Parabolic partial differential equation - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T13:23:46Z

References: replace mr template with mr parameter in CS1 templates; using AWB

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	Nice to meet you, ~~my name is Refugia. Doing ceramics is what my family and~~ I ~~enjoy~~. ~~Bookkeeping~~ is ~~her day job now~~. South Dakota is ~~exactly where me and my spouse live~~.<br><br>~~Here is my web site~~: [http://www.~~gaysphere~~.~~net~~/~~user~~/~~Z5147 over the counter~~ std test]		Nice to meet you, I am Marvella Shryock. To play baseball is the pastime he will by no means quit doing. South Dakota is her beginning place but she requirements to transfer simply because of her family members. I am a meter reader but I strategy on altering it.<br><br>My webpage: [http://www.pornextras.info/blog/187567 home std test kit]

en>Larry Doolittle: avoid linking to a disambiguation page

2014-02-23T17:19:29Z

avoid linking to a disambiguation page

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	~~In [[mathematics]]~~, ~~'''Levinson's inequality '''~~ is ~~the following inequality, due to [[Norman Levinson]], involving positive numbers~~. ~~Let <math>a>0</math>~~ and ~~let <math>f</math> be a given function having a third derivative on the range <math>(0,2a)</math>,~~ and ~~such that~~		Nice to meet you, my name is Refugia. Doing ceramics is what my family and I enjoy. Bookkeeping is her day job now. South Dakota is exactly where me and my spouse live.<br><br>Here is my web site: [http://www.gaysphere.net/user/Z5147 over the counter std test]

	~~:<math>f'''(x)\geq 0</math>~~

	~~for all <math>x\in (0,2a)</math>~~. ~~Suppose~~ <~~math~~>0<~~x_i\leq a</math~~> ~~for <math> i = 1, \ldots, n<~~/~~math> and <math>0<p<~~/~~math>~~. ~~Then~~

	: <math>\frac{\sum_{i=1}^np_i f(x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_ix_i}{\sum_{i=1}^np_i}\right)\le\frac{\sum_{i=1}^np_if(2a-x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_i(2a-x_i)}{\sum_{i=1}^np_i}\right).</~~math>~~

	~~The [[Ky Fan inequality]] is the special case of Levinson's inequality where~~

	~~:<math>p_i=1,\ a=\frac{1}{2},<~~/~~math>~~

	~~and~~

	~~:<math>f(x)=\log x. \, </math>~~

	~~==References==~~
	*Scott Lawrence and Daniel Segalman: ''A generalization of two inequalities involving means'', Proceedings of the ~~American Mathematical Society. Vol 35 No. 1, September 1972.~~
	*Norman Levinson: ''Generalization of an inequality of Ky Fan'', Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134.

	~~[[Category:Inequalities]~~]

68.14.229.249 at 21:04, 30 December 2013

2013-12-30T21:04:52Z

← Older revision		Revision as of 23:04, 30 December 2013
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	~~I would like to introduce myself to you~~, ~~I am Jayson Simcox but I don~~'~~t like when people use my complete name. To climb is some thing she would never give up. I~~'~~ve usually cherished residing in Kentucky but now I~~'~~m contemplating other options. Distributing manufacturing~~ is ~~how he tends~~ to ~~make~~ a ~~residing.~~<br><br>~~Here is my page~~ :~~: phone psychic readings~~ (~~[http:~~//~~formalarmour~~.~~com~~/~~index~~.~~php?do~~=/~~profile-26947~~/~~info~~/ ~~Read Significantly more~~])		In [[mathematics]], '''Levinson's inequality ''' is the following inequality, due to [[Norman Levinson]], involving positive numbers. Let <math>a>0</math> and let <math>f</math> be a given function having a third derivative on the range <math>(0,2a)</math>, and such that

			:<math>f'''(x)\geq 0</math>

			for all <math>x\in (0,2a)</math>. Suppose <math>0<x_i\leq a</math> for <math> i = 1, \ldots, n</math> and <math>0<p</math>. Then

			: <math>\frac{\sum_{i=1}^np_i f(x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_ix_i}{\sum_{i=1}^np_i}\right)\le\frac{\sum_{i=1}^np_if(2a-x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_i(2a-x_i)}{\sum_{i=1}^np_i}\right).</math>

			The [[Ky Fan inequality]] is the special case of Levinson's inequality where

			:<math>p_i=1,\ a=\frac{1}{2},</math>

			and

			:<math>f(x)=\log x. \, </math>

			==References==
			*Scott Lawrence and Daniel Segalman: ''A generalization of two inequalities involving means'', Proceedings of the American Mathematical Society. Vol 35 No. 1, September 1972.
			*Norman Levinson: ''Generalization of an inequality of Ky Fan'', Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134.

			[[Category:Inequalities]]

en>HRoestBot: r2.6.5) (Robot: Adding it:Equazione differenziale alle derivate parziali parabolica

2012-05-18T16:45:38Z

r2.6.5) (Robot: Adding it:Equazione differenziale alle derivate parziali parabolica

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