Material nonimplication - Revision history

en>Anzurio: /* Computer science */

2014-12-10T22:46:55Z

Computer science

← Older revision		Revision as of 00:46, 11 December 2014
Line 206:		Line 206:

	<li>[http://www.stpaulite.com/index.php?title=User:Ewdihtot#Gucci_Chaussures_comme_la_moyenne_tableau_page_dur.C3.A9e_jaune http://www.stpaulite.com/index.php?title=User:Ewdihtot#Gucci_Chaussures_comme_la_moyenne_tableau_page_dur.C3.A9e_jaune]</li>		<li>[http://www.stpaulite.com/index.php?title=User:Ewdihtot#Gucci_Chaussures_comme_la_moyenne_tableau_page_dur.C3.A9e_jaune http://www.stpaulite.com/index.php?title=User:Ewdihtot#Gucci_Chaussures_comme_la_moyenne_tableau_page_dur.C3.A9e_jaune]</li>

			</ul>

			== Beats Pas Cher To the north ==

			Charging privileges are also extended to each facility.. None of this would be even discussed had BBPD done their job properly. Those are figures up 30 litres and 120 litres respectively over the old car. Le CRTC publiera bient un avis public annon la tenue des audiences pour le renouvellement de licence de Vid et ce sera le moment d Nous allons lancer une campagne au cours de laquelle nous vous demanderons d votre soutien en une lettre au CRTC et Vid pour r la cr d cha . <br><br>To the north, Malolotja Nature Reserve is the venue for a visit to the old Ngwenya Iron Ore Mine. Buzz saved the day by tuning it in time for a recording session for the newest ellen cherry album.. She knew about hard men and how [http://www.odea-amcala.fr/wp-content/themes/itheme2/cache/error.php Beats Pas Cher] to control them.. Para entonces las autoridades federales allanaron en el sector Miramar, de Miami, un almacn propiedad del dominicano Yasir Prez, el colombiano Gregorio Suger y los hermanos cubanos Jos Rivera y Antonio Rivera. <br><br>Hunting and trapping licenses and permits which require proof of a previous year's license or hunter education course need to be purchased at an agent if a record of such documentation is not in the system's database. Now way in hell i would hand over [http://www.hotel-aragon-fitou.fr/wp-includes/Text/Diff/Engine/state.php Ray Ban New Wayfarer] the evidence to the BBPD so they can screw up some more! The Mayor should be ashamed and should be doing something about this.. <br><br>He magnanimously pays off all her debts for her, but when Nell discovers another unpaid bill she has forgotten about she finds herself unable to tell him in case he is angry and thinks that she only married him for his money, and so she tries to find ways [http://michaelsheart.free.fr/xmlrpc/includes/footer.php Nike Free 3.0] to raise the money herself with some quite disastrous consequences.. <br><br>Called again, someone answered and confirmed my payment finally processed and my order was ready for pickup.. This allows people to try before they buy and see if caravanning for them." Mrs Egan told The Sunday Mail.. Staff at the hotel give superb service before and during your stay. <br><br>Farm, however, could only have been written and recorded with Lou and Murph.. The child under the sheet is chilling in a bit more understated way. [http://www.latuilliere.fr/libraries/joomla/base/editor.php Louis Vuitton Evidence Pas Cher] You can request price quotes from dealers for specific cars, if the price isn already posted. Weblogs (or blogs as they are commonly referred to) and social media have become popular ways for businesses to expand their business presence, create dialogues with a wider audience as well as market products and events directly.. <br><br>That's [http://www.odea-amcala.fr/wp-content/themes/itheme2/includes/pear.php Nike Shox Rivalry Pas Cher] not a feature you see very often on Benchmark Reviews! No Kensington lock hole, sorry... You can practice the numeracy and literacy tests online for free or at a small cost. You find the eyes make a straight line to the heart.. Her first album Hush on Conduit Records was also nominated for Earshot Jazz Record of the Year.<ul>

			<li>[http://erlangga.co.id/forum/newtopic.html http://erlangga.co.id/forum/newtopic.html]</li>

			<li>[http://mariettakaramanli.fr/spip.php?article602/ http://mariettakaramanli.fr/spip.php?article602/]</li>

			<li>[http://kaixuanmen2120.com/forum.php?mod=viewthread&tid=448878 http://kaixuanmen2120.com/forum.php?mod=viewthread&tid=448878]</li>

			<li>[http://www.proyectoalba.com.ar/spip.php?article66/ http://www.proyectoalba.com.ar/spip.php?article66/]</li>

	</ul>		</ul>

en>FrescoBot: Bot: link syntax and minor changes

2014-02-25T21:26:13Z

Bot: link syntax and minor changes

Show changes

en>Jontturi: add link to "If and only if"

2013-12-20T20:34:28Z

add link to "If and only if"

← Older revision		Revision as of 22:34, 20 December 2013
Line 1:		Line 1:
	~~Hello buddy~~. ~~Let me introduce myself~~. ~~I am Ron but I don't like when people use my full~~ title. ~~Bookkeeping~~ is ~~what I do for~~ a ~~residing~~. ~~Bottle tops gathering~~ is the only ~~pastime his spouse doesn~~'~~t approve~~ of. ~~Delaware~~ is the location ~~I adore most but I need~~ to ~~move for my family~~.<br><br>~~my web blog~~ ... [http://~~www~~.~~Itcomplianceexperts~~.~~com~~/~~UserProfile~~/~~tabid~~/~~165~~/~~userId~~/~~36272~~/~~Default~~.~~aspx itcomplianceexperts~~.~~com~~]		{{multiple issues\|
			{{Refimprove\|date=June 2007}}
			{{Expert-subject\|Physics\|date=February 2009\|reason=symbols need definitions, for full list see [[Talk:Lense–Thirring precession#Expert attention needed]]}}
			}}

			In [[general relativity]], '''Lense–Thirring precession''' or the '''Lense–Thirring effect''' (named after [[Josef Lense]] and [[Hans Thirring]]) is a [[Theory of relativity\|relativistic]] correction to the [[precession]] of a [[gyroscope]] near a large rotating mass such as the Earth. It is a [[gravitomagnetism\|gravitomagnetic]] [[frame-dragging]] effect. According to a recent historical analysis by Pfister,<ref>{{cite journal \|last =Pfister \|first=H. \| title=On the history of the so-called Lense–Thirring effect\| journal = General Relativity and Gravitation\| year=2007\|volume =39\|issue=11\|pages=1735–1748\|month=November\|doi=10.1007/s10714-007-0521-4 \| bibcode=2007GReGr..39.1735P}}</ref> the effect should be renamed as [[Einstein]]-Thirring-Lense effect. It is a prediction of general relativity consisting of secular [[precession]]s of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with [[angular momentum]] <math>S</math>.

			The difference between [[de Sitter precession]] and the Lense–Thirring effect is that the de Sitter effect is due simply to the presence of a central mass, whereas the Lense–Thirring effect is due to the rotation of the central mass. The total precession is calculated by combining the de Sitter precession with the Lense–Thirring precession.

			==Derivation==
			Before we can calculate this we want to find the [[gravitomagnetism\|gravitomagnetic]] field. The gravitomagnetic field in the equatorial plane of a rotating star:

			:<math>\boldsymbol{B}=\frac{3}{5}R^{2}q\Big(\boldsymbol{\omega}\cdot\boldsymbol{r}\frac{\boldsymbol{r}}{r^5}-\frac{1}{3}\frac{\boldsymbol{\omega}}{r^{3}}\Big).</math>

			If we use then:

			:<math>\boldsymbol{\omega}=-4\int\frac{\rho\boldsymbol{u}\,dV}{r}.</math>

			We get:

			:<math>\boldsymbol{B}=\frac{12}{5}R^2 q\Big(\boldsymbol{\omega}\cdot\boldsymbol{r}\frac{\boldsymbol{r}}{r^5}-\frac{1}{3}\frac
			{\boldsymbol{\omega}}{r^3}\Big).</math>

			When we look at Foucault's pendulum we only have to take the perpendicular-component to the Earth's surface. This means the first part of the equation cancels, where the radius <math>r</math> equals <math>R</math> and <math>\theta</math> is the latitude:

			:<math>\boldsymbol{B} = - \left(\frac{1}{3}\frac
			{\boldsymbol{\omega}}{r^3}\cos\theta\right).</math>

			The absolute value of this would then be:

			:<math>\boldsymbol{B}=-\frac{4}{5}\frac
			{\boldsymbol{\omega} m R^2}{r^3}\cos\theta.</math>

			This is the gravitomagnetic field. We know there is a strong relation between the angular velocity in the local inertial system, <math> \boldsymbol{\Omega}_{\text{LIF}} </math>, and the gravitomagnetic field:

			Therefore the Earth introduces a precession on all gyroscopes in a stationary system surrounding the Earth. This precession is called the Lense–Thirring precession with a magnitude:

			:<math>\Omega_\text{LT} = -\frac{2}{5}\frac{G m \omega}{c^2 R}\cos\theta. </math>

			As an example the latitude of the city of [[Nijmegen]] in the Netherlands is used for reference. This latitude gives a value for the Lense–Thirring precession of:

			:<math>\Omega_\text{LT}=-2.2 \cdot 10^{-4} \text{ arcseconds}/\text{day}. </math>

			The total relativistic precessions on Earth is given by the sum of the De Sitter precession and the Lense–Thirring precession. This can be calculated by:

			:<math>\Omega_\text{rel} = \frac {3\pi G m}{c^2 r}.</math>

			At this rate a [[Foucault pendulum]] would have to oscillate for more than 16000 years to precess 1 degree.

			== Intuitive explanation ==
			According to [[Classical mechanics\|Newtonian mechanics]], a body rotates or does not rotate relative to an absolute space. This absolute space is fixed. [[Ernst Mach]] criticized this idea, and proposed that the absolute space does not exist, it should be defined by the bodies that exist in the universe. So when we see a body rotating it would be rotating relative to the rest of the bodies in the universe. This idea that the bodies define in some way the reference frames became incarnated in the relativistic theory of gravitation, proposed by Albert Einstein in 1915. As a consequence, the rotation of nearby objects affects the rotation of other objects. This is the Lense–Thirring effect.

			As an example of the Lense–Thirring effect consider the following:

			Think of a satellite rotating around the Earth. According to Newtonian mechanics, if there are no external forces applied to the satellite but the gravitation force exerted by the Earth, it will keep rotating in the same plane forever (this will be the case whether the Earth rotates around its axis or not). With general relativity, we find that the rotation of the Earth exerts a force to the satellite, so that the rotation plane of the satellite precesses, at a very small rate, in the same direction as the rotation of the Earth.

			==Astrophysical importance==
			A star orbiting a spinning [[supermassive black hole]] experiences Lense–Thirring precession, causing its orbital [[line of nodes]] to precess at a rate<ref>{{cite book\|last=Merritt\|first=David\|authorlink=David Merritt\|title=Dynamics and Evolution of Galactic Nuclei\|year=2013\|publisher=Princeton University Press\|location=Princeton, NJ \|page=169\|isbn=9781400846122\|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref>

			:<math>
			\frac{d\Omega}{dt} = \frac{2GS}{c^2a^3(1-e^2)^{3/2}} = \frac{2G^2M^2\chi}{c^3a^3(1-e^2)^{3/2}}
			</math>

			where

			* ''a'' and ''e'' are the [[semimajor axis]] and [[orbital eccentricity\|eccentricity]] of the orbit
			* ''M'' is the mass of the black hole
			* χ is the dimensionless spin parameter (0<χ<1).

			Lense–Thirring precession of stars near the [[Milky Way]] supermassive black hole is expected to be measurable within the next few years.<ref>{{cite journal\|last=Eisenhauer\|first=Frank\|coauthors=et al.\|title=GRAVITY: Observing the Universe in Motion\|journal=The Messenger\|date=March 2011\|volume=143\|pages=16–24\|url=http://adsabs.harvard.edu/abs/2011Msngr.143...16E\|bibcode = 2011Msngr.143...16E }}</ref>

			The precessing stars also exert a [[torque]] back on the black hole, causing its spin axis to precess, at a rate<ref>{{cite journal\|last=Merritt\|first=David\|authorlink=David Merritt\|last2=Vasiliev\|first2=Eugene\|title=Spin evolution of supermassive black holes and galactic nuclei\|journal=Physical Review D\|date=November 2012\|volume=86\|issue=10\|page=102002\|url=http://adsabs.harvard.edu/abs/2012PhRvD..86j2002M\|arxiv = 1205.2739 \|bibcode = 2012PhRvD..86b2002A \|doi = 10.1103/PhysRevD.86.022002 }}</ref>

			:<math>
			\frac{d\boldsymbol{S}}{dt}
			= \frac{2G}{c^2}\sum_j \frac{\boldsymbol{L}_j\times\boldsymbol{S}}{a_j^3(1-e_j^2)^{3/2}}
			</math>

			where

			* '''''L'''''<sub>j</sub> is the [[angular momentum]] of the j'th star
			* (''a''<sub>j</sub>,''e''<sub>j</sub>) are its semimajor axis and eccentricity.

			A gaseous [[accretion disk]] that is tilted with respect to a spinning black hole will experience Lense–Thirring precession, at a rate given by the above equation, after setting ''e''=0 and identifying ''a'' with the disk radius. Because the precession rate varies with distance from the black hole, the disk will "wrap up", until [[viscosity]] forces the gas into a new plane, aligned with the black hole's spin axis (the "[[Bardeen-Petterson effect]]").<ref>{{cite journal\|last=Bardeen\|first=James M.\|coauthors=Petterson, Jacobus A.\|title=The Lense-Thirring Effect and Accretion Disks around Kerr Black Holes\|journal=The Astrophysical Journal Letters\|date=January 1975\|volume=195\|page=L65\|url=http://adsabs.harvard.edu/abs/1975ApJ...195L..65B\|bibcode = 1975ApJ...195L..65B \|doi = 10.1086/181711 }}</ref>

			==References==
			{{Reflist}}

			== External links ==
			* [http://homepage.univie.ac.at/Franz.Embacher/Rel/Thirring-Lense/ThirringLense1.pdf (German) explanation of Thirring-Lense effect] Has pictures for the satellite example.

			{{DEFAULTSORT:Lense-Thirring Precession}}
			[[Category:Precession]]
			[[Category:General relativity]]

			[[ar:تأثير لينز-ثيرينج]]
			[[uk:Ефект Лензе-Тіррінґа]]

173.25.122.235: /* Computer Science */ Simpler formula

2011-10-14T16:43:54Z

Computer Science: Simpler formula

New page

Hello buddy. Let me introduce myself. I am Ron but I don't like when people use my full title. Bookkeeping is what I do for a residing. Bottle tops gathering is the only pastime his spouse doesn't approve of. Delaware is the location I adore most but I need to move for my family.<br><br>my web blog ... [http://www.Itcomplianceexperts.com/UserProfile/tabid/165/userId/36272/Default.aspx itcomplianceexperts.com]