formulasearchengine - User contributions [en]

M-tree

2014-10-16T15:55:46Z

137.138.48.160: changed small typo for kNN input

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Golomb coding

2014-07-02T09:09:12Z

137.138.78.218: Added N after the "to divide an input value" because N in the formula was not explained anywhere.

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Scattering parameters

2014-01-30T14:28:35Z

137.138.193.170: /* 4-Port S-Parameters */

In [[linguistics]], a ''quantized expression'' is such that, whenever it is true of some entity, it is ''not'' true of any proper subparts of that entity. Example: If something is an "apple", then no proper subpart of that thing is an "apple". If something is "water", then many of its subparts will also be "water". Hence, "apple" is quantized, while "water" is not. Quantization has proven relevant to the proper characterization of grammatical [[telicity]] (roughly, sentences that present events as '''bounded/unbounded''' in time) and the [[mass noun|mass/count]] distinction for [[nouns]]. The notion was first applied to linguistic [[semantics]] by the linguist [[Manfred Krifka]].

Formally, a '''quantization''' predicate ''QUA'' can be defined as follows, where <math>U</math> is the [[universe of discourse]], and <math>F</math> is a variable over [[set (mathematics)|sets]], and <math>p</math> is a [[mereology|mereological]] part [[mathematical structure|structure]] on <math>U</math> with <math> <_p</math> the [[mereology|mereological]] part-of [[relation (mathematics)|relation]].

<center>
<math>(\forall F\subseteq U_p)(QUA(F) \iff (\forall x,y)(F(x)\wedge F(y) \Rightarrow \neg x<_p y))</math>
</center>

==See also==
*[[Fewer vs. less]]

==References==

Krifka, Manfred 1989. Nominal reference, temporal constitution and quantification in event semantics.
In Renate Bartsch, Johan van Benthem and Peter van Emde Boas (eds.), ''Semantics and
Contextual Expressions'' 75-115. Dordrecht: Foris.

[[Category:Logic]]
[[Category:Semantics]]
[[Category:Grammar]]

Collinearity equation

2013-11-13T09:43:18Z

137.138.117.212:

In [[mathematics]], more precisely in [[algebra]], a '''prosolvable group''' (less common: '''prosoluble group''') is a [[group (mathematics)|group]] that is [[isomorphic]] to the [[inverse limit]] of an [[inverse system]] of [[solvable group]]s. Equivalently, a group is called '''prosolvable''', if, viewed as a [[topological group]], every [[open neighborhood]] of the identity contains a [[normal subgroup]] whose corresponding [[quotient group]] is a [[solvable group]].

== Examples ==
* Let ''p'' be a [[prime]], and denote the [[Field (mathematics)|field]] of [[p-adic numbers]], as usually, by <math>\mathbf{Q}_p</math>. Then the [[Galois group]] <math>\text{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)</math>, where <math>\overline{\mathbf{Q}}_p</math> denotes the [[algebraic closure]] of <math>\mathbf{Q}_p</math>, is prosolvable. This follows from the fact that, for any finite [[Galois extension]] <math>L</math> of <math>\mathbf{Q}_p</math>, the [[Galois group]] <math>\text{Gal}(L/\mathbf{Q}_p)</math> can be written as [[semidirect product]] <math>\text{Gal}(L/\mathbf{Q}_p)=(R \rtimes Q) \rtimes P</math>, with <math>P</math> cyclic of order <math>f</math> for some <math>f\in\mathbf{N}</math>, <math>Q</math> cyclic of order dividing <math>p^f-1</math>, and <math>R</math> of <math>p</math>-power order. Therefore, <math>\text{Gal}(L/\mathbf{Q}_p)</math> is [[solvable group|solvable]].<ref>{{citation|last=Boston|first=Nigel|title=The Proof of Fermat's Last Theorem|year=2003|publisher=University of Wisconsin Press|location=Madison, Wisconsin, USA}}</ref>

== See also ==
* [[Solvable group]]
* [[Galois theory]]
* [[p-adic integers]]

==References==
{{reflist}}

[[Category:Mathematical structures]]
[[Category:Algebra]]
[[Category:Number theory]]
[[Category:Topology]]
[[Category:Group theory]]
[[Category:Topological groups]]

Band gap

2012-08-24T13:15:48Z

137.138.27.142: /* List of band gaps */

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Direct simulation Monte Carlo

2012-06-14T08:03:49Z

137.138.122.18: /* DSMC Software */

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