Conditional mutual information - Revision history

en>Rjwilmsi: Journal cites, Added 1 doi to a journal cite using AWB (10498)

2014-11-22T12:16:33Z

Journal cites, Added 1 doi to a journal cite using AWB (10498)

← Older revision		Revision as of 14:16, 22 November 2014
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85.171.168.212: edit multivariate mutual information formula for consistency

2014-03-05T12:29:07Z

edit multivariate mutual information formula for consistency

← Older revision		Revision as of 14:29, 5 March 2014
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	~~In [[sheaf theory]] (an area of mathematics)~~, ~~a '''sheaf extension''~~' ~~is a way of describing a [[sheaf (mathematics)\|sheaf]]~~ in ~~terms~~ of ~~a [[subsheaf]] and a [[quotient sheaf]]~~, ~~analogous~~ to a ~~how~~ a ~~[[group extension]] describes a [[group (mathematics)\|group]] in terms~~ of ~~a [[subgroup]],~~ and ~~a [[quotient~~ group]].		By investing in a premium Word - Press theme, you're investing in the future of your website. Also, you may want to opt for a more professioanl theme if you are planning on showing your site off to a high volume of potential customers each day. Your parishioners and certainly interested audience can come in to you for further information from the group and sometimes even approaching happenings and systems with the church. They found out all the possible information about bringing up your baby and save money at the same time. You can customize the appearance with PSD to Word - Press conversion ''. <br><br>Thus, it is imperative that you must Hire Word - Press Developers who have the expertise and proficiency in delivering theme integration and customization services. Infertility can cause a major setback to the couples due to the inability to conceive. A Wordpress plugin is a software that you can install into your Wordpress site. Now, I want to anxiety that not every single query will be answered. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business. <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. We can active Akismet from wp-admin > Plugins > Installed Plugins. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. Converting HTML to Word - Press theme for your website can allow you to enjoy the varied Word - Press features that aid in consistent growth your online business. <br><br>Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. The templates are designed to be stand alone pages that have a different look and feel from the rest of your website. Word - Press is the most popular open source content management system (CMS) in the world today. This includes enriching the content with proper key words, tactfully defining the tags and URL. <br><br>You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Word - Press can also be quickly extended however improvement API is not as potent as Joomla's. Word - Press is the most popular personal publishing platform which was launched in 2003. Your topic is going to be the basis of your site's name If you beloved this article so you would like to be given more info regarding [http://webmdbook.com/index.php?do=/profile-13417/info/ backup plugin] generously visit the web site. .

	~~==Definition==~~
	~~Let ''X'' be a scheme,~~ and ~~let ''F'', ''H'' be sheaves (of modules) on ''X''~~. ~~An '''extension''' of ''H'' by ''F'' is a [[short exact sequence]] of sheaves~~

	~~: <math>0 \rightarrow F \rightarrow G \rightarrow H \rightarrow 0.</math>~~

	~~Note that an extension is not determined by~~ the ~~sheaf~~ ''~~G'' alone: The morphisms are also important~~.

	~~A simple example of an extension of ''H'' by ''F'' is the sequence~~

	: <~~math~~>~~0 \rightarrow F \rightarrow F \bigoplus H \rightarrow H \rightarrow 0~~ <~~/math~~>

	~~where the second arrow~~ is the ~~inclusion~~ and the ~~fourth arrow is~~ the ~~projection onto the second summand~~. ~~This extension~~ is ~~sometimes called '''trivial'''~~.

	~~==Properties==~~
	~~As with group extensions~~, ~~if we fix ''F'' and ''H''~~, ~~then all (equivalence classes of) possible extensions of ''H'' by ''F'' form an [[abelian group]]~~. ~~This group is isomorphic to the [[Ext functor\|Ext group]]~~ <~~math~~>~~\mathrm{Ext}^1(H,F)~~<~~/math~~>, ~~where~~ the ~~identity element~~ in ~~<math~~>~~\mathrm{Ext}^1(H~~,~~F)</math> corresponds~~ to the ~~trivial extension~~.

	In the ~~case where ''H'' is the [[structure sheaf]]~~ <~~math~~> ~~\mathcal{O}_X~~ <~~/math~~>~~, we~~ have ~~<math>H^1(X, F) \cong \mathrm{Ext}^1~~(~~\mathcal{O}_X,F~~) ~~</math>~~, so the ~~group of extensions of~~ <~~math~~>~~\mathcal{O}_X~~<~~/math~~> ~~by ''F'' is also isomorphic to the first [[sheaf cohomology]] group with coefficients~~ in ~~''F''~~.

	~~==Generalization==~~

	~~The definition of~~ an ~~extension~~ and ~~the correspondence between extensions~~ and ~~Ext groups~~ can be ~~generalized~~ to [~~[abelian category\|abelian categories]], of which sheaves of modules are special instances~~.

	=~~= See also ==~~
	*[[Ext functor]]

	~~==References==~~
	* {{Citation \| last1=Hartshorne \| first1=Robin \| author1-~~link=Robin Hartshorne \| title=[[Algebraic Geometry (book)\|Algebraic Geometry]~~] ~~\| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| isbn=978-0-387-90244-9 \| oclc=13348052 \| id={{MathSciNet \| id = 0463157}} \| year=1977}}, in~~ the ~~algebraic-geometric setting, i~~.e. ~~referring to the [[Zariski topology]]~~
	* {{Weibel IHA}}


	~~[[Category:Sheaf theory]]~~
	~~[[Category:Algebraic geometry]]~~
	~~[[Category:Homological algebra]]~~

109.67.12.191: /* Definition */

2013-09-05T16:11:59Z

Definition

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en>Yobot: /* More general definition */WP:CHECKWIKI error fix 61 ixes + general fixes (BRFA 16) using AWB (7800)

2011-08-04T20:28:18Z

More general definition: WP:CHECKWIKI error fix 61 ixes + general fixes (BRFA 16) using AWB (7800)

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