翻訳と辞書 Words near each other ・ List of Oricon number-one albums of 1999 ・ List of Oricon number-one albums of 2000 ・ List of Oricon number-one albums of 2001 ・ List of Oricon number-one albums of 2002 ・ List of Oricon number-one albums of 2003 ・ List of Oricon number-one albums of 2004 ・ List of Oricon number-one albums of 2005 ・ List of Oricon number-one albums of 2006 ・ List of Oricon number-one albums of 2007 ・ List of Oricon number-one albums of 2008 ・ List of Oricon number-one albums of 2009 ・ List of Oricon number-one albums of 2010 ・ List of Oricon number-one albums of 2011 ・ List of Oricon number-one albums of 2012 ・ List of Oricon number-one albums of 2013 ・ List of operators ・ List of operators of double decker buses ・ List of Operclipygus species ・ List of operetta composers ・ List of operettas and operas by Millöcker ・ List of operettas by Johann Strauss II ・ List of operettas by Offenbach ・ List of operettas by Ziehrer ・ List of Opeth band members ・ List of ophiolites ・ List of Opiliones of Trinidad and Tobago ・ List of Opinion episodes ・ List of opioids ・ List of OPJHL standings (1972–81) ・ List of Opperhoofden of Delagoa Bay 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 List of operators ： ウィキペディア英語版 List of operators In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators. In the following ''L'' is an operator :$L:\backslash mathcal\backslash to\backslash mathcal$ which takes a function $y\backslash in\backslash mathcal$ to another function $L()\backslash in\backslash mathcal$. Here, $\backslash mathcal$ and $\backslash mathcal$ are some unspecified function spaces, such as Hardy space, ''L''p space, Sobolev space, or, more vaguely, the space of holomorphic functions. || || ||Even component |- | $L()=\backslash frac$|| || ||Odd component |- | $L()=y\backslash circ\; (t+1)\; -\; y\backslash circ\; t\; =\; \backslash Delta\; y$|| || ||Difference operator |- | $L()=y\backslash circ\; (t)\; -\; y\backslash circ\; (t-1)\; =\; \backslash nabla\; y$|| || ||Backward difference (Nabla operator) |- | $L()=\backslash sum\; y=\backslash Delta^y$|| || ||Indefinite sum operator (inverse operator of difference) |- | $L()\; =-(py\text{'})\text{'}+qy\; \backslash ,$|| || ||Sturm–Liouville operator |- ! style="background:#eafaea" colspan=4|Non-linear transformations |- | $F()=y^\; \backslash$ || || ||Inverse function |- | $F()=t\backslash ,y\text{'}^\; -\; y\backslash circ\; y\text{'}^$|| || ||Legendre transformation |- | $F()=f\backslash circ\; y$|| || ||Left composition |- | $F()=\backslash prod\; y$|| || ||Indefinite product |- | $F()=\backslash frac$|| || ||Logarithmic derivative |- | $F()=\}$|| || ||Elasticity |- | $F()=-\backslash left(\backslash right)^2$|| || || Schwarzian derivative |- | $F()=\backslash int\_a^t\; |y\text{'}|\; \backslash ,dt$|| || ||Total variation |- | $F()=\backslash frac\backslash int\_a^t\; y\backslash ,dt$|| || ||Arithmetic mean |- | $F()=\backslash exp\; \backslash left(\; \backslash frac\backslash int\_a^t\; \backslash ln\; y\backslash ,dt\; \backslash right)$ || || ||Geometric mean |- | $F()=\; -\backslash frac$|| Cartesian||$y=y(x)$ $x=t$||rowspan=3|Subtangent |- | $F()=\; -\backslash frac$|| Parametric Cartesian||$x=x(t)$ $y=y(t)$ |- | $F()=\; -\backslash frac$||Polar||$r=r(\backslash phi)$ $\backslash phi=t$ |- | $F()=\backslash frac\backslash int\_a^t\; r^2\; dt$||Polar||$r=r(\backslash phi)$ $\backslash phi=t$ ||Sector area |- | $F()=\; \backslash int\_a^t\; \backslash sqrt\; \backslash ,\; dt$|| Cartesian||$y=y(x)$ $x=t$||rowspan=3|Arc length |- | $F()=\; \backslash int\_a^t\; \backslash sqrt\; \backslash ,\; dt$|| Parametric Cartesian||$x=x(t)$ $y=y(t)$ |- | $F()=\; \backslash int\_a^t\; \backslash sqrt\; \backslash ,\; dt$||Polar||$r=r(\backslash phi)$ $\backslash phi=t$ |- | $F()\; =\; \backslash int\_a^t\backslash sqrt()\backslash ,\; dt$ || Cartesian||$y=y(x)$ $x=t$||rowspan=3|Affine arc length |- | $F()\; =\; \backslash int\_a^t\backslash sqrt()\backslash ,\; dt$ || Parametric Cartesian||$x=x(t)$ $y=y(t)$ |- | $F()=\backslash int\_a^t\backslash sqrt()$||Parametric Cartesian||$x=x(t)$ $y=y(t)$ $z=z(t)$ |- | |- | $X()=\backslash frac$ $Y()=\backslash frac$||Parametric Cartesian||$x=x(t)$ $y=y(t)$||Dual curve (tangent coordinates) |- | $X()=x+\backslash frac$ $Y()=y+x\text{'}\backslash frac$||Parametric Cartesian||$x=x(t)$ $y=y(t)$||rowspan=2|Evolute |- | $F()=t\; (r\text{'}\backslash circ\; r^)$||Intrinsic||$r=r(s)$ $s=t$ |- |$X()=x-\backslash frac\backslash ,\; dt\}$ $Y()=\backslash frac$|| Parametric Cartesian||$x=x(t)$ $y=y(t)$|||Pedal curve with pedal point (0;0) |- |$X()=\backslash frac$ $Y()=\backslash frac$|| Parametric Cartesian||$x=x(t)$ $y=y(t)$|||Negative pedal curve with pedal point (0;0) |- | $X()\; =\; \backslash int\_a^t\; \backslash cos\; \backslash left(\backslash frac\; \backslash ,dt\backslash right)\; dt$ $Y()\; =\; \backslash int\_a^t\; \backslash sin\; \backslash left(\backslash frac\; \backslash ,dt\backslash right)\; dt$||Intrinsic||$y=r(s)$ $s=t$||Intrinsic to Cartesian transformation |- ! style="background:#eafaea" colspan=4|Metric functionals |- | $F()=||y||=\backslash sqrt$|| || ||Norm |- | $F()=\backslash int\_E\; xy\; \backslash ,\; dt$|| || ||Inner product |- | (inner angle) |- ! style="background:#eafaea" colspan=4|Distribution functionals |- | $F()\; =\; x$ * y = \int_E x(s) y(t - s)\, ds|| || ||Convolution |- | $F()\; =\; \backslash int\_E\; y\; \backslash ln\; y\; \backslash ,\; dy$|| || ||Differential entropy |- | $F()\; =\; \backslash int\_E\; yt\backslash ,dt$|| || ||Expected value |- | $F()\; =\; \backslash int\_E\; (t-\backslash int\_E\; yt\backslash ,dt)^2y\backslash ,dt$|| || ||Variance |} ==See also== * List of transforms * List of Fourier-related transforms * Transfer operator * Fredholm operator * Borel transform * Table of mathematical symbols 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「List of operators」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.