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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 Singularity function ： ウィキペディア英語版 Singularity function Singularity functions are a class of discontinuous functions that contain singularities, i.e. they are discontinuous at their singular points. Singularity functions have been heavily studied in the field of mathematics under the alternative names of generalized functions and distribution theory. The functions are notated with brackets, as $\backslash langle\; x-a\backslash rangle\; ^n$ where ''n'' is an integer. The "$\backslash langle\; \backslash rangle$" are often referred to as singularity brackets . The functions are defined as: :}\delta(x-a)\, |- | -2 |$\backslash frac\backslash delta(x-a)\backslash ,$ |- | -1 |$\backslash delta(x-a)\backslash ,$ |- | 0 | $H(x-a)\backslash ,$ |- | 1 | $(x-a)H(x-a)\backslash ,$ |- | 2 | $(x-a)^2H(x-a)$ |- | $\backslash ge\; 0$ | $(x-a)^nH(x-a)$ |} where: δ(x) is the Dirac delta function, also called the unit impulse. The first derivative of δ(x) is also called the unit doublet. The function $H(x)$ is the Heaviside step function: H(x)=0 for x<0 and H(x)=1 for x>0. The value of H(0) will depend upon the particular convention chosen for the Heaviside step function. Note that this will only be an issue for ''n=0'' since the functions contain a multiplicative factor of ''x-a'' for n>0. $\backslash langle\; x-a\backslash rangle^1$ is also called the Ramp function. == Integration == Integrating $\backslash langle\; x-a\; \backslash rangle^n$ can be done in a convenient way in which the constant of integration is automatically included so the result will be 0 at x=a. 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「Singularity function」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.