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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 Round function ： ウィキペディア英語版 Round function In topology and in calculus, a round function is a scalar function $M\backslash to\{\backslash mathbb\{R\}\}$, over a manifold $M$, whose critical points form one or several connected components, each homeomorphic to the circle $S^1$, also called critical loops. They are special cases of Morse-Bott functions. ==For instance== For example, let $M$ be the torus. Let :$K=(0,2\backslash pi)\backslash times(0,2\backslash pi).\backslash ,$ Then we know that a map :$X\backslash colon\; K\backslash to\}^3\backslash to\},\; (\backslash theta,\backslash phi)\; \backslash mapsto\; \backslash sin\; \backslash theta\; \backslash ,$ $G=G(\backslash theta,\backslash phi)=\backslash sin\backslash theta$ is a function whose critical sets are determined by :$\backslash \; G(\backslash theta,\backslash phi)=$ \left( we get the restriction :$G=\backslash pi\_3|\_M\backslash colon\; M\backslash to\backslash \; G(\backslash theta,\backslash phi)=$ \left(G\over \theta},G\over \phi}\right)\!\left(\theta,\phi\right)=(0,0),\, this is if and only if $\backslash theta=,\backslash$. These two values for $\backslash theta$ give the critical sets :$X(,\backslash phi)=(2\backslash cos\backslash phi,2\backslash sin\backslash phi,1)\backslash ,$ :$X(,\backslash phi)=(2\backslash cos\backslash phi,2\backslash sin\backslash phi,-1)\backslash ,$ which represent two extremal circles over the torus $M$. Observe that the Hessian for this function is :$(G)=$ \begin -\sin\theta & 0 \\ 0 & 0 \end which clearly it reveals itself as rank of $(G)$ equal to one at the tagged circles, making the critical point degenerate, that is, showing that the critical points are not isolated. 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「Round 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.