翻訳と辞書 Words near each other ・ Jacobs Well Theatre ・ Jacobs Well, Queensland ・ Jacobs Well, Surrey ・ Jacobs Wind ・ Jacobs, Louisville ・ Jacobs, Pennsylvania ・ Jacobs, Wisconsin ・ Jacobs-Hutchinson Block ・ Jacobsbaai ・ Jacobsburg Environmental Education Center ・ Jacobsburg, Ohio ・ Jacobsdal ・ Jacobi polynomials ・ Jacobi Robinson ・ Jacobi rotation ・ Jacobi set ・ Jacobi sum ・ Jacobi symbol ・ Jacobi theta functions (notational variations) ・ Jacobi triple product ・ Jacobi zeta function ・ Jacobi's formula ・ Jacobi's four-square theorem ・ Jacobi's theorem ・ Jacobian ・ Jacobian conjecture ・ Jacobian curve ・ Jacobian ideal ・ Jacobian matrix and determinant ・ Jacobian variety 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 Jacobi set ： ウィキペディア英語版 Jacobi set In Morse theory, a mathematical discipline, Jacobi sets provide a method of studying the relationship between two or more Morse functions. For two Morse functions, the Jacobi set is defined as the set of critical points of the restriction of one function to the level sets of the other function. The Jacobi set can also be defined as the set of points where the gradients of the two functions are parallel. If both the functions are generic, the Jacobi set is a smoothly embedded 1-manifold. == Definition == Consider two generic Morse functions $f,\; g:\; M\; \backslash to\; \backslash R$ defined on a smooth $d$-manifold. Let the restriction of $f$ to the level set $g^(t)$ for $t\; \backslash in\; \backslash R$ a regular value, be called $f\_t:\; g^(t)\; \backslash to\; \backslash R$; it is a Morse function. Then the Jacobi set $J$ of $f$ and $g$ is $J\; =\; cl\}$, Alternatively, the Jacobi set is the collection of points where the gradients of the functions align with each other or one of the gradients vanish (cite?), for some $\backslash lambda\; \backslash in\; \backslash R$, $$ J = \ = 0 \mbox \lambda \nabla + \nabla = 0\}. Equivalently, the Jacobi set can be described as the collection of critical points of the family of functions $f+\; \backslash lambda\; g$, for some $\backslash lambda\; \backslash in\; \backslash R$, $$ J = \ \lambda f + g\}. 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「Jacobi set」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.