翻訳と辞書 Words near each other ・ Picoli ・ Picoline ・ Picolinic acid ・ PicoLisp ・ Picolit ・ Picoliva ・ Picoliva ryalli ・ Picoliva zelindae ・ Picollator ・ Picolo ・ Picometre ・ Picon ・ Picon (footballer) ・ Picon Pie ・ Picon Punch ・ Picone identity ・ Piconet ・ Picong ・ Picong, Lanao del Sur ・ Piconzé ・ Picoo Z ・ Picopict ・ Picoplankton ・ Picoplatin ・ Picorandan ・ Picornain 2A ・ Picornain 3C ・ Picornavirales ・ Picornavirus ・ Picornavirus internal ribosome entry site (IRES) 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 Picone identity ： ウィキペディア英語版 Picone identity In the field of ordinary differential equations, the Picone identity, named after Mauro Picone, is a classical result about homogeneous linear second order differential equations. Since its inception in 1910 it has been used with tremendous success in association with an almost immediate proof of the Sturm comparison theorem, a theorem whose proof took up many pages in Sturm's original memoir of 1836. It is also useful in studying the oscillation of such equations and has been generalized to other type of differential equations and difference equations. The Picone identity is used to prove the Sturm comparison theorem (see also Sturm–Picone comparison theorem). == Picone identity == Suppose that ''u'' and ''v'' are solutions of the two homogeneous linear second order differential equations in self-adjoint form :$(p\_1(x)\; u\text{'})\text{'}\; +\; q\_1(x)\; u\; =\; 0\; \backslash ,$ and :$(p\_2(x)\; v\text{'})\text{'}\; +\; q\_2(x)\; v\; =\; 0.\; \backslash ,$ Then, for all ''x'' with ''v''(''x'') ≠ 0, the following identity holds :$\backslash left(\backslash frac(p\_1\; u\text{'}\; v\; -\; p\_2\; u\; v\text{'})\backslash right)\text{'}\; =\; \backslash left(q\_2\; -\; q\_1\backslash right)\; u^2\; +\; \backslash left(p\_1\; -\; p\_2\backslash right)u\text{'}^2\; +\; p\_2\backslash left(u\text{'}-v\text{'}\backslash frac\backslash right)^2.$ 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「Picone identity」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.