Kernel principal component analysis - Revision history

en>Richard V. Wang at 07:38, 4 September 2014

2014-09-04T07:38:55Z

← Older revision		Revision as of 09:38, 4 September 2014
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	~~Jayson Berryhill~~ is ~~how I'm~~ called and ~~my spouse doesn~~'~~t like~~ it ~~at all~~. ~~Invoicing is what~~ I ~~do. North Carolina is the place he loves most~~ but now ~~he is considering~~ other choices. ~~Playing badminton~~ is ~~a factor that he is completely addicted to~~.<br><br>~~Feel~~ free ~~to surf to my blog; clairvoyants~~ [[http://~~gcjcteam~~.~~org~~/index.php?~~mid=etc_video&~~document_srl=~~696611~~&~~sort_index~~=~~regdate&order_type=desc gcjcteam~~.~~org]~~]		The writer is called Wilber Pegues. The preferred hobby for him and his children is to play lacross and he'll be starting something else alongside with it. My spouse and I live in Mississippi but now I'm contemplating other choices. Invoicing is what I do.<br><br>Look at my web site :: [http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ free online tarot card readings] [http://help.ksu.edu.sa/node/65129 online psychic chat] ([http://c045.danah.co.kr/home/index.php?document_srl=1356970&mid=qna Enter your text here and click the "Remove Empty Lines" button above.])

38.127.164.2: /* Large Datasets */ "your" is inappropriate here

2014-02-12T18:51:13Z

Large Datasets: "your" is inappropriate here

← Older revision		Revision as of 20:51, 12 February 2014
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	~~[[Image:Star domain.svg\|right\|thumb\|A star domain (equivalently, a star-convex or star-shaped set)~~ is ~~not necessarily [[convex set\|convex]] in the ordinary sense.]]~~		Jayson Berryhill is how I'm called and my spouse doesn't like it at all. Invoicing is what I do. North Carolina is the place he loves most but now he is considering other choices. Playing badminton is a factor that he is completely addicted to.<br><br>Feel free to surf to my blog; clairvoyants [[http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc gcjcteam.org]]
	~~[[Image:Not-star-shaped.svg\|right\|thumb\|An [[annulus (mathematics)\|annulus]] is not a star domain.]]~~
	~~In [[mathematics]], a [[Set (mathematics)\|set]] <math>S</math> in the [[Euclidean space]] '''R'''<sup>~~'~~'n''</sup> is~~ called a '~~''star domain''' (or '''star-convex set''', '''star-shaped''' or '''radially convex set''') if there exists ''x''<sub>0</sub> in ''S'' such that for~~ all ~~''x'' in ''S'' the [[line segment]] from ''x''<sub>0</sub> to ''x'' is in ''S''~~. ~~This definition~~ is ~~immediately generalizable to any [[real number\|real]] or [[complex number\|complex]] [[vector space]]~~.

	~~Intuitively, if one thinks of ''S'' as of a region surrounded by a wall, ''S''~~ is ~~a star domain if one can find a vantage point ''x''<sub>0</sub> in ''S'' from which any point ''x'' in ''S''~~ is ~~within line-of-sight~~.

	~~==Examples==~~

	* Any line or plane in '''R'''<sup>''n''</sup> is a ~~star domain.~~
	* A line or a plane with a single point removed is ~~not a star domain~~.
	* If ''A'' is a set in '''R'''<~~sup~~>~~''n''~~<~~/sup~~>~~, the set~~
	~~:: <math>B= \{ ta : a\in A, t\in[0,1] \}</math>~~
	~~: obtained by connecting any point in ''A''~~ to ~~the origin is a star domain.~~
	* Any [[non-empty]] [[convex set]] is a star domain. A set is convex if and only if it is a star domain with respect to ~~any point in that set.~~
	* A [[~~cross]]-shaped figure is a star domain but is not convex~~.

	~~==Properties==~~

	* The [[closure (topology)\|closure]] of a star domain is a star domain, but the [[interior (topology)\|interior]] of a star domain is not necessarily a star domain.
	* Any star domain is a [[contractible_space\|contractible]] set, via a straight-line [[homotopy]]. In particular, any star domain is a [[simply connected set]].
	* The union and intersection of two star domains is not necessarily a star domain.
	* A nonempty open star domain ''S'' in '''R'''<sup>''n''</~~sup> is [[diffeomorphism\|diffeomorphic]] to '''R'''<sup>''n''</sup>~~.

	==~~See also~~==
	* [[Art gallery problem]]
	* [[Star polygon]] &~~mdash; an unrelated term~~
	* [[Star-shaped polygon]]
	* [[Balanced set]]

	==~~References==~~

	* Ian Stewart, David Tall, ''Complex Analysis''. Cambridge University Press, 1983, ISBN 0-521-28763-4, {{mr\|0698076}}

	* C.R. Smith, ''A characterization of star-shaped sets'', [[American Mathematical Monthly]], Vol. 75, No. 4 (April 1968). p.~~ 386, {{mr\|0227724}}, {{jstor\|2313423}}~~

	~~==External links==~~
	~~{{commonscat\|Star-shaped sets}}~~
	* {{mathworld\|urlname=StarConvex\|title=Star convex}}

	~~{{Functional Analysis}}~~

	~~[[Category:Euclidean geometry~~]]

en>Mark viking: alphabetize See also section per WP:ALSO

2014-01-30T01:04:24Z

alphabetize See also section per WP:ALSO

← Older revision		Revision as of 03:04, 30 January 2014
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	~~The author~~ is ~~called Wilber Pegues~~. ~~North Carolina~~ is the ~~location he loves most but now he~~ is ~~contemplating other options~~. ~~I am currently~~ a ~~travel agent~~. It's not a ~~typical factor but what I like performing~~ is ~~to climb but I don~~'~~t have~~ the ~~time lately.~~<br><br>~~Review my blog~~ - ~~psychic readings online~~ ([~~http://netwk~~.~~hannam~~.ac.kr/xe/~~data_2/85669 netwk~~.~~hannam~~.ac.kr])		[[Image:Star domain.svg\|right\|thumb\|A star domain (equivalently, a star-convex or star-shaped set) is not necessarily [[convex set\|convex]] in the ordinary sense.]]
			[[Image:Not-star-shaped.svg\|right\|thumb\|An [[annulus (mathematics)\|annulus]] is not a star domain.]]
			In [[mathematics]], a [[Set (mathematics)\|set]] <math>S</math> in the [[Euclidean space]] '''R'''<sup>''n''</sup> is called a '''star domain''' (or '''star-convex set''', '''star-shaped''' or '''radially convex set''') if there exists ''x''<sub>0</sub> in ''S'' such that for all ''x'' in ''S'' the [[line segment]] from ''x''<sub>0</sub> to ''x'' is in ''S''. This definition is immediately generalizable to any [[real number\|real]] or [[complex number\|complex]] [[vector space]].

			Intuitively, if one thinks of ''S'' as of a region surrounded by a wall, ''S'' is a star domain if one can find a vantage point ''x''<sub>0</sub> in ''S'' from which any point ''x'' in ''S'' is within line-of-sight.

			==Examples==

			* Any line or plane in '''R'''<sup>''n''</sup> is a star domain.
			* A line or a plane with a single point removed is not a star domain.
			* If ''A'' is a set in '''R'''<sup>''n''</sup>, the set
			:: <math>B= \{ ta : a\in A, t\in[0,1] \}</math>
			: obtained by connecting any point in ''A'' to the origin is a star domain.
			* Any [[non-empty]] [[convex set]] is a star domain. A set is convex if and only if it is a star domain with respect to any point in that set.
			* A [[cross]]-shaped figure is a star domain but is not convex.

			==Properties==

			* The [[closure (topology)\|closure]] of a star domain is a star domain, but the [[interior (topology)\|interior]] of a star domain is not necessarily a star domain.
			* Any star domain is a [[contractible_space\|contractible]] set, via a straight-line [[homotopy]]. In particular, any star domain is a [[simply connected set]].
			* The union and intersection of two star domains is not necessarily a star domain.
			* A nonempty open star domain ''S'' in '''R'''<sup>''n''</sup> is [[diffeomorphism\|diffeomorphic]] to '''R'''<sup>''n''</sup>.

			==See also==
			* [[Art gallery problem]]
			* [[Star polygon]] — an unrelated term
			* [[Star-shaped polygon]]
			* [[Balanced set]]

			==References==

			* Ian Stewart, David Tall, ''Complex Analysis''. Cambridge University Press, 1983, ISBN 0-521-28763-4, {{mr\|0698076}}

			* C.R. Smith, ''A characterization of star-shaped sets'', [[American Mathematical Monthly]], Vol. 75, No. 4 (April 1968). p. 386, {{mr\|0227724}}, {{jstor\|2313423}}

			==External links==
			{{commonscat\|Star-shaped sets}}
			* {{mathworld\|urlname=StarConvex\|title=Star convex}}

			{{Functional Analysis}}

			[[Category:Euclidean geometry]]

195.221.233.130: minor correction (forgotten transpose and typo)

2012-08-21T14:03:50Z

minor correction (forgotten transpose and typo)

New page

The author is called Wilber Pegues. North Carolina is the location he loves most but now he is contemplating other options. I am currently a travel agent. It's not a typical factor but what I like performing is to climb but I don't have the time lately.<br><br>Review my blog - psychic readings online ([http://netwk.hannam.ac.kr/xe/data_2/85669 netwk.hannam.ac.kr])