| 翻訳と辞書 |
| Uniformly discrete set ： ウィキペディア英語版 |
Delone set
In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are. These sets have applications in coding theory, approximation algorithms, and the theory of quasicrystals.
==Definitions==
If (''M'',''d'') is a metric space, and ''X'' is a subset of ''M'', then the packing radius of ''X'' is half of the infimum of distances between distinct members of ''X''. If the packing radius is ''r'', then open balls of radius ''r'' centered at the points of ''X'' will all be disjoint from each other, and each open ball centered at one of the points of ''X'' with radius ''2r'' will be disjoint from the rest of ''X''. The covering radius of ''X'' is the infimum of the numbers ''r'' such that every point of ''M'' is within distance ''r'' of at least one point in ''X''; that is, it is the smallest radius such that closed balls of that radius centered at the points of ''X'' have all of ''M'' as their union. An ε-packing is a set ''X'' of packing radius ≥ ε/2 (equivalently, minimum distance ≥ ε), an ε-covering is a set ''X'' of covering radius ≤ ε, and an ε-net is a set that is both an ε-packing and an ε-covering. A set is uniformly discrete if it has a nonzero packing radius, and relatively dense if it has a finite covering radius. A Delone set is a set that is both uniformly discrete and relatively dense; thus, every ε-net is Delone, but not vice versa.〔.〕〔Some sources use "ε-net" for what is here called an "ε-covering"; see, e.g. .〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Delone set」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|