Liquid air cycle engine: Difference between revisions
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en>Khazar2 →Principle of operation: clean up, typos fixed: on-board → on board using AWB (8097) |
en>Speaker to wolves Added comment that the reduction in gravity losses comes at the price of added drag and heating. |
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In mathematics, '''characteristic function''' can refer to any of several distinct concepts: | |||
* As a synonym for [[indicator function]], that is the function | |||
::<math>\mathbf{1}_A\colon X \to \{0, 1\},</math> | |||
:which for a given subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''. | |||
* In probability theory, the [[characteristic function (probability theory) | characteristic function]] of any probability distribution on the real line is given by the following formula, where ''X'' is any random variable with the distribution in question: | |||
::<math>\varphi_X(t) = \operatorname{E}\left(e^{itX}\right)</math>, | |||
:where E means expected value. This concept extends to multivariate distributions. | |||
* The [[characteristic function (convex analysis) | characteristic function]] in convex analysis: | |||
::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math> | |||
* The [[characteristic state function]] in statistical mechanics. | |||
* The [[characteristic polynomial]] in linear algebra. | |||
* The [[Euler characteristic]], a topological invariant. | |||
* The [[cooperative game]] in game theory. | |||
* The [[Receiver operating characteristic]] in statistical decision theory. | |||
{{disambig}} | |||
{{DEFAULTSORT:Characteristic Function}} | |||
[[Category:Mathematical disambiguation]] | |||
Revision as of 21:40, 22 July 2013
In mathematics, characteristic function can refer to any of several distinct concepts:
- As a synonym for indicator function, that is the function
- In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question:
- The characteristic function in convex analysis:
- The characteristic state function in statistical mechanics.
- The characteristic polynomial in linear algebra.
- The Euler characteristic, a topological invariant.
- The cooperative game in game theory.
- The Receiver operating characteristic in statistical decision theory.