翻訳と辞書 Words near each other ・ Effective (album) ・ Effective (database) ・ Effective action ・ Effective altruism ・ Effective arterial blood volume ・ Effective atomic number ・ Effective circulating volume ・ Effective competition ・ Effective complexity ・ Effective Cycling ・ Effective data transfer rate ・ Effective date ・ Effective demand ・ Effective descriptive set theory ・ Effective diffusion coefficient ・ Effective dimension ・ Effective domain ・ Effective dose ・ Effective dose (pharmacology) ・ Effective dose (radiation) ・ Effective evolutionary time ・ Effective exchange rate ・ Effective exchange rate index ・ Effective field goal percentage ・ Effective field theory ・ Effective fitness ・ Effective frequency ・ Effective gross income ・ Effective group decision-making ・ Effective half-life Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Effective dimension ： ウィキペディア英語版 Effective dimension In mathematics, effective dimension is a modification of Hausdorff dimension and other fractal dimensions which places it in a computability theory setting. There are several variations (various notions of effective dimension) of which the most common is effective Hausdorff dimension. Dimension, in mathematics, is a particular way of describing the size of an object (contrasting with measure and other, different, notions of size). Hausdorff dimension generalizes the well-known integer dimensions assigned to points, lines, planes, etc. by allowing one to distinguish between objects of intermediate size between these integer-dimensional objects. For example, fractal subsets of the plane may have intermediate dimension between 1 and 2, as they are "larger" than lines or curves, and yet "smaller" than filled circles or rectangles. Effective dimension modifies Hausdorff dimension by requiring that objects with small effective dimension be not only small but also locatable (or partially locatable) in a computable sense. As such, objects with large Hausdorff dimension also have large effective dimension, and objects with small effective dimension have small Hausdorff dimension, but an object can have small Hausdorff but large effective dimension. An example is an algorithmically random point on a line, which has Hausdorff dimension 0 (since it is a point) but effective dimension 1 (because, roughly speaking, it can't be effectively localized any better than a small interval, which has Hausdorff dimension 1). == Rigorous definitions == This article will define effective dimension for subsets of Cantor space 2ω; closely related definitions exist for subsets of Euclidean space R''n''. We will move freely between considering a set ''X'' of natural numbers, the infinite sequence $\backslash chi\_X$ given by the characteristic function of ''X'', and the real number with binary expansion 0.''X''. 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「Effective dimension」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.