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2014-09-03T15:28:25Z

Removing Link GA template (handled by wikidata)

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96.57.132.179: Links to Quality Metrics added.

2014-02-21T19:48:33Z

Links to Quality Metrics added.

← Older revision		Revision as of 21:48, 21 February 2014
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	'''Nielsen theory''' is a branch of mathematical research with its origins in [[topological]] [[fixed point theory]]. Its central ideas were developed by Danish mathematician [[Jakob Nielsen (mathematician)\|Jakob Nielsen]], and bear his name.

	The theory developed in the study of the so-called ''minimal number'' of a [[map (mathematics)\|map]] ''f'' from a [[compact (topology)\|compact]] space to itself, denoted ''MF''[''f'']. This is defined as:
	~~:<math>\mathit{MF}[f] = \min \{ \# \mathrm{Fix}(g) \, \| \, g \sim f \},</math>~~
	where ''~'' indicates [[homotopy]] of mappings, and #Fix(''g'') indicates the number of fixed points of ''g''. The minimal number was very difficult to compute in Nielsen's time, and remains so today. Nielsen's approach is to group the fixed point set into classes, which are judged "essential" or "nonessential" according to whether or not they can be "removed" by a homotopy.

	~~Nielsen~~'~~s original formulation~~ is ~~equivalent~~ to the ~~following~~:		Manage your time wisely when you are trying to make money online. You may have a real-world job, which means you have to budget time wisely. Set a schedule that will allow you enough time to balance the two. Also make sure that you are being efficient in that time, so you don't run into stress [http://www.comoganhardinheiro101.com/index.php como ganhar dinheiro] about working online. Becoming a ghost writer is a great way to earn money online. There are people who need content for their websites, but who lack good writing skills. You can write for them and earn money for what you write. Many people are earning a good income writing for others this way. <br><br><br>If you have the ability to type quickly, you may consider transcription jobs. You need to have good headphones and the ability to keep up with what is being said. Often, the companies will have their own formatting guidelines. 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	~~We define an [[equivalence relation~~]~~] on the set~~ of ~~fixed~~ points of a ~~self~~-~~map ''f''~~ on a ~~space ''X~~''. ~~We say that ''x'~~' is ~~equivalent~~ to ~~''y''~~ if and ~~only~~ if ~~there exists~~ a [~~[path (topology)\|path]~~] '~~'c''~~ from ~~''x''~~ to ~~''y'' with ''f''(''c'') homotopic~~ to '~~'c'' as paths~~. ~~The equivalence classes with respect~~ to ~~this relation~~ are ~~called~~ the ~~'''Nielsen classes''' of ''f''~~, and the '~~''Nielsen number''' ''N''(''f'') is defined as~~ the ~~number~~ of ~~Nielsen classes having non~~-~~zero [[fixed point index~~]~~] sum~~.

	~~Nielsen proved~~ that		Several websites out there pay for people to do tasks that cannot be handled by a computer. It might be flagging inappropriate activity or finding the name of a business on a receipt. These tasks require human intelligence to find the answer. They are reasonably simple to perform and can provide you with some extra [http://www.comoganhardinheiro101.com/?p=8 ganhe dinheiro] money. If you're ready to check out more information about [http://comoganhardinheiro.comoganhardinheiro101.com como ganhar dinheiro] look at http://comoganhardinheiro.comoganhardinheiro101.com Translate documents if you are fluent in a second language and want to make money on the side. Check out the freelancing sites to find people who will need things altered into a different language. This can be anyone from a large corporation to an individual who wants to [http://Ganhedinheiro.Comoganhardinheiro101.com/ translate] something for a friend.<br><br>When you work online, the world is your oyster. You are free to do, act and be as you wish, but only if you know what you're doing. If you want to turn your online work into a profitable career, use the tips you've read today and make it happen. When you are in a [http://www.comoganhardinheiro101.com/?p=10 como ganhar dinheiro na internet] hurry to make money, reading about the topic may seem frustrating. The fact is that the more you know, the faster and better you will be at bringing in income. This article has given you the foundation you need, so build on it with experience and more learning.<br><br>that's a lie. Don't fall prey to these types of websites and always read the reviews before joining. Talking to experts in their field can help you to use [http://www.comoganhardinheiro101.com/2013/11/ como ficar rico] the Internet successfully. Try to network with people who do what you want to do. Doing these things can help give you an advantage over your competition.
	~~:<math>N(f) \le \mathit{MF}[f],</math>~~
	~~making his invariant~~ a ~~good tool for estimating~~ the ~~much more difficult ''MF''~~[~~''f''~~]. ~~This leads immediately~~ to ~~what is now known as the '''Nielsen fixed point theorem~~:~~''' ''Any map f has~~ at ~~least N(f) fixed points~~.''

	~~Because of its definition~~ in ~~terms of~~ the [~~[fixed point index]~~], the ~~Nielsen number~~ is ~~closely related~~ to ~~the [[Lefschetz number]]. Indeed~~, ~~shortly after Nielsen~~'~~s initial~~ work~~, the two invariants were combined~~ into a ~~single "generalized Lefschetz number" (more recently called~~ the ~~[[Reidemeister trace]]) by [[Wecken]]~~ and [~~[Reidemeister]]~~.

	~~==Bibliography==~~
	*{{cite book
	~~\| last~~=~~[[Werner Fenchel\|Fenchel~~]]
	~~\| first=[[Werner Fenchel\|Werner]]~~
	~~\| coauthors=[[Jakob Nielsen (mathematician)\|Nielsen~~, ~~Jakob]]; edited by Asmus L~~. ~~Schmidt~~
	~~\| title=Discontinuous groups~~ of ~~isometries in~~ the ~~hyperbolic plane~~
	~~\| series=De Gruyter Studies~~ in ~~mathematics~~
	~~\| volume=29~~
	~~\| publisher=Walter de Gruyter & Co.~~
	~~\| location=Berlin~~
	~~\| year=2003~~
	}}

	~~==External links==~~
	*[http://at.~~yorku~~.~~ca/t~~/a/i/~~c/39~~.~~htm Survey article on Nielsen theory] by Robert F~~. ~~Brown at [[Topology Atlas]]~~

	~~[[Category:Fixed-point theorems]]~~
	~~[[Category:Fixed points (mathematics)]]~~
	~~[[Category:Topology]]~~

80.82.201.37: /* Vastness of the problem */

2013-10-11T09:03:31Z

Vastness of the problem

← Older revision		Revision as of 11:03, 11 October 2013
Line 1:		Line 1:
	~~36 years old Make Up Artist Judson~~ from ~~Rexton~~, ~~has hobbies which includes shark fishing~~, ~~ganhando dinheiro na internet~~ and ~~keep~~. ~~Likes~~ to go to ~~new locations like Natural System~~ of ~~Wrangel Island Reserve~~.<br><br>~~Also visit my website~~ [http://~~comoganhardinheiro~~.~~comoganhardinheiro101~~.~~com como ganhar dinheiro~~]		'''Nielsen theory''' is a branch of mathematical research with its origins in [[topological]] [[fixed point theory]]. Its central ideas were developed by Danish mathematician [[Jakob Nielsen (mathematician)\|Jakob Nielsen]], and bear his name.

			The theory developed in the study of the so-called ''minimal number'' of a [[map (mathematics)\|map]] ''f'' from a [[compact (topology)\|compact]] space to itself, denoted ''MF''[''f'']. This is defined as:
			:<math>\mathit{MF}[f] = \min \{ \# \mathrm{Fix}(g) \, \| \, g \sim f \},</math>
			where ''~'' indicates [[homotopy]] of mappings, and #Fix(''g'') indicates the number of fixed points of ''g''. The minimal number was very difficult to compute in Nielsen's time, and remains so today. Nielsen's approach is to group the fixed point set into classes, which are judged "essential" or "nonessential" according to whether or not they can be "removed" by a homotopy.

			Nielsen's original formulation is equivalent to the following:
			We define an [[equivalence relation]] on the set of fixed points of a self-map ''f'' on a space ''X''. We say that ''x'' is equivalent to ''y'' if and only if there exists a [[path (topology)\|path]] ''c'' from ''x'' to ''y'' with ''f''(''c'') homotopic to ''c'' as paths. The equivalence classes with respect to this relation are called the '''Nielsen classes''' of ''f'', and the '''Nielsen number''' ''N''(''f'') is defined as the number of Nielsen classes having non-zero [[fixed point index]] sum.

			Nielsen proved that
			:<math>N(f) \le \mathit{MF}[f],</math>
			making his invariant a good tool for estimating the much more difficult ''MF''[''f'']. This leads immediately to what is now known as the '''Nielsen fixed point theorem:''' ''Any map f has at least N(f) fixed points.''

			Because of its definition in terms of the [[fixed point index]], the Nielsen number is closely related to the [[Lefschetz number]]. Indeed, shortly after Nielsen's initial work, the two invariants were combined into a single "generalized Lefschetz number" (more recently called the [[Reidemeister trace]]) by [[Wecken]] and [[Reidemeister]].

			==Bibliography==
			*{{cite book
			\| last=[[Werner Fenchel\|Fenchel]]
			\| first=[[Werner Fenchel\|Werner]]
			\| coauthors=[[Jakob Nielsen (mathematician)\|Nielsen, Jakob]]; edited by Asmus L. Schmidt
			\| title=Discontinuous groups of isometries in the hyperbolic plane
			\| series=De Gruyter Studies in mathematics
			\| volume=29
			\| publisher=Walter de Gruyter & Co.
			\| location=Berlin
			\| year=2003
			}}

			==External links==
			*[http://at.yorku.ca/t/a/i/c/39.htm Survey article on Nielsen theory] by Robert F. Brown at [[Topology Atlas]]

			[[Category:Fixed-point theorems]]
			[[Category:Fixed points (mathematics)]]
			[[Category:Topology]]

en>Khazar2: Help needed: Dilatation

2012-04-17T11:57:50Z

Help needed: Dilatation

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