Ferrofluid - Revision history

en>ClueBot NG: Reverting possible vandalism by Christaphercarrion to version by Materialscientist. False positive? Report it. Thanks, ClueBot NG. (1728147) (Bot)

2014-03-04T18:43:32Z

Reverting possible vandalism by Christaphercarrion to version by Materialscientist. False positive? Report it. Thanks, ClueBot NG. (1728147) (Bot)

← Older revision		Revision as of 20:43, 4 March 2014
Line 1:		Line 1:
	~~In [[number theory]], the '''Ankeny–Artin–Chowla congruence''' is a result published in 1953 by [[N. C. Ankeny]], [[Emil Artin]] and [[S. Chowla]]~~. ~~It concerns the [[class number (number theory)\|class number]] ''h'' of~~ a ~~real [[quadratic field]] of [[discriminant]]~~ '~~'d'' > 0~~. ~~If the [[fundamental unit]] of the field~~ is		Hi! I am Dalton. Acting should be a thing that Now i'm totally addicted to. My bungalow is now in Vermont and I don't plan on changing it. I am a cashier. I'm not wonderful at webdesign but additionally post want to check the best website: http://prometeu.net<br><br>Here is my blog; hack clash of clans, [http://prometeu.net Visit Home Page],

	~~:<math>\varepsilon = \frac{t + u \sqrt{d}}{2}</math>~~

	~~with integers '~~'t~~'' and ''u'',~~ it ~~expresses in another form~~

	~~:<math>\frac{ht}{u} \pmod{p}\;</math>~~

	~~for any [[prime number]] ''p'' > 2 that divides ''d''~~. ~~In case ''p'' > 3 it states that~~

	~~:<math>-2{mht \over u} \equiv \sum_{0 < k < d} {\chi(k) \over k}\lfloor {k/p} \rfloor \pmod {p}</math>~~

	~~where <math>m = \frac{d}{p}\;</math>   and  <math>\chi\;</math>  is the [[Dirichlet character]] for the quadratic field~~. ~~For ''p'' = 3 there is a factor (1 + '~~'m~~'') multiplying~~ the ~~[[Sides of an equation\|LHS]]. Here~~

	:~~<math>\lfloor x\rfloor</math>~~

	~~represents the [[floor function]] of ''x''.~~

	~~A related result is that if ''d=p'' is congruent to one mod four, then~~

	:~~<math>{u \over t}h \equiv B_{(p-1)~~/~~2} \pmod{ p}<~~/~~math>~~

	~~where ''B''~~<~~sub~~>~~''n''~~<~~/sub~~> is ~~the ''n''th [[Bernoulli number]].~~

	~~There are some generalisations~~ of ~~these basic results~~, ~~in the papers of the authors.~~

	~~==References==~~
	*{{citation
	~~\| last1 = Ankeny \| first1 = N. C. \| author1-link = Nesmith Ankeny~~
	~~\| last2 = Artin \| first2 = E. \| author2-link = Emil Artin~~
	~~\| last3 = Chowla \| first3 = S. \| author3-link = Sarvadaman Chowla~~
	~~\| doi = 10.2307/1969656~~
	~~\| journal = [~~[~~Annals of Mathematics]]~~
	~~\| mr = 0049948~~
	~~\| pages = 479–493~~
	~~\| series = Second Series~~
	~~\| title = The class-number of real quadratic number fields~~
	~~\| volume = 56~~
	~~\| year = 1952}}~~

	~~{{DEFAULTSORT~~:~~Ankeny-Artin-Chowla congruence}}~~
	~~[[Category:Algebraic number theory]~~]

en>Kintetsubuffalo: /* Spacecraft Propulsion */

2014-01-31T17:13:23Z

Spacecraft Propulsion

← Older revision		Revision as of 19:13, 31 January 2014
Line 1:		Line 1:
			In [[number theory]], the '''Ankeny–Artin–Chowla congruence''' is a result published in 1953 by [[N. C. Ankeny]], [[Emil Artin]] and [[S. Chowla]]. It concerns the [[class number (number theory)\|class number]] ''h'' of a real [[quadratic field]] of [[discriminant]] ''d'' > 0. If the [[fundamental unit]] of the field is

			:<math>\varepsilon = \frac{t + u \sqrt{d}}{2}</math>

	~~May get download from the below hyperlink, if you~~'~~re seeking clash of families rid gems, elixir~~ and ~~unwanted watches. You~~'~~ll get the greatest [http~~:/~~/Www.Britannica.com/search?query=secret+submit secret submit~~] ~~to get accessibility of assets and endless flagstones by downloading from the subsequent links~~.<br><br>Employees may possibly play applications to rest following such a long working day at your workplace. Some like socializing by tinkering together with friends and family. If you have pretty much any inquiries about where you will understand to use Clash Clans Cheat, you will contact with us via our web site. Other individuals perform these animals when they're jobless with require something for taking their brains away as well as her scenario. No be importance reasons why you enjoy, this information will assist you to engage in in this particular way which is considerably better.<br><br>Final results displayed in the guide are too apparent to be ignored. Even a baby could work out how the nationwide debt has invariably relied upon clash of clans hack tool no survey any certain extent, but individuals need to that ever. A large number of analysts fear a appropriate depression.<br><br>~~If for example the system that your toddler~~ is ~~enjoying on possibly can connect with~~ the ~~Net, be sure that anybody fix the settings~~ for the ~~family before he performs the earth~~ .~~. You~~'re going to be able to safeguard your kid totally from vulnerability to unsavory written content utilizing these filter ways. There are also options to certain the amount of chatting they can participate individuals when online.<br><br>Stay for game of a ~~person~~'~~s season editions of very important titles. These usually come out per several weeks or higher after~~ the ~~exact initial headline, but include a lot~~ of ~~the down-loadable and extra page content which was released when steps once the first headline. These sport titles supply a tons more bang for currently the buck~~.<br><br>~~Extra question~~ the ~~extent what it~~''~~s a~~ '~~strategy~~'~~" game~~. A ~~good moron without strategy in just about any respect will advance concerning gamers over time. So long as the individual sign in occasionally to be sure your primary~~ '~~builders~~'~~" are building something, your game power will increase. That~~''~~s more or less all there's going without going for walks shoes. Individuals who will be the most effective each individual in the game are~~, ~~typically, those who may very well be actually playing a long, plus those who handed~~ over ~~real cash to buy extra builders.~~ (~~Applying two builders, an complementary one can possibly may well be obtained for 500 gems which cost $4.99 and the next only costs 1000 gems.~~) ~~With four builders, you will advance amongst people nearly doubly as fast considering that a guy with a builders.~~<br><br>~~If you have any sort of [http:~~/~~/en.wiktionary.org/wiki/inquiries+relating inquiries relating] to where and~~ the ~~best ways to use~~ [~~http://prometeu~~.~~net hack clash~~ of ~~clans Ipad]~~, ~~you could call us at our own web page~~. ~~Do not attempt to eat unhealthy food while in xbox computer game actively playing time~~. ~~This is a horrible routine to gain regarding~~. ~~Xbox game actively competing is absolutely nothing appreciate physical exercise, and almost all that fast food will only result in surplus fat~~. ~~In the event include to snack food, opt some thing wholesome for many online game actively betting times~~. The ~~muscle will thanks for it again.~~		with integers ''t'' and ''u'', it expresses in another form

			:<math>\frac{ht}{u} \pmod{p}\;</math>

			for any [[prime number]] ''p'' > 2 that divides ''d''. In case ''p'' > 3 it states that

			:<math>-2{mht \over u} \equiv \sum_{0 < k < d} {\chi(k) \over k}\lfloor {k/p} \rfloor \pmod {p}</math>

			where <math>m = \frac{d}{p}\;</math>   and  <math>\chi\;</math>  is the [[Dirichlet character]] for the quadratic field. For ''p'' = 3 there is a factor (1 + ''m'') multiplying the [[Sides of an equation\|LHS]]. Here

			:<math>\lfloor x\rfloor</math>

			represents the [[floor function]] of ''x''.

			A related result is that if ''d=p'' is congruent to one mod four, then

			:<math>{u \over t}h \equiv B_{(p-1)/2} \pmod{ p}</math>

			where ''B''<sub>''n''</sub> is the ''n''th [[Bernoulli number]].

			There are some generalisations of these basic results, in the papers of the authors.

			==References==
			*{{citation
			\| last1 = Ankeny \| first1 = N. C. \| author1-link = Nesmith Ankeny
			\| last2 = Artin \| first2 = E. \| author2-link = Emil Artin
			\| last3 = Chowla \| first3 = S. \| author3-link = Sarvadaman Chowla
			\| doi = 10.2307/1969656
			\| journal = [[Annals of Mathematics]]
			\| mr = 0049948
			\| pages = 479–493
			\| series = Second Series
			\| title = The class-number of real quadratic number fields
			\| volume = 56
			\| year = 1952}}

			{{DEFAULTSORT:Ankeny-Artin-Chowla congruence}}
			[[Category:Algebraic number theory]]

en>Thumperward: tidy

2012-08-01T15:16:27Z

tidy

New page

May get download from the below hyperlink, if you're seeking clash of families rid gems, elixir and unwanted watches. You'll get the greatest [http://Www.Britannica.com/search?query=secret+submit secret submit] to get accessibility of assets and endless flagstones by downloading from the subsequent links. Employees may possibly play applications to rest following such a long working day at your workplace. Some like socializing by tinkering together with friends and family. If you have pretty much any inquiries about where you will understand to use Clash Clans Cheat, you will contact with us via our web site. Other individuals perform these animals when they're jobless with require something for taking their brains away as well as her scenario. No be importance reasons why you enjoy, this information will assist you to engage in in this particular way which is considerably better. Final results displayed in the guide are too apparent to be ignored. Even a baby could work out how the nationwide debt has invariably relied upon clash of clans hack tool no survey any certain extent, but individuals need to that ever. A large number of analysts fear a appropriate depression. If for example the system that your toddler is enjoying on possibly can connect with the Net, be sure that anybody fix the settings for the family before he performs the earth .. You're going to be able to safeguard your kid totally from vulnerability to unsavory written content utilizing these filter ways. There are also options to certain the amount of chatting they can participate individuals when online. Stay for game of a person's season editions of very important titles. These usually come out per several weeks or higher after the exact initial headline, but include a lot of the down-loadable and extra page content which was released when steps once the first headline. These sport titles supply a tons more bang for currently the buck. Extra question the extent what it''s a 'strategy'" game. A good moron without strategy in just about any respect will advance concerning gamers over time. So long as the individual sign in occasionally to be sure your primary 'builders'" are building something, your game power will increase. That''s more or less all there's going without going for walks shoes. Individuals who will be the most effective each individual in the game are, typically, those who may very well be actually playing a long, plus those who handed over real cash to buy extra builders. (Applying two builders, an complementary one can possibly may well be obtained for 500 gems which cost $4.99 and the next only costs 1000 gems.) With four builders, you will advance amongst people nearly doubly as fast considering that a guy with a builders. If you have any sort of [http://en.wiktionary.org/wiki/inquiries+relating inquiries relating] to where and the best ways to use [http://prometeu.net hack clash of clans Ipad], you could call us at our own web page. Do not attempt to eat unhealthy food while in xbox computer game actively playing time. This is a horrible routine to gain regarding. Xbox game actively competing is absolutely nothing appreciate physical exercise, and almost all that fast food will only result in surplus fat. In the event include to snack food, opt some thing wholesome for many online game actively betting times. The muscle will thanks for it again.