Vacuum solution (general relativity) - Revision history

en>Colonies Chris: sp, date & link fixes; unlinking common words, replaced: stress-energy tensor → stress–energy tensor using AWB

2014-03-13T17:10:19Z

sp, date & link fixes; unlinking common words, replaced: stress-energy tensor → stress–energy tensor using AWB

← Older revision		Revision as of 19:10, 13 March 2014
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	~~{{about\|a mathematical concept\|the psychological concept\|Dual representation (psychology)}}~~		It is a good suggestion to have your personal consultant with you while going to buy a newly constructed apartment. You might not be aware of this, however when you method the gross sales workplace concerning [http://www.nexuschamp.com/groups/rivertrees-residences/ singapore property prices] a brand new condominium growth; the gross sales employees is there to characterize the interests of the builder.<br><br>Anticipated to change into up and achieved between 2017, the brand new construction throughout the market of condo, has been stated for being considered one of a number of personal websites in Katong. Both for particular person dwelling or for expense, it is basically an excellent option for expense. 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	~~In [[mathematics]], if ''G''~~ is a ~~[[group (mathematics)\|group]] and ρ is~~ a ~~[[linear representation]]~~ of ~~it on~~ the ~~real~~ [~~[vector space~~]~~] ''V'', then~~ the ~~'''dual representation''' {{Overline\|ρ}}~~ is ~~defined over~~ the ~~[[dual vector space]] {{Overline\|''V''}} as follows:~~<~~ref~~>~~Lecture 1 of {{Fulton-Harris}}~~<~~/ref~~>

	~~:{{Overline\|ρ}}(''g'')~~ is the ~~[[transpose~~ of a ~~linear map\|transpose]]~~ of ~~ρ(''g''~~<~~sup~~>~~−1~~<~~/sup~~>)

	~~for all ''g''~~ in ''~~G''~~. ~~Then {{Overline\|ρ}}~~ is ~~also~~ a ~~representation, as may be checked explicitly~~. The ~~dual representation is also known as~~ the ~~'''contragredient representation'''. For~~ a ~~complex vector space~~, ~~take~~ <~~math~~> ~~\overline{\rho}(g) := \rho(g)^{\dagger}~~<~~/math~~>

	If <~~math~~>~~\mathfrak{g}~~<~~/math~~> is a ~~[[Lie algebra]] and ρ is~~ a ~~representation~~ of ~~it over~~ the ~~vector~~ space ~~''V''~~, ~~then~~ the ~~dual representation {{Overline\|ρ}}~~ is ~~defined over the dual vector space {{Overline\|''V''}} as follows:~~<~~ref~~>~~Lecture 8 of {{Fulton-Harris}}~~<~~/ref~~>

	~~:{{Overline\|ρ}}(~~'~~'u'') is~~ the ~~transpose~~ of ~~−ρ(u)~~ for ~~all u in~~ <~~math~~>~~\mathfrak{g}~~<~~/math~~>.

	~~:{{Overline\|ρ}}~~ is ~~also~~ a ~~representation~~, ~~as can be explicitly checked~~.

	For ~~a [[unitary representation]]~~, the ~~conjugate representation~~ and the ~~dual representation coincide~~, ~~up to equivalence~~ of ~~representations~~.

	~~==Generalization==~~

	~~A general ring [[Module (mathematics)\|module]] does not admit~~ a ~~dual representation~~. ~~Modules~~ of ~~[[Hopf algebra]]~~s ~~do, however~~.

	~~==See also==~~
	* [[Complex conjugate representation]]
	* [[Kirillov Character Formula]]

	~~==References==~~
	~~<references/>~~

	~~[[Category:Representation theory of groups]]~~

en>KLBot2: Bot: Migrating 2 interwiki links, now provided by Wikidata on :d:Q7908077

2013-03-21T20:59:08Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:Q7908077

← Older revision		Revision as of 22:59, 21 March 2013
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	~~Cold sweats are characterized by extreme perspiration~~, ~~nervousness~~ and ~~low body temperature. In many~~ of the ~~circumstances~~, ~~they~~'~~re skilled at evening. This situation might be accompanied by other signs, depending on~~ the ~~trigger.~~<br><br>Mainly, white coat hypertension should be handled by life-style modifications without drug treatment. Patients must be examined periodically, attention should be paid detox diet to traumatic situations in each day lives, and modifications in way of ~~life and self-measurement~~ of house blood strain should be encouraged. Antihypertensive medicine may be required in sufferers with high-danger white coat hypertension in whom out-of-clinic blood strain is comparatively high or is complicated by cardiovascular disease, organ harm, diabetes mellitus or metabolic syndrome. b. Masked hypertension<br><br>~~Identifying an nervousness assault is a very important should you really feel as if you~~'~~re experiencing one~~. ~~This manner you can higher understand what~~ is ~~occurring to you~~ as ~~well as knowing what you are able to do to forestall from having one other one~~. It is ~~vitally essential to seek medical attention when you really feel~~ as ~~if you might be having chest pains. Even though this symptom will be interrelated with an anxiety assault it is at all times greatest to have~~ the ~~doctor determine why the chest pains are occurring~~.<br><br>~~Lastly, some ladies with exceedingly extreme panic disorder will want to flip to medications or surgery for reduction. It's necessary to consult~~ a healthcare skilled before administering this remedy possibility. Although medication might be the only strategy to attain relief for some women, they typically include harsh side effects. Symptoms in kids may be mistaken for behavioral issues (taking too long to do homework because of perfectionism, refusing to perform a ~~chore due to fear~~ of ~~germs). Youngsters do not often recognize that their obsessions or compulsions are extreme. Gastrointestinal Problems. Nervousness often accompanies gastrointestinal conditions~~, ~~notably irritable bowel syndrome. You are not alone, these symptoms are common.~~<br><br>~~GAD impacts about 1 - 5% of Americans in~~ the ~~low carb diet middle~~ of ~~their lives and is more widespread~~ in ~~girls than in men~~. It is ~~the commonest nervousness disorder among the elderly. GAD often begins in childhood and often becomes~~ a ~~chronic ailment~~, ~~particularly when left untreated. Depression commonly accompanies this nervousness disorder, and melancholy in adolescence may~~ be ~~a powerful predictor of GAD in maturity. Specific Danger Factors for Panic Dysfunction Kids with nervousness issues often suffer from recurrent stomach aches~~. ~~Anxiety is related to~~ a ~~better danger for sleep problems in youngsters, comparable to frequent nightmares, stressed legs syndrome~~, and ~~bruxism (~~the ~~grinding and gnashing~~ of ~~the teeth during sleep~~). ~~Prognosis Panic dysfunction can't be prevented~~.		{{about\|a mathematical concept\|the psychological concept\|Dual representation (psychology)}}
			In [[mathematics]], if ''G'' is a [[group (mathematics)\|group]] and ρ is a [[linear representation]] of it on the real [[vector space]] ''V'', then the '''dual representation''' {{Overline\|ρ}} is defined over the [[dual vector space]] {{Overline\|''V''}} as follows:<ref>Lecture 1 of {{Fulton-Harris}}</ref>

			:{{Overline\|ρ}}(''g'') is the [[transpose of a linear map\|transpose]] of ρ(''g''<sup>−1</sup>)

			for all ''g'' in ''G''. Then {{Overline\|ρ}} is also a representation, as may be checked explicitly. The dual representation is also known as the '''contragredient representation'''. For a complex vector space, take <math> \overline{\rho}(g) := \rho(g)^{\dagger}</math>

			If <math>\mathfrak{g}</math> is a [[Lie algebra]] and ρ is a representation of it over the vector space ''V'', then the dual representation {{Overline\|ρ}} is defined over the dual vector space {{Overline\|''V''}} as follows:<ref>Lecture 8 of {{Fulton-Harris}}</ref>

			:{{Overline\|ρ}}(''u'') is the transpose of −ρ(u) for all u in <math>\mathfrak{g}</math>.

			:{{Overline\|ρ}} is also a representation, as can be explicitly checked.

			For a [[unitary representation]], the conjugate representation and the dual representation coincide, up to equivalence of representations.

			==Generalization==

			A general ring [[Module (mathematics)\|module]] does not admit a dual representation. Modules of [[Hopf algebra]]s do, however.

			==See also==
			* [[Complex conjugate representation]]
			* [[Kirillov Character Formula]]

			==References==
			<references/>

			[[Category:Representation theory of groups]]

83.44.91.227 at 00:39, 17 August 2011

2011-08-17T00:39:42Z

New page

Cold sweats are characterized by extreme perspiration, nervousness and low body temperature. In many of the circumstances, they're skilled at evening. This situation might be accompanied by other signs, depending on the trigger. Mainly, white coat hypertension should be handled by life-style modifications without drug treatment. Patients must be examined periodically, attention should be paid detox diet to traumatic situations in each day lives, and modifications in way of life and self-measurement of house blood strain should be encouraged. Antihypertensive medicine may be required in sufferers with high-danger white coat hypertension in whom out-of-clinic blood strain is comparatively high or is complicated by cardiovascular disease, organ harm, diabetes mellitus or metabolic syndrome. b. Masked hypertension Identifying an nervousness assault is a very important should you really feel as if you're experiencing one. This manner you can higher understand what is occurring to you as well as knowing what you are able to do to forestall from having one other one. It is vitally essential to seek medical attention when you really feel as if you might be having chest pains. Even though this symptom will be interrelated with an anxiety assault it is at all times greatest to have the doctor determine why the chest pains are occurring. Lastly, some ladies with exceedingly extreme panic disorder will want to flip to medications or surgery for reduction. It's necessary to consult a healthcare skilled before administering this remedy possibility. Although medication might be the only strategy to attain relief for some women, they typically include harsh side effects. Symptoms in kids may be mistaken for behavioral issues (taking too long to do homework because of perfectionism, refusing to perform a chore due to fear of germs). Youngsters do not often recognize that their obsessions or compulsions are extreme. Gastrointestinal Problems. Nervousness often accompanies gastrointestinal conditions, notably irritable bowel syndrome. You are not alone, these symptoms are common. GAD impacts about 1 - 5% of Americans in the low carb diet middle of their lives and is more widespread in girls than in men. It is the commonest nervousness disorder among the elderly. GAD often begins in childhood and often becomes a chronic ailment, particularly when left untreated. Depression commonly accompanies this nervousness disorder, and melancholy in adolescence may be a powerful predictor of GAD in maturity. Specific Danger Factors for Panic Dysfunction Kids with nervousness issues often suffer from recurrent stomach aches. Anxiety is related to a better danger for sleep problems in youngsters, comparable to frequent nightmares, stressed legs syndrome, and bruxism (the grinding and gnashing of the teeth during sleep). Prognosis Panic dysfunction can't be prevented.