Quadratic unconstrained binary optimization - Revision history

en>Yobot: Tagging using AWB (10469)

2014-09-21T18:13:42Z

Tagging using AWB (10469)

← Older revision		Revision as of 20:13, 21 September 2014
Line 1:		Line 1:
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en>SamuelRiv: clarified quantum computing reference as per talk.

2014-02-16T21:42:19Z

clarified quantum computing reference as per talk.

← Older revision		Revision as of 23:42, 16 February 2014
Line 1:		Line 1:
	~~In [[mathematics]],~~ the ~~'''Russo–Dye theorem'''~~ is ~~a result~~ in the ~~field of [[functional analysis]]~~. ~~It states that in~~ a [[unital algebra\|unital]] [[C*-~~algebra]]~~, the ~~closure~~ of ~~the [[convex hull]]~~ of the ~~[[unitary element]]s~~ is ~~the closed [[unit ball]]~~.<~~ref name="Doran Belfi"~~>		The main advantage of using the blog is that anyone can use the Word - Press blog and customize the elements in the theme regardless to limited knowledge about internet and website development. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. This is a service where people write articles using a specific keyword you have given them. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. Some of the Wordpress development services offered by us are:. It sorts the results of a search according to category, tags and comments. t need to use the back button or the URL to get to your home page. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer. <br><br>You can down load it here at this link: and utilize your FTP software program to upload it to your Word - Press Plugin folder. For those who have any concerns regarding in which and the best way to employ [http://s.do-dance.com/wordpressdropboxbackup624465 wordpress dropbox backup], you can e-mail us at our own page. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. Those who cannot conceive with donor eggs due to some problems can also opt for surrogacy option using the services of surrogate mother. To turn the Word - Press Plugin on, click Activate on the far right side of the list. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. Russell HR Consulting provides expert knowledge in the practical application of employment law as well as providing employment law training and HR support services. Enterprise, when they plan to hire Word - Press developer resources still PHP, My - SQL and watch with great expertise in codebase. Fast Content Update - It's easy to edit or add posts with free Wordpress websites. OSDI, a Wordpress Development Company based on ahmedabad, India. <br><br>More it extends numerous opportunities where your firm is at comfort and rest assured of no risks & errors. Automated deal feed integration option to populate your blog with relevant deals. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. Thus, Word - Press is a good alternative if you are looking for free blogging software. Get started today so that people searching for your type of business will be directed to you.
	~~{{cite book \| last = Doran \| first = Robert S~~. ~~\|coauthors = Victor A. Belfi \| title = Characterizations~~ of ~~C*-Algebras~~: ~~The Gelfand–Naimark Theorems \| publisher = Marcel Dekker \| location = New York \| year = 1986 \| isbn = 0-8247-7569-4 }}~~
	~~</ref>{{Rp\|44}}~~
	~~The theorem was published by B~~. ~~Russo~~ and H. A. ~~Dye in 1966~~.<~~ref name="Russo Dye"~~>
	{{cite journal \|last=Russo \|first=B. \|coauthors=H. A. Dye \|year=1966\|title=A Note on Unitary Operators in C*-Algebras \|journal=Duke Mathematical Journal \|volume=33 \|pages=413–416 \|doi=10.1215/S0012-7094-66-03346-1 \|issue=2 }}
	<~~/ref~~>

	~~==Other formulations~~ and ~~generalizations==~~

	~~Results similar~~ to ~~the Russo–Dye theorem hold in more general contexts~~. For ~~example,~~ in ~~a unital *-Banach algebra,~~ the ~~closed~~ [~~[unit ball]~~] is ~~contained in~~ the ~~closed [[convex hull]] of~~ the ~~[[unitary element]]s~~.~~<ref name="Doran Belfi" />{{Rp\|73}}~~

	~~A more precise result is true~~ for the [[C*-~~algebra]]~~ of ~~all [[bounded linear operator]]s on a [[Hilbert space]]: If ''T'' is such an operator~~ and ~~\|\|''T''\|\| < 1 − 2/''n'' for some integer ''n'' > 2~~, ~~then ''T''~~ is the ~~mean of ''n'' [[unitary operator]]s~~.<~~ref name="Analysis Now"~~>
	~~{{cite book \| last = Pedersen \| first = Gert K. \| title = Analysis Now \| publisher = Springer-Verlag \| location = Berlin \| year = 1989 \| isbn = 0-387-96788-5 }}~~
	<~~/ref~~>~~{{Rp\|98}}~~

	~~==Applications==~~

	~~This example is due to Russo & Dye~~,~~<ref name="Russo Dye" /> Corollary 1: If~~ '~~'U''(''A'') denotes~~ the ~~[[unitary element]]s~~ of a [[C*-~~algebra]] ''A''~~, ~~then the [[Operator norm\|norm]] of a [[linear mapping]] ''f'' from ''A'~~' to a ~~[[normed linear space]] ''B'' is~~
	:<~~math~~>~~\sup_{U \in U(A)} \|\|f(U)\|\|.~~<~~/math~~>
	~~In other words, the norm~~ of ~~an operator can be calculated using only~~ the ~~unitary elements of~~ the ~~algebra.~~

	~~==Further reading==~~
	* An especially simple proof of the ~~theorem~~ is ~~given in: {{cite journal \|last=Gardner \|first=L~~. T. ~~\|year=1984 \|title=An elementary proof~~ of ~~the Russo–Dye theorem \|jstor=2044692 \|journal=Proceedings of the American Mathematical Society \|volume=90 \|issue=1\|pages=171 \|doi=10~~.~~2307/2044692 }}~~

	~~==Notes==~~
	~~<references />~~

	~~{{DEFAULTSORT:Russo-Dye theorem}}~~
	~~[[Category:C*-algebras]]~~
	~~[[Category:Theorems in functional analysis]]~~
	~~[[Category:Unitary operators]]~~

en>Johnmperry: check/correct/improve cites

2013-05-12T07:07:56Z

check/correct/improve cites

← Older revision		Revision as of 09:07, 12 May 2013
Line 1:		Line 1:
	~~Cell phones have come~~ a ~~lengthy way~~ in the ~~past decade in terms~~ of ~~technology~~. It ~~appears like each and every day there is some thing~~ that ~~new to discover. If you are nonetheless stuck with outdated cell telephone information, or possibly you just want to get~~ in ~~on the newest hot technologies~~, ~~then you will want to study~~ the ~~following report. Continue on for excellent ideas on all~~ the ~~latest gadgets in~~ the ~~cell telephone globe.<br><br>At times signing a longer term contract~~ is ~~worth it to get~~ the ~~phone you want. Discover further on~~ [~~http://www~~.~~tgmplus~~.co.~~il/mobile~~-~~phone~~-~~parts/samsung/galaxy~~-s2-~~i9100~~/~~msk-lglaqsi-2~~.~~html discount ????? 2 ???] by navigating to our thrilling article directory~~. ~~Some providers will provide the best prices if you are willing to sign on for their service for a year or two~~. ~~Just make certain you are willing to commit to the contract, simply because ending the term early can cost a lot~~ in ~~penalties~~.<br>~~<br>Do not feel the require to commit the additional funds on a cell telephone screen protector~~. ~~Today"s cell phones are made from scratch resistant glass~~. ~~To explore additional information, we understand you peep at: [http://www~~.~~tgmplus~~.~~co.il~~/~~mobile~~-~~phone~~-~~parts/samsung/galaxy~~-s3-~~i9300~~/~~msk-lgalqsi-3.html ??? ???? ??? ?????? 3]. This glass is so powerful that even keys won"t scratch it when they are subsequent~~ to ~~a telephone~~ in ~~your pocket~~. ~~That screen protector is most likely wasted cash.<br><br>If you decide to get~~ in ~~touch with details on your cell telephone, you never have to spend exorbitant costs connected with that. You can just dial 1-800-411~~-~~Free. Following you listen to a quick advertisement~~, ~~you will get all~~ the ~~information you requested.<br><br>Think about getting a utilized telephone if you are seeking to upgrade ahead of your contract makes it possible for you to. This~~ is ~~typically much less expensive than buying new, and you will not be locked~~ in ~~to a distinct contract period. Just make certain your provider supports~~ the ~~telephone you want to get, and that you can very easily add it to your strategy~~.<br>~~<br>Check online critiques before acquiring your cell telephone. There are lots of new phones coming on the industry all the time, and it is at times challenging to know which~~ is ~~ideal~~ for ~~you. By checking on~~-~~line reviews, you can see what attributes a variety~~ of ~~phones provide, as properly as how~~ a ~~lot other folks like them. This can help you to make~~ an ~~educated selection.~~<br>~~<br>When purchasing a used cell telephone~~, ~~make sure you know who you are acquiring from. Think about only getting from a reliable company that will back your acquire with some sort of guarantee. This will shield you if the telephone~~ is ~~defective. If you get from an individual, think about trying~~ the ~~phone out just before handing over any funds~~.<br><br>~~If you are in the industry for a new cell phone and are unsure about which path~~ to ~~take~~, do your self a favor and ask your buddies and family members for opinions. By seeking personal suggestions for each brands and models, the approach will be a lot easier. Acquiring some thing you know people like can be a excellent way to end up happy with your new phone.<~~br><br~~>If ~~you"re concerned about cell telephone radiation, use~~ a ~~headset rather of holding your cell phone to your ear. Usually~~, ~~every cell telephone comes prepackaged with a head set. You can commence making use of it proper out of~~ the ~~box. Consider getting a second for the auto so that you constantly have a single handy.<br><br>Do not be afraid to switch cell telephone brands. Even though you might be utilised to making use~~ of a ~~particular screen layout or interface, be positive~~ to ~~have an open thoughts. There could be~~ a ~~lot more function out there that you don"t recognize.~~<~~br><br~~>A screen protector could not be necessary. The latest screens usually have a protective layer currently included. A screen protector might make it hard for you to see your screen or even make it tougher for you to touch and interact with your device. For that reason, when getting your phone, ask about the screen and how it was made to decide if further protection is needed.<br>~~<br>If you like to take pictures with your cell phone~~, be ~~leery~~ of ~~using~~ the ~~zoom~~. ~~It does not zoom in~~ the ~~way cameras do. You might just end up with an image that~~ is ~~fuzzy~~. ~~This is because it enlarges the pixels rather than actually receiving closer to the image~~.~~<br><br>Scroll by way~~ of ~~your cell telephone directory and see which numbers you dial~~ the ~~most usually or are~~ the most essential. Create or variety out this short list, and maintain it in your wallet or purse. Losing your cell telephone can be negative adequate, but losing all your telephone numbers with it is even worse. This is specifically accurate if you just left it at a friend"s house and could find it in 1 ~~telephone contact~~.<br><br>As you can see from the above report, there is a lot to learn when it comes to the latest cell phone technologies. Fortunately, you came across these great ideas that ought to give you a good notion on the newest technologies. Get further about [~~http~~:~~//www.tgmplus.co.il/mobile~~-~~phone-parts/samsung/galaxy-s3-i9300/msk-lgalqsi-3.html ??? ????? 3 ????~~] ~~by browsing our pictorial web page. Possibly you may possibly want to get a single of these new fancy phones oneself? Hold these ideas~~ in ~~mind anytime you go buying for that new cell telephone..<br><br>If you have any inquiries regarding in which and how to use~~ [~~http~~:~~//relievedmovie3697.jimdo.com health website~~]~~, you can get hold of us at the webpage.~~		In [[mathematics]], the '''Russo–Dye theorem''' is a result in the field of [[functional analysis]]. It states that in a [[unital algebra\|unital]] [[C*-algebra]], the closure of the [[convex hull]] of the [[unitary element]]s is the closed [[unit ball]].<ref name="Doran Belfi">
			{{cite book \| last = Doran \| first = Robert S. \|coauthors = Victor A. Belfi \| title = Characterizations of C*-Algebras: The Gelfand–Naimark Theorems \| publisher = Marcel Dekker \| location = New York \| year = 1986 \| isbn = 0-8247-7569-4 }}
			</ref>{{Rp\|44}}
			The theorem was published by B. Russo and H. A. Dye in 1966.<ref name="Russo Dye">
			{{cite journal \|last=Russo \|first=B. \|coauthors=H. A. Dye \|year=1966\|title=A Note on Unitary Operators in C*-Algebras \|journal=Duke Mathematical Journal \|volume=33 \|pages=413–416 \|doi=10.1215/S0012-7094-66-03346-1 \|issue=2 }}
			</ref>

			==Other formulations and generalizations==

			Results similar to the Russo–Dye theorem hold in more general contexts. For example, in a unital *-Banach algebra, the closed [[unit ball]] is contained in the closed [[convex hull]] of the [[unitary element]]s.<ref name="Doran Belfi" />{{Rp\|73}}

			A more precise result is true for the [[C*-algebra]] of all [[bounded linear operator]]s on a [[Hilbert space]]: If ''T'' is such an operator and \|\|''T''\|\| < 1 − 2/''n'' for some integer ''n'' > 2, then ''T'' is the mean of ''n'' [[unitary operator]]s.<ref name="Analysis Now">
			{{cite book \| last = Pedersen \| first = Gert K. \| title = Analysis Now \| publisher = Springer-Verlag \| location = Berlin \| year = 1989 \| isbn = 0-387-96788-5 }}
			</ref>{{Rp\|98}}

			==Applications==

			This example is due to Russo & Dye,<ref name="Russo Dye" /> Corollary 1: If ''U''(''A'') denotes the [[unitary element]]s of a [[C*-algebra]] ''A'', then the [[Operator norm\|norm]] of a [[linear mapping]] ''f'' from ''A'' to a [[normed linear space]] ''B'' is
			:<math>\sup_{U \in U(A)} \|\|f(U)\|\|.</math>
			In other words, the norm of an operator can be calculated using only the unitary elements of the algebra.

			==Further reading==
			* An especially simple proof of the theorem is given in: {{cite journal \|last=Gardner \|first=L. T. \|year=1984 \|title=An elementary proof of the Russo–Dye theorem \|jstor=2044692 \|journal=Proceedings of the American Mathematical Society \|volume=90 \|issue=1\|pages=171 \|doi=10.2307/2044692 }}

			==Notes==
			<references />

			{{DEFAULTSORT:Russo-Dye theorem}}
			[[Category:C*-algebras]]
			[[Category:Theorems in functional analysis]]
			[[Category:Unitary operators]]

en>AnomieBOT: Dating maintenance tags: {{Orphan}}

2011-11-01T16:48:12Z

Dating maintenance tags: {{Orphan}}

New page

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