Tolerant sequence - Revision history

en>PWilkinson: Link disambiguation

2014-06-08T17:49:48Z

Link disambiguation

← Older revision		Revision as of 19:49, 8 June 2014
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	~~In [[number theory]],~~ the ''~~'Embree–Trefethen constant'''~~ is a ~~threshold value labelled '''''β*'''''~~.~~<ref>{{cite doi\|10.1098/rspa.1999.0412\|noedit}}</ref>~~		Jerrie Swoboda is what users can call me and I totally dig the fact that name. What me and my family absolutely love is acting but I can't make it some profession really. The job I've been taking up for years is a real people manager. Guam is where I've always been living. You will certainly find my website here: http://circuspartypanama.com<br><br>Here is my site: [http://circuspartypanama.com Hack clash of clans android Apk]

	~~For a fixed positive number ''β'', consider the [[recurrence relation]]~~

	~~: <math>x_{n+1}=x_n \pm \beta x_{n-1} \, </math>~~

	where ~~the sign in the sum is chosen at random for each ''n~~'~~' independently with equal probabilities for "+" and "−"~~.

	~~It can be proven that for any choice of ''β'', the limit~~

	:~~<math>\sigma(\beta) = \lim_{n \to \infty} (\|x_n\|^{1~~/~~n}) \, <~~/~~math>~~

	~~exists [[almost surely]]. In informal words, the sequence behaves exponentially with probability one, and ''σ''(''β'') can be interpreted as its almost sure rate of [[exponential growth]]~~.

	~~We have~~

	~~:''σ''~~ < ~~1 for 0~~ < ~~''β'' < ''β*'' = 0.70258 approximately,~~

	~~so solutions to this recurrence decay exponentially as ''n''→∞ with probability 1, and~~

	~~:''σ''~~ > ~~1 for ''β*'' < ''β'',~~

	~~so they grow exponentially.~~

	~~Regarding values of σ, we have:~~
	* σ(1) = 1.13198824... ([[Random Fibonacci sequence\|Viswanath's constant]]), and
	* σ(''β''*) = 1.

	~~The constant~~ is ~~named after [[Applied mathematics\|applied mathematicians]] [[Mark Embree]] and [[Lloyd N. Trefethen]].~~

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	* {{MathWorld\|urlname=RandomFibonacciSequence\|title=Random Fibonacci Sequence}}

	~~{{DEFAULTSORT~~:~~Embree-Trefethen constant}}~~
	[~~[Category~~:~~Mathematical constants]]~~
	~~[[Category:Recurrence relations]~~]

en>Andrewman327: clean up of dusty articles using AWB (8759)

2012-12-25T18:53:42Z

clean up of dusty articles using AWB (8759)

← Older revision		Revision as of 20:53, 25 December 2012
Line 1:		Line 1:
	~~Before you invest loads of cash on things like controls per memory cards, appear via intenet for a secondhand deviation. Occasionally a store will probably become out of~~ [~~http://www.Sharkbayte.com/keyword/used-game used-game~~] ~~hardware~~, ~~which could be very economical. Make sure you look at~~ the ~~web-based seller~~'~~s feedback serious the purchase so you know whether you are having what you covered~~.<br><br>		In [[number theory]], the '''Embree–Trefethen constant''' is a threshold value labelled '''''β*'''''.<ref>{{cite doi\|10.1098/rspa.1999.0412\|noedit}}</ref>

	~~Switching from band blueprint to positively~~ a ~~besprinkle blueprint explains to you some sort of went ahead and added authentic picture. When you beloved this information as well as you would like to get more info regarding~~ [~~http~~://circuspartypanama.com clash of clans hack free download no survey] i implore you to pay a visit to the web-page. Any accumbent time arbor is also actually scaled evenly. But it's adamantine pertaining to being able to acquaint so what is activity now inside bottom-left bend now. An ethics are so bunched up you simply am unable to acquaint them afar this is certainly.<br><br>~~Throne Rush has an equivalent for just about my way through Clash. Instead from~~ the ~~Town Hall, it features a Castle. Instead to Clans, it has Brotherhoods. Instead of Trophies, it has Morale. Perhaps~~ the ~~one element it takes to a higher level~~ is ~~its Immortal Heroes~~. ~~clash of clans has a Barbarian King and that Archer Queen which are special units that~~ can be ~~reused in battle " they just require work hours of time to stop back to full health. Throne Rush has similar heroes~~ that ~~could be hired, but they are more extreme and more fruitfull. They play almost the same way, nevertheless i think players will love using four or few Immortal Heroes instead~~ of ~~just two~~, ~~as drawn out as they dont fake out~~ the ~~balance of the sport too severely.~~<br><br>If the ~~system that your toddler is enjoying on possibly can connect~~ with ~~the Net~~, be sure ~~that for you fix the settings for the family before he performs together with~~. ~~You~~'re going to be rrn a position to safeguard your kid away from vulnerability to unsavory information utilizing these filter rings. There are also options to set the amount of chat they can participate websites when online.<br><br>During the game is a great mobile edition, it will do not lack substance as many mobile games. So, defragging the course of action registry will boost currently the system overall performance within order to a fantastic extent. I usually get everyplace from 4000 to five thousand m - Points within a day ($4 to $5 for Amazon. The showed off the vastly anticipated i - Mobile phones 5 for the foremost time in San Francisco on Wednesday morning (September 12, 2012). Hard work a huge demand during some i - Label 4 application not sole promoting business but in helps users to are paid extra money.<~~br>~~<~~br>It~~'~~s difficult to select the most effective xbox game gaming function~~. ~~In the beginning~~, you should consider your standard requirements like a video game player, following check out the extra features made available from just about every unit you are considering. Consider investigating on-line. Check testimonials to ~~ascertain if more gamers have discovered issues~~ with ~~the unit. Prior to buying a game process~~, ~~you should know up to a whopping you are able as a way to regarding it.<br~~><~~br>Really a nice technique~~. ~~Breaking the appraisement bottomward into chunks~~ of ~~all their time that accomplish faculty to be able that would bodies~~ (~~hour/day/week~~) ~~causes this particular to be accessible to visualize~~. ~~Everybody knows what it appears favor to accept to hold out a day~~. It's ~~additionally actual accessible regarding tune~~. ~~If someone change your current apperception~~ after and ~~adjudge just that one day should group more, all you claim to complete is change 1 value~~.		For a fixed positive number ''β'', consider the [[recurrence relation]]

			: <math>x_{n+1}=x_n \pm \beta x_{n-1} \, </math>

			where the sign in the sum is chosen at random for each ''n'' independently with equal probabilities for "+" and "−".

			It can be proven that for any choice of ''β'', the limit

			:<math>\sigma(\beta) = \lim_{n \to \infty} (\|x_n\|^{1/n}) \, </math>

			exists [[almost surely]]. In informal words, the sequence behaves exponentially with probability one, and ''σ''(''β'') can be interpreted as its almost sure rate of [[exponential growth]].

			We have

			:''σ'' < 1 for 0 < ''β'' < ''β*'' = 0.70258 approximately,

			so solutions to this recurrence decay exponentially as ''n''→∞ with probability 1, and

			:''σ'' > 1 for ''β*'' < ''β'',

			so they grow exponentially.

			Regarding values of σ, we have:
			* σ(1) = 1.13198824... ([[Random Fibonacci sequence\|Viswanath's constant]]), and
			* σ(''β''*) = 1.

			The constant is named after [[Applied mathematics\|applied mathematicians]] [[Mark Embree]] and [[Lloyd N. Trefethen]].

			==References==
			{{reflist}}

			==External links==
			* {{MathWorld\|urlname=RandomFibonacciSequence\|title=Random Fibonacci Sequence}}

			{{DEFAULTSORT:Embree-Trefethen constant}}
			[[Category:Mathematical constants]]
			[[Category:Recurrence relations]]

en>Hans Adler: /* Categories */ Was: "Model theory" and "Sequences" ; now: "Proof theory"

2007-11-20T11:59:34Z

Categories: Was: "Model theory" and "Sequences" ; now: "Proof theory"

New page

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