Cnoidal wave - Revision history

en>John of Reading: /* Korteweg–de Vries equation */Typo fixing, replaced: its is → it is using AWB

2014-10-08T16:59:36Z

Korteweg–de Vries equation: Typo fixing, replaced: its is → it is using AWB

← Older revision		Revision as of 18:59, 8 October 2014
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	In [[real algebraic geometry]], the ''' Łojasiewicz inequality''', named after [[Stanisław Łojasiewicz]], gives an upper bound for the distance of a point to the nearest zero of a given [[real analytic function]]. Specifically, let ƒ : ''U'' → '''R''' be a real-analytic function on an [[open set]] ''U'' in '''R'''<sup>''n''</sup>, and ~~let ''Z'' be the zero [[locus (mathematics)\|locus]] of ƒ. Assume that ''Z'' is not empty. Then for any [[compact set]] ''K'' in ''U'', there exist positive constants α~~ and ~~''C'' such that, for all ''x'' in ''K''~~		My name is Numbers and I am studying Social Service and Modern Languages and Classics at Fruitport / United States.<br><br>my webpage: [http://bit.ly/1tn2bLa Best treadmills 2014]

	~~:<math>\operatorname{dist}(x,Z)^\alpha \le C\|f(x)\|. \, <~~/~~math>~~

	~~Here α can be large~~.

	The following form of this inequality is often seen in more analytic contexts: with the same assumptions on ƒ, for every ''p'' ∈ ''U'' there is a possibly smaller open neighborhood ''W'' of ''p'' and constants θ ∈ (0,1) and ''c'' > 0 such that

	:<~~math~~>~~\|f(x)-f(p)\|^\theta\le c\|\nabla f(x)\|. \,~~ <~~/math~~>

	~~==References==~~
	*{{Citation \| last1=Bierstone \| first1=Edward \| last2=Milman \| first2=Pierre D. \| title=Semianalytic and subanalytic sets \| id={{MathSciNet \| id = 972342}} \| year=1988 \| journal=[[Publications Mathématiques de l'IHÉS]] \| issn=1618-1913 \| issue=67 \| pages=5–42\|url=http:~~//www.numdam.org/item?id=PMIHES_1988__67__5_0}}~~
	*{{Citation \| doi=10.2307/2153965 \| last1=Ji \| first1=Shanyu \| last2=Kollár \| first2=János \| last3=Shiffman \| first3=Bernard \| title=A global Łojasiewicz inequality for algebraic varieties \| id={{MathSciNet \| id = 1046016}} \| url=http://www.ams.org/journals/tran/1992-329-02/S0002-9947-1992-1046016-6/ \| year=1992 \| journal=[[Transactions of the American Mathematical Society]] \| issn=0002-9947 \| volume=329 \| issue=2 \| pages=813–818 \| jstor=2153965}}

	~~==External links==~~
	*[http://~~www~~.~~encyclopediaofmath.org~~/~~index.php/Lojasiewicz_inequality Lojasiewicz inequality] at [http://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]~~

	~~{{mathanalysis-stub}}~~
	~~{{DEFAULTSORT:Lojasiewicz inequality}}~~
	~~[[Category:Inequalities]]~~
	~~[[Category:Mathematical analysis]]~~
	~~[[Category:Real algebraic geometry]~~]

en>Rjwilmsi: /* References */Journal cites, added 1 DOI using AWB (9887)

2014-01-25T21:37:59Z

References: Journal cites, added 1 DOI using AWB (9887)

← Older revision		Revision as of 23:37, 25 January 2014
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	~~Hi!~~ <br>~~My name~~ is ~~Crystal~~ and I'm a ~~29 years old girl from France.~~<br><br>~~my web~~-~~site~~ :: [http://~~www2~~.~~energybulletin~~.~~net~~/~~node~~/~~69786 бессолевая диета отзывы~~]		In [[real algebraic geometry]], the ''' Łojasiewicz inequality''', named after [[Stanisław Łojasiewicz]], gives an upper bound for the distance of a point to the nearest zero of a given [[real analytic function]]. Specifically, let ƒ : ''U'' → '''R''' be a real-analytic function on an [[open set]] ''U'' in '''R'''<sup>''n''</sup>, and let ''Z'' be the zero [[locus (mathematics)\|locus]] of ƒ. Assume that ''Z'' is not empty. Then for any [[compact set]] ''K'' in ''U'', there exist positive constants α and ''C'' such that, for all ''x'' in ''K''

			:<math>\operatorname{dist}(x,Z)^\alpha \le C\|f(x)\|. \, </math>

			Here α can be large.

			The following form of this inequality is often seen in more analytic contexts: with the same assumptions on ƒ, for every ''p'' ∈ ''U'' there is a possibly smaller open neighborhood ''W'' of ''p'' and constants θ ∈ (0,1) and ''c'' > 0 such that

			:<math>\|f(x)-f(p)\|^\theta\le c\|\nabla f(x)\|. \, </math>

			==References==
			*{{Citation \| last1=Bierstone \| first1=Edward \| last2=Milman \| first2=Pierre D. \| title=Semianalytic and subanalytic sets \| id={{MathSciNet \| id = 972342}} \| year=1988 \| journal=[[Publications Mathématiques de l'IHÉS]] \| issn=1618-1913 \| issue=67 \| pages=5–42\|url=http://www.numdam.org/item?id=PMIHES_1988__67__5_0}}
			*{{Citation \| doi=10.2307/2153965 \| last1=Ji \| first1=Shanyu \| last2=Kollár \| first2=János \| last3=Shiffman \| first3=Bernard \| title=A global Łojasiewicz inequality for algebraic varieties \| id={{MathSciNet \| id = 1046016}} \| url=http://www.ams.org/journals/tran/1992-329-02/S0002-9947-1992-1046016-6/ \| year=1992 \| journal=[[Transactions of the American Mathematical Society]] \| issn=0002-9947 \| volume=329 \| issue=2 \| pages=813–818 \| jstor=2153965}}

			==External links==
			*[http://www.encyclopediaofmath.org/index.php/Lojasiewicz_inequality Lojasiewicz inequality] at [http://www.encyclopediaofmath.org/ Encyclopedia of Mathematics]

			{{mathanalysis-stub}}
			{{DEFAULTSORT:Lojasiewicz inequality}}
			[[Category:Inequalities]]
			[[Category:Mathematical analysis]]
			[[Category:Real algebraic geometry]]

en>Crowsnest: /* Background */ +wiki link

2012-08-28T15:26:05Z

Background: +wiki link

New page

Hi! <br>My name is Crystal and I'm a 29 years old girl from France.<br><br>my web-site :: [http://www2.energybulletin.net/node/69786 бессолевая диета отзывы]