NumXL - Revision history

en>Cranberry Products: Reverted 1 edit by Cab driver Champion (talk) to last revision by Filedelinkerbot. (TW)

2014-11-29T00:49:45Z

Reverted 1 edit by Cab driver Champion (talk) to last revision by Filedelinkerbot. (TW)

← Older revision		Revision as of 02:49, 29 November 2014
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	~~A certain family~~ of ~~[[BCH code]]s have a particularly useful property, which is~~ that		Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. When you loved this short article along with you wish to get details with regards to [http://ad4.fr/wordpress_backup_2669238 wordpress dropbox backup] kindly go to the site. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>
	~~treated as [[linear operator]]s~~, ~~their [[dual basis\|dual operators]] turns their input into an <math>\ell</math>-wise [[pairwise independence\|independent source]]~~. ~~That~~ is, the ~~set of vectors from the input [[vector space]] are mapped~~ to ~~an <math>\ell</math>~~-~~wise independent source~~. ~~The proof of~~ this ~~fact below as~~ the ~~following Lemma~~ and ~~Corollary is useful~~ in ~~derandomizing~~ the ~~algorithm for a~~ <~~math~~>~~1-2^{-\ell}~~<~~/math~~>~~-approximation to [[MAXEkSAT]].~~

	~~==Lemma==~~		Creating a website from scratch can be such a pain. If a newbie missed a certain part of the video then they could always rewind. Which is perfect for building a mobile site for business use. You can add new functionalities and edit the existing ones to suit your changing business needs. 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>Minor and medium sized corporations also have a lot to obtain by shelling out in a very good website. As of now, Pin2Press is getting ready to hit the market. You've got invested a great cope of time developing and producing up the topic substance. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. After that the developer adds the unordered list for navigations. <br><br>Whether your Word - Press themes is premium or not, but nowadays every theme is designed with widget-ready. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. However, you may not be able to find a theme that is in sync with your business. It's now become a great place to sell it thanks to Woo - Commerce. The Pakistani culture is in demand of a main surgical treatment. <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. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. 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.

	~~Let <math>C\subseteq F_2^n</math>~~ be a ~~linear code such that <math>C^\perp </math> has distance greater than <math> \ell +1</math>~~. ~~Then <math>C</math> is an <math>\ell</math>-wise independent source.~~

	~~==Proof~~ of ~~Lemma==~~

	~~It is sufficient to show that given any <math>k \times l</math> matrix ''M'', where ''k'' is greater than or equal to ''l'', such that~~ the ~~rank of ''M''~~ is ~~''l'',~~ for ~~all <math>x\in F_2^k</math>, <math>xM</math> takes every value in <math>F_2^l</math>~~ the ~~same number of times~~.

	~~Since ''M''~~ has ~~rank ''l''~~, ~~we can write ''M'' as two matrices of~~ the ~~same size,~~ <~~math~~>~~M_1~~<~~/math~~> and ~~<math>M_2</math>~~, ~~where <math>M_1</math> has rank equal~~ to '~~'l''. This means that <math>xM</math> can be rewritten as <math>x_1M_1 + x_2M_2</math> for some <math>x_1</math>~~ and ~~<math>x_2</math>~~.

	~~If we consider ''M'' written with respect to~~ a ~~basis where~~ the ~~first ''l'' rows are~~ the ~~identity matrix, then <math>x_1</math> has zeros wherever <math>M_2</math> has nonzero rows, and <math>x_2</math> has zeros wherever <math>M_1</math> has nonzero rows.~~

	~~Now any value ''y'', where <math>y=xM</math>,~~ can be ~~written as <math>x_1M_1+x_2M_2</math> for some vectors <math>x_1, x_2</math>~~.

	~~We can rewrite this as:~~

	~~<math>x_1M_1 = y - x_2M_2</math>~~

	~~Fixing~~ the ~~value of~~ the ~~last <math>k-l</math> coordinates of~~
	~~<math>x_2\in F_2^k</math> (note that there are exactly <math>2^{k-l}</math>~~
	~~such choices), we can rewrite this equation again as:~~

	~~<math>x_1M_1 = b</math>~~ for ~~some ''b''~~.

	~~Since~~ <~~math~~>~~M_1~~<~~/math~~> ~~has rank equal to ''l'', there~~
	is ~~exactly one solution <math>x_1</math>~~, ~~so the total number of solutions~~ is ~~exactly <math>2^{k~~-~~l}</math>, proving~~ the ~~lemma~~.

	~~==Corollary==~~

	~~Recall~~ that ~~BCH<sub>2,~~'~~'m'',''d''</sub>~~ is ~~an <math> [n=2^m, n-1 -\lceil {d-2}/2\rceil m, d]_2</math> linear code~~.

	~~Let~~ <~~math~~>~~C^\perp~~<~~/math~~> ~~be BCH<sub~~>2,~~log ''n''~~,~~''ℓ''+1</sub>. Then <math>C</math>~~ is ~~an <math>\ell</math>-wise independent source of size <math>O(n^{\lfloor \ell/2 \rfloor})</math>~~.

	~~==Proof of Corollary==~~

	~~The dimension ''d'~~' of ~~''C'' is just <math>\lceil{(\ell +1~~ -~~2)/{2}}\rceil \log n +1 </math>~~. ~~So <math>d = \lceil {(\ell -1)}/2\rceil \log n +1 = \lfloor \ell/2 \rfloor \log n +1</math>.~~

	~~So the cardinality~~ of ~~<math>C</math> considered as~~ a ~~set~~ is ~~just~~
	~~<math> 2^{d}=O(n^{\lfloor \ell/2 \rfloor})</math>, proving~~ the ~~Corollary~~.

	~~== References ==~~
	~~[http://www.cse.buffalo.edu/~atri/courses/coding~~-~~theory/ Coding Theory notes at University at Buffalo]~~

	~~[http://people~~.~~csail.mit.edu/madhu/FT01/course.html/ Coding Theory notes at MIT]~~

	~~[[Category:Article proofs]]~~

en>Spiderfinancial: linked feature with an existing wiki page

2013-08-07T12:56:47Z

linked feature with an existing wiki page

← Older revision		Revision as of 14:56, 7 August 2013
Line 1:		Line 1:
	~~53 year old Osteopath Gordon Pale~~ from St. ~~Catharines~~, has ~~several pursuits including genealogy~~, ~~pawn shop~~ and ~~horse racing~~. ~~Recollects what~~ a ~~striking location it was having gone~~ to ~~Comoé National Park~~.<br><br>~~my site~~: [~~https~~://~~b5b6a2804591849e9557635b349492d48bbc6965~~.~~googledrive~~.~~com~~/~~host~~/~~0B0ArFwQ_4S04VVpodHdkb25kN0k~~/~~Pawn-Shop-Phoenix Extra resources~~]		A certain family of [[BCH code]]s have a particularly useful property, which is that
			treated as [[linear operator]]s, their [[dual basis\|dual operators]] turns their input into an <math>\ell</math>-wise [[pairwise independence\|independent source]]. That is, the set of vectors from the input [[vector space]] are mapped to an <math>\ell</math>-wise independent source. The proof of this fact below as the following Lemma and Corollary is useful in derandomizing the algorithm for a <math>1-2^{-\ell}</math>-approximation to [[MAXEkSAT]].

			==Lemma==

			Let <math>C\subseteq F_2^n</math> be a linear code such that <math>C^\perp </math> has distance greater than <math> \ell +1</math>. Then <math>C</math> is an <math>\ell</math>-wise independent source.

			==Proof of Lemma==

			It is sufficient to show that given any <math>k \times l</math> matrix ''M'', where ''k'' is greater than or equal to ''l'', such that the rank of ''M'' is ''l'', for all <math>x\in F_2^k</math>, <math>xM</math> takes every value in <math>F_2^l</math> the same number of times.

			Since ''M'' has rank ''l'', we can write ''M'' as two matrices of the same size, <math>M_1</math> and <math>M_2</math>, where <math>M_1</math> has rank equal to ''l''. This means that <math>xM</math> can be rewritten as <math>x_1M_1 + x_2M_2</math> for some <math>x_1</math> and <math>x_2</math>.

			If we consider ''M'' written with respect to a basis where the first ''l'' rows are the identity matrix, then <math>x_1</math> has zeros wherever <math>M_2</math> has nonzero rows, and <math>x_2</math> has zeros wherever <math>M_1</math> has nonzero rows.

			Now any value ''y'', where <math>y=xM</math>, can be written as <math>x_1M_1+x_2M_2</math> for some vectors <math>x_1, x_2</math>.

			We can rewrite this as:

			<math>x_1M_1 = y - x_2M_2</math>

			Fixing the value of the last <math>k-l</math> coordinates of
			<math>x_2\in F_2^k</math> (note that there are exactly <math>2^{k-l}</math>
			such choices), we can rewrite this equation again as:

			<math>x_1M_1 = b</math> for some ''b''.

			Since <math>M_1</math> has rank equal to ''l'', there
			is exactly one solution <math>x_1</math>, so the total number of solutions is exactly <math>2^{k-l}</math>, proving the lemma.

			==Corollary==

			Recall that BCH<sub>2,''m'',''d''</sub> is an <math> [n=2^m, n-1 -\lceil {d-2}/2\rceil m, d]_2</math> linear code.

			Let <math>C^\perp</math> be BCH<sub>2,log ''n'',''ℓ''+1</sub>. Then <math>C</math> is an <math>\ell</math>-wise independent source of size <math>O(n^{\lfloor \ell/2 \rfloor})</math>.

			==Proof of Corollary==

			The dimension ''d'' of ''C'' is just <math>\lceil{(\ell +1 -2)/{2}}\rceil \log n +1 </math>. So <math>d = \lceil {(\ell -1)}/2\rceil \log n +1 = \lfloor \ell/2 \rfloor \log n +1</math>.

			So the cardinality of <math>C</math> considered as a set is just
			<math> 2^{d}=O(n^{\lfloor \ell/2 \rfloor})</math>, proving the Corollary.

			== References ==
			[http://www.cse.buffalo.edu/~atri/courses/coding-theory/ Coding Theory notes at University at Buffalo]

			[http://people.csail.mit.edu/madhu/FT01/course.html/ Coding Theory notes at MIT]

			[[Category:Article proofs]]

en>FrescoBot: Bot: link syntax/spacing and minor changes

2012-08-12T13:58:01Z

Bot: link syntax/spacing and minor changes

New page

53 year old Osteopath Gordon Pale from St. Catharines, has several pursuits including genealogy, pawn shop and horse racing. Recollects what a striking location it was having gone to Comoé National Park.<br><br>my site: [https://b5b6a2804591849e9557635b349492d48bbc6965.googledrive.com/host/0B0ArFwQ_4S04VVpodHdkb25kN0k/Pawn-Shop-Phoenix Extra resources]