Dixmier trace - Revision history

en>Yobot: /* Definition */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T09:59:54Z

Definition: WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 11:59, 5 May 2014
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	In [~~[mathematics]~~]~~, the '''collage theorem''' characterises an~~ [~~[iterated function system]~~] ~~whose~~ [~~[attractor~~]~~] is close, relative to the [~~[~~Hausdorff metric]], to a given set~~. The IFS described is composed of [[contraction mapping\|contractions]] whose images, as a '''collage''' or [[Union (set theory)\|union]] when mapping the given set, are arbitrarily close to the given set. ~~It is typically used in [[fractal compression~~]].		I am 34 years old and my name is Alfonzo Shores. I life in Groningen (Netherlands).<br>xunjie 女性と指摘していることを発見の品質に関する調査を実施したアンジェラベイビーとジョーイ。
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	~~== Statement of the theorem ==~~		Visit my webpage: [http://www.rheintalverlag.ch/newsletter/gaga.php ガガミラノ]
	Let <math>\mathbb{X}</math> be a [[complete metric space]]. Let <math>L \in H(\mathbb{X})</math> be given, and let <math>\epsilon \geq 0</math> be given. Choose an [[iterated function system]] (IFS) <math>\{ \mathbb{X} ; w_1, w_2, \dots, w_N\}</math> with contractivity factor <math>0 \leq s < 1</math>, so that

	~~:<math>h\left( L, \bigcup_{n=1}^N w_n (L) \right) \leq \varepsilon,</math>~~

	~~where <math>h(d)</math> is the Hausdorff metric. Then~~

	:~~<math>h(L,A) \leq \frac{\varepsilon}{1-s}</math>~~

	~~where ''A'' is the attractor of the IFS. Equivalently,~~

	~~:<math>h(L,A) \leq (1-s)^{-1} h\left(L,\cup_{n=1}^N w_n(L)\right) \quad \text{for all } L \in {H}(\mathbb{X}).</math>~~

	~~==See also==~~
	* [[Michael Barnsley]]

	~~== References ==~~

	*{{cite book
	~~\| author = Barnsley, Michael.~~
	~~\| title = Fractals Everywhere~~
	~~\| year = 1988~~
	~~\| publisher = Academic Press, Inc.~~
	~~\| isbn = 0-12-079062-9~~
	}}
	~~==External links==~~
	* [http://www.~~cut-the-knot~~.~~org~~/~~ctk~~/~~ifs~~.~~shtml A description of the collage theorem and interactive Java applet] at [[cut-the-knot]].~~
	* [http://www.math.okstate.edu/mathdept/dynamics/lecnotes/node47.html Notes on designing IFSs to approximate real images.] {{Dead link\|date=August 2010}}
	* [http://scimath.unl.edu/MIM/files/MATExamFiles/Snyder_MAT_Exam_ExpositoryPaper.pdf Expository Paper on Fractals and Collage theorem]

	~~{{DEFAULTSORT:Collage Theorem}}~~
	~~[[Category:Fractals]]~~
	~~[[Category:Theorems in geometry]~~]


	~~{{math-stub}}~~

en>Dr.steven.lord: Added hyperlinks to page Singular trace

2013-10-02T23:58:25Z

Added hyperlinks to page Singular trace

← Older revision		Revision as of 01:58, 3 October 2013
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	~~If you are looking for a specific plugin~~, ~~then you can just search for~~ the ~~name of~~ the ~~plugin~~. ~~Affilo - Theme~~ is the ~~guaranteed mixing of wordpress theme that Mark Ling use for his internet marketing career~~. ~~Step-4 Testing:~~ It is ~~the foremost important~~ of ~~your Plugin development process. After confirming~~ the ~~account, login with your username and password at Ad - Mob. The top 4 reasons to use Business Word - Press Themes for a business website are:.~~ <br><br>Always remember that an effective linkwheel strategy strives to answer all the demands of popular search engines while reacting to the latest marketing number trends. Wordpress have every reason with it which promote wordpress development. Our Daily Deal Software plugin brings the simplicity of setting up a ~~Word - Press blog to the daily deal~~ space. ~~So if you want to create blogs or have a website for your business or for personal reasons~~, ~~you can take advantage of free Word - Press installation to get started. Akismet is really a sophisticated junk e-mail blocker~~ and ~~it's also very useful thinking about I recieve many junk e-mail comments day-to-day across my various web-sites.~~ <br><br>~~Here are a few reasons as to why people prefer Word - Press over other software's~~. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,~~which demands a experienced wordpress designer. After age 35~~, ~~18% of pregnancies will end in miscarriage. Storing write-ups in advance would have to be neccessary~~ with ~~the auto blogs. Websites using this content based strategy are always given top scores by Google.~~ <br><br>~~If you loved this informative article in addition to you want to obtain more info concerning [https~~://~~pendek~~.ga/~~wordpress_dropbox_backup_713590 wordpress dropbox backup] kindly go to~~ the ~~web site~~. ~~Whether your Word~~ - ~~Press themes is premium or not, but nowadays every theme is designed with widget~~-~~ready. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. However~~, ~~you may not be able to find a theme that is~~ in ~~sync with your business~~. ~~Fast Content Update~~ ~~- It's easy to edit or add posts with free Wordpress websites~~. ~~OSDI, a~~ ~~Wordpress Development Company~~ ~~based on ahmedabad~~, ~~India~~. ~~<br><br>Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts~~. ~~It can run as plugin~~ and ~~you can still get to that whole database just in circumstance your webhost does not have a c~~ - ~~Panel area~~. ~~Must being, it's beneficial because I don't know about you, but loading an old website~~ on ~~a mobile, having~~ to ~~scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline~~. ~~And, it is better that you leave it on for the duration you are writing plugin code~~. ~~Verify whether your company has a team of developers or programmers having hands-~~on ~~experience~~ and ~~knowledge about all Word~~ - ~~Press concepts.~~		In [[mathematics]], the '''collage theorem''' characterises an [[iterated function system]] whose [[attractor]] is close, relative to the [[Hausdorff metric]], to a given set. The IFS described is composed of [[contraction mapping\|contractions]] whose images, as a '''collage''' or [[Union (set theory)\|union]] when mapping the given set, are arbitrarily close to the given set. It is typically used in [[fractal compression]].

			== Statement of the theorem ==
			Let <math>\mathbb{X}</math> be a [[complete metric space]]. Let <math>L \in H(\mathbb{X})</math> be given, and let <math>\epsilon \geq 0</math> be given. Choose an [[iterated function system]] (IFS) <math>\{ \mathbb{X} ; w_1, w_2, \dots, w_N\}</math> with contractivity factor <math>0 \leq s < 1</math>, so that

			:<math>h\left( L, \bigcup_{n=1}^N w_n (L) \right) \leq \varepsilon,</math>

			where <math>h(d)</math> is the Hausdorff metric. Then

			:<math>h(L,A) \leq \frac{\varepsilon}{1-s}</math>

			where ''A'' is the attractor of the IFS. Equivalently,

			:<math>h(L,A) \leq (1-s)^{-1} h\left(L,\cup_{n=1}^N w_n(L)\right) \quad \text{for all } L \in {H}(\mathbb{X}).</math>

			==See also==
			* [[Michael Barnsley]]

			== References ==

			*{{cite book
			\| author = Barnsley, Michael.
			\| title = Fractals Everywhere
			\| year = 1988
			\| publisher = Academic Press, Inc.
			\| isbn = 0-12-079062-9
			}}
			==External links==
			* [http://www.cut-the-knot.org/ctk/ifs.shtml A description of the collage theorem and interactive Java applet] at [[cut-the-knot]].
			* [http://www.math.okstate.edu/mathdept/dynamics/lecnotes/node47.html Notes on designing IFSs to approximate real images.] {{Dead link\|date=August 2010}}
			* [http://scimath.unl.edu/MIM/files/MATExamFiles/Snyder_MAT_Exam_ExpositoryPaper.pdf Expository Paper on Fractals and Collage theorem]

			{{DEFAULTSORT:Collage Theorem}}
			[[Category:Fractals]]
			[[Category:Theorems in geometry]]


			{{math-stub}}

en>Chris Howard: added link noncommutative geometry

2012-07-09T20:22:47Z

added link noncommutative geometry

New page

If you are looking for a specific plugin, then you can just search for the name of the plugin. Affilo - Theme is the guaranteed mixing of wordpress theme that Mark Ling use for his internet marketing career. Step-4 Testing: It is the foremost important of your Plugin development process. After confirming the account, login with your username and password at Ad - Mob. The top 4 reasons to use Business Word - Press Themes for a business website are:. Always remember that an effective linkwheel strategy strives to answer all the demands of popular search engines while reacting to the latest marketing number trends. Wordpress have every reason with it which promote wordpress development. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. Akismet is really a sophisticated junk e-mail blocker and it's also very useful thinking about I recieve many junk e-mail comments day-to-day across my various web-sites. Here are a few reasons as to why people prefer Word - Press over other software's. Now if we talk about them one by one then -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,which demands a experienced wordpress designer. After age 35, 18% of pregnancies will end in miscarriage. Storing write-ups in advance would have to be neccessary with the auto blogs. Websites using this content based strategy are always given top scores by Google. If you loved this informative article in addition to you want to obtain more info concerning [https://pendek.ga/wordpress_dropbox_backup_713590 wordpress dropbox backup] kindly go to the web site. Whether your Word - Press themes is premium or not, but nowadays every theme is designed with widget-ready. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. However, you may not be able to find a theme that is in sync with your business. Fast Content Update - It's easy to edit or add posts with free Wordpress websites. OSDI, a Wordpress Development Company based on ahmedabad, India. Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. And, it is better that you leave it on for the duration you are writing plugin code. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts.