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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 Reynolds operator ： ウィキペディア英語版 Reynolds operator In fluid dynamics and invariant theory, a Reynolds operator is a mathematical operator given by averaging something over a group action, that satisfies a set of properties called Reynolds rules. In fluid dynamics Reynolds operators are often encountered in models of turbulent flows, particularly the Reynolds-averaged Navier–Stokes equations, where the average is typically taken over the fluid flow under the group of time translations. In invariant theory the average is often taken over a compact group or reductive algebraic group acting on a commutative algebra, such as a ring of polynomials. Reynolds operators were introduced into fluid dynamics by and named by . ==Definition== Reynolds operators are used in fluid dynamics, functional analysis, and invariant theory, and the notation and definitions in these areas differ slightly. A Reynolds operator acting on φ is sometimes denoted by ''R''(''φ''), ''P''(''φ''), ''ρ''(''φ''), 〈''φ''〉, or . Reynolds operators are usually linear operators acting on some algebra of functions, satisfying the identity : ''R''(''R''(''φ'')''ψ'') = ''R''(''φ'')''R''(''ψ'') for all ''φ'', ''ψ'' and sometimes some other conditions, such as commuting with various group actions. 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「Reynolds operator」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.