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| Author | : Kenneth Stephenson |
| Publisher | : Cambridge University Press |
| Total Pages | : 380 |
| Release | : 2005-04-18 |
| Genre | : Mathematics |
| ISBN | : 9780521823562 |
Publisher Description
| Author | : Péter Gábor Szabó |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2007-05-31 |
| Genre | : Mathematics |
| ISBN | : 0387456767 |
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 | : Asaf Nachmias |
| Publisher | : Springer Nature |
| Total Pages | : 120 |
| Release | : 2019-10-04 |
| Genre | : Mathematics |
| ISBN | : 3030279685 |
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 | : Guntram Scheithauer |
| Publisher | : Springer |
| Total Pages | : 429 |
| Release | : 2017-10-20 |
| Genre | : Business & Economics |
| ISBN | : 3319644033 |
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 | : Itai Benjamini |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1199 |
| Release | : 2011-08-12 |
| Genre | : Mathematics |
| ISBN | : 1441996753 |
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 | : Thomas Callister Hales |
| Publisher | : Cambridge University Press |
| Total Pages | : 286 |
| Release | : 2012-09-06 |
| Genre | : Mathematics |
| ISBN | : 0521617707 |
The definitive account of the recent computer solution of the oldest problem in discrete geometry.
| Author | : Francis Bonahon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 403 |
| Release | : 2009-07-14 |
| Genre | : Mathematics |
| ISBN | : 082184816X |
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 |
| Publisher | : Springer |
| Total Pages | : 330 |
| Release | : 2018-12-04 |
| Genre | : Mathematics |
| ISBN | : 3319991426 |
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 | : Chuanming Zong |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2008-01-20 |
| Genre | : Mathematics |
| ISBN | : 0387227806 |
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 | : Nora Hartsfield |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 2013-04-15 |
| Genre | : Mathematics |
| ISBN | : 0486315525 |
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.
