Baskakov operator - Revision history

en>Monkbot: /* References */Task 6f: add |script-title=; replace {{xx icon}} with |language= in CS1 citations; clean up language icons;

2014-11-17T22:52:59Z

References: Task 6f: add |script-title=; replace {{xx icon}} with |language= in CS1 citations; clean up language icons;

← Older revision		Revision as of 00:52, 18 November 2014
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	~~My name~~ is ~~Lindsay Suter but everybody calls me Lindsay~~. I'~~m from Canada~~. I'~~m studying at~~ the ~~college (final~~ year) and ~~I play~~ the ~~Guitar~~ for ~~9 years. Usually I choose songs from my famous films ;)~~. <br>~~I have two sister~~. ~~I love Microscopy~~, ~~watching movies~~ and ~~Meteorology~~.<br><br>~~My webpage~~ [http://wallpaperpicker.com/profile/jedobbins backup plugin]		Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. 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. s and intelligently including a substantial amount of key words in the title tags, image links, etc. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner. <br><br>Thus, it is imperative that you must Hire Word - Press Developers who have the expertise and proficiency in delivering theme integration and customization services. When you write a new post, you'll see a small bar that goes across the text input area. Several claim that Wordpress just isn't an preferred tool to utilise when developing a professional site. You can add new functionalities and edit the existing ones to suit your changing business needs. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business. <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. It was also the very first year that the category of Martial Arts was included in the Parents - Connect nationwide online poll, allowing parents to vote for their favorite San Antonio Martial Arts Academy. You can now search through the thousands of available plugins to add all kinds of functionality to your Word - Press site. Enough automated blog posts plus a system keeps you and your clients happy. 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>There has been a huge increase in the number of developers releasing free premium Word - Press themes over the years. 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. The Pakistani culture is in demand of a main surgical treatment. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. An ease of use which pertains to both internet site back-end and front-end users alike. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. Thus, Word - Press is a good alternative if you are looking for free blogging software. If you liked this article and you also would like to be given more info with regards to [http://wallpaperpicker.com/profile/jedobbins backup plugin] please visit our own website. For your information, it is an open source web content management system.

en>Trappist the monk: /* Basic results */Fix CS1 deprecated coauthor parameter errors using AWB

2014-03-04T14:05:15Z

Basic results: Fix CS1 deprecated coauthor parameter errors using AWB

← Older revision		Revision as of 16:05, 4 March 2014
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	~~In [[mathematics]] '''leapfrog integration'''~~ is ~~a simple method for numerically integrating [[differential equation]]s of the form~~		My name is Lindsay Suter but everybody calls me Lindsay. I'm from Canada. I'm studying at the college (final year) and I play the Guitar for 9 years. Usually I choose songs from my famous films ;). <br>I have two sister. I love Microscopy, watching movies and Meteorology.<br><br>My webpage [http://wallpaperpicker.com/profile/jedobbins backup plugin]
	~~:<math>\ddot x=F(x)</math>,~~
	~~or equivalently of the form~~
	~~:<math>\dot v=F(x),\;\dot x \equiv v</math>,~~
	~~particularly in the case of a [[dynamical system]] of [[classical mechanics]]~~. ~~Such problems often take the form~~
	~~:<math>\ddot x=-\nabla V(x)</math>,~~
	~~with energy function~~
	~~:<math>E(x,v)=\tfrac12\|v\|^2+V(x)</math>,~~
	~~where~~ '~~'V'' is the [[potential energy]] of the system. The method is known by different names in different disciplines~~. ~~In particular, it is similar to the '''Velocity Verlet'~~'~~' method, which is a variant of [[Verlet integration]]. Leapfrog integration is equivalent to updating positions <math>x(t)</math> and velocities <math>v(t)=\dot x(t)</math>~~ at interleaved time points, staggered in such a way that they 'leapfrog' over each other. For example, the position is updated at integer time steps and the velocity is updated at integer-plus-a-half time steps.

	Leapfrog integration is a second order method, in contrast to [[Euler integration]], which is only first order, yet requires the same number of function evaluations per step. Unlike Euler integration, it is stable for oscillatory motion, as long as the time-step <math>\Delta t</math> is constant, and <math>\Delta t \leq 2/\omega</math>.<ref>[C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulations, McGraw-Hill Book Company, 1985, p. 56]</ref>

	~~In leapfrog integration, the equations for updating position and velocity are~~
	~~:<math>\begin{align}~~
	~~x_i &= x_{i-1} + v_{i-1/2}\, \Delta t , \\[0.4em]~~
	~~a_i &= F~~(~~x_i~~) ~~\\[0.4em]~~
	~~v_{i+1/2} &= v_{i-1/2} + a_{i}\, \Delta t ,~~
	~~\end{align}</math>~~

	where <math>x_i</math> is position at step <math>i</math>, <math>v_{i+1/2\,}</math> is the velocity, or first derivative of <math>x</math>, at step <math>i+1/2\,</math>, <math>a_{i}=F(x_i)</math> is the acceleration, or second derivative of <math>x</math>, at step <math>i</math> and ~~<math>\Delta t</math> is~~ the ~~size of each time step~~. These equations can be expressed in a form which gives velocity at integer steps as well.<ref>[http://www.artcompsci.org/vol_1/v1_web/node34.html 4.1 Two Ways to Write the Leapfrog]</ref> However, even in this synchronized form, the time-step <math>\Delta t</math> must be constant to maintain stability.<ref>[Skeel, R. D., "Variable Step Size Destabilizes the Stömer/Leapfrog/Verlet Method," BIT Numerical Mathematics, Vol. 33, 1993, pp. 172-175.]</ref>
	~~:<math>\begin{align}~~
	~~x_{i+1} &= x_i + v_i\, \Delta t + \tfrac{1}{2}\,a_i\, \Delta t^{\,2} , \\[0.4em]~~
	~~v_{i+1} &= v_i + \tfrac{1}{2}\,(a_i + a_{i+1}~~)~~\,\Delta t~~ .
	~~\end{align}~~<~~/math~~>

	One use of this equation is in gravity simulations, since in that case the acceleration depends only on the positions of the gravitating masses, although higher order integrators (such as [[Runge–Kutta methods]]) are more frequently used.

	~~There are~~ two ~~primary strengths to Leapfrog integration when applied to mechanics problems~~. ~~The first is the [[time-reversibility]] of the Leapfrog method. One can integrate forward ''n'' steps~~, and then reverse the direction of integration and integrate backwards ''n'' steps to arrive at the same starting position. The second strength of Leapfrog integration is its [[Symplectic integrator\|symplectic]] nature, which implies that it conserves the (slightly modified) energy of dynamical systems. This is especially useful when computing orbital dynamics, as many other integration schemes, such as the (order 4) Runge-Kutta method, do not conserve energy and allow the system to drift substantially over time.

	Because of its time-reversibility, and because it is a [[symplectic integrator]], leapfrog integration is also used in [[Hybrid Monte Carlo\|Hamiltonian Monte Carlo]], a method for drawing random samples from a probability distribution whose overall normalization is unknown.<~~ref~~>{{cite book \| last=Bishop \| first=Christopher \| title=Pattern Recognition and Machine Learning \| year=2006 \| publisher=[[Springer-Verlag]] \| location=New York \| isbn=978-0-387-31073-2 \| pages=548–554}}<~~/ref~~>

	~~==See also==~~
	*[[Numerical ordinary differential equations]]
	*[[Symplectic integrator\|Symplectic integration]]
	*[[Euler integration]]
	*[[Verlet integration]]
	*[[Runge–Kutta methods\|Runge–Kutta integration]]

	~~==References==~~
	~~{{Reflist}}~~

	~~==External links==~~
	*[http://~~einstein~~.~~drexel.edu/courses/Comp_Phys~~/~~Integrators~~/~~leapfrog/ The Leapfrog Integrator], Drexel University Physics~~

	~~{{Numerical integrators}}~~

	~~[[Category:Numerical differential equations]~~]

en>Mdd: + Link(s)

2013-09-09T23:31:01Z

+ Link(s)

← Older revision		Revision as of 01:31, 10 September 2013
Line 1:		Line 1:
	~~e - Shop Word - Press~~ is a ~~excellent cart~~ for ~~your on~~ the ~~web shopping organization. Online available for hiring are most qualified~~, ~~well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company~~. ~~Step~~-~~4 Testing~~: It is the ~~foremost important~~ of ~~your Plugin development process~~. ~~Out of the various designs of photography identified these days~~, ~~sports photography~~ is ~~preferred most, probably for~~ the ~~enjoyment and enjoyment associated with it. By using this~~ method ~~one can see whether the theme has the potential to become popular or not and~~ is ~~their any scope~~ of ~~improvement in the theme~~. <br><br>~~purcase~~ and ~~download - WPZOOM Tribune wordpress Theme~~, ~~find~~ and ~~use~~ the ~~WPZOOM Discount Code~~. ~~WPTouch~~ is ~~among the more well known Word - Press smartphone plugins~~ which is ~~currently in use by thousands~~ of ~~users~~. ~~With~~ the ~~free Word~~ - ~~Press blog~~, ~~you have the liberty to come up with your own personalized domain name~~. ~~E-commerce websites are meant to be buzzed with fresh contents~~, ~~graphical enhancements~~, ~~and functionalities. By using Word~~ - ~~Press~~, ~~you can develop very rich~~, ~~user-friendly and full-functional website~~. <br><br>~~Your Word~~ - ~~Press blog or site will also require a domain name which many hosting companies can also provide. Now if we talk about them one by one then~~ -wordpress blog customization means customization of your blog such as installation of wordpress on your server by wordpress developer which will help you to acquire the SEO friendly blog application integrated with your site design as well as separate blog administration panel for starting up your own business blog,~~which demands a experienced wordpress designer~~. ~~Are you considering getting your website redesigned~~. ~~Storing write~~-~~ups in advance would have to be neccessary with~~ the ~~auto blogs. Purchase these from our site~~, or ~~bring your own~~, ~~it doesn't matter~~, ~~we will still give you free installation~~ and ~~configuration.~~ <br><br>~~There has been a huge increase in~~ the ~~number~~ of ~~developers releasing free premium Word - Press themes over the years~~. ~~If you loved this post and you wish to receive details relating to~~ [http://~~flashgameaddiction~~.~~com~~/~~profile~~/~~553407~~/~~erdesmond~~.html ~~wordpress dropbox backup~~] ~~please visit~~ the ~~site~~. ~~Cameras with a pentaprism~~ (~~as in comparison to pentamirror~~) ~~ensure that little mild~~ is ~~lost before it strikes your eye~~, ~~however these often increase~~ the ~~cost~~ of the ~~digital camera considerably~~. ~~One~~ of the ~~great features of Wordpress is its ability to integrate SEO into your site~~. ~~Contact Infertility Clinic Providing~~ One ~~stop Fertility Solutions at:. Make sure you have~~ the ~~latest versions~~ of ~~all your plugins are updated. <br><br>Instead, you can easily just include it with our bodies~~ integration ~~field in e - Panel. I don~~'~~t want that for my visitors and I~~'~~m quite sure they don~~'~~t either~~. ~~However~~, ~~there are a few other Wordpress plugins also for its development~~ which ~~requires adding files in your Wordpress setup~~. ~~Word - Press~~ is ~~an open source content management system which is easy to use and offers~~ many ~~user friendly features. As for performing online business~~, ~~websites~~ and ~~blogs are~~ the ~~only medium that are available~~ to ~~interact with customers and Word - Press perform this work with the help~~ of ~~cross~~-~~blog communication tools~~, ~~comments~~ and ~~full user registration plug~~-~~ins~~.		In [[mathematics]] '''leapfrog integration''' is a simple method for numerically integrating [[differential equation]]s of the form
			:<math>\ddot x=F(x)</math>,
			or equivalently of the form
			:<math>\dot v=F(x),\;\dot x \equiv v</math>,
			particularly in the case of a [[dynamical system]] of [[classical mechanics]]. Such problems often take the form
			:<math>\ddot x=-\nabla V(x)</math>,
			with energy function
			:<math>E(x,v)=\tfrac12\|v\|^2+V(x)</math>,
			where ''V'' is the [[potential energy]] of the system. The method is known by different names in different disciplines. In particular, it is similar to the '''Velocity Verlet''' method, which is a variant of [[Verlet integration]]. Leapfrog integration is equivalent to updating positions <math>x(t)</math> and velocities <math>v(t)=\dot x(t)</math> at interleaved time points, staggered in such a way that they 'leapfrog' over each other. For example, the position is updated at integer time steps and the velocity is updated at integer-plus-a-half time steps.

			Leapfrog integration is a second order method, in contrast to [[Euler integration]], which is only first order, yet requires the same number of function evaluations per step. Unlike Euler integration, it is stable for oscillatory motion, as long as the time-step <math>\Delta t</math> is constant, and <math>\Delta t \leq 2/\omega</math>.<ref>[C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulations, McGraw-Hill Book Company, 1985, p. 56]</ref>

			In leapfrog integration, the equations for updating position and velocity are
			:<math>\begin{align}
			x_i &= x_{i-1} + v_{i-1/2}\, \Delta t , \\[0.4em]
			a_i &= F(x_i) \\[0.4em]
			v_{i+1/2} &= v_{i-1/2} + a_{i}\, \Delta t ,
			\end{align}</math>

			where <math>x_i</math> is position at step <math>i</math>, <math>v_{i+1/2\,}</math> is the velocity, or first derivative of <math>x</math>, at step <math>i+1/2\,</math>, <math>a_{i}=F(x_i)</math> is the acceleration, or second derivative of <math>x</math>, at step <math>i</math> and <math>\Delta t</math> is the size of each time step. These equations can be expressed in a form which gives velocity at integer steps as well.<ref>[http://www.artcompsci.org/vol_1/v1_web/node34.html 4.1 Two Ways to Write the Leapfrog]</ref> However, even in this synchronized form, the time-step <math>\Delta t</math> must be constant to maintain stability.<ref>[Skeel, R. D., "Variable Step Size Destabilizes the Stömer/Leapfrog/Verlet Method," BIT Numerical Mathematics, Vol. 33, 1993, pp. 172-175.]</ref>
			:<math>\begin{align}
			x_{i+1} &= x_i + v_i\, \Delta t + \tfrac{1}{2}\,a_i\, \Delta t^{\,2} , \\[0.4em]
			v_{i+1} &= v_i + \tfrac{1}{2}\,(a_i + a_{i+1})\,\Delta t .
			\end{align}</math>

			One use of this equation is in gravity simulations, since in that case the acceleration depends only on the positions of the gravitating masses, although higher order integrators (such as [[Runge–Kutta methods]]) are more frequently used.

			There are two primary strengths to Leapfrog integration when applied to mechanics problems. The first is the [[time-reversibility]] of the Leapfrog method. One can integrate forward ''n'' steps, and then reverse the direction of integration and integrate backwards ''n'' steps to arrive at the same starting position. The second strength of Leapfrog integration is its [[Symplectic integrator\|symplectic]] nature, which implies that it conserves the (slightly modified) energy of dynamical systems. This is especially useful when computing orbital dynamics, as many other integration schemes, such as the (order 4) Runge-Kutta method, do not conserve energy and allow the system to drift substantially over time.

			Because of its time-reversibility, and because it is a [[symplectic integrator]], leapfrog integration is also used in [[Hybrid Monte Carlo\|Hamiltonian Monte Carlo]], a method for drawing random samples from a probability distribution whose overall normalization is unknown.<ref>{{cite book \| last=Bishop \| first=Christopher \| title=Pattern Recognition and Machine Learning \| year=2006 \| publisher=[[Springer-Verlag]] \| location=New York \| isbn=978-0-387-31073-2 \| pages=548–554}}</ref>

			==See also==
			*[[Numerical ordinary differential equations]]
			*[[Symplectic integrator\|Symplectic integration]]
			*[[Euler integration]]
			*[[Verlet integration]]
			*[[Runge–Kutta methods\|Runge–Kutta integration]]

			==References==
			{{Reflist}}

			==External links==
			*[http://einstein.drexel.edu/courses/Comp_Phys/Integrators/leapfrog/ The Leapfrog Integrator], Drexel University Physics

			{{Numerical integrators}}

			[[Category:Numerical differential equations]]

en>Helpful Pixie Bot: ISBNs (Build KG)

2012-05-11T09:40:58Z

ISBNs (Build KG)

New page

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