Single displacement reaction - Revision history

77.71.177.4: Sodium (Na) is more reactive than Calcium (Ca)

2015-01-04T13:13:40Z

Sodium (Na) is more reactive than Calcium (Ca)

← Older revision		Revision as of 15:13, 4 January 2015
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	~~Production Manager~~ (~~Forestry~~ ) ~~Ensley from Matachewan~~, has ~~hobbies~~ which ~~include acting~~, new launch property ~~singapore and rc model cars~~. ~~Has enrolled~~ in a ~~global contiki tour~~. ~~Is quite ecstatic particularly about traveling~~ to ~~Bagrati Cathedral~~ and ~~Gelati Monastery~~.<br><br>~~Also visit my site ::~~ [http://noblecow.com/members/bruce8995/activity/95504/ The Skywoods vacancy]		The Sorrento condominium ( pictured ) will officially launch next Saturday (19 April), marketing agent CBRE stated. The 2014 Singaporean property market is already coping with an increasing provide, so the weakened demand is worrisome for home developers. Results 1 - 15 of about a hundred for singapore pool four d result To satisfy the demand for multigenerational residing, Roxy-Pacific Holdings will launch Trilive soon this year. 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174.20.216.236 at 18:07, 23 February 2014

2014-02-23T18:07:17Z

← Older revision		Revision as of 20:07, 23 February 2014
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	~~{{for\|preliminary discussion\|Cartan connection applications}}~~		Production Manager (Forestry ) Ensley from Matachewan, has hobbies which include acting, new launch property singapore and rc model cars. Has enrolled in a global contiki tour. Is quite ecstatic particularly about traveling to Bagrati Cathedral and Gelati Monastery.<br><br>Also visit my site :: [http://noblecow.com/members/bruce8995/activity/95504/ The Skywoods vacancy]
	~~In [[Riemannian geometry]], we can introduce a [[coordinate system]] over the [[Riemannian manifold]]~~ (~~at least, over a [[Chart (topology)\|chart]]~~), ~~giving ''n'' coordinates~~

	~~:<math>x_{i}\;\text{~~,~~}\qquad i = 1, \dots, n</math>~~

	~~for an n-dimensional manifold~~. ~~Locally, at least, this gives~~ a ~~basis for the 1-forms, dx<sup>i</sup> where d is the [[exterior derivative]]. The [[dual basis]] for the [[tangent space]] T is '''e'''<sub>i</sub>.~~

	~~Now, let's choose an [[orthonormal basis]] for the [[fiber bundle\|fibers]] of T. The rest is index manipulation~~.

	~~==Example==~~

	~~Take a [[3-sphere]] with the [[radius]] ''R''~~ and ~~give it [[polar coordinate]]s α, θ, φ~~.

	~~:e('''e'''~~<~~sub~~>~~α~~<~~/sub~~>~~)/R,~~
	:~~e('''e'''<sub>θ</sub>)/R sin(α) and~~
	:~~e('''e'''<sub>φ</sub>)/R sin(α) sin(θ)~~

	~~form an orthonormal basis of T.~~

	~~Call these '''e'''<sub>1</sub>, '''e'''<sub>2</sub> and '''e'''<sub>3</sub>. Given the metric η, we can ignore the [[Covariance\|covariant]] and [~~[~~contravariant]] distinction for T.~~

	~~Then, the dreibein (triad),~~

	~~:<math>e_1 = R\, d\alpha</math>~~
	~~:<math>e_2 = R\, \sin{(\alpha)} d\theta</math>~~
	:~~<math>e_3 = R\, \sin{(\alpha)} \sin{(\theta)} d\phi<~~/~~math>.~~

	~~So,~~

	~~:<math>de_1=0</math>~~
	~~:<math>de_2=R \cos{(\alpha)} d\alpha \wedge d\theta<~~/~~math>~~
	~~:<math>de_3=R (\cos{(\alpha)} \sin{(\theta)} d\alpha \wedge d\phi + \sin{(\alpha)} \cos{(\theta)} d\theta \wedge d\phi)</math>~~.

	~~from the relation~~

	~~:<math>d_\mathbf{A} e = de + A \wedge e = 0<~~/~~math>,~~

	~~we get~~

	~~:<math>A_{12} = -\cos{(\alpha)} \, d\theta<~~/~~math>~~
	~~:<math>A_{13} = -\cos{(\alpha)} \, \sin{(\theta)} d\phi</math>~~
	~~:<math>A_{23} = -\cos{(\theta)} \, d\phi<~~/~~math>.~~

	~~(d<sub>'''A'''<~~/~~sub>η=0 tells us A is antisymmetric)~~

	~~So, <math>\mathbf{F} = d\mathbf{A} + \mathbf{A} \wedge \mathbf{A}<~~/~~math>,~~

	~~:<math>F_{12}=\sin{(\alpha)} d\alpha\wedge d\theta</math>~~
	~~:<math>F_{13}=\sin{(\alpha)} \sin{(\theta)} d\alpha\wedge d\phi</math>~~
	~~:<math>F_{23}=\sin^2{(\alpha)} \sin{(\theta)} d\theta\wedge d\phi</math>~~

	~~{{tensors}}~~
	~~{{differential-geometry-stub}}~~

	~~[[Category:Differential geometry]]~~
	~~[[Category:Mathematical notation]~~]

en>Denisarona: Reverted 1 edit by 207.219.43.34 (talk) to last revision by Nruddz. (TW)

2014-01-10T18:42:28Z

Reverted 1 edit by 207.219.43.34 (talk) to last revision by Nruddz. (TW)

← Older revision		Revision as of 20:42, 10 January 2014
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	~~Greetings! I am Marvella and I feel comfy when people use~~ the ~~complete name~~. ~~Managing people~~ is ~~his occupation~~. ~~Her family members life in Minnesota~~. ~~His wife doesn~~'~~t like it~~ the ~~way he does but what he truly likes performing~~ is ~~to do aerobics~~ and ~~he'~~s ~~been performing it for fairly a while~~.<br><br>~~my web page~~: [~~http~~://~~url~~.~~5base~~.~~com~~/~~dietmealsdelivered20142 url~~.~~5base.com~~]		{{for\|preliminary discussion\|Cartan connection applications}}
			In [[Riemannian geometry]], we can introduce a [[coordinate system]] over the [[Riemannian manifold]] (at least, over a [[Chart (topology)\|chart]]), giving ''n'' coordinates

			:<math>x_{i}\;\text{,}\qquad i = 1, \dots, n</math>

			for an n-dimensional manifold. Locally, at least, this gives a basis for the 1-forms, dx<sup>i</sup> where d is the [[exterior derivative]]. The [[dual basis]] for the [[tangent space]] T is '''e'''<sub>i</sub>.

			Now, let's choose an [[orthonormal basis]] for the [[fiber bundle\|fibers]] of T. The rest is index manipulation.

			==Example==

			Take a [[3-sphere]] with the [[radius]] ''R'' and give it [[polar coordinate]]s α, θ, φ.

			:e('''e'''<sub>α</sub>)/R,
			:e('''e'''<sub>θ</sub>)/R sin(α) and
			:e('''e'''<sub>φ</sub>)/R sin(α) sin(θ)

			form an orthonormal basis of T.

			Call these '''e'''<sub>1</sub>, '''e'''<sub>2</sub> and '''e'''<sub>3</sub>. Given the metric η, we can ignore the [[Covariance\|covariant]] and [[contravariant]] distinction for T.

			Then, the dreibein (triad),

			:<math>e_1 = R\, d\alpha</math>
			:<math>e_2 = R\, \sin{(\alpha)} d\theta</math>
			:<math>e_3 = R\, \sin{(\alpha)} \sin{(\theta)} d\phi</math>.

			So,

			:<math>de_1=0</math>
			:<math>de_2=R \cos{(\alpha)} d\alpha \wedge d\theta</math>
			:<math>de_3=R (\cos{(\alpha)} \sin{(\theta)} d\alpha \wedge d\phi + \sin{(\alpha)} \cos{(\theta)} d\theta \wedge d\phi)</math>.

			from the relation

			:<math>d_\mathbf{A} e = de + A \wedge e = 0</math>,

			we get

			:<math>A_{12} = -\cos{(\alpha)} \, d\theta</math>
			:<math>A_{13} = -\cos{(\alpha)} \, \sin{(\theta)} d\phi</math>
			:<math>A_{23} = -\cos{(\theta)} \, d\phi</math>.

			(d<sub>'''A'''</sub>η=0 tells us A is antisymmetric)

			So, <math>\mathbf{F} = d\mathbf{A} + \mathbf{A} \wedge \mathbf{A}</math>,

			:<math>F_{12}=\sin{(\alpha)} d\alpha\wedge d\theta</math>
			:<math>F_{13}=\sin{(\alpha)} \sin{(\theta)} d\alpha\wedge d\phi</math>
			:<math>F_{23}=\sin^2{(\alpha)} \sin{(\theta)} d\theta\wedge d\phi</math>

			{{tensors}}
			{{differential-geometry-stub}}

			[[Category:Differential geometry]]
			[[Category:Mathematical notation]]

75.168.41.160: Undid revision 501208230 by 203.87.162.18 (talk)

2012-07-09T16:10:43Z

Undid revision 501208230 by 203.87.162.18 (talk)

New page

Greetings! I am Marvella and I feel comfy when people use the complete name. Managing people is his occupation. Her family members life in Minnesota. His wife doesn't like it the way he does but what he truly likes performing is to do aerobics and he's been performing it for fairly a while.<br><br>my web page: [http://url.5base.com/dietmealsdelivered20142 url.5base.com]