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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク interval exchange transformation ： ウィキペディア英語版 interval exchange transformation In mathematics, an interval exchange transformation〔.〕 is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals. ==Formal definition== Let $n\; >\; 0$ and let $\backslash pi$ be a permutation on $1,\; \backslash dots,\; n$. Consider a vector $\backslash lambda\; =\; (\backslash lambda\_1,\; \backslash dots,\; \backslash lambda\_n)$ of positive real numbers (the widths of the subintervals), satisfying :$\backslash sum\_^n\; \backslash lambda\_i\; =\; 1.$ Define a map $T\_:()\backslash rightarrow\; (),$ called the interval exchange transformation associated to the pair $(\backslash pi,\backslash lambda)$ as follows. For $1\; \backslash leq\; i\; \backslash leq\; n$ let :$a\_i\; =\; \backslash sum\_\; \backslash lambda\_j\; \backslash quad\; \backslash text\; \backslash quad\; a\text{'}\_i\; =\; \backslash sum\_\; \backslash lambda\_.$ Then for $x\; \backslash in\; ()$, define :$$ T_(x) = x - a_i + a'_i if $x$ lies in the subinterval $[a\_i,a\_i+\backslash lambda\_i)$. Thus $T\_$ acts on each subinterval of the form $[a\_i,a\_i+\backslash lambda\_i)$ by a translation, and it rearranges these subintervals so that the subinterval at position $i$ is moved to position $\backslash pi(i)$. 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「interval exchange transformation」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.