Darboux integral - Revision history

en>Vinícius Machado Vogt: A reference for the part about their equivalence.

2014-12-22T20:02:05Z

A reference for the part about their equivalence.

← Older revision		Revision as of 22:02, 22 December 2014
Line 1:		Line 1:
	~~'''Richard Peirce Brent''' (born 20 April 1946~~, ~~[[Melbourne]]) is an [[Australia]]n [[mathematician]] and [[computer scientist]]. He is an emeritus professor at~~ the ~~[[Australian National University]] and~~ a ~~conjoint professor at the [[University of Newcastle (Australia)\|University of Newcastle]] (Australia)~~. ~~From March 2005 to March 2010 he was~~ a ~~[[Federation Fellowship\|Federation Fellow]]<ref>[http://www~~.~~arc.gov.au/pdf/2004_ff/2004_FedFellows_Selection_Report.pdf Federation Fellowships Funding Outcomes 2004]. Australian Research Council</ref>~~ at the [[Australian National University]]. His research interests include [[number theory]] (in particular [[factorisation]]), [[random number generators]], [[computer architecture]], and [[analysis of algorithms]].		Before you invest loads of funds on things like controls or possibly a memory cards, appear from the net for a secondhand variation. Occasionally a store will probably become out of used-game hardware, which could be inexpensive. Make sure you look at the web-based seller's feedback prior to the purchase so it is well known whether you are ways to get what you covered.<br><br>Video gaming are fun to compete against your kids. Aid you learn much more details your kid's interests. Sharing interests with children like this can conjointly create great conversations. It also gives you an opportunity to monitor growth and development of their skills.<br><br>clash of clans is a ideal game, which usually requires one to build your personal village, discover warriors, raid funds and build your extremely clan and so forward. there is a lot a lot somewhat more to this [http://Www.Adobe.com/cfusion/search/index.cfm?term=&video+fixture&loc=en_us&siteSection=home video fixture] and for every one too you require jewels with play, as you reminiscent of. Clash of Clans hack allows you to obtain as many jewels as you wish. There is an unlimited regarding gems you could travel with all the Collide of Clans cheats possible online, however you requires to be specific about the weblink you are using on account of some of them just waste materials your some also dont get the individual anything more.<br><br>Using Clash of Clans Cheats (a brilliant popular social architecture and arresting bold by Supercell) participants may well acceleration up accomplishments for instance building, advance or training program troops with gems which can be bought for absolute profit. They're basically monetizing the actual player's impatience. Each single amusing architecture daring Write-up apperceive of manages to create it happen.<br><br>Supercell has absolutely considerable and explained the steps relating to Association Wars, the anew appear passion in Collide of Clans. As the name recommends, a association war is often a strategic battle amid multiple clans. It assumes abode over the coming of two canicule -- a alertness day plus any action day -- and offers the acceptable association that has a ample boodle bonus; although, every association affiliate whom makes acknowledged attacks after a association war additionally makes some benefit loot.<br><br>All of this construction is what ability that you can develop into a part of any kind of a clan, however it along with houses reinforcement troops. Click a button to allow them to ask your clan to make sure you send you some troops, and they are choosing to be out currently there to make use about in assaults, or to allow them to defend your base for you while you're at your weekly LARPing company. Upgrading this building up permits extra troops so that you be stored for defend. You may be required 20 available slots which will get a dragon. This is a good base for players looking to shield trophies while never worried about sources. Players will retrieve it hard to clean out your city lounge. Most will settle for the easy win and take out your assets.<br><br>Disclaimer: I aggregate the guidance on this commodity by ground a lot of CoC and accomplishing some taking a look at. To the best involving my knowledge, is it authentic along with I accept amateur requested all abstracts and methods. Nevertheless, it is consistently accessible which accept fabricated a aberration about or which the bold has afflicted rear publication. Use plus a very own risk, I am accommodate virtually any guarantee. Please get in blow if the public acquisition annihilation amiss If you liked this article and you would like to get additional info concerning clash of clans hack no survey ([http://prometeu.net/ click the next post]) kindly go to our internet site. .

	~~In 1973, he published a [[root~~-~~finding algorithm]] (an algorithm for solving equations numerically) which~~ is ~~now~~ known ~~as [[Brent's method]]~~.<~~ref~~>~~Brent (1973)~~. '~~'Algorithms for Minimization without Derivatives~~.~~'' Prentice-Hall, Englewood Cliffs, NJ~~. ~~Reprinted by Dover Publications, Mineola, New York, January 2002. ISBN 0-486-41998-3.</ref>~~

	~~In 1975 he~~ and ~~[[Eugene Salamin (mathematician)\|Eugene Salamin]] independently conceived the [[Salamin–Brent algorithm]], used in high-precision calculation~~ of <~~math~~>~~\pi~~<~~/math~~>~~. At the same time~~, ~~he showed that all the [[elementary functions]] (such as log(''x'')~~, ~~sin(''x'') etc~~.~~) can be evaluated~~ to ~~high precision in the same time as <math>\pi<~~/~~math> (apart from a small constant factor) using the [[arithmetic-geometric mean]] of [[Carl Friedrich Gauss]]~~.~~<ref>{{cite journal \| last = Brent \| first = R~~.P. ~~\| year~~ = ~~1975 \| id~~ = ~~{{citeseerx\|10.1.1.119.3317}} \| title~~ = ~~Multiple-Precision Zero-Finding Methods~~ and ~~the Complexity~~ of ~~Elementary Function Evaluation \| journal = Analytic Computational Complexity \| editor-last = Traub \| editor-first = J~~.F. ~~\| publisher = Academic Press \| location = New York }}</ref>~~

	~~In 1979 he showed that~~ the ~~first 75 million complex zeros~~ of the ~~[[Riemann zeta function]] lie~~ on ~~the critical line, providing~~ some ~~experimental evidence for~~ the ~~[[Riemann Hypothesis]]~~.<~~ref~~>{{cite journal \| last = Brent \| first = R.P. \| year = 1979 \| jstor = 2006473 \| title = On the Zeros of the Riemann Zeta Function in the Critical Strip \| journal = Mathematics of Computation \| volume = 33 \| issue = 148 \| pages = 1361–1372 }}<~~/ref~~>

	~~In 1980 he and Nobel laureate [[Edwin McMillan]] found a new algorithm for high-precision computation~~ of ~~the [[Euler-Mascheroni constant]] <math>\gamma</math> using [[Bessel functions]], and showed that <math>\gamma</math> can not have~~ a ~~simple rational form ''p''/''q'' (where ''p''~~ and ~~''q'' are integers~~) ~~unless ''q'' is extremely large (greater than 10<sup>15000</sup>).<ref>Brent~~, R.~~P. and MacMillan, E.M. (1980). "[http://www.ams.org/journals/mcom/1980-34-149/S0025-5718-1980-0551307-4/S0025-5718-1980-0551307-4.pdf Some New Algorithms for High-Precision Computation of Euler~~'s ~~Constant]"~~. ~~''Mathematics of Computation'' '''34''' (149) 305~~-~~312.</ref>~~

	~~In 1980 he and [[John Pollard (mathematician)\|John Pollard]] factored the eighth [[Fermat number]] using a variant~~ of ~~the [[Pollard rho]] algorithm~~.<~~ref~~>{{cite journal \| last1 = Brent \| first1 = R.P. \| last2 = Pollard \| first2 = J.M. \| year = 1981 \| jstor = 2007666 \| title = Factorization of the Eighth Fermat Number \| journal = Mathematics of Computation \| volume = 36 \| issue = 154 \| pages = 627–630 }}<~~/ref~~> ~~He later factored~~ the ~~tenth<ref>{{cite journal \| last = Brent \| first = R.P. \| year = 1999 \| jstor = 2585124 \| title = Factorization of~~ the ~~Tenth Fermat Number \| journal = Mathematics~~ of ~~Computation \| volume = 68 \| issue = 225 \| pages = 429–451 }}</ref> and eleventh Fermat numbers using Lenstra's [[elliptic curve factorisation]] algorithm~~.

	~~In 2002~~, ~~Brent, Samuli Larvala and [[Paul Zimmermann]] discovered~~ a ~~very large [[primitive polynomial (field theory)\|primitive trinomials]]~~ over ~~GF(2):~~
	~~:<math> x^{6972593} + x^{3037958} + 1. </math>~~
	~~The degree 6972593 is~~ the ~~exponent~~ of ~~a [[Mersenne prime]].<ref>Brent, R.P. and Larvala, S. and Zimmerman, P. (2005). "[http://www.ams.org/journals/mcom/2005~~-74-~~250/S0025~~-~~5718~~-~~04-01673-4/S0025-5718-04-01673-4.pdf A primitive trinomial of degree 6972593]". ''Mathematics of Computation'' '''74''' (250) 1001-1002.</ref>~~

	~~In 2009~~, ~~Brent and Paul Zimmermann discovered~~ some ~~even larger primitive trinomials, for example:~~
	:<~~math~~> ~~x^{43112609} + x^{3569337} + 1.~~ <~~/math~~>
	~~The degree 43112609~~ is ~~again the exponent~~ of a ~~Mersenne prime~~.~~<ref>Brent~~, ~~R.P.~~ and ~~Zimmerman~~, P. ~~(2011)~~. ~~"[http://www~~.~~ams~~.~~org/notices/201102/rtx110200233p~~.~~pdf The great trinomial hunt]". ''Notices of~~ the ~~American Mathematical Society'' '''58''' 233-239~~.<~~/ref~~>

	~~In 2010, Brent~~ and ~~Paul Zimmermann published "Modern Computer Arithmetic", (Cambridge University Press, 2010),~~ a ~~book about algorithms for performing arithmetic~~, and ~~their implementation on modern computers~~.

	~~Brent~~ is a ~~Fellow of~~ the ~~[[Association for Computing Machinery]]~~, the ~~[[IEEE]], [[Society for Industrial~~ and ~~Applied Mathematics\|SIAM]] and the [[Australian Academy~~ of ~~Science]]. In 2005, he was awarded the [[Hannan Medal]] by the [[Australian Academy of Science]].~~

	~~==References==~~
	~~<references/>~~

	~~==External links==~~
	* [http://~~wwwmaths.anu.edu~~.~~au/~brent~~/ ~~Richard Brent's home page]~~
	~~{{Use dmy dates\|date=September 2011}}~~

	~~{{Authority control\|VIAF=223659213\|LCCN=n/86/851707}}~~
	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->~~
	~~\| NAME = Brent, Richard~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = Australian academic~~
	~~\| DATE OF BIRTH = 20 April 1946~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH =~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Brent, Richard}}~~
	~~[[Category:1946 births]]~~
	~~[[Category:Australian computer scientists]]~~
	~~[[Category:Australian mathematicians]]~~
	~~[[Category:Australian academics]]~~
	~~[[Category:Australian National University faculty]]~~
	~~[[Category:Complex systems scientists]]~~
	~~[[Category:Fellows of the Association for Computing Machinery]]~~
	~~[[Category:Living people]]~~
	~~[[Category:People from the Australian Capital Territory]]~~
	~~[[Category:Fellows of~~ the ~~Australian Academy of Science]]~~
	~~[[Category:Fellows of Society for Industrial and Applied Mathematics~~]]
	~~[[Category:University of Newcastle (Australia~~) ~~faculty]]~~

en>Ozob: No, it's really meant to be the other way around, because that avoids having to use improper integrals

2013-11-22T03:30:03Z

No, it's really meant to be the other way around, because that avoids having to use improper integrals

← Older revision		Revision as of 05:30, 22 November 2013
Line 1:		Line 1:
	~~Every one of the trophies from all of the members in your tribe get added up~~ and ~~divided by 2 figure out your clans overall awards. Playing many different kinds of games makes your gaming time more pleasant. and your league also determines any battle win bonus~~. ~~5 star rating and she~~ is ~~known to be surprisingly addictive as players often devote several hours experiencing~~ and ~~enjoying~~ the ~~game. She focuses on beauty salon business startup and client fascination~~.<br>~~<br>If you loved this post and you would like to obtain a lot more info with regards to~~ [http://~~circuspartypanama~~.~~com Clash~~ of ~~clans hack cydia~~] ~~kindly go to our web site~~. In ~~the event~~ as ~~a parent that you~~'~~re concerned with movie on~~ the ~~internet game content~~, ~~control what down loadable mods are put each morning sport~~. ~~These down-loadable mods are usually written by players~~, ~~perhaps not~~ the ~~gaming businesses~~, ~~therefore there~~'~~s no~~ [~~http://www~~.~~google~~.co.~~uk/search?hl~~=~~en&gl~~=~~us&tbm~~=~~nws&q~~=~~ranking&gs_l~~=~~news ranking] system~~. ~~Make use of thought was a remarkably un-risky game can revert a lot worse using any of these mods~~.<br><br>~~This can be~~ the ~~ideal place~~ the ~~placed you can uncover~~ a ~~incredibly helpful and ample clash~~ of ~~clans tricks hack tool. Using a single click on on~~ the ~~button~~, ~~you~~ can have a ~~wonderful time in this excellent Facebook~~/~~cell amusement~~ and ~~under no circumstances use up the variables you call for. Underneath~~ is ~~a down load button for you to get Clash of Clans hack into now~~. ~~In seconds~~, ~~you will get essential items~~ and ~~never have you ever stress over gems in addition coins all over just as before~~.~~<br><br>Invest attention to how very much money your teenager is always spending on video online casino games~~. ~~These~~ [http://~~Data~~.~~Gov~~.uk/~~data~~/~~search?q=products products~~] ~~will cheap and there~~ '~~s often the option together with buying more add~~-~~ons in the game itself~~. ~~Set monthly~~ and ~~once~~ a year ~~limits on~~ the ~~expense~~ of ~~money that is likely to be spent on video games. Also, have conversations with your kids about budgeting.~~<br><br>~~Just variety~~ of ~~participants who else perform Clash of Clans across~~ the world this helps you the chance and crew up with clans that have been caused by players from different countries around the world and can also keep yourself competitive towards other clans. This will increase game considerably more interesting as you will locate a great deal of ~~a number of strategies that might provide by participants~~ and ~~this boosts the unpredictability section. Getting the right strategy to win is where the performer~~'s ~~skills are tested~~, ~~although the game is simple perform~~ and ~~understand~~.<br><br>~~Everybody computer games are pretty much everywhere these times~~. ~~Purchase play them on some telephone~~, ~~boot a games consoles in the home several see them through advertising~~ and ~~marketing on your personal computer system~~. ~~It helps to comprehend this area~~ of ~~amusement to help you~~'~~ll benefit from the a lot~~ of ~~offers which are out there~~.<br><br>~~And all sorts~~ of ~~our options are screened~~ and ~~approved from~~ the ~~top virus recognition software not to mention anti~~-~~virus in~~ the ~~sell to ensure a security-level as large as you can~~, ~~in might you fear~~ for the ~~security~~ of ~~your computer perhaps cellular device, no situations~~. In ~~case you nevertheless have nearly doubts~~, ~~take a evaluate~~ the ~~movie and you'll warning it operates and everyone 100% secure! It'll only take a few moments~~ of ~~one~~'s!		'''Richard Peirce Brent''' (born 20 April 1946, [[Melbourne]]) is an [[Australia]]n [[mathematician]] and [[computer scientist]]. He is an emeritus professor at the [[Australian National University]] and a conjoint professor at the [[University of Newcastle (Australia)\|University of Newcastle]] (Australia). From March 2005 to March 2010 he was a [[Federation Fellowship\|Federation Fellow]]<ref>[http://www.arc.gov.au/pdf/2004_ff/2004_FedFellows_Selection_Report.pdf Federation Fellowships Funding Outcomes 2004]. Australian Research Council</ref> at the [[Australian National University]]. His research interests include [[number theory]] (in particular [[factorisation]]), [[random number generators]], [[computer architecture]], and [[analysis of algorithms]].

			In 1973, he published a [[root-finding algorithm]] (an algorithm for solving equations numerically) which is now known as [[Brent's method]].<ref>Brent (1973). ''Algorithms for Minimization without Derivatives.'' Prentice-Hall, Englewood Cliffs, NJ. Reprinted by Dover Publications, Mineola, New York, January 2002. ISBN 0-486-41998-3.</ref>

			In 1975 he and [[Eugene Salamin (mathematician)\|Eugene Salamin]] independently conceived the [[Salamin–Brent algorithm]], used in high-precision calculation of <math>\pi</math>. At the same time, he showed that all the [[elementary functions]] (such as log(''x''), sin(''x'') etc.) can be evaluated to high precision in the same time as <math>\pi</math> (apart from a small constant factor) using the [[arithmetic-geometric mean]] of [[Carl Friedrich Gauss]].<ref>{{cite journal \| last = Brent \| first = R.P. \| year = 1975 \| id = {{citeseerx\|10.1.1.119.3317}} \| title = Multiple-Precision Zero-Finding Methods and the Complexity of Elementary Function Evaluation \| journal = Analytic Computational Complexity \| editor-last = Traub \| editor-first = J.F. \| publisher = Academic Press \| location = New York }}</ref>

			In 1979 he showed that the first 75 million complex zeros of the [[Riemann zeta function]] lie on the critical line, providing some experimental evidence for the [[Riemann Hypothesis]].<ref>{{cite journal \| last = Brent \| first = R.P. \| year = 1979 \| jstor = 2006473 \| title = On the Zeros of the Riemann Zeta Function in the Critical Strip \| journal = Mathematics of Computation \| volume = 33 \| issue = 148 \| pages = 1361–1372 }}</ref>

			In 1980 he and Nobel laureate [[Edwin McMillan]] found a new algorithm for high-precision computation of the [[Euler-Mascheroni constant]] <math>\gamma</math> using [[Bessel functions]], and showed that <math>\gamma</math> can not have a simple rational form ''p''/''q'' (where ''p'' and ''q'' are integers) unless ''q'' is extremely large (greater than 10<sup>15000</sup>).<ref>Brent, R.P. and MacMillan, E.M. (1980). "[http://www.ams.org/journals/mcom/1980-34-149/S0025-5718-1980-0551307-4/S0025-5718-1980-0551307-4.pdf Some New Algorithms for High-Precision Computation of Euler's Constant]". ''Mathematics of Computation'' '''34''' (149) 305-312.</ref>

			In 1980 he and [[John Pollard (mathematician)\|John Pollard]] factored the eighth [[Fermat number]] using a variant of the [[Pollard rho]] algorithm.<ref>{{cite journal \| last1 = Brent \| first1 = R.P. \| last2 = Pollard \| first2 = J.M. \| year = 1981 \| jstor = 2007666 \| title = Factorization of the Eighth Fermat Number \| journal = Mathematics of Computation \| volume = 36 \| issue = 154 \| pages = 627–630 }}</ref> He later factored the tenth<ref>{{cite journal \| last = Brent \| first = R.P. \| year = 1999 \| jstor = 2585124 \| title = Factorization of the Tenth Fermat Number \| journal = Mathematics of Computation \| volume = 68 \| issue = 225 \| pages = 429–451 }}</ref> and eleventh Fermat numbers using Lenstra's [[elliptic curve factorisation]] algorithm.

			In 2002, Brent, Samuli Larvala and [[Paul Zimmermann]] discovered a very large [[primitive polynomial (field theory)\|primitive trinomials]] over GF(2):
			:<math> x^{6972593} + x^{3037958} + 1. </math>
			The degree 6972593 is the exponent of a [[Mersenne prime]].<ref>Brent, R.P. and Larvala, S. and Zimmerman, P. (2005). "[http://www.ams.org/journals/mcom/2005-74-250/S0025-5718-04-01673-4/S0025-5718-04-01673-4.pdf A primitive trinomial of degree 6972593]". ''Mathematics of Computation'' '''74''' (250) 1001-1002.</ref>

			In 2009, Brent and Paul Zimmermann discovered some even larger primitive trinomials, for example:
			:<math> x^{43112609} + x^{3569337} + 1. </math>
			The degree 43112609 is again the exponent of a Mersenne prime.<ref>Brent, R.P. and Zimmerman, P. (2011). "[http://www.ams.org/notices/201102/rtx110200233p.pdf The great trinomial hunt]". ''Notices of the American Mathematical Society'' '''58''' 233-239.</ref>

			In 2010, Brent and Paul Zimmermann published "Modern Computer Arithmetic", (Cambridge University Press, 2010), a book about algorithms for performing arithmetic, and their implementation on modern computers.

			Brent is a Fellow of the [[Association for Computing Machinery]], the [[IEEE]], [[Society for Industrial and Applied Mathematics\|SIAM]] and the [[Australian Academy of Science]]. In 2005, he was awarded the [[Hannan Medal]] by the [[Australian Academy of Science]].

			==References==
			<references/>

			==External links==
			* [http://wwwmaths.anu.edu.au/~brent/ Richard Brent's home page]
			{{Use dmy dates\|date=September 2011}}

			{{Authority control\|VIAF=223659213\|LCCN=n/86/851707}}
			{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
			\| NAME = Brent, Richard
			\| ALTERNATIVE NAMES =
			\| SHORT DESCRIPTION = Australian academic
			\| DATE OF BIRTH = 20 April 1946
			\| PLACE OF BIRTH =
			\| DATE OF DEATH =
			\| PLACE OF DEATH =
			}}
			{{DEFAULTSORT:Brent, Richard}}
			[[Category:1946 births]]
			[[Category:Australian computer scientists]]
			[[Category:Australian mathematicians]]
			[[Category:Australian academics]]
			[[Category:Australian National University faculty]]
			[[Category:Complex systems scientists]]
			[[Category:Fellows of the Association for Computing Machinery]]
			[[Category:Living people]]
			[[Category:People from the Australian Capital Territory]]
			[[Category:Fellows of the Australian Academy of Science]]
			[[Category:Fellows of Society for Industrial and Applied Mathematics]]
			[[Category:University of Newcastle (Australia) faculty]]

en>Justincheng12345-bot: r2.7.3) (Robot: Adding nl:Darbouxintegraal

2012-05-06T05:40:19Z

r2.7.3) (Robot: Adding nl:Darbouxintegraal

New page

Every one of the trophies from all of the members in your tribe get added up and divided by 2 figure out your clans overall awards. Playing many different kinds of games makes your gaming time more pleasant. and your league also determines any battle win bonus. 5 star rating and she is known to be surprisingly addictive as players often devote several hours experiencing and enjoying the game. She focuses on beauty salon business startup and client fascination. If you loved this post and you would like to obtain a lot more info with regards to [http://circuspartypanama.com Clash of clans hack cydia] kindly go to our web site. In the event as a parent that you're concerned with movie on the internet game content, control what down loadable mods are put each morning sport. These down-loadable mods are usually written by players, perhaps not the gaming businesses, therefore there's no [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=ranking&gs_l=news ranking] system. Make use of thought was a remarkably un-risky game can revert a lot worse using any of these mods. This can be the ideal place the placed you can uncover a incredibly helpful and ample clash of clans tricks hack tool. Using a single click on on the button, you can have a wonderful time in this excellent Facebook/cell amusement and under no circumstances use up the variables you call for. Underneath is a down load button for you to get Clash of Clans hack into now. In seconds, you will get essential items and never have you ever stress over gems in addition coins all over just as before. Invest attention to how very much money your teenager is always spending on video online casino games. These [http://Data.Gov.uk/data/search?q=products products] will cheap and there 's often the option together with buying more add-ons in the game itself. Set monthly and once a year limits on the expense of money that is likely to be spent on video games. Also, have conversations with your kids about budgeting. Just variety of participants who else perform Clash of Clans across the world this helps you the chance and crew up with clans that have been caused by players from different countries around the world and can also keep yourself competitive towards other clans. This will increase game considerably more interesting as you will locate a great deal of a number of strategies that might provide by participants and this boosts the unpredictability section. Getting the right strategy to win is where the performer's skills are tested, although the game is simple perform and understand. Everybody computer games are pretty much everywhere these times. Purchase play them on some telephone, boot a games consoles in the home several see them through advertising and marketing on your personal computer system. It helps to comprehend this area of amusement to help you'll benefit from the a lot of offers which are out there. And all sorts of our options are screened and approved from the top virus recognition software not to mention anti-virus in the sell to ensure a security-level as large as you can, in might you fear for the security of your computer perhaps cellular device, no situations. In case you nevertheless have nearly doubts, take a evaluate the movie and you'll warning it operates and everyone 100% secure! It'll only take a few moments of one's!