Open-circuit time constant method - Revision history

en>Faizhaider: Disambiguated: Kirchhoff's laws → Kirchhoff's circuit laws

2014-02-05T18:56:47Z

Disambiguated: Kirchhoff's laws → Kirchhoff's circuit laws

← Older revision		Revision as of 20:56, 5 February 2014
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	In [~~[functional analysis]~~], a ~~branch~~ of ~~mathematics,~~ the ~~'''Goldstine theorem'''~~, ~~named~~ after ~~[[Herman Goldstine]]~~, ~~asserts that the image~~ of ~~the closed unit ball~~ <~~math~~>~~B_X~~<~~/math~~> ~~of a [[Banach space]]~~ <~~math~~>X<~~/math~~> ~~under~~ the ~~canonical imbedding into~~ the ~~closed unit ball <math>B_{X^{}}<~~/~~math> of~~ the ~~[[Dual space\|bidual space]~~] <~~math~~>~~X^{}~~<~~/math~~> ~~is [[Weak topology\|weakly*]]~~-~~[[Dense set\|dense]]~~.		Iѕ nutritional imрrovement on the "to complete" list, however you are not sure [http://games.cool-radio.in/profile/gaearle vigrx plus where to buy in the philippines] to begin? Maintaining a healthy diet food items and dоing exercises will make ʏou feel more lively and check bettеr than ever before. This post offers some significant nourishment suggestions, some tҺаt deserve reiteratіng and a fеա you may possibly not know. 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	~~The conclusion of the theorem is not true~~ for ~~the norm topology~~, ~~which can be seen by considering the Banach space of real sequences~~ that ~~converge to zero~~ [~~[c0 space\|''c''<sub>0<~~/~~sub>]~~], ~~and its bi-dual space [[Lp space\|ℓ~~<~~sub~~>∞<~~/sub~~>]].

	~~== Proof ==~~
	~~Given an~~ <~~math~~>~~x^{} \in B_{X^{}}~~<~~/math~~>, ~~a tuple~~ <~~math~~>~~(\phi_1, \dots, \phi_n)~~<~~/math~~> of ~~linearly independent elements~~ of <~~math~~>X^<~~/math~~> ~~and~~ a ~~<math>\delta>0<~~/~~math> we shall find an <math>x \in (1+\delta) B_{X}<~~/~~math> such that <math>\phi_i(x)~~=~~x^{*}(\phi_i)</math> for every <math>i~~=1,~~\dots~~,n</~~math>~~.

	If the ~~requirement~~ <~~math~~>~~\\|x\\| \leq 1+\delta~~<~~/math~~> ~~is dropped~~, the ~~existence~~ of ~~such an~~ <~~math~~>x<~~/math~~> ~~follows from~~ the ~~surjectivity~~ of
	~~:<math>\Phi : X \to \mathbb{C}^{n}~~, ~~x \mapsto (\phi_1(x)~~, ~~\dots~~, ~~\phi_n(x))~~.<~~/math~~>

	~~Let now~~ <~~math>Y := \bigcap_i \ker \phi_i = \ker \Phi</math~~>.
	~~Every element of~~ <~~math~~>~~(x+Y) \cap (1+\delta) B_{X}~~<~~/math~~> ~~has the required property~~, ~~so that it suffices~~ to ~~show that the latter~~ set ~~is not empty~~.

	~~Assume that it is empty. Then <math>\mathrm{dist}(x,Y) \geq 1+\delta<~~/~~math> and by the Hahn~~-~~Banach theorem there exists a linear form <math>\phi \~~in ~~X^<~~/~~math> such that~~ <~~math~~>~~\phi\|_Y = 0~~<~~/math~~>, <~~math~~>~~\phi(x) \geq 1+\delta~~<~~/math~~> and <~~math~~>~~\\|\phi\\|_{X^}=1~~<~~/math~~>. ~~Then <math>\phi \in \mathrm{span}(\phi_1~~, ~~\dots~~, ~~\phi_n)~~<~~/math~~> ~~and therefore~~
	:<~~math~~>~~1+\delta \leq \phi(x) = x^{*}(\phi) \leq \\|\phi\\|_{X^} \\|x^{}\\|_{X^{}} \leq 1~~,~~</math>~~
	~~which~~ is ~~a contradiction.~~

	~~==See also==~~
	*[[Banach–Alaoglu theorem]]
	*[[Bishop–Phelps theorem]]
	*[[Eberlein–Šmulian theorem]]
	*[[Mazur's ~~lemma]]~~
	*[[James' ~~theorem]]~~

	~~{{Functional Analysis}}~~

	~~[[Category:Banach spaces]]~~
	~~[[Category:Functional analysis]]~~
	~~[[Category:Theorems in functional analysis]]~~

	~~[[de:Schwach-*-Topologie#Eigenschaften]]~~

en>Yworo: belongs in section

2013-10-04T22:14:07Z

belongs in section

@@ Line 1: / Line 1: @@
-Nikola Tesla has announced a volunteer remember touching to a greater extent than 29,000 of its nursing home charging adapters all over potential fuel concerns. The NEMA 14-50 adapter is an optional home initiation that�allows for 240-volt recharging of the company's Modeling S. "Electrical resistance heating in the adapter or at the interface to the wall socket may lead to melting of the adapter, cord or wall receptacle, and possible electrical arcing that could lead to fire," reads Tesla's [http://imageshack.us/photos/January January] 12th missive to the�Home Main road Dealings Condom Giving medication.
+In [[functional analysis]], a branch of mathematics, the '''Goldstine theorem''', named after [[Herman Goldstine]], asserts that the image of the closed unit ball <math>B_X</math> of a [[Banach space]] <math>X</math> under the canonical imbedding into the closed unit ball <math>B_{X^{**}}</math> of the [[Dual space|bidual space]] <math>X^{**}</math> is [[Weak topology|weakly*]]-[[Dense set|dense]].
-  Just this isn't a think in the traditional sense; Nikola Tesla owners don't penury to contain their cars or adapters in for inspection and repair. (1/2) The terminal figure "recall" is obsolete. No vehicles are beingness physically [http://en.search.wordpress.com/?q=recalled recalled] by Tesla. ?? Tesla Motors (@TeslaMotors) January 14, 2014 The automaker says the trouble has been completely remedied�with an over-the-aviation software update. That update has already made its way of life to ended 99 percent of cars, according to Tesla's Saint Jerome Guillen.
+The conclusion of the theorem is not true for the norm topology, which can be seen by considering the Banach space  of real sequences that converge to zero [[c0 space|''c''<sub>0</sub>]], and its bi-dual space [[Lp space|ℓ<sub>∞</sub>]].
- If your Simulation S happens to be come out of meshwork range, the companionship bequeath set up the computer software at whatever of its serve locations. On that point was an over-the-transmit software package update (through with net month) and an upgraded US 14-50 arranger wish be mail-clad to customers. ?? Elon Musk (@elonmusk) January 14, 2014 Prior to the update, Tesla says that around 2.7 per centum of returned adapters showed signs of internal price.
+== Proof ==
- Simply a to a greater extent thorough depth psychology establish that "defective or improperly installed wall receptacles" could lead in melted adapters and tied elicit "in the worst case scenario."�In plus to the software package update, Tesla has engineered a revised adapter hoopla that includes an national fountain mix. "The improved design and addition of the fuse will act to provide a higher level of reliability thereby demonstrating Tesla's commitment to full customer satisfaction.
+If the requirement <math>\|x\| \leq 1+\delta</math> is dropped, the existence of such an <math>x</math> follows from the surjectivity of
-" Tesla says it wish Menachem Begin delivering the updated arranger to customers as trite becomes useable. "It is a very safe car," aforementioned Guillen. "To date, there has been no serious injury in the Model S, ever."<br><br>For those who have any concerns about wherever and also the way to use [http://batuiti.com/shop/smartwatch/smart-bracelet-watch-for-iphone-android-phones-bluetooth-anti-theft-smart-watch-wristwatch/ smart bracelet], it is possible to e-mail us on our web site.
+Let now <math>Y := \bigcap_i \ker \phi_i = \ker \Phi</math>.

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-05T23:52:41Z

ISBNs (Build KC)

New page

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