Author : Kenneth Stephenson
Publisher : Cambridge University Press
Page : 380 pages
File Size : 20,63 MB
Release : 2005-04-18
Category : Mathematics
ISBN : 9780521823562
Publisher Description
Author : Asaf Nachmias
Publisher : Springer Nature
Page : 126 pages
File Size : 33,96 MB
Release : 2019-10-04
Category : 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 : Itai Benjamini
Publisher : Springer Science & Business Media
Page : 1199 pages
File Size : 43,2 MB
Release : 2011-08-12
Category : 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 : Guntram Scheithauer
Publisher : Springer
Page : 429 pages
File Size : 24,31 MB
Release : 2017-10-20
Category : 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 : Michael A. Brilleslyper
Publisher : American Mathematical Soc.
Page : 373 pages
File Size : 45,97 MB
Release : 2012-12-31
Category : Mathematics
ISBN : 1614441081
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 49,86 MB
Release : 2009-07-14
Category : 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 : Yoshiaki Itoh
Publisher : World Scientific
Page : 255 pages
File Size : 19,5 MB
Release : 2011-01-26
Category : Mathematics
ISBN : 9814464783
In this volume very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem, which is known by the pioneering works by Flory (1939), Renyi (1958), Dvoretzky and Robbins (1962). To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. This book introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings./a
Author : Dominik Volland
Publisher : Springer
Page : 110 pages
File Size : 32,42 MB
Release : 2017-12-01
Category : Mathematics
ISBN : 3658204575
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
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 16,64 MB
Release : 2004
Category : Mathematics
ISBN : 0821835238
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 : Haeng Kon Kim
Publisher : Springer
Page : 778 pages
File Size : 44,42 MB
Release : 2014-07-02
Category : Technology & Engineering
ISBN : 9401791155
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.
