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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 Asano contraction ： ウィキペディア英語版 Asano contraction In complex analysis, a discipline in mathematics, and in statistical physics, the Asano contraction or Asano–Ruelle contraction is a transformation on a separately affine multivariate polynomial. It was first presented in 1970 by Taro Asano to prove the Lee–Yang theorem in the Heisenberg spin model case. This also yielded a simple proof of the Lee–Yang theorem in the Ising model. David Ruelle proved a general theorem relating the location of the roots of a contracted polynomial to that of the original. Asano contractions have also been used to study polynomials in graph theory. ==Definition== Let $\backslash Phi(z\_1,z\_2,\backslash ldots,z\_n)$ be a polynomial which, when viewed as a function of only one of these variables is an affine function. Such functions are called separately affine. For example, $a+bz\_1+cz\_2+dz\_1z\_2$ is the general form of a separately affine function in two variables. Any separately affine function can be written in terms of any two of its variables as $\backslash Phi(z\_i,z\_j)=a+bz\_i+cz\_j+dz\_iz\_j$. The Asano contraction $(z\_i,z\_j)\backslash mapsto\; z$ sends $\backslash Phi$ to $\backslash tilde=a+dz$. 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「Asano contraction」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.