P-adic L-function - Revision history

en>K9re11: /* Definition using interpolation */

2014-05-29T08:53:09Z

Definition using interpolation

← Older revision		Revision as of 10:53, 29 May 2014
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	~~{{Unreferenced\|date=March 2009}}~~		I'm Fabian and I live in a seaside city in northern Poland, Lublin. I'm 20 and I'm will soon finish my study at English Literature.<br><br>Look at my webpage; [http://touredition.com/uncategorized/%d0%b4%d0%b8%d0%b5%d1%82%d1%8b-%d0%ba%d0%b0%d0%ba-%d0%bf%d0%be%d1%85%d1%83%d0%b4%d0%b5%d1%82%d1%8c-%d1%80%d1%83%d0%ba%d0%b8-%d0%b8-%d0%b4%d0%b8%d0%b5%d1%82%d1%83-%d1%87%d1%82%d0%be%d0%b1%d1%8b/ поджелудочная железа диета]

	~~The~~ '~~''Weierstrass–Erdmann condition''' is~~ a ~~technical tool from the [[calculus of variations]]~~. ~~This condition gives the sufficient conditions for an [[extremal]] to have a corner.~~

	~~== Conditions ==~~

	~~The condition says that, along a [[piecewise smooth]] extremal~~ ''~~x''(''t'') (i~~.~~e. an extremal which is smooth except at a finite number of corners) for an [[integral]]~~ <~~math~~>~~J=\int f(t,x,y)\,dt~~<~~/math~~>~~, the~~ [~~[partial derivative]] <math>\partial f~~/~~\partial x<~~/~~math> must be [[Continuous function\|continuous]] at a corner ''T''~~. ~~That is, if one takes the [[Limit of a function\|limit]] of partials on both sides of the corner as one approaches the corner ''T'', the result must~~ be ~~the same answer.~~

	~~== Applications ==~~

	The condition allows one to prove that a corner exists along a given extremal. As a result, there are many applications to [[differential geometry]]. In calculations of the [[Weierstrass's elliptic functions\|Weierstrass E-~~Function]], it is often helpful to find where corners exist along the curves. Similarly, the condition allows for one to find a minimizing curve for a given integral.~~

	~~{{DEFAULTSORT:Weierstrass~~-~~Erdmann Condition}}~~
	~~[[Category:Calculus of variations]~~]

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2013-03-20T05:11:18Z

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← Older revision		Revision as of 07:11, 20 March 2013
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			{{Unreferenced\|date=March 2009}}

			The '''Weierstrass–Erdmann condition''' is a technical tool from the [[calculus of variations]]. This condition gives the sufficient conditions for an [[extremal]] to have a corner.

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			The condition says that, along a [[piecewise smooth]] extremal ''x''(''t'') (i.e. an extremal which is smooth except at a finite number of corners) for an [[integral]] <math>J=\int f(t,x,y)\,dt</math>, the [[partial derivative]] <math>\partial f/\partial x</math> must be [[Continuous function\|continuous]] at a corner ''T''. That is, if one takes the [[Limit of a function\|limit]] of partials on both sides of the corner as one approaches the corner ''T'', the result must be the same answer.

			== Applications ==

			The condition allows one to prove that a corner exists along a given extremal. As a result, there are many applications to [[differential geometry]]. In calculations of the [[Weierstrass's elliptic functions\|Weierstrass E-Function]], it is often helpful to find where corners exist along the curves. Similarly, the condition allows for one to find a minimizing curve for a given integral.

			{{DEFAULTSORT:Weierstrass-Erdmann Condition}}
			[[Category:Calculus of variations]]

76.120.181.41: improve

2012-08-08T21:23:06Z

improve

New page

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