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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 Hobby–Rice theorem ： ウィキペディア英語版 Hobby–Rice theorem In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain solutions. It was proved in 1965 by Charles R. Hobby and John R. Rice; a simplified proof was given in 1976 by A. Pinkus. ==The theorem== Given an integer ''k'', define a ''partition'' of the interval () as a sequence of numbers which divide the interval to $k+1$ subintervals: : Define a ''signed partition'' as a partition in which each subinterval $i$ has an associated sign $\backslash delta\_i$: : $\backslash delta\_1,\backslash dotsc,\backslash delta\_\backslash in\backslash left\backslash$ The Hobby-Rice theorem says that for every ''k'' continuously integrable functions: : $g\_1,\backslash dotsc,g\_k\backslash colon()\backslash longrightarrow\backslash Bbb$ there exists a signed partition of () such that: : $\backslash sum\_^\backslash delta\_i\backslash !\backslash int\_\; g\_j(z)\backslash ,dz=0\backslash text1\backslash leq\; j\backslash leq\; k.$ (in other words: for each of the ''k'' functions, its integral over the positive subintervals equals its integral over the negative subintervals). 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「Hobby–Rice theorem」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.