Weak gravitational lensing - Revision history

en>Tom.Reding: Removed 12 accessdate/format/url errors to unique, persistent, available sources as per Help:CS1 errors#accessdate missing url

2015-01-12T21:20:09Z

Removed 12 accessdate/format/url errors to unique, persistent, available sources as per Help:CS1 errors#accessdate missing url

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128.189.187.104: /* Weak lensing by clusters of galaxies */ links

2014-02-12T09:18:42Z

Weak lensing by clusters of galaxies: links

← Older revision		Revision as of 11:18, 12 February 2014
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	~~In [[mathematics]]~~, ~~a collection of [[real number]]s is '''rationally independent''' if none of them can be written as a linear combination~~ of the ~~other numbers in the collection with~~ [~~[rational number\|rational]] coefficients. A collection of numbers which is not rationally independent is called '''rationally dependent'''~~. ~~For instance we have the following example~~.		World Monetary Community National Bank (WFNNB), issuer of Vogue Bug Credit score Playing cards, sent an e mail assertion to customers on April 5 relating to the Epsilon email hack last week. The company warned customers “your e mail handle and/or your title could have been included on this [http://Www.Ehow.com/search.html?s=compromised+email compromised email] file.”<br><br>After skipping a day, on April 25 Sony realized that user knowledge was compromised, however they did not make that announcement until Tuesday, April 26. Lastly, Sony lets PS3 PSN customers know that their data had been stolen. Finally, on Friday, April 29, hackers try to hold PS3 PSN consumer's bank cards for ransom. Nevertheless, Sony claimed that the credit card data was encrypted, so they did not pay the ransom. For me, playing the Monk looks like practicing Kungfu. He performs melee actions when encountering enemies. His skills principally remind me of Kungfu-themed movies. But overall, I believe he isn't a most popular choice for any old avid gamers of Eternity Warriors. Throughout the game, unveil the mysteries surrounding your warriors<br><br>This could indicate that whoever took Holly may very well be on the run, and maybe just isn't even a local. Why would a neighborhood to the Darden and Parsons area want a resort pass key? Perhaps they lived at home with mother and father, or maybe it was a traveler, simply passing by means of. Hopefully, investigators will keep on prime of this and extra updates will come from this significant piece of proof.<br><br>Connectez votre appareil iOS ou Android à l'ordinateur through USB. (Dungeon Hunter 4 doit être installé et fonctionner avec une connexion Web.) Each day updates to ensure the functionality of the hacking device. However that isn't enough. On September 26, 2013, Glu Video games quietly tender-launched Eternity Warriors 3 in the New Zealand App Retailer. It's one more spectacularly rendered effort that makes an attempt to blow its fans away with two extra characters (Mage and Monk), [http://www.britannica.com/search?query=incredibly+beautiful incredibly beautiful] visuals and in-game real-time chat. LOOT countless items Choose from 4 types of warriors with unique fight types Bear in mind the sole function of the leaked letter to publishers and developers is for creating open strains of communication. Trendy Fight 3 IDA Greatest Cydia Apps Greatest Cydia Sources<br><br>If you cherished this information in addition to you would want to obtain more information concerning Dungeon Hunter 4 Hack ([http://www.pinterest.com/pin/420805158906719506/ www.pinterest.com]) generously go to the internet site.
	~~:<math>~~
	~~\begin{matrix}~~
	~~\mbox{independent}\qquad\\~~
	~~\underbrace{~~
	~~\overbrace{~~
	~~3,\quad~~
	~~\sqrt{8}\quad~~
	},
	~~1+\sqrt{2}~~
	~~}\\~~
	~~\mbox{dependent}\\~~
	~~\end{matrix}~~
	</~~math>~~

	=~~=Formal definition==~~

	~~The [[real number~~]~~]s ω~~<~~sub~~>1<~~/sub~~>, ~~ω<sub>2</sub>~~, ... , ~~ω<sub>''n''</sub> are said~~ to be '~~'rationally dependent'' if there exist integers ''k''<sub>1</sub>~~, ~~''k''<sub>2</sub>~~, ... , '~~'k''<sub>''n''</sub>, not all~~ of ~~which are zero~~, ~~such that~~

	:<~~math~~> ~~k_1 \omega_1 + k_2 \omega_2 + \cdots + k_n \omega_n = 0.~~ <~~/math~~>

	~~If such integers do not exist~~, ~~then the vectors are said to be ''rationally independent'~~'. ~~This condition can be reformulated as follows: ω<sub>1</sub>~~, ~~ω<sub>2</sub>~~, ..~~. , ω~~<~~sub~~>~~''n''~~<~~/sub~~> ~~are rationally independent if~~ the ~~only ''n'~~'-~~tuple of integers~~ '~~'k''<sub>1<~~/~~sub>, ''k''<sub>2<~~/~~sub>, .~~.. ~~, ''k''<sub>''n''<~~/~~sub> such that~~

	~~:<math> k_1 \omega_1 + k_2 \omega_2 + \cdots~~ + ~~k_n \omega_n = 0 </math>~~
	~~is the [[trivial (mathematics)\|trivial solution]~~] in ~~which every ''k''~~<~~sub~~>~~''i''~~<~~/sub~~> ~~is zero.~~

	~~The real numbers form a [[vector space]] over the [[rational number]]s, and~~ this ~~is equivalent~~ to ~~the usual definition of~~ [~~[linear independence]] in this vector space~~.

	~~== See also ==~~

	*[[Linear flow on the torus]]

	~~==Bibliography==~~

	* {{cite book \| author=Anatole Katok and Boris Hasselblatt \| title= Introduction to the ~~modern theory of dynamical systems \| publisher= Cambridge \| year= 1996 \| isbn=0-521-57557-5}}~~

	~~[[Category:Dynamical systems]]~~


	~~{{mathanalysis-stub}}~~

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-31T17:08:45Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 19:08, 31 January 2014
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	~~Video Producer Grimmer from Pinawa~~, ~~really likes cryptography~~, ~~Dungeon Hunter 4 Hack (~~[~~http~~://~~www~~.~~pinterest~~.~~com~~/~~pin~~/~~420805158906719506~~/ ~~www~~.~~pinterest~~.~~com~~]~~) and cosplay~~. ~~Finished~~ a ~~cruiseship experience that included passing by Sian Ka'an~~.		In [[mathematics]], a collection of [[real number]]s is '''rationally independent''' if none of them can be written as a linear combination of the other numbers in the collection with [[rational number\|rational]] coefficients. A collection of numbers which is not rationally independent is called '''rationally dependent'''. For instance we have the following example.
			:<math>
			\begin{matrix}
			\mbox{independent}\qquad\\
			\underbrace{
			\overbrace{
			3,\quad
			\sqrt{8}\quad
			},
			1+\sqrt{2}
			}\\
			\mbox{dependent}\\
			\end{matrix}
			</math>

			==Formal definition==

			The [[real number]]s ω<sub>1</sub>, ω<sub>2</sub>, ... , ω<sub>''n''</sub> are said to be ''rationally dependent'' if there exist integers ''k''<sub>1</sub>, ''k''<sub>2</sub>, ... , ''k''<sub>''n''</sub>, not all of which are zero, such that

			:<math> k_1 \omega_1 + k_2 \omega_2 + \cdots + k_n \omega_n = 0. </math>

			If such integers do not exist, then the vectors are said to be ''rationally independent''. This condition can be reformulated as follows: ω<sub>1</sub>, ω<sub>2</sub>, ... , ω<sub>''n''</sub> are rationally independent if the only ''n''-tuple of integers ''k''<sub>1</sub>, ''k''<sub>2</sub>, ... , ''k''<sub>''n''</sub> such that

			:<math> k_1 \omega_1 + k_2 \omega_2 + \cdots + k_n \omega_n = 0 </math>
			is the [[trivial (mathematics)\|trivial solution]] in which every ''k''<sub>''i''</sub> is zero.

			The real numbers form a [[vector space]] over the [[rational number]]s, and this is equivalent to the usual definition of [[linear independence]] in this vector space.

			== See also ==

			*[[Linear flow on the torus]]

			==Bibliography==

			* {{cite book \| author=Anatole Katok and Boris Hasselblatt \| title= Introduction to the modern theory of dynamical systems \| publisher= Cambridge \| year= 1996 \| isbn=0-521-57557-5}}

			[[Category:Dynamical systems]]


			{{mathanalysis-stub}}

en>John of Reading: /* Observational products */Typo fixing, replaced: classifed → classified using AWB (8097)

2012-08-01T09:38:41Z

Observational products: Typo fixing, replaced: classifed → classified using AWB (8097)

New page

Video Producer Grimmer from Pinawa, really likes cryptography, Dungeon Hunter 4 Hack ([http://www.pinterest.com/pin/420805158906719506/ www.pinterest.com]) and cosplay. Finished a cruiseship experience that included passing by Sian Ka'an.