Fresnel diffraction - Revision history

en>Tom.Reding: Gen fixes (page/s, endash, , et al., unicodify, concising wikilinks, etc.), ref cleanup using AWB

2014-12-27T02:21:15Z

Gen fixes (page/s, endash, &nbsp, et al., unicodify, concising wikilinks, etc.), ref cleanup using AWB

← Older revision		Revision as of 04:21, 27 December 2014
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132.66.51.110: Very well, but, F>>1 is not a sufficient condition for the validity of the Fresnel approximation. See Saleh and Teich pg.119 eq.(4.1-10) and the text on pg.123 below eq.(4.2-4) !

2014-02-19T09:02:34Z

Very well, but, F>>1 is not a sufficient condition for the validity of the Fresnel approximation. See Saleh and Teich pg.119 eq.(4.1-10) and the text on pg.123 below eq.(4.2-4) !

← Older revision		Revision as of 11:02, 19 February 2014
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	~~{{lowercase\|title=utm theorem}}~~		The author is called Wilber Pegues. Mississippi is exactly where her house is but her spouse desires them to move. To climb is something I really appreciate doing. Invoicing is my profession.<br><br>My page [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 free psychic]
	~~In [[computability theory]] the '''utm theorem''', or '''[[Universal Turing machine]] theorem''',~~ is ~~a basic result about [[Gödel numbering]]s of the set of [[computable function]]s~~. ~~It affirms the existence of a computable '''universal function''' which~~ is ~~capable of calculating any other computable function~~. ~~The universal function~~ is ~~an abstract version of the [[universal turing machine]], thus the name of the theorem~~.

	~~[[Roger's equivalence theorem\|Rogers equivalence theorem]] provides a characterization of the Gödel numbering of the computable functions in terms of the [[smn theorem]] and the utm theorem~~.

	~~== utm theorem ==~~

	~~Let~~ <~~math~~>~~\varphi_1, \varphi_2, \varphi_3, ...~~<~~/math~~> ~~be an enumeration of Gödel numbers of computable functions. Then the partial function~~
	~~:<math>u~~: ~~\mathbb{N}^2 \to \mathbb{N}<~~/~~math>~~
	~~defined as~~
	~~:<math>u(i,x) := \varphi_i(x) \qquad i,x \in \mathbb{N}<~~/~~math>~~
	~~is computable~~.

	~~<math>u<~~/~~math> is called the '''universal function'''~~.

	~~== References =~~=
	*{{cite book \| author = ~~Rogers, H. \| title = The Theory of Recursive Functions and Effective Computability \| publisher = First MIT press paperback edition \| year = 1987 \| origyear = 1967 \| isbn = 0-262-68052-1 }}~~
	*{{cite book \| author = Soare, R.\| title = Recursively enumerable sets and degrees \| series = Perspectives in Mathematical Logic \| publisher = Springer-Verlag \| year = 1987 \| isbn = 3-540-15299-7 }}

	~~[[Category:Theory of computation]]~~
	~~[[Category:Computability theory]~~]

en>Chetvorno: Added mention of Fraunhofer diffraction to the introduction

2014-01-01T10:46:46Z

Added mention of Fraunhofer diffraction to the introduction

← Older revision		Revision as of 12:46, 1 January 2014
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	~~The author~~ is ~~called Wilber Pegues~~. ~~Credit authorising~~ is ~~where my primary income comes from~~. ~~Alaska~~ is ~~exactly where I~~'~~ve always been living~~. ~~I am truly fond~~ of ~~handwriting but I can't make it my occupation really~~.<br><br>~~my page~~: ~~accurate psychic predictions; [http~~://~~galab-work~~.cs.~~pusan~~.~~ac.kr/Sol09B/?document_srl~~=~~1489804 mouse click the up coming internet site~~],		{{lowercase\|title=utm theorem}}
			In [[computability theory]] the '''utm theorem''', or '''[[Universal Turing machine]] theorem''', is a basic result about [[Gödel numbering]]s of the set of [[computable function]]s. It affirms the existence of a computable '''universal function''' which is capable of calculating any other computable function. The universal function is an abstract version of the [[universal turing machine]], thus the name of the theorem.

			[[Roger's equivalence theorem\|Rogers equivalence theorem]] provides a characterization of the Gödel numbering of the computable functions in terms of the [[smn theorem]] and the utm theorem.

			== utm theorem ==

			Let <math>\varphi_1, \varphi_2, \varphi_3, ...</math> be an enumeration of Gödel numbers of computable functions. Then the partial function
			:<math>u: \mathbb{N}^2 \to \mathbb{N}</math>
			defined as
			:<math>u(i,x) := \varphi_i(x) \qquad i,x \in \mathbb{N}</math>
			is computable.

			<math>u</math> is called the '''universal function'''.

			== References ==
			*{{cite book \| author = Rogers, H. \| title = The Theory of Recursive Functions and Effective Computability \| publisher = First MIT press paperback edition \| year = 1987 \| origyear = 1967 \| isbn = 0-262-68052-1 }}
			*{{cite book \| author = Soare, R.\| title = Recursively enumerable sets and degrees \| series = Perspectives in Mathematical Logic \| publisher = Springer-Verlag \| year = 1987 \| isbn = 3-540-15299-7 }}

			[[Category:Theory of computation]]
			[[Category:Computability theory]]

en>ChrisGualtieri: TypoScan Project / General Fixes, typos fixed: , → , using AWB

2012-05-30T02:54:46Z

TypoScan Project / General Fixes, typos fixed: , → , using AWB

New page

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