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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 Discrete Morse theory ： ウィキペディア英語版 Discrete Morse theory Discrete Morse theory is a combinatorial adaptation of Morse theory developed by (Robin Forman ). The theory has various practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces,〔F. Mori and M. Salvetti: ((Discrete) Morse theory for Configuration spaces )〕 homology computation,〔(Perseus ): the Persistent Homology software.〕 denoising,〔U. Bauer, C. Lange, and M. Wardetzky: (Optimal Topological Simplification of Discrete Functions on Surfaces )〕 and mesh compression.〔T Lewiner, H Lopez and G Tavares: (Applications of Forman's discrete Morse theory to topological visualization and mesh compression )〕 ==Notation regarding CW complexes== Let $\backslash mathcal$ be a CW complex. Define the ''incidence function'' $\backslash kappa:\backslash mathcal\; \backslash times\; \backslash mathcal\; \backslash to\; \backslash mathbb$ in the following way: given two cells $\backslash sigma$ and $\backslash tau$ in $\backslash mathcal$, let $\backslash kappa(\backslash sigma,~\backslash tau)$ be the degree of the attaching map from the boundary of $\backslash sigma$ to $\backslash tau$. The boundary operator $\backslash partial$ on $\backslash mathcal$ is defined by :$\backslash partial(\backslash sigma)\; =\; \backslash sum\_\; \backslash in\; \backslash mathcal$ :$\backslash sum\_)\; =\; 0$ which is a corollary of the above definition of the boundary operator and the requirement that $\backslash partial\backslash circ\backslash partial\; \backslash equiv\; 0$. 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「Discrete Morse theory」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.