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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 Positive-real function ： ウィキペディア英語版 Positive-real function Positive-real functions, often abbreviated to PR function, are a kind of mathematical function that first arose in electrical network analysis. They are complex functions, ''Z''(''s''), of a complex variable, ''s''. A rational function is defined to have the PR property if it has a positive real part and is analytic in the right halfplane of the complex plane and takes on real values on the real axis. In symbols the definition is, :$\backslash begin$ & \Re()>0 \quad\text\quad \Re(s) > 0 \\ & \Im()=0 \quad\text\quad \Im(s)=0 \end In electrical network analysis, ''Z''(''s'') represents an impedance expression and ''s'' is the complex frequency variable, often expressed as its real and imaginary parts; :$s=\backslash sigma+i\backslash omega\; \backslash ,\backslash !$ in which terms the PR condition can be stated; :$\backslash begin$ & \Re()>0 \quad\text\quad \sigma > 0 \\ & \Im()=0 \quad\text\quad \omega=0 \end The importance to network analysis of the PR condition lies in the realisability condition. ''Z''(''s'') is realisable as a one-port rational impedance if and only if it meets the PR condition. Realisable in this sense means that the impedance can be constructed from a finite (hence rational) number of discrete ideal passive linear elements (resistors, inductors and capacitors in electrical terminology).〔E. Cauer, W. Mathis, and R. Pauli, "Life and Work of Wilhelm Cauer (1900 – 1945)", ''Proceedings of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems (MTNS2000)'', Perpignan, June, 2000. (Retrieved online ) 19 September 2008.〕 ==Definition== The term ''positive-real function'' was originally defined by〔 Otto Brune to describe any function ''Z''(''s'') which〔Brune, O, "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency", Doctoral thesis, MIT, 1931. (Retrieved online ) 3 June 2010.〕 *is rational (the quotient of two polynomials), *is real when ''s'' is real *has positive real part when ''s'' has a positive real part Many authors strictly adhere to this definition by explicitly requiring rationality, or by restricting attention to rational functions, at least in the first instance. However, a similar more general condition, not restricted to rational functions had earlier been considered by Cauer,〔 and some authors ascribe the term ''positive-real'' to this type of condition, while other consider it to be a generalization of the basic definition.〔 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「Positive-real 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.