Igusa zeta-function - Revision history

en>Yobot: /* Congruences modulo powers of $P$ */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T09:46:27Z

Congruences modulo powers of <math>P</math>: WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 11:46, 5 May 2014
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	~~In [[linear programming]],~~ a '~~''Hilbert basis'''~~ for ~~a [[convex cone]] ''C''~~ is ~~an integer [[cone basis]]: minimal set of integer [[vector (mathematics)\|vector]]s such that every integer vector in~~ '~~'C'' is~~ a ~~[[conical combination]] of the vectors in the Hilbert basis~~ with ~~integer coefficients~~.		Hello. Let me introduce the author. Her title is Refugia Shryock. For a while I've been in South Dakota and my parents reside close by. The preferred pastime for my kids and me is to play baseball but I haven't made a dime with it. Hiring is her working day occupation now and she will not alter it whenever soon.<br><br>Feel free to visit my site; [http://hotporn123.com/blog/150819 at home std test]

	~~== Definition ==~~
	~~A set <math>A=\{a_1,\ldots,a_n\}</math> of integer vectors~~ is ~~a Hilbert basis of its [[convex cone]]~~

	:<~~math~~>~~C=\{ \lambda_1 a_1 + \ldots + \lambda_n a_n \mid \lambda_1,\ldots,\lambda_n \geq 0, \lambda_1,\ldots,\lambda_n \in\mathbb{R}\}~~<~~/math~~>

	~~if every integer vector from ''C'' belongs~~ to ~~the integer convex cone of ''A''~~:

	~~:<math>\{ \alpha_1 a_1 + \ldots + \alpha_n a_n \mid \alpha_1,\ldots,\alpha_n \geq 0, \alpha_1,\ldots,\alpha_n \in\mathbb{Z}\},<~~/~~math>~~

	~~and no vector from ''A'' belongs to the integer convex cone of the others.~~

	~~== References ==~~

	* {{Citation \| last1=Bruns \| first1=Winfried \|last2=Gubeladze \| first2=Joseph \| last3=Henk \| first3=Martin \| last4=Martin \| first4=Alexander \| last5=Weismantel \| first5=Robert \| title=A counterexample to an integer analogue of Carathéodory's theorem \| doi=10.1515/~~crll~~.~~1999.045 \| year=1999 \| journal=[[Journal für die reine und angewandte Mathematik]] \| volume=510 \| pages=179–185 \| issue=510}}~~
	* {{Citation \| last1=Cook \| first1=William John \| last2=Fonlupt \| first2=Jean \| last3=Schrijver \| first3=Alexander \| authorlink3=Alexander Schrijver\|title=An integer analogue of Carathéodory's theorem \| doi=10.1016/0095-8956(86)90064-X \| year=1986 \| journal=Journal of Combinatorial Theory. Series B \| volume=40 \| issue=1 \| pages=63–70}}
	* {{Citation \| last1=Eisenbrand \| first1=Friedrich \| last2=Shmonin \| first2=Gennady \| title=Carathéodory bounds for integer cones \| doi=10.1016/~~j.orl.2005.09.008 \| year=2006 \| journal=Operations Research Letters \| volume=34 \| issue=5 \| pages=564–568}}~~
	* {{cite journal \|author = D. V. Pasechnik \|title=On computing the Hilbert bases via the Elliott—MacMahon algorithm \|journal=Theoretical Computer Science \|volume=263 \|year=2001 \|pages=37–46 \|doi=10.1016/~~S0304-3975(00)00229-2}}~~

	~~{{mathapplied-stub}}~~

	~~[[Category:Mathematical optimization]]~~
	~~[[Category:Operations research]]~~
	~~[[Category:Linear programming]~~]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5994475

2013-03-16T10:09:44Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5994475

← Older revision		Revision as of 12:09, 16 March 2013
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	~~Greetings! I am Myrtle Shroyer. Managing people has been his working day job~~ for a ~~while. One~~ of the ~~extremely best things~~ in the ~~world for me is to do aerobics and now I'm trying to earn cash~~ with ~~it. Years in the past we moved to North Dakota and I adore each day residing right here~~.<br><br>~~Also visit my website~~ :: ~~[http~~://~~Product~~-~~Dev~~.~~Younetco~~.~~com~~/~~xuannth/fox_ios1/index~~.~~php?do~~=/~~profile~~-~~1539/info/ at home std test~~]		In [[linear programming]], a '''Hilbert basis''' for a [[convex cone]] ''C'' is an integer [[cone basis]]: minimal set of integer [[vector (mathematics)\|vector]]s such that every integer vector in ''C'' is a [[conical combination]] of the vectors in the Hilbert basis with integer coefficients.

			== Definition ==
			A set <math>A=\{a_1,\ldots,a_n\}</math> of integer vectors is a Hilbert basis of its [[convex cone]]

			:<math>C=\{ \lambda_1 a_1 + \ldots + \lambda_n a_n \mid \lambda_1,\ldots,\lambda_n \geq 0, \lambda_1,\ldots,\lambda_n \in\mathbb{R}\}</math>

			if every integer vector from ''C'' belongs to the integer convex cone of ''A'':

			:<math>\{ \alpha_1 a_1 + \ldots + \alpha_n a_n \mid \alpha_1,\ldots,\alpha_n \geq 0, \alpha_1,\ldots,\alpha_n \in\mathbb{Z}\},</math>

			and no vector from ''A'' belongs to the integer convex cone of the others.

			== References ==

			* {{Citation \| last1=Bruns \| first1=Winfried \|last2=Gubeladze \| first2=Joseph \| last3=Henk \| first3=Martin \| last4=Martin \| first4=Alexander \| last5=Weismantel \| first5=Robert \| title=A counterexample to an integer analogue of Carathéodory's theorem \| doi=10.1515/crll.1999.045 \| year=1999 \| journal=[[Journal für die reine und angewandte Mathematik]] \| volume=510 \| pages=179–185 \| issue=510}}
			* {{Citation \| last1=Cook \| first1=William John \| last2=Fonlupt \| first2=Jean \| last3=Schrijver \| first3=Alexander \| authorlink3=Alexander Schrijver\|title=An integer analogue of Carathéodory's theorem \| doi=10.1016/0095-8956(86)90064-X \| year=1986 \| journal=Journal of Combinatorial Theory. Series B \| volume=40 \| issue=1 \| pages=63–70}}
			* {{Citation \| last1=Eisenbrand \| first1=Friedrich \| last2=Shmonin \| first2=Gennady \| title=Carathéodory bounds for integer cones \| doi=10.1016/j.orl.2005.09.008 \| year=2006 \| journal=Operations Research Letters \| volume=34 \| issue=5 \| pages=564–568}}
			* {{cite journal \|author = D. V. Pasechnik \|title=On computing the Hilbert bases via the Elliott—MacMahon algorithm \|journal=Theoretical Computer Science \|volume=263 \|year=2001 \|pages=37–46 \|doi=10.1016/S0304-3975(00)00229-2}}

			{{mathapplied-stub}}

			[[Category:Mathematical optimization]]
			[[Category:Operations research]]
			[[Category:Linear programming]]

76.120.181.41: edit

2012-08-08T20:02:38Z

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New page

Greetings! I am Myrtle Shroyer. Managing people has been his working day job for a while. One of the extremely best things in the world for me is to do aerobics and now I'm trying to earn cash with it. Years in the past we moved to North Dakota and I adore each day residing right here.<br><br>Also visit my website :: [http://Product-Dev.Younetco.com/xuannth/fox_ios1/index.php?do=/profile-1539/info/ at home std test]

Igusa zeta-function - Revision history

en>Yobot: /* Congruences modulo powers of P */WP:CHECKWIKI error fixes using AWB (10093)

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q5994475

76.120.181.41: edit

en>Yobot: /* Congruences modulo powers of $P$ */WP:CHECKWIKI error fixes using AWB (10093)