Free-electron laser - Revision history

en>Maderthaner: /* External links */ bad quality webpage.

2014-11-13T02:36:20Z

External links: bad quality webpage.

← Older revision		Revision as of 04:36, 13 November 2014
Line 1:		Line 1:
	~~Glazier Alfonzo~~ from ~~Alma~~, ~~spends time~~ with ~~hobbies~~ and ~~interests for instance snowshoeing~~, ~~property developers in singapore~~ and ~~creating a house~~. ~~Will~~ soon ~~undertake~~ a ~~contiki journey~~ that will ~~consist~~ of taking a ~~trip to~~ the ~~Lumbini~~.<br><br>~~Here is my web blog:~~ [http://tukarposisi.com/groups/property-news-in-singapore/ tukarposisi.com]		I'm a property agent from DTZ, a worldwide chief in property companies. My providers embrace leasing, rental, sale and purchase of economic and residential properties. I worth relationships and hope to serve you with Sincerity, Honesty and Integrity. My aim is to supply the highest degree of skill, service and care to every consumer during each transaction.<br><br>As soon as one has completed some research, that's, compiled a shortlist of criteria that they'd like their future residence to satisfy, expats can move this record to their property agent. The agent will use this to assemble quite a lot of obtainable addresses that match all their listed points. The screening course of that follows involves the agent taking expats on viewings so that they'll acquaint themselves in particular person with the sorts of houses which might be out there. As a result of they take care of property consumers, sellers, landlords and tenants, and because the transactions they handle can involve large sums of money, the necessity for professionalism is of utmost significance. Overseas Member of the Chartered Institute of Patent Brokers within the UK My Featured Properties of the Day! Click it! View it!<br><br>15.2.1 All definitions [http://tukarposisi.com/groups/property-news-in-singapore/ tukarposisi.com] suffer from inadequacies however basically agency is defined as the relationship which arises where one individual referred to as the agent acts for an additional referred to as the principal. By way of the acts of the agent, the principal and a 3rd celebration may be introduced right into a contractual relationship. The agent may also have the facility to dispose of property of the principal to a 3rd get together. Typically the agent´s acts have such effect as a result of the principal has licensed the agent to do the acts in question and the agent has agreed.<br><br>Correct planning - Pen down your objectives and the steps you'll take to achieve them. Train some creativity and let your greatest ideas deliver you results. Observe up – So essential but often ignored. Some of the most successful brokers have clients who give them referrals, so they don't have to maintain prospecting new clients. Why? It is as a result of they keep in contact with their clients. It can be as simple as month-to-month SMS messages to remind your customer that you're nonetheless in the enterprise. Such an action grows your referral base. The drop out fee in our trade is relatively excessive. After about three to six months, newbie brokers lose their steam and their preliminary "Can do" perspective turns into a "Can I do it?" perspective. Celebration Fee / Payment Payable to Agency<br><br>Basically, documents corresponding to gross sales order, pro-forma invoice, statement of accounts and letter/statement of claims usually are not thought of as invoices for GST time of provide functions. It is because these paperwork are sometimes not billing for payments and would due to this fact not be handled as invoices based mostly on normal business practices. The rental of the naked residential unit is exempt from GST. Nevertheless, you might want to cost GST on the rental of the furniture and fittings. Complete rental of the furnished flat = $4,500 per month Alternatively, if you want to treat the rental as inclusive of GST, you can account for the GST based on the tax fraction of 7/107 of $1,500. HDB Transaction with extra details for your CMA Browse by Location Choose Area and District<br><br>How do you choose a property company and the way do you make sure that you might have made the precise selection at first? Is it true that the larger the true property company, the higher it is? Or can a smaller agency be higher for the development of an agent? There are professionals and cons on the subject of measurement, and dimension does make a difference. Actual property can be a lonely enterprise and it is straightforward to really feel demoralised, particularly when there aren't any enquiries regardless of your finest effort in advertising your shopper's property. That is where having the best assist from fellow associates is vital. JLL has been named Finest Performing Property Brand at the twelfth Annual MPF Awards for Management Excellence. Whether new or resale properties are higher investments Project Gallery Supervisor<br><br>The opposite merchandise you may want to consider or negotiate with your employers is transportation. Automobiles and their running prices are expensive in Singapore. On average, expect to incur S$2500 to S$3000.00 a month to hire a 1600-2000 cc automotive with some petrol leftover for the automobile. Career improvement programmes, in-house valuation, auctions and administrative help, project advertising and marketing, skilled talks and traisning are always deliberate for the gross sales associates to help them achieve higher outcomes for their shoppers while at Knight Frank Singapore. Instances have modified. We don't see those unlawful hawkers anymore. Instead, well dressed property agents have been seen reaching out to people visiting the market in the morning. UE Sq. (D09) – Condominium For Rent

en>JorisvS: /* top */ terms are coined not invented

2014-02-21T08:23:41Z

top: terms are coined not invented

← Older revision		Revision as of 10:23, 21 February 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, ~~the '''multivariate gamma function''', Γ<sub>''p''</sub>(·), is a generalization of the [[gamma function]]. It is useful in [[multivariate statistics]]~~, ~~appearing~~ in ~~the [[probability density function]] of the [[Wishart distribution\|Wishart]]~~ and ~~[[inverse Wishart distribution]]s.~~		Glazier Alfonzo from Alma, spends time with hobbies and interests for instance snowshoeing, property developers in singapore and creating a house. Will soon undertake a contiki journey that will consist of taking a trip to the Lumbini.<br><br>Here is my web blog: [http://tukarposisi.com/groups/property-news-in-singapore/ tukarposisi.com]

	~~It has two equivalent definitions. One is~~

	~~:<math>~~
	~~\Gamma_p(~~a)=
	~~\int_{S>0} \exp\left(~~
	~~-{\rm trace}(S)\right)~~
	~~\left\|S\right\|^{a-(p+1)/2}~~
	~~dS ,~~
	~~</math>~~
	~~where S>0 means S is [[positive-definite matrix\|positive-definite]]~~. ~~The other one, more useful in practice, is~~

	~~:<math>~~
	~~\Gamma_p(~~a)=
	~~\pi^{p(p-1)/4}\prod_{j=1}^p~~
	~~\Gamma\left[~~ a~~+(1-j)/2\right].~~
	~~</math>~~
	~~From this, we have~~ the ~~recursive relationships:~~
	~~:<math>~~
	~~\Gamma_p(a) = \pi^{(p-1)/2} \Gamma(a) \Gamma_{p-1}(a-\tfrac{1}{2}) = \pi^{(p-1)/2} \Gamma_{p-1}(a) \Gamma[a+(1-p)/2]~~ .
	<~~/math~~>

	~~Thus~~

	* <~~math~~>~~\Gamma_1(a)=\Gamma(a)</math>~~
	* <math>\Gamma_2(a)=\pi^{1/2}\Gamma(a)\Gamma(a-1/2)</math>
	* <math>\Gamma_3(a)=\pi^{3/2}\Gamma(a)\Gamma(a-1/2)\Gamma(a-1)</math>

	~~and so on.~~

	~~== Derivatives ==~~

	~~We may define the multivariate [[digamma function]] as~~
	:~~<math>\psi_p(a) = \frac{\partial \log\Gamma_p(a)}{\partial a} = \sum_{i=1}^p \psi(a+(1-i)/2) ,</math>~~
	~~and the general [~~[~~polygamma function]] as~~
	~~:<math>\psi_p^{(n)}(a) = \frac{\partial^n \log\Gamma_p(a)}{\partial a^n} = \sum_{i=1}^p \psi^{(n)}(a+(1-i)/2).</math>~~

	~~=== Calculation steps ===~~

	* Since
	::~~<math>\Gamma_p(a) = \pi^{p(p-1)/4}\prod_{j=1}^p \Gamma(a+\frac{1-j}{2}),<~~/~~math>~~
	~~:it follows that~~
	~~::<math>\frac{\partial \Gamma_p(a)}{\partial a} = \pi^{p(p-1)~~/~~4}\sum_{i=1}^p \frac{\partial\Gamma(a+\frac{1-i}{2})}{\partial a}\prod_{j=1, j\neq i}^p\Gamma(a+\frac{1-j}{2})~~.</~~math>~~

	* By definition of the [[digamma function]], ψ,
	~~::<math>\frac{\partial\Gamma(a+(1-i)~~/~~2)}{\partial a} = \psi(a+(i~~-~~1)/2)\Gamma(a+(i~~-~~1)/2)</math>~~

	~~:it follows that~~
	~~::<math>\frac{\partial \Gamma_p(a)}{\partial a} = \pi^{p(p-1)/4}\prod_{j=1}^p \Gamma(a+(1-j)/2) \sum_{i=1}^p \psi(a+(1~~-~~i)/2) = \Gamma_p(a)\sum_{i=1}^p \psi(a+(1-i)/2).<~~/~~math>~~

	~~{{single source\|date=May 2012}}~~
	~~{{inline\|date=May 2012}}~~
	~~==References==~~
	* {{cite journal
	~~\|title=Distributions of Matrix Variates and Latent Roots Derived from Normal Samples~~
	~~\|last=James \|first=A.~~
	~~\|journal=[[Annals of Mathematical Statistics]]~~
	~~\|volume=35 \|issue=2 \|year=1964 \|pages=475–501~~
	~~\|doi=10~~.~~1214/aoms/1177703550 \|mr=181057 \| zbl = 0121.36605~~
	}}

	~~[[Category:Gamma and related functions]~~]

en>JorisvS: /* External links */

2014-01-11T09:09:58Z

External links

New page

In [[mathematics]], the '''multivariate gamma function''', Γ<sub>''p''</sub>(·), is a generalization of the [[gamma function]]. It is useful in [[multivariate statistics]], appearing in the [[probability density function]] of the [[Wishart distribution|Wishart]] and [[inverse Wishart distribution]]s.

It has two equivalent definitions. One is

:<math>
\Gamma_p(a)=
\int_{S>0} \exp\left(
-{\rm trace}(S)\right)
\left|S\right|^{a-(p+1)/2}
dS ,
</math>
where S>0 means S is [[positive-definite matrix|positive-definite]]. The other one, more useful in practice, is

:<math>
\Gamma_p(a)=
\pi^{p(p-1)/4}\prod_{j=1}^p
\Gamma\left[ a+(1-j)/2\right].
</math>
From this, we have the recursive relationships:
:<math>
\Gamma_p(a) = \pi^{(p-1)/2} \Gamma(a) \Gamma_{p-1}(a-\tfrac{1}{2}) = \pi^{(p-1)/2} \Gamma_{p-1}(a) \Gamma[a+(1-p)/2] .
</math>

Thus

* <math>\Gamma_1(a)=\Gamma(a)</math>
* <math>\Gamma_2(a)=\pi^{1/2}\Gamma(a)\Gamma(a-1/2)</math>
* <math>\Gamma_3(a)=\pi^{3/2}\Gamma(a)\Gamma(a-1/2)\Gamma(a-1)</math>

and so on.

== Derivatives ==

We may define the multivariate [[digamma function]] as
:<math>\psi_p(a) = \frac{\partial \log\Gamma_p(a)}{\partial a} = \sum_{i=1}^p \psi(a+(1-i)/2) ,</math>
and the general [[polygamma function]] as
:<math>\psi_p^{(n)}(a) = \frac{\partial^n \log\Gamma_p(a)}{\partial a^n} = \sum_{i=1}^p \psi^{(n)}(a+(1-i)/2).</math>

=== Calculation steps ===

* Since
::<math>\Gamma_p(a) = \pi^{p(p-1)/4}\prod_{j=1}^p \Gamma(a+\frac{1-j}{2}),</math>
:it follows that
::<math>\frac{\partial \Gamma_p(a)}{\partial a} = \pi^{p(p-1)/4}\sum_{i=1}^p \frac{\partial\Gamma(a+\frac{1-i}{2})}{\partial a}\prod_{j=1, j\neq i}^p\Gamma(a+\frac{1-j}{2}).</math>

* By definition of the [[digamma function]], ψ,
::<math>\frac{\partial\Gamma(a+(1-i)/2)}{\partial a} = \psi(a+(i-1)/2)\Gamma(a+(i-1)/2)</math>

:it follows that
::<math>\frac{\partial \Gamma_p(a)}{\partial a} = \pi^{p(p-1)/4}\prod_{j=1}^p \Gamma(a+(1-j)/2) \sum_{i=1}^p \psi(a+(1-i)/2) = \Gamma_p(a)\sum_{i=1}^p \psi(a+(1-i)/2).</math>

{{single source|date=May 2012}}
{{inline|date=May 2012}}
==References==
* {{cite journal
|title=Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
|last=James |first=A.
|journal=[[Annals of Mathematical Statistics]]
|volume=35 |issue=2 |year=1964 |pages=475–501
|doi=10.1214/aoms/1177703550 |mr=181057 | zbl = 0121.36605
}}

[[Category:Gamma and related functions]]