Self-phase modulation - Revision history

131.169.134.242: /* Theory */

2014-07-02T10:23:34Z

Theory

← Older revision		Revision as of 12:23, 2 July 2014
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	Hi there. ~~Allow~~ [http://~~cpacs~~.~~org~~/~~index.php~~?~~document_srl~~=~~90091&mid=board_zTGg26 online psychic chat~~] ~~me begin by introducing~~ the ~~author, her title is Sophia~~. ~~North Carolina is~~ the ~~location he loves most but now he~~ is ~~considering other options. My day job is an invoicing officer but I've currently~~ ~~good psychic (~~[http://www.~~familysurvivalgroup~~.com/~~easy~~-~~methods-planting-looking-backyard~~/ ~~click the next post~~]~~) utilized for an additional one. It's not a common factor~~ but ~~what I like doing~~ is to ~~climb but I don't have the~~ time ~~lately~~.<br><br>~~Also visit~~ my ~~page - psychic phone readings~~ ([http://~~www.article-galaxy~~.com/~~profile.php?a=143251 www.article-galaxy.com~~])		Hello. Allow me introduce the author. Her name is Emilia Shroyer but it's not the most feminine title out there. California is home std test kit where I've always been living and I adore each working day residing here. Managing people has been his day occupation for a while. One of [http://www.alhuloul.com/?p=235037 http://www.alhuloul.com/] the [http://Homestdtests.org/ extremely] best issues in the world for him is to gather [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=182582 http://www.january-yjm.com/xe/index.php?mid=video&document_srl=182582] badges but he is struggling to find time for it.<br><br>Visit my homepage; at home at home std test std testing ([http://Xrambo.com/user/NEme click this link here now])

en>BG19bot: /* Theory */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{2 → ² using AWB (9957)}

2014-03-01T08:48:59Z

Theory: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 2 → 2 using AWB (9957)

← Older revision		Revision as of 10:48, 1 March 2014
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	A [~~[bounded sequence\|bounded]] [[real number\|real]] [[sequence]] <math>(x_n)<~~/~~math> is said to be ''almost convergent'' to <math>L<~~/~~math> if each [[Banach limit]~~] ~~assigns~~		Hi there. Allow [http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 online psychic chat] me begin by introducing the author, her title is Sophia. North Carolina is the location he loves most but now he is considering other options. My day job is an invoicing officer but I've currently good psychic ([http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ click the next post]) utilized for an additional one. It's not a common factor but what I like doing is to climb but I don't have the time lately.<br><br>Also visit my page - psychic phone readings ([http://www.article-galaxy.com/profile.php?a=143251 www.article-galaxy.com])
	the ~~same value <math>L</math> to the sequence <math>(x_n)</math>~~.

	~~Lorentz proved that <math>(x_n)</math>~~ is ~~almost convergent if and only if~~
	~~:<math>\lim\limits_{p\to\infty} \frac{x_{n}+\ldots+x_{n+p-1}}p=L</math>~~
	~~uniformly in <math>n</math>.~~

	~~The above limit can be rewritten in detail as~~
	~~:<math>(\forall \varepsilon>0) (\exists p_0) (\forall p>p_0) (\forall n) \left\|\frac{x_{n}+\ldots+x_{n+p-1}}p-L\right\|<\varepsilon.</math>~~
	~~Almost convergence~~ is ~~studied in [[summability theory]]~~. It is an ~~example of a summability method~~
	~~which cannot be represented as a matrix method.~~

	~~==References==~~
	* G. Bennett and [[~~Nigel Kalton\|N.J. Kalton]]~~: ~~"Consistency theorems for almost convergence~~.~~" Trans~~. ~~Amer. Math. Soc., 198:23~~--~~43, 1974.~~
	* J. Boos: "Classical and modern methods in summability." Oxford University Press, New York, 2000.
	* J. Connor and K.-~~G. Grosse~~-~~Erdmann: "Sequential definitions of continuity~~ for ~~real functions~~.~~" Rocky Mt~~. ~~J. Math., 33~~(1):93-~~-121, 2003~~.
	* G.~~G. Lorentz: "A contribution to the theory of divergent sequences~~.~~" Acta Math., 80:167~~-~~-190, 1948~~.

	~~{{PlanetMath attribution\|id=7356\|title=Almost convergent}}~~

	~~[[Category:Convergence (mathematics~~)]]
	~~[[Category:Sequences and series]]~~

50.53.15.59: refs

2013-05-23T20:48:00Z

refs

← Older revision		Revision as of 22:48, 23 May 2013
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	~~Jayson Berryhill~~ is ~~how I~~'~~m called and my wife doesn~~'~~t like it at all. One of~~ the ~~extremely love psychics~~ (~~[http:~~/~~/kpupf~~.~~com~~/xe/~~talk~~/~~735373 kpupf~~.~~com]~~) ~~best things~~ in ~~the world for him~~ is ~~doing ballet~~ and ~~he'll be starting some thing else alongside with it~~. ~~North Carolina is exactly where we've been residing~~ for ~~years~~ and ~~will by no means move~~. ~~Credit authorising is [http~~:~~//Www~~.~~onbizin~~.co.~~kr/xe/?document_srl=320614 love psychics] where my main income comes from~~.~~<br><br>Here is my blog~~ - ~~online psychic ([http~~:~~//gcjcteam~~.~~org/index~~.~~php?mid~~=~~etc_video&document_srl~~=~~696611&sort_index=regdate&order_type=desc gcjcteam.org~~])		A [[bounded sequence\|bounded]] [[real number\|real]] [[sequence]] <math>(x_n)</math> is said to be ''almost convergent'' to <math>L</math> if each [[Banach limit]] assigns
			the same value <math>L</math> to the sequence <math>(x_n)</math>.

			Lorentz proved that <math>(x_n)</math> is almost convergent if and only if
			:<math>\lim\limits_{p\to\infty} \frac{x_{n}+\ldots+x_{n+p-1}}p=L</math>
			uniformly in <math>n</math>.

			The above limit can be rewritten in detail as
			:<math>(\forall \varepsilon>0) (\exists p_0) (\forall p>p_0) (\forall n) \left\|\frac{x_{n}+\ldots+x_{n+p-1}}p-L\right\|<\varepsilon.</math>
			Almost convergence is studied in [[summability theory]]. It is an example of a summability method
			which cannot be represented as a matrix method.

			==References==
			* G. Bennett and [[Nigel Kalton\|N.J. Kalton]]: "Consistency theorems for almost convergence." Trans. Amer. Math. Soc., 198:23--43, 1974.
			* J. Boos: "Classical and modern methods in summability." Oxford University Press, New York, 2000.
			* J. Connor and K.-G. Grosse-Erdmann: "Sequential definitions of continuity for real functions." Rocky Mt. J. Math., 33(1):93--121, 2003.
			* G.G. Lorentz: "A contribution to the theory of divergent sequences." Acta Math., 80:167--190, 1948.

			{{PlanetMath attribution\|id=7356\|title=Almost convergent}}

			[[Category:Convergence (mathematics)]]
			[[Category:Sequences and series]]

130.149.239.47: /* Theory */

2011-11-04T13:08:11Z

Theory

New page

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Self-phase modulation - Revision history

131.169.134.242: /* Theory */

en>BG19bot: /* Theory */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 2 → 2 using AWB (9957)

50.53.15.59: refs

130.149.239.47: /* Theory */

en>BG19bot: /* Theory */WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{2 → ² using AWB (9957)}