Semiring - Revision history

en>BethNaught: clean up, typo(s) fixed: et al → et al. using AWB

2015-01-11T15:57:47Z

clean up, typo(s) fixed: et al → et al. using AWB

← Older revision		Revision as of 17:57, 11 January 2015
Line 1:		Line 1:
	Hi, ~~everybody!~~ <br>~~I'm Korean female :D~~. <br>I really ~~love Freerunning!~~<br><br>~~my page;~~ [http://~~www~~.~~enbasit~~.~~com~~/32-~~temiz-ve-minimal-website-tasarim-ornegi~~.~~html architect~~ in ~~gurgaon]~~		All the trophies from all of your members in your group get added up and as well as divided by 2 ascertain your clans overall awards. [http://Www.alexa.com/search?q=Playing&r=topsites_index&p=bigtop Playing] many different kinds of games makes your gaming time more enjoyable. and your league also determines your primary battle win bonus. 5 star rating and is defined as known to be very addictive as players frequently devote several hours enjoying the game. She specializes in beauty salon business startup company and client fascination.<br><br>Towards conclude, clash of clans hack tool no survey must not be left to get in during of the bigger question: what makes we above? Putting this particular in addition its of great necessity. It replenishes the self, provides financial security advantage always chips in.<br><br>Crystals are known as the games primary forex. The Jewels are acquainted with purchase resources along to speeding up numerous imperative tasks. The Jewels can also be once buy bonus items. Apart from that, additionally, it can let the leader alleged any undesired debris in order to obtain a lot more gems. Players can easily obtain Gems through rounding out numerous tasks or it could be that using the clash of clans hack into available online.<br><br>If you beloved this report and you would like to receive more facts concerning [http://prometeu.net Clash Of Clans Cheats Ipad Gems] kindly go to the site. Purchase attention to how really money your teenager is generally spending on video games. These products might not be cheap and there is very much often the option of a buying more add-ons for the game itself. Set monthly and every year limits on the wide variety of money that is likely to be spent on video playback games. Also, have conversations with your toddlers about budgeting.<br><br>Second, when your husband decides to commit adultery, he creates a problem that forces you to have some serious decisions. Step one turn at your Xbox sign during the dash board. It is unforgivable and also disappointing to say the very. I think we end up being start differentiating between unquestionably the public interest, and a proper definition of what that means, and stories that the media conclude the public people 'd be interested in. Ford introduced the [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=foremost+production&Submit=Go foremost production] woodie in 1929. The varieties associated fingers you perform on the inside No-Limit Holdem vary as opposed to what all those in Prohibit.<br><br>Everybody computer games are everywhere these times. Perfect play them on an telephone, boot a console in the home several see them through social media optimisation on your personal computer system. It helps to comprehend this area of amusement to help you benefit from the pretty offers which are around the market.<br><br>One particular amend additionally permits you to access the ability with your Sensei application buffs available with the Dojo because. Dojo win band technique. Furthermore, it introduces fresh, new customized headgear and equipment, new barrio and safeguarding, and new assemblage progress.

Deltahedron: /* Specific examples */ name Boolean semiring

2014-02-17T19:42:35Z

Specific examples: name Boolean semiring

← Older revision		Revision as of 21:42, 17 February 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, a '~~''real tree''', or an~~ <~~math~~>~~\mathbb R~~<~~/math~~>~~-'''tree''', is a [[metric space]] (''M'',''d'') such that~~		Hi, everybody! <br>I'm Korean female :D. <br>I really love Freerunning!<br><br>my page; [http://www.enbasit.com/32-temiz-ve-minimal-website-tasarim-ornegi.html architect in gurgaon]
	for any ''x'', ''y'' in ''M'' there is a unique ''arc'' from ''x'' to ''y'' and this arc is a [[Geodesic#Metric_geometry\|geodesic segment]]. Here by an ''arc'' from ''x'' to ''y'' we mean the image in ''M'' of a [[homeomorphism\|topological embedding]] ''f'' from an [[Interval (mathematics)\|interval]] [''a'',''b''] to ''M'' such that ''f''(''a'')=''x'' and ''f''(''b'')=''y''. The condition that the arc is a geodesic segment means that the map ''f'' above can be chosen to be an [[isometry\|isometric]] [[embedding]], that is it can be chosen so that for every ''z, t'' in [''a'',''b''] we have ''d(f(z), f(t))''=\|''z-t''\| and that ''f(a)=x'', ''f(b)=y''.

	~~Equivalently, a [[geodesic metric space]] ''M'' is a real tree if and only if ''M'' is a [[δ-hyperbolic space]] with δ=0.~~

	~~Complete real trees are [[injective metric space]]s {{harv\|Kirk\|1998}}.~~

	~~There is a theory of [[group action]]s on '''R'''-trees, known as the [[Rips machine]], which is part of [[geometric group theory]].~~

	~~== Simplicial R-trees ==~~
	~~A '''simplicial''' '''R'''-tree is an '''R'''-tree that is free from certain "topological strangeness". More precisely, a point ''x'' in an '''R'''-tree ''T'' is called '''ordinary''' if ''T''&minus~~;''x'' has exactly two components. The points which are not ordinary are '''singular'''. We define a simplicial '''R'''-tree to be an '''R'''-tree whose set of singular points is [[Discrete space\|discrete]] and [[Closed set\|closed]].

	~~== Examples ==~~
	* Each discrete [[Tree (graph theory)\|tree]] can be regarded as an '''R'''-tree by a simple construction such that neighboring vertices have distance one.
	* The [[Paris metric]] makes the plane into an '''R'''-tree. If two points are on the same ray in the plane, their distance is defined as the [[Euclidean distance]]. Otherwise, their distance is defined to be the sum of the Euclidian distances of these two points to the origin. More generally any [[hedgehog space]] is an example of a real tree.
	* The '''R'''-tree obtained in the following way is nonsimplicial. Start with the interval [0,2] and [[Quotient space#Examples\|glue]], for each positive integer ''n'', an interval of length 1/''n'' to the point 1−1/''n'' in the original interval. The set of singular points is discrete, but fails to be closed since 1 is an ordinary point in this '''R'''-tree. Gluing an interval to 1 would result in a [[closed set]] of singular points at the expense of discreteness.

	~~==See also==~~
	*[[Dendroid (topology)]]
	*[[Tree-graded space]]

	~~== References ==~~

	*{{citation
	~~\| last = Bestvina \| first = Mladen \| authorlink = Mladen Bestvina~~
	~~\| contribution = ℝ-trees in topology, geometry, and group theory~~
	~~\| location = Amsterdam~~
	~~\| mr = 1886668~~
	~~\| pages = 55–91~~
	~~\| publisher = North-Holland~~
	~~\| title = Handbook of geometric topology~~
	~~\| url =~~ http://www.~~math~~.~~utah.edu/~bestvina/eprints~~/~~handbook.ps~~
	~~\| year = 2002}}.~~
	*{{citation
	~~\| last = Chiswell \| first = Ian~~
	~~\| isbn = 981~~-02-~~4386~~-3
	~~\| location = River Edge, NJ~~
	~~\| mr = 1851337~~
	~~\| publisher = World Scientific Publishing Co. Inc.~~
	~~\| title = Introduction to Λ~~-~~trees~~
	~~\| year = 2001}}.~~
	*{{citation
	~~\| last = Kirk \| first = W. A.~~
	~~\| issue = 1~~
	~~\| journal = Fundamenta Mathematicae~~
	~~\| mr = 1610559~~
	~~\| pages = 67–72~~
	~~\| title = Hyperconvexity of '''R'''~~-~~trees~~
	~~\| volume = 156~~
	~~\| url = http://matwbn.icm.edu.pl/ksiazki/fm/fm156/fm15613.pdf~~
	~~\| year = 1998}}.~~
	*{{citation
	~~\| last = Shalen \| first = Peter B.~~
	~~\| editor~~-~~last = Gersten \| editor-first = S~~. M.
	~~\| contribution = Dendrology of groups: an introduction~~
	~~\| isbn = 978-0-387-96618-2~~
	~~\| mr = 919830~~
	~~\| pages = 265–319~~
	~~\| publisher = [[Springer-Verlag]]~~
	~~\| series = Math. Sci. Res. Inst. Publ.~~
	~~\| title = Essays~~ in ~~group theory~~
	~~\| volume = 8~~
	~~\| year = 1987}}.~~

	~~[[Category:Group theory]]~~
	~~[[Category:Geometry]]~~
	~~[[Category:Topology]]~~
	~~[[Category:Trees (topology)]~~]

Deltahedron: /* In general */ Boolean semiring, cite Guterman (2008)

2014-02-01T21:32:04Z

In general: Boolean semiring, cite Guterman (2008)

← Older revision		Revision as of 23:32, 1 February 2014
Line 1:		Line 1:
	~~Adrianne~~ is ~~what you has~~ the ~~capability~~ to ~~call me but I don~~'t ~~like when guys~~ and ~~women use my full address~~. ~~What I love doing~~ is ~~always to play croquet~~ ~~now I have time to take~~ on ~~issues~~. The ~~job I~~'~~ve been occupying~~ to ~~find years~~ is an [~~http://Sequenceclerk~~.~~org/ sequence clerk~~]. ~~My husband~~ and ~~I decide~~ to ~~reside~~ in ~~Guam~~ but ~~I will have~~ to ~~move~~ in a ~~trustworthy year or two~~. ~~You can find my~~ [http://~~Www~~.~~Bing~~.~~com~~/~~search?q~~=~~website&form~~=~~MSNNWS&mkt~~=en-~~us&pq~~=~~website website] here:~~ http://~~prometeu~~.~~net<br><br>my homepage~~ - [~~http~~:~~//prometeu.net Clash Of Clans Cheats Ipad Gems~~]		In [[mathematics]], a '''real tree''', or an <math>\mathbb R</math>-'''tree''', is a [[metric space]] (''M'',''d'') such that
			for any ''x'', ''y'' in ''M'' there is a unique ''arc'' from ''x'' to ''y'' and this arc is a [[Geodesic#Metric_geometry\|geodesic segment]]. Here by an ''arc'' from ''x'' to ''y'' we mean the image in ''M'' of a [[homeomorphism\|topological embedding]] ''f'' from an [[Interval (mathematics)\|interval]] [''a'',''b''] to ''M'' such that ''f''(''a'')=''x'' and ''f''(''b'')=''y''. The condition that the arc is a geodesic segment means that the map ''f'' above can be chosen to be an [[isometry\|isometric]] [[embedding]], that is it can be chosen so that for every ''z, t'' in [''a'',''b''] we have ''d(f(z), f(t))''=\|''z-t''\| and that ''f(a)=x'', ''f(b)=y''.

			Equivalently, a [[geodesic metric space]] ''M'' is a real tree if and only if ''M'' is a [[δ-hyperbolic space]] with δ=0.

			Complete real trees are [[injective metric space]]s {{harv\|Kirk\|1998}}.

			There is a theory of [[group action]]s on '''R'''-trees, known as the [[Rips machine]], which is part of [[geometric group theory]].

			== Simplicial R-trees ==
			A '''simplicial''' '''R'''-tree is an '''R'''-tree that is free from certain "topological strangeness". More precisely, a point ''x'' in an '''R'''-tree ''T'' is called '''ordinary''' if ''T''−''x'' has exactly two components. The points which are not ordinary are '''singular'''. We define a simplicial '''R'''-tree to be an '''R'''-tree whose set of singular points is [[Discrete space\|discrete]] and [[Closed set\|closed]].

			== Examples ==
			* Each discrete [[Tree (graph theory)\|tree]] can be regarded as an '''R'''-tree by a simple construction such that neighboring vertices have distance one.
			* The [[Paris metric]] makes the plane into an '''R'''-tree. If two points are on the same ray in the plane, their distance is defined as the [[Euclidean distance]]. Otherwise, their distance is defined to be the sum of the Euclidian distances of these two points to the origin. More generally any [[hedgehog space]] is an example of a real tree.
			* The '''R'''-tree obtained in the following way is nonsimplicial. Start with the interval [0,2] and [[Quotient space#Examples\|glue]], for each positive integer ''n'', an interval of length 1/''n'' to the point 1−1/''n'' in the original interval. The set of singular points is discrete, but fails to be closed since 1 is an ordinary point in this '''R'''-tree. Gluing an interval to 1 would result in a [[closed set]] of singular points at the expense of discreteness.

			==See also==
			*[[Dendroid (topology)]]
			*[[Tree-graded space]]

			== References ==

			*{{citation
			\| last = Bestvina \| first = Mladen \| authorlink = Mladen Bestvina
			\| contribution = ℝ-trees in topology, geometry, and group theory
			\| location = Amsterdam
			\| mr = 1886668
			\| pages = 55–91
			\| publisher = North-Holland
			\| title = Handbook of geometric topology
			\| url = http://www.math.utah.edu/~bestvina/eprints/handbook.ps
			\| year = 2002}}.
			*{{citation
			\| last = Chiswell \| first = Ian
			\| isbn = 981-02-4386-3
			\| location = River Edge, NJ
			\| mr = 1851337
			\| publisher = World Scientific Publishing Co. Inc.
			\| title = Introduction to Λ-trees
			\| year = 2001}}.
			*{{citation
			\| last = Kirk \| first = W. A.
			\| issue = 1
			\| journal = Fundamenta Mathematicae
			\| mr = 1610559
			\| pages = 67–72
			\| title = Hyperconvexity of '''R'''-trees
			\| volume = 156
			\| url = http://matwbn.icm.edu.pl/ksiazki/fm/fm156/fm15613.pdf
			\| year = 1998}}.
			*{{citation
			\| last = Shalen \| first = Peter B.
			\| editor-last = Gersten \| editor-first = S. M.
			\| contribution = Dendrology of groups: an introduction
			\| isbn = 978-0-387-96618-2
			\| mr = 919830
			\| pages = 265–319
			\| publisher = [[Springer-Verlag]]
			\| series = Math. Sci. Res. Inst. Publ.
			\| title = Essays in group theory
			\| volume = 8
			\| year = 1987}}.

			[[Category:Group theory]]
			[[Category:Geometry]]
			[[Category:Topology]]
			[[Category:Trees (topology)]]

en>R'n'B: Fix links to disambiguation page Infinite

2012-08-23T16:18:35Z

Fix links to disambiguation page Infinite

New page

Adrianne is what you has the capability to call me but I don't like when guys and women use my full address. What I love doing is always to play croquet now I have time to take on issues. The job I've been occupying to find years is an [http://Sequenceclerk.org/ sequence clerk]. My husband and I decide to reside in Guam but I will have to move in a trustworthy year or two. You can find my [http://Www.Bing.com/search?q=website&form=MSNNWS&mkt=en-us&pq=website website] here: http://prometeu.net<br><br>my homepage - [http://prometeu.net Clash Of Clans Cheats Ipad Gems]

← Older revision		Revision as of 21:42, 17 February 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, a '~~''real tree''', or an~~ <~~math~~>~~\mathbb R~~<~~/math~~>~~-'''tree''', is a [[metric space]] (''M'',''d'') such that~~		Hi, everybody! <br>I'm Korean female :D. <br>I really love Freerunning!<br><br>my page; [http://www.enbasit.com/32-temiz-ve-minimal-website-tasarim-ornegi.html architect in gurgaon]
	for any ''x'', ''y'' in ''M'' there is a unique ''arc'' from ''x'' to ''y'' and this arc is a [[Geodesic#Metric_geometry\|geodesic segment]]. Here by an ''arc'' from ''x'' to ''y'' we mean the image in ''M'' of a [[homeomorphism\|topological embedding]] ''f'' from an [[Interval (mathematics)\|interval]] [''a'',''b''] to ''M'' such that ''f''(''a'')=''x'' and ''f''(''b'')=''y''. The condition that the arc is a geodesic segment means that the map ''f'' above can be chosen to be an [[isometry\|isometric]] [[embedding]], that is it can be chosen so that for every ''z, t'' in [''a'',''b''] we have ''d(f(z), f(t))''=\|''z-t''\| and that ''f(a)=x'', ''f(b)=y''.

	~~Equivalently, a [[geodesic metric space]] ''M'' is a real tree if and only if ''M'' is a [[δ-hyperbolic space]] with δ=0.~~

	~~Complete real trees are [[injective metric space]]s {{harv\|Kirk\|1998}}.~~

	~~There is a theory of [[group action]]s on '''R'''-trees, known as the [[Rips machine]], which is part of [[geometric group theory]].~~

	~~== Simplicial R-trees ==~~
	~~A '''simplicial''' '''R'''-tree is an '''R'''-tree that is free from certain "topological strangeness". More precisely, a point ''x'' in an '''R'''-tree ''T'' is called '''ordinary''' if ''T''&minus~~;''x'' has exactly two components. The points which are not ordinary are '''singular'''. We define a simplicial '''R'''-tree to be an '''R'''-tree whose set of singular points is [[Discrete space\|discrete]] and [[Closed set\|closed]].

	~~== Examples ==~~
	* Each discrete [[Tree (graph theory)\|tree]] can be regarded as an '''R'''-tree by a simple construction such that neighboring vertices have distance one.
	* The [[Paris metric]] makes the plane into an '''R'''-tree. If two points are on the same ray in the plane, their distance is defined as the [[Euclidean distance]]. Otherwise, their distance is defined to be the sum of the Euclidian distances of these two points to the origin. More generally any [[hedgehog space]] is an example of a real tree.
	* The '''R'''-tree obtained in the following way is nonsimplicial. Start with the interval [0,2] and [[Quotient space#Examples\|glue]], for each positive integer ''n'', an interval of length 1/''n'' to the point 1−1/''n'' in the original interval. The set of singular points is discrete, but fails to be closed since 1 is an ordinary point in this '''R'''-tree. Gluing an interval to 1 would result in a [[closed set]] of singular points at the expense of discreteness.

	~~==See also==~~
	*[[Dendroid (topology)]]
	*[[Tree-graded space]]

	~~== References ==~~

	*{{citation
	~~\| last = Bestvina \| first = Mladen \| authorlink = Mladen Bestvina~~
	~~\| contribution = ℝ-trees in topology, geometry, and group theory~~
	~~\| location = Amsterdam~~
	~~\| mr = 1886668~~
	~~\| pages = 55–91~~
	~~\| publisher = North-Holland~~
	~~\| title = Handbook of geometric topology~~
	~~\| url =~~ http://www.~~math~~.~~utah.edu/~bestvina/eprints~~/~~handbook.ps~~
	~~\| year = 2002}}.~~
	*{{citation
	~~\| last = Chiswell \| first = Ian~~
	~~\| isbn = 981~~-02-~~4386~~-3
	~~\| location = River Edge, NJ~~
	~~\| mr = 1851337~~
	~~\| publisher = World Scientific Publishing Co. Inc.~~
	~~\| title = Introduction to Λ~~-~~trees~~
	~~\| year = 2001}}.~~
	*{{citation
	~~\| last = Kirk \| first = W. A.~~
	~~\| issue = 1~~
	~~\| journal = Fundamenta Mathematicae~~
	~~\| mr = 1610559~~
	~~\| pages = 67–72~~
	~~\| title = Hyperconvexity of '''R'''~~-~~trees~~
	~~\| volume = 156~~
	~~\| url = http://matwbn.icm.edu.pl/ksiazki/fm/fm156/fm15613.pdf~~
	~~\| year = 1998}}.~~
	*{{citation
	~~\| last = Shalen \| first = Peter B.~~
	~~\| editor~~-~~last = Gersten \| editor-first = S~~. M.
	~~\| contribution = Dendrology of groups: an introduction~~
	~~\| isbn = 978-0-387-96618-2~~
	~~\| mr = 919830~~
	~~\| pages = 265–319~~
	~~\| publisher = [[Springer-Verlag]]~~
	~~\| series = Math. Sci. Res. Inst. Publ.~~
	~~\| title = Essays~~ in ~~group theory~~
	~~\| volume = 8~~
	~~\| year = 1987}}.~~

	~~[[Category:Group theory]]~~
	~~[[Category:Geometry]]~~
	~~[[Category:Topology]]~~
	~~[[Category:Trees (topology)]~~]