翻訳と辞書 Words near each other ・ Dinhata (Vidhan Sabha constituency) ・ Dinhata College ・ Dinhata High School ・ Dinhata I (community development block) ・ Dinhata II (community development block) ・ Dinhata subdivision ・ Dinheirosaurus ・ Dinhing Dapita Sadya ・ Dinho Chingunji ・ Dini ・ Dini Beyk ・ Dini Cabinet ・ Dini continuity ・ Dini criterion ・ Dini Daniel ・ Dini derivative ・ Dini Dimakos ・ Dini Petty ・ Dini test ・ Dini Ya Msambwa ・ Dini's Lucky Club ・ Dini's surface ・ Dini's theorem ・ DinI-like protein family ・ Dinia ・ Dinia (moth) ・ Dinia eagrus ・ Dinia mena ・ Dinia subapicalis ・ Dinic 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 Dini derivative ： ウィキペディア英語版 Dini derivative In mathematics and, specifically, real analysis, the Dini derivatives (or Dini derivates) are a class of generalizations of the derivative. They were introduced by Ulisse Dini. The upper Dini derivative, which is also called an upper right-hand derivative, of a continuous function :$f:\; \backslash rightarrow\; ,$ is denoted by $f\text{'}\_+,\backslash ,$ and defined by :$f\text{'}\_+(t)\; \backslash triangleq\; \backslash limsup\_$ where $\backslash limsup$ is the supremum limit and the limit is a one-sided limit. The lower Dini derivative, $f\text{'}\_-,\backslash ,$, is defined by :$f\text{'}\_-(t)\; \backslash triangleq\; \backslash liminf\_$ where $\backslash liminf$ is the infimum limit. If $f$ is defined on a vector space, then the upper Dini derivative at $t$ in the direction $d$ is defined by :$f\text{'}\_+\; (t,d)\; \backslash triangleq\; \backslash limsup\_.$ If $f$ is locally Lipschitz, then $f\text{'}\_+\backslash ,$ is finite. If $f$ is differentiable at $t$, then the Dini derivative at $t$ is the usual derivative at $t$. ==Remarks== * Sometimes the notation $D^+\; f(t)\backslash ,$ is used instead of $f\text{'}\_+(t),\backslash ,$ and $D\_+f(t)\backslash ,$ is used instead of $f\text{'}\_-(t).\backslash ,$〔 * Also, :$D^-f(t)\; \backslash triangleq\; \backslash limsup\_$ and :$D\_-f(t)\; \backslash triangleq\; \backslash liminf\_.$ * So when using the $D$ notation of the Dini derivatives, the plus or minus sign indicates the left- or right-hand limit, and the placement of the sign indicates the infimum or supremum limit. * On the extended reals, each of the Dini derivatives always exist; however, they may take on the values $+\; \backslash infty$ or $-\; \backslash infty$ at times (i.e., the Dini derivatives always exist in the extended sense). 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「Dini derivative」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.