Trans-tubular potassium gradient - Revision history

en>Rjwilmsi: Journal cites, Added 1 doi to a journal cite using AWB (10473)

2014-09-25T10:05:50Z

Journal cites, Added 1 doi to a journal cite using AWB (10473)

← Older revision		Revision as of 12:05, 25 September 2014
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	~~In [[mathematics]]~~ and ~~[[game theory]], '''Bulgarian solitaire''' is a [[playing card\|card]] game that was introduced by [[Martin Gardner]]~~.		Greetings! I am Marvella and I really feel comfy when people use the complete name. Managing individuals is his profession. The factor she adores most is body developing and now she is trying to earn cash with it. Years in the past we moved to Puerto Rico and my family members enjoys it.<br><br>Feel free to surf to my blog :: [http://www.uknewsx.com/what-you-want-to-do-when-confronted-with-candida-albicans/ home std test kit]

	~~In the game, a pack of <math>N</math> cards~~ is ~~divided into several piles~~. ~~Then for each pile, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored).~~

	~~If <math>N</math>~~ is ~~a [[triangular number]] (that~~ is~~, <math>N=1+2+\cdots+k</math> for some <math>k</math>), then~~ it ~~is known that Bulgarian solitaire will reach a stable configuration~~ in ~~which~~ the ~~sizes of the piles are <math>1,2,\ldots, k</math>~~. ~~This state is reached in~~ <~~math~~>~~k^2-k~~<~~/math~~> ~~moves or fewer. If <math>N</math> is not triangular, no stable configuration exists and a~~ [~~[limit cycle]] is reached.~~

	~~==Random Bulgarian solitaire==~~
	~~In ''random Bulgarian solitaire'' or ''stochastic Bulgarian solitaire'' a pack of <math>N<~~/~~math> cards is divided into several piles. Then for each pile, either leave it intact or, with a fixed [[probability]] <math>p<~~/~~math>, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored). This is a [[finite set\|finite]] irreducible [[Markov chain]].~~

	~~In 2004, [[Brazil]]ian [[probability\|probabilist]] of [[Russia]]n origin [[Serguei Popov]] showed that stochastic Bulgarian solitaire spends "most" of its time in a "roughly" triangular distribution~~.

	~~==References==~~

	*{{cite journal \| author= Serguei Popov\| title= Random Bulgarian solitaire\| journal= [[Random Structures and Algorithms]]\| year=2005\| volume=27 \| pages=310–330 \| doi= 10.~~1002~~/~~rsa.20076 \| issue=3}}~~
	* {{cite journal \| doi = 10.2307/2323643 \| author = [[Ethan Akin]] and [[Morton Davis]] \| title = Bulgarian solitaire \| journal = [[American Mathematical Monthly]] \| year = 1985 \| volume = 92 \| pages=237–250 \| issue=4 \| jstor = 2323643}}

	~~[[Category:20th century card games]]~~
	~~[[Category:Recreational mathematics]]~~
	~~[[Category:Combinatorial game theory]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-31T01:30:07Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 03:30, 31 January 2014
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	~~The title~~ of the ~~author~~ is ~~Jayson. Credit authorising~~ is ~~how she makes~~ a ~~residing. Some time~~ in the ~~past he chose to reside~~ in ~~North Carolina and he doesn't strategy on altering it~~. ~~What me~~ and ~~my family love~~ is ~~performing ballet but I~~'~~ve been taking on new issues lately~~.<br><br>~~my homepage: clairvoyants~~ ([~~http://appin~~.co.kr/~~board_Zqtv22/688025 appin~~.co.kr])		In [[mathematics]] and [[game theory]], '''Bulgarian solitaire''' is a [[playing card\|card]] game that was introduced by [[Martin Gardner]].

			In the game, a pack of <math>N</math> cards is divided into several piles. Then for each pile, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored).

			If <math>N</math> is a [[triangular number]] (that is, <math>N=1+2+\cdots+k</math> for some <math>k</math>), then it is known that Bulgarian solitaire will reach a stable configuration in which the sizes of the piles are <math>1,2,\ldots, k</math>. This state is reached in <math>k^2-k</math> moves or fewer. If <math>N</math> is not triangular, no stable configuration exists and a [[limit cycle]] is reached.

			==Random Bulgarian solitaire==
			In ''random Bulgarian solitaire'' or ''stochastic Bulgarian solitaire'' a pack of <math>N</math> cards is divided into several piles. Then for each pile, either leave it intact or, with a fixed [[probability]] <math>p</math>, remove one card; collect the removed cards together to form a new pile (piles of zero size are ignored). This is a [[finite set\|finite]] irreducible [[Markov chain]].

			In 2004, [[Brazil]]ian [[probability\|probabilist]] of [[Russia]]n origin [[Serguei Popov]] showed that stochastic Bulgarian solitaire spends "most" of its time in a "roughly" triangular distribution.

			==References==

			*{{cite journal \| author= Serguei Popov\| title= Random Bulgarian solitaire\| journal= [[Random Structures and Algorithms]]\| year=2005\| volume=27 \| pages=310–330 \| doi= 10.1002/rsa.20076 \| issue=3}}
			* {{cite journal \| doi = 10.2307/2323643 \| author = [[Ethan Akin]] and [[Morton Davis]] \| title = Bulgarian solitaire \| journal = [[American Mathematical Monthly]] \| year = 1985 \| volume = 92 \| pages=237–250 \| issue=4 \| jstor = 2323643}}

			[[Category:20th century card games]]
			[[Category:Recreational mathematics]]
			[[Category:Combinatorial game theory]]

210.0.231.224: /* See also */

2011-08-09T06:37:26Z