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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 Mixed volume ： ウィキペディア英語版 Mixed volume In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an ''n''-tuple of convex bodies in the ''n''-dimensional space. This number depends on the size of the bodies and their relative positions. ==Definition== Let ''K''1, ''K''2, ..., ''K''''r'' be convex bodies in R''n'', and consider the function :$f(\backslash lambda\_1,\; \backslash ldots,\; \backslash lambda\_r)$ = \mathrm_n (\lambda_1 K_1 + \cdots + \lambda_r K_r), \qquad \lambda_i \geq 0, where Vol''n'' stands for the ''n''-dimensional volume and its argument is the Minkowski sum of the scaled convex bodies ''Ki''. One can show that ''f'' is a homogeneous polynomial of degree ''n'', therefore it can be written as :$f(\backslash lambda\_1,\; \backslash ldots,\; \backslash lambda\_r)$ = \sum_^r V(K_, \ldots, K_) \lambda_ \cdots \lambda_, where the functions ''V'' are symmetric. Then ''V''(''T''1, ..., ''T''''n'') is called the mixed volume of ''T''1, ''T''2, ..., ''T''''n''. Equivalently, :$$ V(T_1, \ldots, T_n) = \left. \frac\right|_ \mathrm_n(\lambda_1 T_1 + \cdots + \lambda_n T_n). 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「Mixed volume」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.