翻訳と辞書 Words near each other ・ Multi-wire saw ・ Multi-word verb ・ Multi-frequency signaling ・ Multi-frequency time division multiple access ・ Multi-fuel stove ・ Multi-function display ・ Multi-function printer ・ Multi-function structure ・ Multi-Functional Transport Satellite ・ Multi-gigabit transceiver ・ Multi-Gun ・ Multi-headed ・ Multi-Housing News ・ Multi-hyphenate ・ Multi-image ・ Multi-index notation ・ Multi-instrumentalist ・ Multi-jackbolt tensioner ・ Multi-junction solar cell ・ Multi-key quicksort ・ Multi-label classification ・ Multi-Lamellar Emulsion ・ Multi-lane free flow in Malaysia ・ Multi-layer CCD ・ Multi-layer insulation ・ Multi-leaded power package ・ Multi-level cell ・ Multi-level governance ・ Multi-level marketing ・ Multi-level technique 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 Multi-index notation ： ウィキペディア英語版 Multi-index notation Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices. ==Definition and basic properties== An ''n''-dimensional multi-index is an ''n''-tuple :$\backslash alpha\; =\; (\backslash alpha\_1,\; \backslash alpha\_2,\backslash ldots,\backslash alpha\_n)$ of non-negative integers (i.e. an element of the ''n''-dimensional set of natural numbers, denoted $\backslash mathbb^n\_0$). For multi-indices $\backslash alpha,\; \backslash beta\; \backslash in\; \backslash mathbb^n\_0$ and $x\; =\; (x\_1,\; x\_2,\; \backslash ldots,\; x\_n)\; \backslash in\; \backslash mathbb^n$ one defines: ;Componentwise sum and difference :$\backslash alpha\; \backslash pm\; \backslash beta=\; (\backslash alpha\_1\; \backslash pm\; \backslash beta\_1,\backslash ,\backslash alpha\_2\; \backslash pm\; \backslash beta\_2,\; \backslash ldots,\; \backslash ,\backslash alpha\_n\; \backslash pm\; \backslash beta\_n)$ ;Partial order :$\backslash alpha\; \backslash le\; \backslash beta\; \backslash quad\; \backslash Leftrightarrow\; \backslash quad\; \backslash alpha\_i\; \backslash le\; \backslash beta\_i\; \backslash quad\; \backslash forall\backslash ,i\backslash in\backslash$ ;Sum of components (absolute value) :$|\; \backslash alpha\; |\; =\; \backslash alpha\_1\; +\; \backslash alpha\_2\; +\; \backslash cdots\; +\; \backslash alpha\_n$ ;Factorial :$\backslash alpha\; !\; =\; \backslash alpha\_1!\; \backslash cdot\; \backslash alpha\_2!\; \backslash cdots\; \backslash alpha\_n!$ ;Binomial coefficient :$\backslash binom\; =\; \backslash binom\backslash binom\backslash cdots\backslash binom\; =\; \backslash frac$ ;Multinomial coefficient :$\backslash binom\; =\; \backslash frac\; =\; \backslash frac$ where $k:=|\backslash alpha|\backslash in\backslash mathbb\_0\backslash ,\backslash !$. ;Power :$x^\backslash alpha\; =\; x\_1^\; x\_2^\; \backslash ldots\; x\_n^$. ;Higher-order partial derivative :$\backslash partial^\backslash alpha\; =\; \backslash partial\_1^\; \backslash partial\_2^\; \backslash ldots\; \backslash partial\_n^$ where $\backslash partial\_i^:=\backslash part^\; /\; \backslash part\; x\_i^$ (see also 4-gradient). 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「Multi-index notation」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.