Diffusion capacitance - Revision history

59.177.77.84 at 17:34, 31 March 2014

2014-03-31T17:34:59Z

← Older revision		Revision as of 19:34, 31 March 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, ~~the~~ '~~''Silverman–Toeplitz theorem''', first proved by [[Otto Toeplitz]], is a result in [[summability theory]] characterizing [[Matrix (mathematics)\|matrix]] summability methods that are regular~~. ~~A regular matrix summability method~~ is ~~a matrix transformation of a [[convergent sequence]] which preserves the [[Limit of a sequence\|limit]]~~.		Hi there, I am Alyson Pomerleau and I believe it seems fairly good when you say it. My working day occupation is an information officer but I've currently applied for an additional 1. The favorite hobby for him and his children is style and he'll be starting some thing else along with it. For a while I've been in Mississippi but now I'm contemplating other options.<br><br>My web site ... [http://rv4x4.com/?q=tips-about-hobbies-easy-follow-along live psychic reading]

	~~An [[infinite matrix]] <math>(a_{i,j})_{i,j \in \mathbb{N}}</math> with [[complex number\|complex]]-valued entries defines~~ a ~~regular summability method [[if and only if]] it satisfies all of the following properties~~
	~~:<math>\lim_{i \to \infty} a_{i,j} = 0 \quad j \~~in ~~\mathbb{N}~~<~~/math~~> ~~(every column sequence converges to 0)~~
	:<~~math~~>~~\lim_{i \to \infty} \sum_{j=0}^{\infty} a_{i,j} = 1</math> (the row sums converge to 1)~~
	~~:<math>\sup_{i} \sum_{j=0}^{\infty} \vert a_{i,j} \vert < \infty</math> (the absolute row sums are bounded)~~.

	~~== References ==~~
	* Toeplitz, Otto (1911) "[http://~~matwbn~~.~~icm.edu.pl~~/~~ksiazki/pmf/pmf22/pmf2219.pdf ''Über die lineare Mittelbildungen.'']" ''Prace mat.~~-~~fiz.'', '''22''', 113–118 (the original paper in [[German language\|German]])~~
	* Silverman, Louis Lazarus (1913) "On the definition of the sum of a divergent series." University of Missouri Studies, Math. Series I, 1–96

	~~{{DEFAULTSORT:Silverman~~-~~Toeplitz theorem}}~~
	~~[[Category:Theorems in analysis]]~~
	~~[[Category:Summability methods]]~~
	~~[[Category:Summability theory]~~]

117.199.194.157 at 11:31, 6 October 2013

2013-10-06T11:31:24Z

← Older revision		Revision as of 13:31, 6 October 2013
Line 1:		Line 1:
	~~I am Ferdinand and was born on 9 August 1977~~. ~~My hobbies are Computer programming~~ and ~~Fantasy Football.~~<br><br>~~Also visit my web blog ..~~. [http://~~Ly8Hxw~~.~~com~~/~~plus~~/~~guestbook~~.~~php fifa coin generator~~]		In [[mathematics]], the '''Silverman–Toeplitz theorem''', first proved by [[Otto Toeplitz]], is a result in [[summability theory]] characterizing [[Matrix (mathematics)\|matrix]] summability methods that are regular. A regular matrix summability method is a matrix transformation of a [[convergent sequence]] which preserves the [[Limit of a sequence\|limit]].

			An [[infinite matrix]] <math>(a_{i,j})_{i,j \in \mathbb{N}}</math> with [[complex number\|complex]]-valued entries defines a regular summability method [[if and only if]] it satisfies all of the following properties
			:<math>\lim_{i \to \infty} a_{i,j} = 0 \quad j \in \mathbb{N}</math> (every column sequence converges to 0)
			:<math>\lim_{i \to \infty} \sum_{j=0}^{\infty} a_{i,j} = 1</math> (the row sums converge to 1)
			:<math>\sup_{i} \sum_{j=0}^{\infty} \vert a_{i,j} \vert < \infty</math> (the absolute row sums are bounded).

			== References ==
			* Toeplitz, Otto (1911) "[http://matwbn.icm.edu.pl/ksiazki/pmf/pmf22/pmf2219.pdf ''Über die lineare Mittelbildungen.'']" ''Prace mat.-fiz.'', '''22''', 113–118 (the original paper in [[German language\|German]])
			* Silverman, Louis Lazarus (1913) "On the definition of the sum of a divergent series." University of Missouri Studies, Math. Series I, 1–96

			{{DEFAULTSORT:Silverman-Toeplitz theorem}}
			[[Category:Theorems in analysis]]
			[[Category:Summability methods]]
			[[Category:Summability theory]]

en>Donald Albury: fixed links

2011-10-29T00:30:32Z

fixed links

New page

I am Ferdinand and was born on 9 August 1977. My hobbies are Computer programming and Fantasy Football.<br><br>Also visit my web blog ... [http://Ly8Hxw.com/plus/guestbook.php fifa coin generator]