Stochastic ordering - Revision history

en>Boriaj: /* Convex order */ The inequality shouldn't be strict (corrected)

2014-04-23T17:03:57Z

Convex order: The inequality shouldn't be strict (corrected)

← Older revision		Revision as of 19:03, 23 April 2014
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	~~{{Expert-subject\|Physics\|date=February 2008}}~~		If you present photography effectively, it helps you look much more properly at the globe around you. Offshore expert Word - Press developers high level of interactivity, accessibility, functionality and usability of our website can add custom online to using. SEO Ultimate - I think this plugin deserves more recognition than it's gotten up till now. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. Over a million people are using Wordpress to blog and the number of Wordpress users is increasing every day. <br><br>Creating a website from scratch can be such a pain. If you loved this post and you would like to receive even more details regarding [http://www.kingz-gaming.com/index.php?mod=users&action=view&id=97895 wordpress backup plugin] kindly check out the website. While direct advertising is limited to few spots in your site and tied to fixed monthly payment by the advertisers, affiliate marketing can give you unlimited income as long as you can convert your traffic to sales. A Wordpress plugin is a software that you can install into your Wordpress site. They provide many such popular products which you can buy for your baby. The biggest advantage of using a coupon or deal plugin is that it gives your readers the coupons and deals within minutes of them becoming available. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. 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. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. To turn the Word - Press Plugin on, click Activate on the far right side of the list. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>Word - Press has plenty of SEO benefits over Joomla and Drupal. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. The company gains commission from the customers' payment. This includes enriching the content with proper key words, tactfully defining the tags and URL. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. And, it is better that you leave it on for the duration you are writing plugin code. However, if you're just starting out your blog site or business site, you can still search for an ideal theme for it without breaking your bank account.

	~~The '''excess chemical potential''' is defined as the difference between the [[chemical potential]] of a given species and that of an [[ideal gas]] under the same conditions (in particular~~, at the ~~same [[pressure]]~~, ~~[[temperature]]~~, and ~~[[wikt:composition\|composition]])~~.<ref>{{cite book \| last = Frenkel \| first = Daan \| authorlink = Daan Frenkel \| coauthors = Smit, Berend \| title = Understanding Molecular Simulation : from algorithms to applications \| publisher = [[Academic Press]] \| year = 2001 \| location = [[San Diego, California]] \| pages = \| url = \| doi = \| id = \| isbn = 0-12-~~267351-4 }}</ref>~~

	~~Chemical potential of pure fluid can~~ be ~~estimated by~~ the ~~[[Widom insertion method]]~~.

	~~For~~ a ~~system~~ of ~~diameter~~ <~~math~~>L<~~/math~~> and ~~volume <math>V<~~/~~math>, at constant temperature :<math>T<~~/~~math>, the classical [[partition function (statistical mechanics)\|partition function]] <math>Q(N,V,T)=\frac{V^{N}}{\Lambda^{dN}N!}\int_{0}^{1}\ldots\int_{0}^{1}ds^{N}\exp[~~-~~\beta U(s^{N};L)]<~~/~~math>~~
	~~s is a scaled coordinate~~.

	~~:<math>F(N,V,T)~~= ~~-k_{B}T\ln Q~~=~~-k_{B}T\ln\left(\frac{V^{N}}{\Lambda^{dN}N!}\right)-k_{B}T \ln{\int ds^{N}\exp[-\beta U(s^{N};L)~~]~~}=</math>~~
	~~::<math>\;=F_{id}(N~~,~~V,T)+F_{ex}(N,V,T)</math>~~

	~~combining~~ the ~~above equation with the definition~~ of ~~chemical potential:~~ <~~math~~>~~\mu_{a}= \left(\frac{\partial G}{\partial N_{a}}\right)_{PTN}~~<~~/math~~>

	we get ~~the chemical potential~~ of a ~~sufficient large system~~ is :

	~~:<math>\mu=~~ -~~k_{B}T\ln(Q_{N+1}/Q_{N})=-k_{B}T\ln\left(\frac{V/\Lambda^{d}}{N+1}\~~right~~) - k_{B}T \ln{\frac{\int ds^{N+1}\exp[-\beta U(s^{N+1})]}{\int ds^{N}\exp[-\beta U(s^{N})]}}=\mu_{id}(\rho) + \mu_{ex}</math>~~

	~~wherein~~ the ~~chemical potential of ideal gas~~ can ~~be evaluated analytically~~.
	~~Now let's focus on~~ <~~math~~>~~\mu_{ex}~~<~~/math~~>~~, since the potential energy~~ of ~~an N+1 particle system can~~ be ~~separated into~~ the ~~potential energy of an N [[particle system]] and~~ the ~~potential of~~ the ~~excess particle interacts~~ with the ~~N particle system, there is~~

	~~:<math>\Delta U\equiv U(s^{N+1}) - U(s^{N})</math>~~

	and

	:<~~math~~>~~\mu_{ex}= -k_{B}T \ln \int ds_{N+1} \langle \exp(-\beta\Delta U)\rangle_{N}~~<~~/math~~>

	~~thus far we converted~~ the ~~excess chemical potential into an ensemble average, and~~ the ~~integral~~ in the ~~above equation can be sampled~~ by ~~brute force [[Monte Carlo method]]~~.

	~~The calculating~~ of ~~excess chemical potential is not only limited to homogeneous system~~, it ~~has also been extended~~ to ~~inhomogeneous system by [[Widom insertion method]]~~, ~~or other [[Statistical ensemble (mathematical physics)\|ensembles]] such as NPT~~, ~~[[Microcanonical ensemble\|NVE]]~~.

	~~==See also==~~
	~~[[Apparent molar property]]~~

	~~==References==~~
	* Note: the ~~equations and presentation in this article~~ are ~~drawn from [http://www~~.~~pages.drexel.edu/~cfa22/msim/node39~~.~~html Excess Chemical Potential via the Widom Method]<!-- not a copyright violation--see talk page and [[Wikipedia talk:Copyright problems#Copyright violations in Excess chemical potential]] -->~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Excess Chemical Potential}}~~
	~~[[Category:Potentials]]~~
	~~[[Category:Thermodynamics]]~~
	~~[[Category:Chemical thermodynamics]]~~

	~~[[ro:Mărimi molare de exces]]~~

en>BG19bot: /* Multivariate stochastic order */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9782)

2013-12-15T08:06:42Z

Multivariate stochastic order: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9782)

← Older revision		Revision as of 10:06, 15 December 2013
Line 1:		Line 1:
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			The '''excess chemical potential''' is defined as the difference between the [[chemical potential]] of a given species and that of an [[ideal gas]] under the same conditions (in particular, at the same [[pressure]], [[temperature]], and [[wikt:composition\|composition]]).<ref>{{cite book \| last = Frenkel \| first = Daan \| authorlink = Daan Frenkel \| coauthors = Smit, Berend \| title = Understanding Molecular Simulation : from algorithms to applications \| publisher = [[Academic Press]] \| year = 2001 \| location = [[San Diego, California]] \| pages = \| url = \| doi = \| id = \| isbn = 0-12-267351-4 }}</ref>

			Chemical potential of pure fluid can be estimated by the [[Widom insertion method]].

			For a system of diameter <math>L</math> and volume <math>V</math>, at constant temperature :<math>T</math>, the classical [[partition function (statistical mechanics)\|partition function]] <math>Q(N,V,T)=\frac{V^{N}}{\Lambda^{dN}N!}\int_{0}^{1}\ldots\int_{0}^{1}ds^{N}\exp[-\beta U(s^{N};L)]</math>
			s is a scaled coordinate.

			:<math>F(N,V,T)= -k_{B}T\ln Q=-k_{B}T\ln\left(\frac{V^{N}}{\Lambda^{dN}N!}\right)-k_{B}T \ln{\int ds^{N}\exp[-\beta U(s^{N};L)]}=</math>
			::<math>\;=F_{id}(N,V,T)+F_{ex}(N,V,T)</math>

			combining the above equation with the definition of chemical potential: <math>\mu_{a}= \left(\frac{\partial G}{\partial N_{a}}\right)_{PTN}</math>

			we get the chemical potential of a sufficient large system is :

			:<math>\mu= -k_{B}T\ln(Q_{N+1}/Q_{N})=-k_{B}T\ln\left(\frac{V/\Lambda^{d}}{N+1}\right) - k_{B}T \ln{\frac{\int ds^{N+1}\exp[-\beta U(s^{N+1})]}{\int ds^{N}\exp[-\beta U(s^{N})]}}=\mu_{id}(\rho) + \mu_{ex}</math>

			wherein the chemical potential of ideal gas can be evaluated analytically.
			Now let's focus on <math>\mu_{ex}</math>, since the potential energy of an N+1 particle system can be separated into the potential energy of an N [[particle system]] and the potential of the excess particle interacts with the N particle system, there is

			:<math>\Delta U\equiv U(s^{N+1}) - U(s^{N})</math>

			and

			:<math>\mu_{ex}= -k_{B}T \ln \int ds_{N+1} \langle \exp(-\beta\Delta U)\rangle_{N}</math>

			thus far we converted the excess chemical potential into an ensemble average, and the integral in the above equation can be sampled by brute force [[Monte Carlo method]].

			The calculating of excess chemical potential is not only limited to homogeneous system, it has also been extended to inhomogeneous system by [[Widom insertion method]], or other [[Statistical ensemble (mathematical physics)\|ensembles]] such as NPT, [[Microcanonical ensemble\|NVE]].

			==See also==
			[[Apparent molar property]]

			==References==
			* Note: the equations and presentation in this article are drawn from [http://www.pages.drexel.edu/~cfa22/msim/node39.html Excess Chemical Potential via the Widom Method]<!-- not a copyright violation--see talk page and [[Wikipedia talk:Copyright problems#Copyright violations in Excess chemical potential]] -->
			{{Reflist}}

			{{DEFAULTSORT:Excess Chemical Potential}}
			[[Category:Potentials]]
			[[Category:Thermodynamics]]
			[[Category:Chemical thermodynamics]]

			[[ro:Mărimi molare de exces]]

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

2012-02-18T17:36:33Z

Dating maintenance tags: {{Cn}}

New page

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