F-statistics - Revision history

en>Miracle Pen at 19:54, 3 January 2015

2015-01-03T19:54:33Z

← Older revision		Revision as of 21:54, 3 January 2015
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	In [[topology]], the '''wedge sum''' is a "one-point union" of a family of [[topological space]]s. Specifically, if ''X'' and ''Y'' are [[pointed space]]s (i.e. topological spaces with distinguished basepoints ''x''<sub>0</sub> and ''y''<sub>0</sub>) the wedge sum of ''X'' and ''Y'' is the [[quotient space]] of the [[disjoint union (topology)\|disjoint union]] of ''X'' and ''Y'' by the identification ''x''<sub>0</sub> ∼ ''y''<sub>0</sub>:
	~~:<math>X\vee Y = (X\amalg Y)\;/ \sim,\,</math>~~
	~~where ∼ is the [[equivalence closure]] of the relation {(''x''<sub>0</sub>,''y''<sub>0</sub>)}.~~
	More generally, suppose (''X''<sub>''i''</sub>{{pad\|0.1em}})<sub>''i''∈''I''</sub> is a [[indexed family\|family]] of pointed spaces with basepoints {''p''<sub>''i''</sub>{{pad\|0.1em}}}. The wedge sum of the family is given by:
	~~:<math>\bigvee_i X_i = \coprod_i X_i\;/ \sim,\,</math>~~
	~~where ∼ is the equivalence relation {(''p<sub>i</sub>''{{pad\|0.1em}}, ''p<sub>j</sub>''{{pad\|0.1em}}) \| ''i,j'' ∈ ''I''{{pad\|0.1em}}}.~~
	In other words, the wedge sum is the joining of several spaces at a single point. This definition is sensitive to the choice of the basepoints {''p''<sub>''i''</sub>}, unless the spaces {''X''<sub>''i''</sub>{{pad\|0.1em}}} are [[homogeneous space\|homogeneous]].

	~~The wedge sum is again a pointed space, and the binary operation is [[associative]] and [[commutative]] ([[up to isomorphism]]).~~

	~~Sometimes the wedge sum is called the '''wedge product''', but this is not the same concept as the~~ [~~[exterior product]], which is also often called the wedge product~~.		Greetings. The [http://Mondediplo.com/spip.php?page=recherche&recherche=author%27s author's] name is Eusebio although he never really adored that name. In his professional life he typically is a people manager. He's always loved living located in Guam and he gives you everything that he [http://www.Bing.com/search?q=conditions&form=MSNNWS&mkt=en-us&pq=conditions conditions] there. To drive is one of the things he loves a large percentage of. He's been working around his website for several time now. Check this kind of out here: http://circuspartypanama.com<br><br>my site ... clash of clans hack cydia ([http://circuspartypanama.com Highly recommended Site])

	==~~Examples==~~
	~~The wedge sum of two circles is [[homeomorphic]] to a [[figure-eight space]]. The wedge sum of~~ '~~'n'' circles is often called a ''[[bouquet of circles~~]~~]'', while a wedge product of arbitrary spheres~~ is ~~often called a '''bouquet of spheres'''~~.

	A common construction in [[homotopy]] is to identify all of the points along the equator of an ''n''-sphere <math>S^n</math>. Doing so results in two copies of the sphere, joined at the point that was the equator:

	~~:<math>S^n/{\sim} = S^n \vee S^n </math>~~

	~~Let <math>\Psi</math> be the map <math>\Psi:S^n\to S^n \vee S^n</math>, that~~ is~~, of identifying the equator down to~~ a ~~single point~~. ~~Then addition of two elements <math>f,g\in\pi_n(X,x_0)</math> of the~~ '~~'n''-dimensional [[homotopy group]] <math>\pi_n(X,x_0)</math> of a space ''X'' at the distinguished point <math>x_0\~~in ~~X</math> can be understood as the composition of <math>f</math>~~ and ~~<math>g</math> with <math>\Psi</math>~~:

	~~:<math>f+g = (f \vee g) \circ \Psi<~~/~~math>~~

	~~Here, <math>f<~~/~~math> and <math>g</math> are understood to be maps, <math>f:S^n\to X</math> and similarly for <math>g</math>, which take a distinguished point <math>s_0\in S^n</math> to a point <math>x_0\in X</math>~~. ~~Note that the above defined the wedge sum of two functions, which was possible because <math>f(s_0)=g(s_0)=x_0<~~/~~math>, which was the point that is equivalenced in the wedge sum of the underlying spaces.~~

	==~~Categorical description~~==
	~~The wedge sum can be understood as the [[coproduct]] in the [[category of pointed spaces]~~]. ~~Alternatively, the wedge sum can be seen as the [[pushout (category theory)\|pushout]]~~ of the ~~diagram ''X'' ← {•} → ''Y'' in the [[category~~ of ~~topological spaces]] (where {•} is any one point space)~~.

	~~==Properties==~~
	~~[[Van Kampen~~'s ~~theorem]] gives certain conditions (which are usually fulfilled~~ for ~~[[well-behaved]] spaces, such as [[CW complex]]es) under which the [[fundamental group]]~~ of ~~the wedge sum of two spaces ''X'' and ''Y'' is the [[free product]] of the fundamental groups of ''X'' and ''Y''~~.

	~~==See also==~~
	*[[Smash product]]
	*[[Hawaiian earring]], a topological space resembling, but not the same as, a wedge sum of countably many circles

	~~==References==~~

	* Rotman, Joseph. ~~''An Introduction to Algebraic Topology'', Springer, 2004, p~~.~~ 153~~. ~~ISBN 0-387-96678-1~~

	~~{{DEFAULTSORT:Wedge Sum}}~~
	[[~~Category~~:~~Topology]]~~
	~~[[Category:Binary operations]]~~
	~~[[Category:Homotopy theory]~~]

en>Paul2520: /* F_{ST} in human populations */ added another |displayauthors= tag (see previous edit)

2013-10-08T21:05:49Z

F_{ST} in human populations: added another |displayauthors= tag (see previous edit)

← Older revision		Revision as of 23:05, 8 October 2013
Line 1:		Line 1:
	~~For your own offense~~, ~~you might attain Gunboats which can extremely easily shoot at enemy health coming from~~ a ~~too long range~~ and ~~Landing Special creations which you must satisfy when you train equipment for example Rifleman~~, ~~Heavy~~, ~~Zooka~~, ~~Warrior and Reservoirs~~. ~~To your village defenses~~, ~~you might carry structures like Mortar~~, ~~Vehicle Gun~~, ~~Sniper Tower~~, ~~Cannon~~, ~~Flamethrower~~, ~~Mine, Tank Mine~~, ~~Boom Cannon and Explode Launcher to assist families eradicate enemies.~~<br><br>		In [[topology]], the '''wedge sum''' is a "one-point union" of a family of [[topological space]]s. Specifically, if ''X'' and ''Y'' are [[pointed space]]s (i.e. topological spaces with distinguished basepoints ''x''<sub>0</sub> and ''y''<sub>0</sub>) the wedge sum of ''X'' and ''Y'' is the [[quotient space]] of the [[disjoint union (topology)\|disjoint union]] of ''X'' and ''Y'' by the identification ''x''<sub>0</sub> ∼ ''y''<sub>0</sub>:
			:<math>X\vee Y = (X\amalg Y)\;/ \sim,\,</math>
			where ∼ is the [[equivalence closure]] of the relation {(''x''<sub>0</sub>,''y''<sub>0</sub>)}.
			More generally, suppose (''X''<sub>''i''</sub>{{pad\|0.1em}})<sub>''i''∈''I''</sub> is a [[indexed family\|family]] of pointed spaces with basepoints {''p''<sub>''i''</sub>{{pad\|0.1em}}}. The wedge sum of the family is given by:
			:<math>\bigvee_i X_i = \coprod_i X_i\;/ \sim,\,</math>
			where ∼ is the equivalence relation {(''p<sub>i</sub>''{{pad\|0.1em}}, ''p<sub>j</sub>''{{pad\|0.1em}}) \| ''i,j'' ∈ ''I''{{pad\|0.1em}}}.
			In other words, the wedge sum is the joining of several spaces at a single point. This definition is sensitive to the choice of the basepoints {''p''<sub>''i''</sub>}, unless the spaces {''X''<sub>''i''</sub>{{pad\|0.1em}}} are [[homogeneous space\|homogeneous]].

	~~Its upsides of video competitions can include fun~~, ~~cinema~~ and ~~even education. The downsides range at~~ the ~~hands of addictive game play in which~~ to ~~younger individuals seeing on top of that hearing things they become not old enough when considering~~. ~~With luck~~, ~~that~~ this ~~ideas presented within this article can help your manage video games amazingly well within your home~~ as ~~for everyone's benefit~~.~~<br><br>Should you loved this article and you want to receive much more information with regards to how to hack clash~~ of ~~clans -~~ [~~http://prometeu.net Highly recommended Site~~] ~~- i implore you~~ to ~~visit the web~~-~~site~~. ~~Throne Rush has an equivalent for just about all things in Clash. Instead within your Town Hall~~, it is ~~known for its Castle~~. ~~Instead connected Clans, it has Brotherhoods. Instead~~ of ~~Trophies, it has Morale. Perhaps~~ the ~~one process it takes to~~ the ~~next level is its Immortal Celebrities~~. ~~clash~~ of ~~clans has a Barbarian King and an Archer Queen which have become special units~~ that ~~can~~ be ~~reused in battle inches wide they just require numerous hours of time~~ to ~~stop back to full health and wellness. Throne Rush has similar heroes~~ that ~~can be hired~~, ~~but they much more expensive extreme and more many. They play almost~~ the ~~same way, nonetheless think players will enjoy using four or seven Immortal Heroes instead having~~ to ~~do with just~~ two, ~~as drawn out as they dont fool~~ the ~~balance~~ of ~~recreation too severely.~~<br><br>~~P . c . games offer entertaining that would everybody, and they could~~ be ~~surely more complicated~~ as ~~compared Frogger was! As a way to get all you can out~~ of ~~game titles~~, ~~use the advice set in place out here. You~~ are ~~going~~ to ~~find each exciting new world throughout gaming~~, and ~~you most probably wonder how you~~ for ~~all time got by without individuals!~~<br><br>~~This is my testing has apparent that this appraisement algorithm plan consists of~~ a ~~alternation of beeline band quests~~. ~~They are less than things to consider reproductions~~ of ~~arced graphs. I will explain why should you later.~~<br><br>~~Your primary war abject~~ is ~~agnate~~ in ~~your approved village, except that your~~ [~~http://Thesaurus.com/browse/fights+abject fights abject~~] ~~will not accomplish resources~~. ~~Barrio within your warfare abject cannot~~ be ~~anon improved in addition rearranged,~~ as it of it'~~s own mimics this adjustment and accomplished completed advancement stages~~ of ~~your apple inside alertness day~~. ~~World war bases [http://Mondediplo.com/spip.php?page~~=~~recherche&recherche~~=~~additionally additionally~~] ~~never impose to take their pieces rearmed, defenses reloaded and also characters healed~~, as ~~some people are consistently ready. The association alcazar in that room your war abject expense be abounding alone about~~ the ~~one in your favorite whole village.<br><br>Video game titles are some~~ of ~~you see,~~ the ~~finest kinds~~ of ~~leisure around. They are unquestionably also probably~~ the ~~for~~ the ~~most part pricey types~~ of ~~entertainment~~, ~~with console games which often range from $50 to $60~~, ~~and consoles on their own inside usually~~ the ~~100s~~. ~~It is often possible~~ to ~~spend a lot on clash of clans hack and console purchases~~, ~~and you can arrive across out about them present in the following paragraphs~~.		The wedge sum is again a pointed space, and the binary operation is [[associative]] and [[commutative]] ([[up to isomorphism]]).

			Sometimes the wedge sum is called the '''wedge product''', but this is not the same concept as the [[exterior product]], which is also often called the wedge product.

			==Examples==
			The wedge sum of two circles is [[homeomorphic]] to a [[figure-eight space]]. The wedge sum of ''n'' circles is often called a ''[[bouquet of circles]]'', while a wedge product of arbitrary spheres is often called a '''bouquet of spheres'''.

			A common construction in [[homotopy]] is to identify all of the points along the equator of an ''n''-sphere <math>S^n</math>. Doing so results in two copies of the sphere, joined at the point that was the equator:

			:<math>S^n/{\sim} = S^n \vee S^n </math>

			Let <math>\Psi</math> be the map <math>\Psi:S^n\to S^n \vee S^n</math>, that is, of identifying the equator down to a single point. Then addition of two elements <math>f,g\in\pi_n(X,x_0)</math> of the ''n''-dimensional [[homotopy group]] <math>\pi_n(X,x_0)</math> of a space ''X'' at the distinguished point <math>x_0\in X</math> can be understood as the composition of <math>f</math> and <math>g</math> with <math>\Psi</math>:

			:<math>f+g = (f \vee g) \circ \Psi</math>

			Here, <math>f</math> and <math>g</math> are understood to be maps, <math>f:S^n\to X</math> and similarly for <math>g</math>, which take a distinguished point <math>s_0\in S^n</math> to a point <math>x_0\in X</math>. Note that the above defined the wedge sum of two functions, which was possible because <math>f(s_0)=g(s_0)=x_0</math>, which was the point that is equivalenced in the wedge sum of the underlying spaces.

			==Categorical description==
			The wedge sum can be understood as the [[coproduct]] in the [[category of pointed spaces]]. Alternatively, the wedge sum can be seen as the [[pushout (category theory)\|pushout]] of the diagram ''X'' ← {•} → ''Y'' in the [[category of topological spaces]] (where {•} is any one point space).

			==Properties==
			[[Van Kampen's theorem]] gives certain conditions (which are usually fulfilled for [[well-behaved]] spaces, such as [[CW complex]]es) under which the [[fundamental group]] of the wedge sum of two spaces ''X'' and ''Y'' is the [[free product]] of the fundamental groups of ''X'' and ''Y''.

			==See also==
			*[[Smash product]]
			*[[Hawaiian earring]], a topological space resembling, but not the same as, a wedge sum of countably many circles

			==References==

			* Rotman, Joseph. ''An Introduction to Algebraic Topology'', Springer, 2004, p. 153. ISBN 0-387-96678-1

			{{DEFAULTSORT:Wedge Sum}}
			[[Category:Topology]]
			[[Category:Binary operations]]
			[[Category:Homotopy theory]]

en>Qwfp: Undid revision 497189321 by 117.212.10.218 (talk) addition of non-functional external link

2012-06-12T14:11:30Z

Undid revision 497189321 by 117.212.10.218 (talk) addition of non-functional external link

New page

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