PSRK - Revision history

129.241.83.209: /* Example Calculation */ Corrected a typo

2014-11-03T15:08:12Z

Example Calculation: Corrected a typo

← Older revision		Revision as of 17:08, 3 November 2014
Line 1:		Line 1:
	~~The '''Andronov–Pontryagin criterion'''~~ is a ~~necessary and sufficient condition for the stability of [[dynamical system]]s~~ in the ~~plane~~. ~~It was derived by [[Aleksandr Andronov]]~~ and [~~[Lev Pontryagin~~]~~] in 1937~~.		Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. In case you loved this post and you would love to receive more info regarding [http://emailsite.de/backup_plugin_1799675 wordpress dropbox backup] please visit our own web-site. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. 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. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner. <br><br>Choosing what kind of links you'll be using is a ctitical aspect of any linkwheel strategy, especially since there are several different types of links that are assessed by search engines. But as expected the level of support you get with them can be hit or miss based on the developer's free time and desire. With the free Word - Press blog, you have the liberty to come up with your own personalized domain name. Apart from these, you are also required to give some backlinks on other sites as well. You can also get a free keyword tool that is to determine how strong other competing sites are and number of the searches on the most popular search sites. <br><br>This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. s cutthroat competition prevailing in the online space won. If Gandhi was empowered with a blogging system, every event in his life would have been minutely documented so that it could be recounted to the future generations. The animation can be quite subtle these as snow falling gently or some twinkling start in the track record which are essentially not distracting but as an alternative gives some viewing enjoyment for the visitor of the internet site. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them. <br><br>It has become a more prevalent cause of infertility and the fertility clinic are having more and more couples with infertility problems. And, make no mistake,India's Fertility Clinics and IVF specialists are amongst the best in the world,and have been for some time. Websites that do rank highly, do so becaue they use keyword-heavy post titles. There are many advantages of hiring Wordpress developers for Wordpress project development:. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>Internet is not only the source for information, it is also one of the source for passive income. Visit our website to learn more about how you can benefit. Just download it from the website and start using the same. In addition, Word - Press design integration is also possible. As with a terminology, there are many methods to understand how to use the terminology.

	~~==Statement==~~

	A ~~dynamical system~~

	: ~~<math>\dot{x} = v(x), </math>~~

	~~where~~ '~~'v'' is~~ a ~~''C''<sup>1</sup>-[[vector field]]~~ on the ~~[[Euclidean plane\|plane]]~~, ''~~x''∈'''R'''~~<~~sup~~>2<~~/sup~~> ,
	~~is [[topological conjugacy\|orbitally topologically stable]] if and only if the following two conditions hold:~~

	~~# All [[equilibrium point]]s and [[periodic orbit]]s~~ are ~~''hyperbolic''.~~
	~~# There~~ are ~~no ''saddle connections''~~.

	~~The same statement holds if~~ the ~~vector field ''v'' is defined~~ on the ~~[[unit disk]]~~ and ~~is transversal~~ to ~~the boundary~~.

	~~==Clarifications==~~

	~~'''Orbital topological stability''' of~~ a ~~dynamical system means~~ that ~~for any sufficiently small perturbation (in~~ the ~~''C''~~<~~sup~~>1<~~/sup~~>~~-metric), there exists~~ a ~~[[homeomorphism]] close to~~ the ~~identity map which transforms~~ the ~~orbits of the original dynamical~~ system to the ~~orbits of the perturbed system (cf [[structural stability]])~~.

	The ~~first condition~~ of the ~~theorem is known as '''global hyperbolicity'''~~. ~~A zero of~~ a ~~vector field ''v''~~, ~~i.e~~. ~~a point ''x''~~<~~sub~~>0<~~/sub~~> ~~where~~ '~~'v''(''x''<sub>0</sub>)=0~~, ~~is said to be '''hyperbolic''' if none~~ of the ~~[[eigenvalue]]s of~~ the ~~linearization of ''v'' at ''x''~~<~~sub~~>0<~~/sub~~> is ~~purely imaginary. A periodic orbit of a flow~~ is ~~said to be hyperbolic if none~~ of the ~~[[eigenvalue]]s of the [[Poincaré map\|Poincaré return map]] at a point on the orbit has absolute value one~~.

	~~Finally, '''saddle connection''' refers~~ to ~~a situation where an orbit~~ from ~~one saddle point enters~~ the same ~~or another saddle point~~, ~~i.e~~. the ~~unstable and stable [[separatrix\|separatrices]] are connected (cf [[homoclinic orbit]] and [[heteroclinic orbit]]).~~

	~~== References ==~~
	* {{cite journal\| last=Andronov \| first=Aleksandr A. \| authorlink=Aleksandr Andronov \| coauthors=[[Lev Pontryagin\|Lev S. Pontryagin]] \| year=1937 \| title=Грубые системы \| trans_title=Coarse systems \| journal=[[Doklady Akademii Nauk SSSR]] \| volume=14 \| issue=5 \| pages=247–250\| ref=harv}} Cited in {{harvtxt\|Kuznetsov\|2004}}.
	* {{Cite book \| first1 = Yuri A. \| last1 = Kuznetsov \| year = 2004 \| title = Elements of Applied Bifurcation Theory \| publisher = Springer \| isbn = 978-0-387-21906-6 \| ref = harv \| postscript = <!--None--> }}. See Theorem 2.5.

	~~{{DEFAULTSORT:Andronov-Pontryagin criterion}}~~
	~~[[Category:Dynamical systems]]~~

en>Mogism: /* Principle */Cleanup/Typo fixing, typo(s) fixed: so called → so-called using AWB

2013-11-29T17:12:17Z

Principle: Cleanup/Typo fixing, typo(s) fixed: so called → so-called using AWB

← Older revision		Revision as of 19:12, 29 November 2013
Line 1:		Line 1:
			The '''Andronov–Pontryagin criterion''' is a necessary and sufficient condition for the stability of [[dynamical system]]s in the plane. It was derived by [[Aleksandr Andronov]] and [[Lev Pontryagin]] in 1937.

			==Statement==

	~~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. You can customize the appearance with PSD to Word - Press conversion~~ ''. <br><br>~~You just download ready made templates to a separate directory~~ and ~~then choose a favorite one in~~ the ~~admin panel~~. ~~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~~. ~~Which is perfect for building~~ a ~~mobile site~~ for business use. 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>~~You can down load it here at this link: and utilize your FTP software program to upload it~~ to ~~your Word - Press Plugin folder. 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. 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~~. ~~There are plenty~~ of ~~tables that are attached to this particular database~~. <br><br>It is ~~the convenient service through which professionals either improve the position or keep the ranking intact. * Robust CRM~~ to ~~control and connect with your subscribers. When we talk about functional suitability, Word - Press proves itself as one~~ of the ~~strongest contestant among its other rivals. Should you have almost any queries about where and the way to work with~~ [~~http://shortener.us/backup_plugin_6890957 wordpress backup~~]~~, it is possible to contact us from~~ the ~~site. IVF ,fertility,infertility expert,surrogacy specialist in India~~ at ~~Rotundaivf. Look for experience: When you are searching for a Word - Press developer you should always look at their experience level.~~ <br><br>~~As a open source platform Wordpress offers distinctive ready to use themes for free along with custom theme support and easy customization~~. ~~I'm~~ a ~~large fan of using Word - Press~~ to ~~create pretty much any sort~~ of ~~web page. Just download it from~~ the ~~website and start using the same. This is because~~ of the ~~customization that works as~~ a ~~keystone for a SEO friendly blogging portal website~~. ~~Likewise~~, ~~professional publishers with~~ a ~~multi author~~ and ~~editor setup often find that Word~~ - ~~Press lack basic user and role management capabilities~~.		A dynamical system

			: <math>\dot{x} = v(x), </math>

			where ''v'' is a ''C''<sup>1</sup>-[[vector field]] on the [[Euclidean plane\|plane]], ''x''∈'''R'''<sup>2</sup> ,
			is [[topological conjugacy\|orbitally topologically stable]] if and only if the following two conditions hold:

			# All [[equilibrium point]]s and [[periodic orbit]]s are ''hyperbolic''.
			# There are no ''saddle connections''.

			The same statement holds if the vector field ''v'' is defined on the [[unit disk]] and is transversal to the boundary.

			==Clarifications==

			'''Orbital topological stability''' of a dynamical system means that for any sufficiently small perturbation (in the ''C''<sup>1</sup>-metric), there exists a [[homeomorphism]] close to the identity map which transforms the orbits of the original dynamical system to the orbits of the perturbed system (cf [[structural stability]]).

			The first condition of the theorem is known as '''global hyperbolicity'''. A zero of a vector field ''v'', i.e. a point ''x''<sub>0</sub> where ''v''(''x''<sub>0</sub>)=0, is said to be '''hyperbolic''' if none of the [[eigenvalue]]s of the linearization of ''v'' at ''x''<sub>0</sub> is purely imaginary. A periodic orbit of a flow is said to be hyperbolic if none of the [[eigenvalue]]s of the [[Poincaré map\|Poincaré return map]] at a point on the orbit has absolute value one.

			Finally, '''saddle connection''' refers to a situation where an orbit from one saddle point enters the same or another saddle point, i.e. the unstable and stable [[separatrix\|separatrices]] are connected (cf [[homoclinic orbit]] and [[heteroclinic orbit]]).

			== References ==
			* {{cite journal\| last=Andronov \| first=Aleksandr A. \| authorlink=Aleksandr Andronov \| coauthors=[[Lev Pontryagin\|Lev S. Pontryagin]] \| year=1937 \| title=Грубые системы \| trans_title=Coarse systems \| journal=[[Doklady Akademii Nauk SSSR]] \| volume=14 \| issue=5 \| pages=247–250\| ref=harv}} Cited in {{harvtxt\|Kuznetsov\|2004}}.
			* {{Cite book \| first1 = Yuri A. \| last1 = Kuznetsov \| year = 2004 \| title = Elements of Applied Bifurcation Theory \| publisher = Springer \| isbn = 978-0-387-21906-6 \| ref = harv \| postscript = <!--None--> }}. See Theorem 2.5.

			{{DEFAULTSORT:Andronov-Pontryagin criterion}}
			[[Category:Dynamical systems]]

en>EmausBot: r2.7.2+) (Robot: Modifying de:PSRK-Zustandsgleichung

2012-08-26T00:13:14Z

r2.7.2+) (Robot: Modifying de:PSRK-Zustandsgleichung

New page

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