mahyar A. Amouzegar
Publisher : Springer
Page : 796 pages
File Size : 50,9 Mb
Release : 2014-07-02
Category : Technology & Engineering
ISBN : 9789401791151
This volume contains fifty-six revised and extended research articles, written by prominent researchers participating in the congress. Topics covered include electrical engineering, chemical engineering, circuits, computer science, communications systems, engineering mathematics, systems engineering, manufacture engineering and industrial applications. This book offers theoretical advances in engineering technologies and presents state of the art applications. It also serves as an excellent source of reference for researchers and graduate students working with/on engineering technologies.
Author : Chuanming Zong
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 40,7 Mb
Release : 2008-01-20
Category : Mathematics
ISBN : 9780387227801
Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.
Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 42,8 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author : J.H. Conway,N.J.A. Sloane
Publisher : Springer Science & Business Media
Page : 724 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722499
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.
Author : Nora Hartsfield,Gerhard Ringel
Publisher : Courier Corporation
Page : 272 pages
File Size : 49,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486315522
Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.