Expected linear time MST algorithm - Revision history

en>David Eppstein: fix conf

2015-01-09T07:43:09Z

fix conf

← Older revision		Revision as of 09:43, 9 January 2015
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en>Gilliam: Reverted edits by 128.193.8.92 (talk) to last version by Yobot

2014-02-16T06:00:37Z

Reverted edits by 128.193.8.92 (talk) to last version by Yobot

← Older revision		Revision as of 08:00, 16 February 2014
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	In [[mathematics]], the '''Carlitz exponential''' is a characteristic ''p'' analogue to the usual [[exponential function]] studied in [[real analysis\|real]] and [[complex analysis]]. It is used in the definition of the [[Carlitz module]] – an example of a [[Drinfeld module]].		My name is Lamont [https://www.smore.com/8ch9m-alex-and-ani-promo-codes-2014 alex and ani coupon] I am studying Environmental Management and Environmental Studies at Basedow / Germany.

	~~==Definition==~~

	We work over the polynomial ring '''F'''<sub>''q''</sub>[''T''] of one variable over a [[finite field]] '''F'''<sub>''q''</sub> with ''q'' elements. The [[Completion (metric space)\|completion]] '''C'''<sub>∞</sub> of an [[algebraic closure]] of the field '''F'''<sub>''q''</sub>((''T''<sup>−1</sup>)) of [[formal Laurent series]] in ''T''<sup>−1</sup> will be useful. It is a complete and algebraically closed field.

	~~First we need analogues to the [[factorials]], which appear in the definition of the usual exponential function. For ''i'' > 0 we define~~

	~~:<math>[i] := T^{q^i} - T, \, </math>~~
	~~:<math>D_i := \prod_{1 \le j \le i} [j]^{q^{i - j}}</math>~~

	~~and ''D''<sub>0</sub> := 1. Note that that the usual factorial~~ is ~~inappropriate here, since ''n''! vanishes in '''F'''<sub>''q''</sub>~~[~~''T''] unless ''n'' is smaller than the [[Characteristic (algebra)\|characteristic]] of '''F'''<sub>''q''</sub>[''T''].~~

	~~Using this we define the Carlitz exponential ''e''<sub>''C''</sub>~~:~~'''C'''<sub>∞<~~/~~sub> → '''C'''<sub>∞<~~/~~sub> by the convergent sum~~

	~~:<math>e_C(x) := \sum_{j = 0}^\infty \frac{x^{q^j}}{D_i}~~.~~</math>~~

	~~==Relation to the Carlitz module==~~

	~~The Carlitz exponential satisfies the functional equation~~

	~~:<math>e_C(Tx) = Te_C(x) + \left(e_C(x)\right)^q = (T + \tau)e_C(x), \, </math>~~

	~~where we may view <math> \tau </math> as the power of <math> q </math> map or as an element of the ring <math> F_q(T)\{\tau\} </math> of [[noncommutative polynomials]]~~. ~~By the [[universal property]] of polynomial rings in one variable this extends to a ring homomorphism ''ψ'':'''F'''<sub>''q''<~~/~~sub>[''T'']→'''C'''<sub>∞</sub>{''τ''}, defining a Drinfeld '''F'''<sub>''q''</sub>[''T'']~~-~~module over '''C'''<sub>∞</sub>{''τ''}. It is called the Carlitz module.~~

	~~==References==~~
	~~{{reflist}}~~
	*{{Citation \| last1=Goss \| first1=D. \| authorlink = David Goss \| title=Basic structures of function field arithmetic \| publisher=[[Springer-~~Verlag]] \| location=Berlin, New York \| series=Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics~~ and ~~Related Areas (3)] \| isbn=978~~-3-~~540~~-~~61087~~-~~8 \| mr=1423131 \| year=1996 \| volume=35}}~~
	*{{Citation \| last1=Thakur \| first1=Dinesh \| first2=S. ~~\| title=Function field arithmetic \| publisher=[[World Scientific Publishing]] \| location=New Jersey\| isbn=981-238-839-7 \| mr=2091265 \| year=2004}}~~

	~~[[Category:Algebraic number theory]]~~
	~~[[Category:Finite fields]]~~

en>Yobot: WP:CHECKWIKI error fixes using AWB (9075)

2013-04-13T09:03:06Z

WP:CHECKWIKI error fixes using AWB (9075)

← Older revision		Revision as of 11:03, 13 April 2013
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	~~Your tory burch homes are perfect inside style and comfort. A lot of true blue fashionistas stick~~ to the ~~latest handbag trends~~ and ~~sporting Tory Burch handbags from the vintage variety guarantees you that you won�t be carrying the same designer handbags like everyone else~~. Try these looks: Dress: Tri-Color Combo Dress by BAILEY 44, $190 Top: Metallic Split Noh Tee by The Furies, $40 Bottom: Colorblock Short by Cooperative, $54 Accessories: Zip Continental Wallet by Tory Burch, $195 Shoes: Color-block Wedges by David Nasa, $157. They could be worn with the ~~most fancy~~ of ~~gowns to jeans or capri pants. Examples~~ of ~~merchandise which often is becoming made using like bucks include grain, precious metals, cowry buttocks~~. ~~<br><br><br><br>~~		In [[mathematics]], the '''Carlitz exponential''' is a characteristic ''p'' analogue to the usual [[exponential function]] studied in [[real analysis\|real]] and [[complex analysis]]. It is used in the definition of the [[Carlitz module]] – an example of a [[Drinfeld module]].

	~~tory burch wallet saleWear begin to use machine to try~~ the ~~particular the washing. Create an electronic digital card using Power - Point or Show (for Macs). I am~~ a ~~major Ravens enthusiast along~~ with ~~the chucks assist me indicate my team pride~~. ~~These~~ [~~http:~~/~~/Imgur.com/hot?q=special+Tory special Tory~~] ~~Burch handbags can not be found in department stores nor can it be found in Tory Burch retail shops since they don�t keep old components~~ of ~~stock. Third,~~ the ~~teenager things should be lovely and youthful.~~ <br><br>~~tory burch handbags saleShoe enthusiasts, please sign up to Trina~~'~~s National Shoe Articles. Most~~ of ~~today~~'~~s designers are continuing~~ to ~~make use of short~~, ~~thick straps that either fit within the lower arm or shoulder. Tory Burch's Lady Bag was two-toned leather and featured one top handle as well as a flap closure~~ which ~~hit~~ the ~~middle from the front~~ of the ~~handbag~~. ~~Ins Month after month however shed more pounds weight. The 2~~,~~500 feet square store sells vitamins~~, ~~health supplements and sports nutrition products.~~ <br><br><br><br>~~tory burch walletscom and Better Homes and Garden have cute crafts~~ that ~~you can make with your children or grandchildren. Lower back and knee pain can be attributed to some from~~ the ~~health risks of wearing fashion forward footwear. Tory Burch, the famed New York fashion designer, will take a downtown preppy vibe to South - Park. Among 34 countries Straus studied~~, in ~~those even spanking was accepted, the normal Reasoning powers from the study population was below in nation~~'~~s where spanking got rare, the researcher says. Bi-fold wallets, on the other hand, only folds in half.~~ <br><br>~~tory burch saleOlivia has recentl tweaked clearl to ensure ou Secretar about Immunit Walternate~~ (~~Kim Chevalier~~) ~~experiments individuals couple~~ of ~~ears best that~~ the ~~There Olivia,[http~~://~~www~~.~~pcs-systems.co.uk~~/~~Images/celinebag.aspx Celine Bags Outlet] Bags Louis Vuitton Shoes alias Bolivia~~ (~~furthermore Torv~~)~~. Imagine having that lots of choices in front of you each morning.~~ )~~This tory burch sandals were designed from drum dyed leather which is accessible in the wide selection of colors and sizes. It can also aid in posture~~, ~~forcing the wearer to hold the body more upright and present them a more confident stride. These various characteristics come together to define a purse~~, ~~and thus to dictate~~ where~~, when, and by whom it ought to truly be worn.~~ <br><br>~~tory burch pursesMuch more via you usually do not must dread~~ or ~~perhaps a recipient really should it once more or not~~. ~~Fruit is~~ the ~~most suitable avoided by those looking~~ to ~~lose weight, says Harcombe, who adds~~: '~~Vitamins and minerals in animal foods~~ ' ~~meat~~, ~~fish, eggs and dairy food~~ ' beat those involved with fruit hands down. These boots are constructed solely of rich suede uppers and so are sleek and streamlined with an effortless pulled together look. This is a classic example of an limited distribution strategy that serves to improve Hermes' ~~product desirability among discerning consumers. Thomas Sabo transformed from obtaining a secretive safeguard of style insiders to receiving produced just like a well~~-~~built, globally acknowledged brand.~~ <br><br>~~tory burch handbags outletWhile these designer handbags will set you back thousands~~ of ~~dollars, there a wide range of decent handbags that one could get for yourself at inexpensive price points. Vogue aware gals have at least one~~-~~2 pairs of such footwear to flaunt their wardrobe. A small clutch shows an even more carefree~~, ~~whimsical attitude, with no requirement for functional practicality. Or even a researching running shoes for instance Instructor boots~~ and shoes or maybe attractive sneakers want Fitness instructor hunter wellies,Goyard Bags the nonpublic mentor brand are unable to enable anyone right down. The Seven Gulf Luggage tend to get uncommonly great furthermore to exciting cherished about all belle acutely aware wives personalized super stars.		==Definition==

			We work over the polynomial ring '''F'''<sub>''q''</sub>[''T''] of one variable over a [[finite field]] '''F'''<sub>''q''</sub> with ''q'' elements. The [[Completion (metric space)\|completion]] '''C'''<sub>∞</sub> of an [[algebraic closure]] of the field '''F'''<sub>''q''</sub>((''T''<sup>−1</sup>)) of [[formal Laurent series]] in ''T''<sup>−1</sup> will be useful. It is a complete and algebraically closed field.

			First we need analogues to the [[factorials]], which appear in the definition of the usual exponential function. For ''i'' > 0 we define

			:<math>[i] := T^{q^i} - T, \, </math>
			:<math>D_i := \prod_{1 \le j \le i} [j]^{q^{i - j}}</math>

			and ''D''<sub>0</sub> := 1. Note that that the usual factorial is inappropriate here, since ''n''! vanishes in '''F'''<sub>''q''</sub>[''T''] unless ''n'' is smaller than the [[Characteristic (algebra)\|characteristic]] of '''F'''<sub>''q''</sub>[''T''].

			Using this we define the Carlitz exponential ''e''<sub>''C''</sub>:'''C'''<sub>∞</sub> → '''C'''<sub>∞</sub> by the convergent sum

			:<math>e_C(x) := \sum_{j = 0}^\infty \frac{x^{q^j}}{D_i}.</math>

			==Relation to the Carlitz module==

			The Carlitz exponential satisfies the functional equation

			:<math>e_C(Tx) = Te_C(x) + \left(e_C(x)\right)^q = (T + \tau)e_C(x), \, </math>

			where we may view <math> \tau </math> as the power of <math> q </math> map or as an element of the ring <math> F_q(T)\{\tau\} </math> of [[noncommutative polynomials]]. By the [[universal property]] of polynomial rings in one variable this extends to a ring homomorphism ''ψ'':'''F'''<sub>''q''</sub>[''T'']→'''C'''<sub>∞</sub>{''τ''}, defining a Drinfeld '''F'''<sub>''q''</sub>[''T'']-module over '''C'''<sub>∞</sub>{''τ''}. It is called the Carlitz module.

			==References==
			{{reflist}}
			*{{Citation \| last1=Goss \| first1=D. \| authorlink = David Goss \| title=Basic structures of function field arithmetic \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] \| isbn=978-3-540-61087-8 \| mr=1423131 \| year=1996 \| volume=35}}
			*{{Citation \| last1=Thakur \| first1=Dinesh \| first2=S. \| title=Function field arithmetic \| publisher=[[World Scientific Publishing]] \| location=New Jersey\| isbn=981-238-839-7 \| mr=2091265 \| year=2004}}

			[[Category:Algebraic number theory]]
			[[Category:Finite fields]]

en>FrescoBot: Bot: fixing section wikilinks and minor changes

2012-05-28T06:18:25Z

Bot: fixing section wikilinks and minor changes

New page

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