Batchelor scale - Revision history

en>Rjwilmsi: Journal cites, Added 1 doi to a journal cite using AWB (10395)

2014-08-23T15:32:25Z

Journal cites, Added 1 doi to a journal cite using AWB (10395)

← Older revision		Revision as of 17:32, 23 August 2014
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	~~{{unreferenced\|date=December 2009}}~~
	'''Lupanov's (''k'', ''s'')-representation''', named after [[Oleg Lupanov]], is a way of representing [[Boolean circuit]]s so as to show that the reciprocal of the [[Claude Shannon\|Shannon effect]]. Shannon had showed that almost all [[Boolean functions]] of ''n'' variables need a [[circuit complexity\|circuit]] of size at least 2<sup>''n''</sup>''n''<sup>−1</sup>. The reciprocal is that:

	~~<blockquote>~~
	~~All Boolean functions of ''n'' variables can be computed with a circuit of at most 2<sup>''n''</sup>''n''<sup>−1</sup> + o(2<sup>''n''</sup>''n''<sup>−1</sup>) gates.~~
	~~</blockquote>~~

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	~~The idea is to represent the values~~ of ~~a boolean function ''&fnof;''~~ in ~~a table of 2<sup>''k''</sup> rows, representing~~ the ~~possible values of~~ the ~~''k'' first variables ''x''<sub>1</sub>~~,~~ ~~..~~., ,~~''~~x''<sub>''k''</sub>~~, and ~~2<sup>''n''−''k''</sup> columns representing~~ the ~~values~~ of the ~~other variables~~.

	~~Let ''A''~~<~~sub~~>1<~~/sub~~>~~, ~~...,~~ ''A'~~'<~~sub~~>~~''p''~~<~~/sub~~> be a ~~partition of~~ the ~~rows~~ of this ~~table~~ such that ~~for ''i'' < ''p''~~, ~~\|''A''<sub>''i''</sub> = ''s''~~ and <~~math~~>~~\|A_p\|=s'\leq s~~<~~/math~~>.
	~~Let ''&fnof;''<sub>''i''</sub>~~(~~''x'') = ''&fnof;''(''x''~~) [~~[iff~~]~~] ''x'' ∈ ''A''<sub>''i''</sub>~~.

	~~Moreover~~, ~~let~~ <~~math~~>~~B_{i,w}~~<~~/math~~> be the ~~set~~ of the ~~columns whose intersection~~ with ~~<math>A_i</math> is <math>w</math>~~.

	~~[[Category:Boolean algebra]]~~
	~~[[Category:Circuit complexity]]~~

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q4868729

2013-03-20T19:11:08Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q4868729

← Older revision		Revision as of 21:11, 20 March 2013
Line 1:		Line 1:
	~~Surely the second option would be more beneficial for any website. It~~ is ~~very easy to customize plugins according~~ to the ~~needs~~ of ~~a particular business. I thought about what would happen by placing a text widget in~~ the ~~sidebar beneath my banner ad, and so it went. If you cherished this article therefore you would like to get more info pertaining to~~ [~~http://teenyweenyurl.com/WordpressDropboxBackup482755 wordpress backup plugin~~] ~~generously visit our own web page~~. ~~s ultimately easy to implement and virtually maintenance free. All this is very simple, and the best thing is~~ that ~~it is totally free, and you don~~'t need a ~~domain name or web hosting.~~ <br><br>~~These websites~~ can be ~~easily customized and can appear in the top rankings of the major search engines. If a newbie missed~~ a ~~certain part~~ of ~~the video then they could always rewind~~. ~~A Wordpress plugin~~ is a ~~software that you can install into your Wordpress site. You can up your site~~'~~s rank with the search engines by simply taking~~ a ~~bit~~ of ~~time with your site. That~~'~~s a total~~ of ~~180$ for each Wordpress theme if you sell 3 links and keep~~ the ~~designer link for your own website~~, ~~or 240$ if you sell all links~~. <br><br>~~But before choosing any one of these~~, ~~let~~'~~s compare between~~ the ~~two~~. ~~Word - Press has different exciting features including a plug-in architecture with a templating system~~. ~~If Gandhi was empowered with a blogging system~~, ~~every event in his life would have been minutely documented so that it could~~ be ~~recounted to~~ the future generations. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for ~~the visitor of the internet site. " Thus working with a Word - Press powered web application~~, ~~making any changes in the website design or website content is really easy~~ and ~~self explanatory~~. <br><br>~~Word - Press installation is very easy and hassle free. php file in the Word - Press root folder and look for this line~~ (~~line 73 in our example~~):. ~~Websites that do rank highly~~, ~~do so becaue they use keyword-heavy post titles. So~~, ~~we have to add our social media sharing buttons in website. Now all you have to do is log into your Word - Press site making use~~ of the ~~very same username and password that you initially had in your previous site.~~ <br><br>Website security has become a major concern among individuals all over the world. Automated deal feed integration option to populate your blog with relevant deals. By the time you get the Gallery Word - Press Themes, the first thing that you should know is ~~on how to install it~~. ~~) Remote Login~~: With the process of PSD to Wordpress conversion comes the advantage of flexibility. Definitely when you wake up from the slumber, you can be sure that you will be lagging behind and getting on track would be a tall order.		{{unreferenced\|date=December 2009}}
			'''Lupanov's (''k'', ''s'')-representation''', named after [[Oleg Lupanov]], is a way of representing [[Boolean circuit]]s so as to show that the reciprocal of the [[Claude Shannon\|Shannon effect]]. Shannon had showed that almost all [[Boolean functions]] of ''n'' variables need a [[circuit complexity\|circuit]] of size at least 2<sup>''n''</sup>''n''<sup>−1</sup>. The reciprocal is that:

			<blockquote>
			All Boolean functions of ''n'' variables can be computed with a circuit of at most 2<sup>''n''</sup>''n''<sup>−1</sup> + o(2<sup>''n''</sup>''n''<sup>−1</sup>) gates.
			</blockquote>

			==Definition==

			The idea is to represent the values of a boolean function ''&fnof;'' in a table of 2<sup>''k''</sup> rows, representing the possible values of the ''k'' first variables ''x''<sub>1</sub>, ..., ,''x''<sub>''k''</sub>, and 2<sup>''n''−''k''</sup> columns representing the values of the other variables.

			Let ''A''<sub>1</sub>, ..., ''A''<sub>''p''</sub> be a partition of the rows of this table such that for ''i'' < ''p'', \|''A''<sub>''i''</sub> = ''s'' and <math>\|A_p\|=s'\leq s</math>.
			Let ''&fnof;''<sub>''i''</sub>(''x'') = ''&fnof;''(''x'') [[iff]] ''x'' ∈ ''A''<sub>''i''</sub>.

			Moreover, let <math>B_{i,w}</math> be the set of the columns whose intersection with <math>A_i</math> is <math>w</math>.

			[[Category:Boolean algebra]]
			[[Category:Circuit complexity]]

en>Magioladitis: clean up using AWB (8279)

2012-08-22T14:17:36Z

clean up using AWB (8279)

New page

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