Stochastic computing - Revision history

en>AnomieBOT: Dating maintenance tags: {{Cn}}

2014-10-09T16:26:56Z

Dating maintenance tags: {{Cn}}

← Older revision		Revision as of 18:26, 9 October 2014
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	~~In [[mathematics]]~~, the '~~''distortion''' is a measure~~ of ~~the amount by which~~ a ~~[[function (mathematics)\|function]] from the [[Euclidean plane]] to itself distorts circles to ellipses~~. If the ~~distortion of a function is equal~~ to ~~one, then it is [[conformal map\|conformal]]; if~~ the ~~distortion is bounded~~ and the ~~function is a [[homeomorphism]], then it is [[quasiconformal mapping\|quasiconformal]]~~. ~~The distortion of a function ƒ of the plane is given by~~		They're always ready to help, and they're always making changes to the site to make sure you won't have troubles in the first place. You may discover this probably the most time-consuming part of building a Word - Press MLM website. The Word - Press Dashboard : an administrative management tool that supports FTP content upload 2. If you are using videos on your site then this is the plugin to use. Also our developers are well convergent with the latest technologies and bitty-gritty of wordpress website design and promises to deliver you the best solution that you can ever have. <br><br>Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. Wordpress have every reason with it which promote wordpress development. Some plugins ask users to match pictures or add numbers, and although effective, they appear unprofessional and unnecessary. 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. Aided by the completely foolproof j - Query color selector, you're able to change the colors of factors of your theme a the click on the screen, with very little previous web site design experience. <br><br>Usually, Wordpress owners selling the ad space on monthly basis and this means a residual income source. As of now, Pin2Press is getting ready to hit the market. I've applied numerous Search engine optimization-ready Word - Press themes and I can say from knowledge that I consider the Genesis Search engine marketing panel one particular of the simplest to use. The first thing you need to do is to choose the right web hosting plan. After that the developer adds the unordered list for navigations. <br><br>Word - Press has plenty of SEO benefits over Joomla and Drupal. 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. In case you loved this article and you want to receive much more information relating to [http://xd03.com/WordpressBackup479451/ wordpress backup plugin] assure visit our own web site. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc, yet some are looking for economical solutions. See a product, take a picture, and it gives you an Amazon price for that product, or related products. <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. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. Word - Press can also be quickly extended however improvement API is not as potent as Joomla's. And, it is better that you leave it on for the duration you are writing plugin code. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.

	:<~~math~~>~~H(z,f) = \limsup_{r\to 0}\frac{\max_{\|h\|=r}\|f(z+h)-f(z)\|}{\min_{\|h\|=r}\|f(z+h)-f(z)\|}~~<~~/math~~>

	~~which~~ is the ~~limiting eccentricity of~~ the ~~ellipse produced~~ by ~~applying ƒ~~ to ~~small circles centered at ''z''~~. ~~This geometrical definition is often very difficult~~ to ~~work with~~, ~~and the necessary analytical features~~ can ~~be extrapolated~~ to the ~~following definition. A mapping ''ƒ'' : Ω → ''~~'~~R'''<sup>2</sup> from an open domain in the plane~~ to the ~~plane has finite distortion at~~ a ~~point ''x'' ∈ Ω if ''ƒ'' is in~~ the ~~[[Sobolev space]] W{{su\|p=1~~,~~1\|b=loc}}(Ω, '''R'''~~<~~sup~~>2<~~/sup~~>), the ~~[[Jacobian matrix~~ and ~~determinant\|Jacobian determinant]] J(''x'',ƒ) is locally integrable and does not change sign in Ω, and there is~~ a ~~measurable function ''K''(''x'') ≥ 1 such that~~

	~~:<math>\|Df(x)\|^2 \le K(x)\|J(x,f)\| \, </math>~~

	~~almost everywhere~~. ~~Here ''Df'' is the [[weak derivative]]~~ of ƒ, ~~and \|''Df''\|~~ is the ~~[[Hilbert–Schmidt norm]]~~.

	~~For functions on a higher~~-~~dimensional [[Euclidean space]] '''R'''<sup>''n''</sup>, there are more measures~~ of ~~distortion because there are more than two [[principal axes]] of a symmetric tensor~~. The ~~pointwise information~~ is ~~contained in~~ the ~~''distortion tensor''~~

	~~:<math>G(x,f) =~~
	~~\begin{cases}~~
	~~\|J(x,f)^{-2/n}D^Tf(x)Df(x)&\text{if }J(x,f)\not=0\\~~
	~~I &\text{if }J(x,f)=0~~.
	~~\end{cases}~~<~~/math~~>

	~~The outer distortion ''K''~~<~~sub>O</sub~~> and ~~inner distortion ''K''<sub>I</sub>~~ are ~~defined via~~ the [~~[Raleigh quotient]]s~~

	:~~<math>K_O(x) = \sup_{\xi\not=0}\frac{\langle G(x)\xi,\xi\rangle^{n~~/~~2}}{\|\xi\|^n},\quad K_O(x) = \sup_{\xi\not=0}\frac{\langle G^{-1}(x)\xi,\xi\rangle^{n~~/~~2}}{\|\xi\|^n}~~.</~~math>~~

	~~The outer distortion~~ can ~~also be characterized by means of an inequality similar~~ to ~~that given in the two-dimensional case~~. ~~If Ω is an open set in '''R'''<sup>''n''</sup>~~, ~~then~~ a ~~function {{nowrap\|&fnof; ∈ W{{su\|p=1~~,~~1\|b=loc}}(Ω~~,~~'''R'''~~<~~sup~~>~~''n''~~<~~/sup~~>~~)}} has finite distortion if its Jacobian is locally integrable~~ and ~~does not change sign, and there is~~ a ~~measurable function ''K''<sub>''O''</sub> (~~the ~~outer distortion) such that~~

	:~~<math>\|Df(x)\|^n \le K_O(x)\|J(x,f)\| \, </math>~~

	~~almost everywhere~~.

	~~==See also==~~
	* [[Deformation (mechanics)]]

	~~==References==~~
	* {{Citation \| last1=Iwaniec \| first1=Tadeusz \| last2=Martin \| first2=Gaven \| title=Geometric function theory and non-~~linear analysis \| publisher=The Clarendon~~ Press ~~Oxford University Press \| series=Oxford Mathematical Monographs \| isbn=978-0-19-850929-5 \| mr=1859913 \| year=2001}}~~.
	*{{Citation \| last1=Reshetnyak \| first1=Yu. ~~G. \| title=Space mappings with bounded distortion \| publisher=[[American Mathematical Society]] \| location=Providence~~, ~~R.I~~. ~~\| series=Translations of Mathematical Monographs \| isbn=978-0-8218-4526-4 \| mr=994644 \| year=1989 \| volume=73}}.~~

	~~[[Category:Conformal mapping]]~~
	~~[[Category:Real analysis]]~~
	~~[[Category:Complex analysis]]~~
	~~[[Category:Topology]]~~
	~~[[Category:Measure theory]]~~
	~~[[Category:Euclidean geometry]]~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-30T10:42:26Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 12:42, 30 January 2014
Line 1:		Line 1:
	~~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~~. ~~2- Ask for~~ the ~~designs and graphics that will be provided along with the Word~~ - ~~Press theme. You can customize the appearance with PSD to Word~~ - ~~Press conversion ''.~~ <br>~~<br>Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. But as expected~~ the ~~level~~ of ~~support you get with them can be hit or miss based on~~ the ~~developer~~'~~s free time and desire~~. ~~With the free Word - Press blog, you have the liberty~~ to ~~come up~~ with ~~your own personalized domain name. By purchasing Word - Press weblogs you can acquire your very own domain title and have total command of your web site. Moreover~~, ~~many Word - Press themes need to be purchased~~ and ~~designing your own WP site~~ can be ~~boring~~. <br><br>~~If you have any questions concerning~~ in ~~which and how~~ to ~~use~~ [~~http:~~/~~/topne.ws/WordpressBackup458163 backup plugin~~], ~~you can speak to us at our own webpage~~. ~~You can down load it here at this link:~~ ~~and utilize your FTP software program to upload it to your Word - Press Plugin folder. It was also~~ the ~~very first year that the category~~ of ~~Martial Arts was included in~~ the ~~Parents~~ - ~~Connect nationwide online poll~~, ~~allowing parents to vote for their favorite San Antonio Martial Arts Academy. You can now search through the thousands~~ of ~~available plugins to add all kinds~~ of ~~functionality to your Word - Press site~~. ~~User friendly features and flexibility that Word - Press has to offer~~ is ~~second to none. Socrates~~: (~~link to~~ ) ~~Originally developed for affiliate marketers~~, ~~I've used this theme again and again to develop full~~-~~fledged web sites that include static pages~~, ~~squeeze pages~~, ~~and a blog~~. <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~~)~~:. Normally~~, ~~the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website~~. ~~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>~~Millions of individuals~~ and ~~organizations are now successfully using this tool throughout the world. If you operate~~ a ~~website that~~'~~s been built on HTML then you might have to witness traffic losses because such a site isn~~'~~t competent enough in grabbing~~ the ~~attention of potential consumers~~. ~~Useful Plugins Uber~~ - ~~Menu Top Megamenu Now it is the time of sticky Top navbar~~. ~~You should stay away from plugins that are full of flaws and bugs~~. 95, ~~and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals~~.		In [[mathematics]], the '''distortion''' is a measure of the amount by which a [[function (mathematics)\|function]] from the [[Euclidean plane]] to itself distorts circles to ellipses. If the distortion of a function is equal to one, then it is [[conformal map\|conformal]]; if the distortion is bounded and the function is a [[homeomorphism]], then it is [[quasiconformal mapping\|quasiconformal]]. The distortion of a function ƒ of the plane is given by

			:<math>H(z,f) = \limsup_{r\to 0}\frac{\max_{\|h\|=r}\|f(z+h)-f(z)\|}{\min_{\|h\|=r}\|f(z+h)-f(z)\|}</math>

			which is the limiting eccentricity of the ellipse produced by applying ƒ to small circles centered at ''z''. This geometrical definition is often very difficult to work with, and the necessary analytical features can be extrapolated to the following definition. A mapping ''ƒ'' : Ω → '''R'''<sup>2</sup> from an open domain in the plane to the plane has finite distortion at a point ''x'' ∈ Ω if ''ƒ'' is in the [[Sobolev space]] W{{su\|p=1,1\|b=loc}}(Ω, '''R'''<sup>2</sup>), the [[Jacobian matrix and determinant\|Jacobian determinant]] J(''x'',ƒ) is locally integrable and does not change sign in Ω, and there is a measurable function ''K''(''x'') ≥ 1 such that

			:<math>\|Df(x)\|^2 \le K(x)\|J(x,f)\| \, </math>

			almost everywhere. Here ''Df'' is the [[weak derivative]] of ƒ, and \|''Df''\| is the [[Hilbert–Schmidt norm]].

			For functions on a higher-dimensional [[Euclidean space]] '''R'''<sup>''n''</sup>, there are more measures of distortion because there are more than two [[principal axes]] of a symmetric tensor. The pointwise information is contained in the ''distortion tensor''

			:<math>G(x,f) =
			\begin{cases}
			\|J(x,f)^{-2/n}D^Tf(x)Df(x)&\text{if }J(x,f)\not=0\\
			I &\text{if }J(x,f)=0.
			\end{cases}</math>

			The outer distortion ''K''<sub>O</sub> and inner distortion ''K''<sub>I</sub> are defined via the [[Raleigh quotient]]s

			:<math>K_O(x) = \sup_{\xi\not=0}\frac{\langle G(x)\xi,\xi\rangle^{n/2}}{\|\xi\|^n},\quad K_O(x) = \sup_{\xi\not=0}\frac{\langle G^{-1}(x)\xi,\xi\rangle^{n/2}}{\|\xi\|^n}.</math>

			The outer distortion can also be characterized by means of an inequality similar to that given in the two-dimensional case. If Ω is an open set in '''R'''<sup>''n''</sup>, then a function {{nowrap\|&fnof; ∈ W{{su\|p=1,1\|b=loc}}(Ω,'''R'''<sup>''n''</sup>)}} has finite distortion if its Jacobian is locally integrable and does not change sign, and there is a measurable function ''K''<sub>''O''</sub> (the outer distortion) such that

			:<math>\|Df(x)\|^n \le K_O(x)\|J(x,f)\| \, </math>

			almost everywhere.

			==See also==
			* [[Deformation (mechanics)]]

			==References==
			* {{Citation \| last1=Iwaniec \| first1=Tadeusz \| last2=Martin \| first2=Gaven \| title=Geometric function theory and non-linear analysis \| publisher=The Clarendon Press Oxford University Press \| series=Oxford Mathematical Monographs \| isbn=978-0-19-850929-5 \| mr=1859913 \| year=2001}}.
			*{{Citation \| last1=Reshetnyak \| first1=Yu. G. \| title=Space mappings with bounded distortion \| publisher=[[American Mathematical Society]] \| location=Providence, R.I. \| series=Translations of Mathematical Monographs \| isbn=978-0-8218-4526-4 \| mr=994644 \| year=1989 \| volume=73}}.

			[[Category:Conformal mapping]]
			[[Category:Real analysis]]
			[[Category:Complex analysis]]
			[[Category:Topology]]
			[[Category:Measure theory]]
			[[Category:Euclidean geometry]]

en>Helpful Pixie Bot: ISBNs (Build KH)

2012-05-11T23:52:50Z

ISBNs (Build KH)

New page

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. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. You can customize the appearance with PSD to Word - Press conversion ''. Most Word - Press web developers can provide quality CMS website solutions and they price their services at reasonable rates. But as expected the level of support you get with them can be hit or miss based on the developer's free time and desire. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. By purchasing Word - Press weblogs you can acquire your very own domain title and have total command of your web site. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. If you have any questions concerning in which and how to use [http://topne.ws/WordpressBackup458163 backup plugin], you can speak to us at our own webpage. You can down load it here at this link: and utilize your FTP software program to upload it to your Word - Press Plugin folder. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. User friendly features and flexibility that Word - Press has to offer is second to none. Socrates: (link to ) Originally developed for affiliate marketers, I've used this theme again and again to develop full-fledged web sites that include static pages, squeeze pages, and a blog. 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):. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. 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. Millions of individuals and organizations are now successfully using this tool throughout the world. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. Useful Plugins Uber - Menu Top Megamenu Now it is the time of sticky Top navbar. You should stay away from plugins that are full of flaws and bugs. 95, and they also supply studio press discount code for their clients, coming from 10% off to 25% off upon all theme deals.