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	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Interior_(topology)&amp;diff=222996</id>
		<title>Interior (topology)</title>
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		<updated>2014-11-09T18:01:48Z</updated>

		<summary type="html">&lt;p&gt;103.21.125.76: /* Examples */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;My name is Adela Hannan. I life in Columbia (United States).&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Look into my webpage ... [http://etudesu.org Blog]&lt;/div&gt;</summary>
		<author><name>103.21.125.76</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Semiperimeter&amp;diff=234898</id>
		<title>Semiperimeter</title>
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		<updated>2014-10-12T10:07:00Z</updated>

		<summary type="html">&lt;p&gt;103.21.127.60: /* Formulas invoking the semipermeter */       semiperimeter had a spelling error.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The initiation of the X games and their rising popularity in China, surprisingly has been a result of a number of businessmen seeking new business opportunities in sports. They do not realize that it is actually a trap for fools because the gold could only be mined by those who held the key. Several of the well-known villains from the series consist of Venom, Carnage, Squid and Sinister Six. They choose the &#039;bad guy&#039; amongst themselves, bikes become horses or motorcycles, and the purpose of the game is to track down or hunt the enemy.&lt;br /&gt;
&lt;br /&gt;
 According to the Disney Family Fun website, fairy parties are popular events that typically involve dressing up like fairy princesses, complete with tulle and satin outfits. The Pyromancer is what portion the Demon controls and you can light weapons on fire and add some hit points. It also benefits us by increasing our smart capability and patient and enduring quality. I was a little sceptical at first on how I could actually earn money playing games as something on the side, that would also fund me to buy pc games online, whether it was through google play store or using the play store app &#039; and of course Steam :-).&lt;br /&gt;
&lt;br /&gt;
 After a bit longer the game will be complete and enter the debugging phase. These peasants and soldiers don&#039;t work for free though (what happened to forced labor. The world of Dominion is about to get way darker and more sinister in Dominion: Intrigue, the first standalone expansion for the hit card game that took the world by storm. They also incorporate other features which include, collection of ammunition, tracing the ammunitions, armors and other puzzle machinery.&lt;br /&gt;
&lt;br /&gt;
 Information that can hopefully be obtained easily is what type of games console they have. The Nikon 7216 Action binoculars have a close focus [https://www.flickr.com/search/?q=advantage advantage] for viewing in the backyard and they&#039;re great for butterfly watching too. The differences between Orochi, Black Chrome and Blade are only visual:. Each one of these rules by itself may be enough to turn losing into winning. It can make no distinction whether you use an overlapping, interlocking, or ten-finger grip.&lt;br /&gt;
&lt;br /&gt;
 operate on rescue operations [http://data.gov.uk/data/search?q=anytime anytime] you get yourself a chance. Minor characters like police officers Marvin Branagh (Resident Evil 2) and Kevin Ryman (the Outbreak sub-series), could also make appearances. While the sniper and shooting games are definitely among the more popular games, there are also many other types of games available as well. These online casino games are scientifically intended that caters to brain training.&lt;br /&gt;
&lt;br /&gt;
 Action rpg games like Fallout 3, Fallout: New Vegas, The Incredible Adventures of Van Helsing and The Witcher 2: Assassins of Kings are few rpg action games which are in huge demand because conventional games are slowly but surely losing their appeal among today&#039;s youth. In short, I thought this game was fun, but it doesn’t really deliver a lot for your money when compared to other games. Sonic the Hedge hog 4 First episode is rocking its users and is a follow up of the original game.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If you loved this write-up and you would certainly like to receive more details concerning [https://www.facebook.com/CrazyTaxiCityRushHackToolCheatsAndroidiOS crazy taxi city rush Hack ios] kindly visit our web page.&lt;/div&gt;</summary>
		<author><name>103.21.127.60</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Vapour_pressure_of_water&amp;diff=14556</id>
		<title>Vapour pressure of water</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Vapour_pressure_of_water&amp;diff=14556"/>
		<updated>2013-12-07T10:17:59Z</updated>

		<summary type="html">&lt;p&gt;103.21.127.55: /* See also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Science with neutrons}}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Neutron reflectometry&#039;&#039;&#039; is a [[neutron diffraction]] technique for measuring the structure of [[thin films]], similar to the often complementary techniques of [[X-ray reflectivity]] and [[ellipsometry]]. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, [[polymer]] and [[surfactant]] [[adsorption]], structure of thin film magnetic systems, biological membranes, etc.&lt;br /&gt;
&lt;br /&gt;
==Technical details==&lt;br /&gt;
The technique involves shining a highly [[Collimator|collimated]] beam of [[neutrons]] onto an extremely flat surface and measuring the intensity of reflected radiation as a function of angle or neutron wavelength. The exact shape of the reflectivity profile provides detailed information about the structure of the surface, including the thickness, density, and roughness of any thin films layered on the substrate.&lt;br /&gt;
&lt;br /&gt;
Neutron reflectometry is a [[specular reflection]] technique, where the angle of the incident beam is equal to the angle of the reflected beam. The reflection is usually described in terms of a [[momentum]] [[momentum transfer|transfer]] [[vector (geometric)|vector]], denoted &amp;lt;math&amp;gt;q_z&amp;lt;/math&amp;gt;, which describes the change in momentum of a neutron after reflecting from the material. Conventionally the &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; direction is defined to be the film normal direction, and for specular reflection, the scattering vector has only a &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt;-component. A typical neutron reflectometry  plot displays the reflected intensity (relative to the incident beam) as a function of the scattering vector:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt; q_z = \frac{4\pi}{\lambda}\sin ( \theta )&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;\lambda&amp;lt;/math&amp;gt;  is the neutron [[wavelength]], and &amp;lt;math&amp;gt;\theta &amp;lt;/math&amp;gt; is the angle of incidence. The [[Abeles matrix formalism]] or the Parratt recursion can be used to describe the specular signal arising from the interface.&lt;br /&gt;
&lt;br /&gt;
The wavelength of the neutrons used for reflectivity are typically on the order of 0.2 to 1 [[Metre#SI_prefixed_forms_of_metre|nm]] (2 to 10 [[Ångström|Å]]). This technique requires a [[neutron source]], which may be either a [[research reactor]] or a [[spallation]] source (based on a [[particle accelerator]]). Like all [[neutron scattering]] techniques, neutron reflectometry is sensitive to contrast arising from different nuclei (as compared to electron density, which is measured in x-ray scattering). This allows the technique to differentiate between various [[isotopes]] of [[chemical element|elements]]. Neutron reflectometry measures the neutron &#039;&#039;scattering length density&#039;&#039; (SLD) and can be used to accurately calculate material [[density]] if the atomic composition is known.&lt;br /&gt;
&lt;br /&gt;
==Comparison to other reflectometry techniques==&lt;br /&gt;
Although other reflectivity techniques (in particular optical reflectivity, x-ray reflectometry) operate using the same general principles, neutron measurements are advantageous in a few significant ways. Most notably, since the technique probes nuclear contrast, rather than electron density, it is more sensitive for measuring some elements, especially lighter elements ([[hydrogen]], [[carbon]], [[nitrogen]], [[oxygen]], etc.). Sensitivity to isotopes also allows contrast to be greatly (and selectively) enhanced for some systems of interest using isotopic substitution, and multiple experiments that differ only by isotopic substitution can be used to resolve the [[phase problem]] that is general to scattering techniques. Finally, neutrons are highly penetrating and typically non-perturbing: which allows for great flexibility in sample environments, and the use of delicate sample materials (e.g., biological specimens). By contrast x-ray exposure may damage some materials, and [[laser]] light can modify some materials (e.g. [[photoresist]]s). Also, optical techniques may include ambiguity due to optical [[anisotropy]] ([[birefringence]]), which complementary neutron measurements can resolve. [[Dual polarisation interferometry]] is one optical method which provides analogous results to neutron reflectometry at comparable resolution although the underpinning mathematical model is somewhat simpler, i.e. it can only derive a thickness (or [[birefringence]]) for a uniform layer density. &lt;br /&gt;
&lt;br /&gt;
Disadvantages of neutron reflectometry include the higher cost of the required infrastructure, the fact that some materials may become [[radioactive]] upon exposure to the beam, and insensitivity to the chemical state of constituent atoms. Moreover, the relatively lower flux and higher background of the technique (when compared to x-ray reflectivity) limit the maximum value of &amp;lt;math&amp;gt;q_z&amp;lt;/math&amp;gt; that can be probed (and hence the measurement resolution).&lt;br /&gt;
&lt;br /&gt;
==Partial list of neutron reflectometers==&lt;br /&gt;
*[http://lansce.lanl.gov/lujan/instruments/Asterix/index.html ASTERIX] at the [[Los Alamos Neutron Science Center]] in [[Los Alamos National Laboratory]]&lt;br /&gt;
*[http://lansce.lanl.gov/lujan/instruments/SPEAR/index.html SPEAR] at the [[Los Alamos Neutron Science Center]] in [[Los Alamos National Laboratory]]&lt;br /&gt;
*[http://www.ansto.gov.au/bragg/facilities/instruments/platypus.html Platypus] at [[ANSTO]] in [[Sydney]], [[Australia]]&lt;br /&gt;
* [http://neutron.nrc-cnrc.gc.ca/c5gen_e.html C5 spectrometer] at [[National Research Council of Canada|NRC Canada]] [[Chalk River Laboratories|Chalk River Labs]] in [[Chalk River, Ontario|Chalk River]], [[Canada]]. &#039;&#039;Note: a new dedicated reflectometer (D3) was commissioned in 2006.&#039;&#039;&lt;br /&gt;
* [http://neutron.nrc-cnrc.gc.ca/d3gen_e.html D3 reflectometer] at [[National Research Council of Canada|NRC Canada]] [[Chalk River Laboratories|Chalk River Labs]] in [[Chalk River, Ontario|Chalk River]], [[Canada]].&lt;br /&gt;
*[http://www.ill.eu/instruments-support/instruments-groups/instruments/d17/ D17], [http://www.ill.eu/instruments-support/instruments-groups/instruments/superadam/ SuperADAM] and [http://www.ill.eu/instruments-support/instruments-groups/instruments/figaro/ Figaro] at the [[Institut Laue-Langevin]] ([http://www.ill.eu/ ILL]) in [[Grenoble]], [[France]]&lt;br /&gt;
* [http://www-llb.cea.fr/spectros/pdf/eros-llb.pdf EROS] and [http://www-llb.cea.fr/spectros/pdf/prism-llb.pdf PRISM] ([http://www-llb.cea.fr/prism/PRISM.html alternate]) at [[Commissariat à l&#039;énergie atomique|CEA]] [[Laboratoire Léon Brillouin]] ([http://www-llb.cea.fr/index_e.html LLB]) in [[Saclay]], [[France]]&lt;br /&gt;
* [http://www.frm2.tum.de/wissenschaft/diffraktometer/n-rex/index.html N-REX+], [http://www.frm2.tum.de/wissenschaft/diffraktometer/mira/index.html MIRA], [http://www.frm2.tum.de/wissenschaft/index.html TREFF@NoSpec], [http://www.hzg.de/central_departments/genf/branch/frm/005265/index_0005265.html REFSANS] and [http://www.jcns.info/jcns_maria/ MARIA] at the [[FRM II|Forschungsneutronenquelle Heinz Maier-Leibnitz]] ([http://www.frm2.tum.de FRM II]) in [[Garching]], [[Germany]]&lt;br /&gt;
* [http://www.gkss.de/central_departments/genf/instruments/003142/index_0003142.html.en NeRo] and [http://www.gkss.de/central_departments/genf/instruments/003138/index_0003138.html.de PNR] at the [[GKSS|GKSS Research Centre]] ([http://www.gkss.de GKSS]) in [[Geesthacht]], [[Germany]]&lt;br /&gt;
* [http://www.hmi.de/bensc/instrumentation/instrumente/v6/v6_en.htm V6 reflectometer] at [[Hahn-Meitner-Institut]] ([http://www.hmi.de/index_en.html HMI]) in [[Berlin]], [[Germany]]&lt;br /&gt;
* [http://www.fz-juelich.de/iff/wns_hadas/ HADAS] at [[Forschungszentrum Jülich]] in [[Jülich]], [[Germany]]&lt;br /&gt;
&lt;br /&gt;
* PNR at the [[Dhruva reactor]], [[Bhabha Atomic Research Centre]] in [[Mumbai]], [[India]]&lt;br /&gt;
* [http://flnp.jinr.ru/140 REFLEX] and [http://flnp.jinr.ru/139/ REMUR] at [[Joint Institute for Nuclear Research]] IBR-2 in [[Dubna]], [[Russia]]&lt;br /&gt;
* [http://kur.web.psi.ch/amor/ AMOR] at the [[Paul Scherrer Institute]] ([http://www.psi.ch PSI]) in [[Villigen]], [[Switzerland]]&lt;br /&gt;
*[http://www.isis.rl.ac.uk/largescale/surf/surf.htm SURF], [http://www.isis.rl.ac.uk/largescale/surf/crisp.htm CRISP], [http://ts-2.isis.rl.ac.uk/instruments/inter/ INTER], [http://ts-2.isis.rl.ac.uk/instruments/offspec/ Offspec] and [http://ts-2.isis.rl.ac.uk/instruments/polref/ polREF] at the [[ISIS neutron source]] ([http://www.isis.rl.ac.uk/ ISIS]) in [[Oxfordshire]], [[United Kingdom]]&lt;br /&gt;
*[http://www.ncnr.nist.gov/instruments/ng1refl/ NG1], [http://www.ncnr.nist.gov/instruments/ng7refl/ NG7] and [http://www.ncnr.nist.gov/programs/reflect/ANDR/ AND/R] at the [[NIST Center for Neutron Research]] ([http://www.ncnr.nist.gov NCNR]) in [[Gaithersburg, Maryland]], [[United States]]&lt;br /&gt;
*[http://neutrons.ornl.gov/instrument_systems/beamline_04b_lr/index.shtml Liquids] and [http://neutrons.ornl.gov/instrument_systems/beamline_04a_mr/index.shtml Magnetic] at the [[Spallation Neutron Source]] ([http://neutrons.ornl.gov/ ORNL]) in [[Oak Ridge, Tennessee]], [[United States]]&lt;br /&gt;
* Neutron Reflectometer at the [http://www.murr.missouri.edu/rd_material_sciences_instrumentation_gans.php  University of Missouri Research Reactor], in [[Columbia, Missouri]]&lt;br /&gt;
&lt;br /&gt;
==Partial list of neutron reflectometry software==&lt;br /&gt;
*[http://www.ncnr.nist.gov/programs/reflect/data_reduction/software/reflred.html Reflred] and [http://www.ncnr.nist.gov/programs/reflect/data_reduction/software/reflfit.html reflfit] ([http://www.ncnr.nist.gov/programs/reflect/data_reduction/software/index.html NIST Center for Neutron Research])&lt;br /&gt;
*[http://motofit.sourceforge.net Motofit]&lt;br /&gt;
*[http://www.hmi.de/bensc/instrumentation/instrumente/v6/refl/parratt_en.htm Parratt32] ([[Hahn-Meitner-Institut|HMI]])&lt;br /&gt;
*[http://www.physics.brocku.ca/~tharroun/yanera Yanera] ([[Brock University]])&lt;br /&gt;
*[http://stochfit.sourceforge.net StochFit]&lt;br /&gt;
*[http://www.fs.kfki.hu FitSuite]&lt;br /&gt;
*[http://genx.sf.net GenX]&lt;br /&gt;
*[http://smmb.usc.es/sangra/sangra.php SANGRA] (web application, no local installation required)&lt;br /&gt;
&lt;br /&gt;
[[Category:Neutron scattering]]&lt;/div&gt;</summary>
		<author><name>103.21.127.55</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Rat-race_coupler&amp;diff=23703</id>
		<title>Rat-race coupler</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Rat-race_coupler&amp;diff=23703"/>
		<updated>2013-10-20T05:25:55Z</updated>

		<summary type="html">&lt;p&gt;103.21.126.77: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Multiple issues|notability=March 2009|unreferenced=February 2009|orphan=February 2009}}&lt;br /&gt;
&#039;&#039;&#039;Block Premium&#039;&#039;&#039; is the [[Buyer&#039;s premium|premiums]] paid in [[Block trade|block transactions]], which is indeed how much the new large minority [[shareholder]] would pay more per [[Share (finance)|share]], than the [[Share price|stock price]] two days after the transaction.&lt;br /&gt;
&lt;br /&gt;
==Block Premium per Share==&lt;br /&gt;
&#039;&#039;Block Premuim per share&#039;&#039; or &#039;&#039;BPS&#039;&#039; is derived as&lt;br /&gt;
:::&amp;lt;math&amp;gt;BPS=\frac{{P_{t}^{*}-P_{t+2}}}{P_{t+2}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
* [[Control premium]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Stock market]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Business-stub}}&lt;/div&gt;</summary>
		<author><name>103.21.126.77</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Spectral_centroid&amp;diff=16941</id>
		<title>Spectral centroid</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Spectral_centroid&amp;diff=16941"/>
		<updated>2013-08-04T06:20:11Z</updated>

		<summary type="html">&lt;p&gt;103.21.125.79: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In [[complex analysis]], a branch of mathematics, the &#039;&#039;&#039;Schwarz integral formula&#039;&#039;&#039;, named after [[Hermann Schwarz]], allows one to recover a [[holomorphic function]], [[up to]] an imaginary constant, from the boundary values of its real part.&lt;br /&gt;
&lt;br /&gt;
==Unit disc==&lt;br /&gt;
Let &#039;&#039;ƒ&#039;&#039;&amp;amp;nbsp;=&amp;amp;nbsp;&#039;&#039;u&#039;&#039;&amp;amp;nbsp;+&amp;amp;nbsp;&#039;&#039;iv&#039;&#039; be a function which is holomorphic on the closed unit disc {&#039;&#039;z&#039;&#039;&amp;amp;nbsp;∈&amp;amp;nbsp;&#039;&#039;&#039;C&#039;&#039;&#039;&amp;amp;nbsp;|&amp;amp;nbsp;|&#039;&#039;z&#039;&#039;|&amp;amp;nbsp;≤&amp;amp;nbsp;1}.  Then&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt; f(z) = \frac{1}{2\pi i} \oint_{|\zeta| = 1} \frac{\zeta + z}{\zeta - z} \text{Re}(f(\zeta)) \, \frac{d\zeta}{\zeta}&lt;br /&gt;
+ i\text{Im}(f(0))&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
for all |&#039;&#039;z&#039;&#039;|&amp;amp;nbsp;&amp;lt;&amp;amp;nbsp;1.&lt;br /&gt;
&lt;br /&gt;
==Upper half-plane==&lt;br /&gt;
Let &#039;&#039;ƒ&#039;&#039;&amp;amp;nbsp;=&amp;amp;nbsp;&#039;&#039;u&#039;&#039;&amp;amp;nbsp;+&amp;amp;nbsp;&#039;&#039;iv&#039;&#039; be a function that is holomorphic on the closed [[upper half-plane]] {&#039;&#039;z&#039;&#039;&amp;amp;nbsp;∈&amp;amp;nbsp;&#039;&#039;&#039;C&#039;&#039;&#039;&amp;amp;nbsp;|&amp;amp;nbsp;Im(&#039;&#039;z&#039;&#039;)&amp;amp;nbsp;≥&amp;amp;nbsp;0} such that, for some &#039;&#039;α&#039;&#039;&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0, |&#039;&#039;z&#039;&#039;&amp;lt;sup&amp;gt;&#039;&#039;α&#039;&#039;&amp;lt;/sup&amp;gt;&amp;amp;nbsp;&#039;&#039;ƒ&#039;&#039;(&#039;&#039;z&#039;&#039;)| is bounded on the closed upper half-plane.  Then&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;&lt;br /&gt;
f(z) &lt;br /&gt;
= &lt;br /&gt;
\frac{1}{\pi i} \int_{-\infty}^\infty \frac{u(\zeta,0)}{\zeta - z} \, d\zeta&lt;br /&gt;
=&lt;br /&gt;
\frac{1}{\pi i} \int_{-\infty}^\infty \frac{Re(f)(\zeta+0i)}{\zeta - z} \, d\zeta&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
for all Im(&#039;&#039;z&#039;&#039;)&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0.&lt;br /&gt;
&lt;br /&gt;
Note that, as compared to the version on the unit disc, this formula does not have an arbitrary constant added to the integral; this is because the additional decay condition makes the conditions for this formula more stringent.&lt;br /&gt;
&lt;br /&gt;
== Corollary of Poisson integral formula ==&lt;br /&gt;
&lt;br /&gt;
The formula follows from [[Poisson integral formula]] applied to&amp;amp;nbsp;&#039;&#039;u&#039;&#039;:&amp;lt;ref&amp;gt;&lt;br /&gt;
{{cite web&lt;br /&gt;
|url=http://books.google.com/books?id=NVrgftOGG1sC&amp;amp;pg=PA9&amp;amp;ots=FTpLISInOP&amp;amp;dq=Schwarz+formula&amp;amp;sig=tYdkW2Mq4IJg-gTIDWVCEI4HKCE&lt;br /&gt;
|title=Lectures on Entire Functions - Google Book Search&lt;br /&gt;
|publisher=books.google.com&lt;br /&gt;
|accessdate=2008-06-26&lt;br /&gt;
|last=&lt;br /&gt;
|first=&lt;br /&gt;
}}&lt;br /&gt;
&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;The derivation without an appeal to the Poisson formula can be found at: http://planetmath.org/encyclopedia/PoissonFormula.html&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;u(z) = \frac{1}{2\pi}\int_0^{2\pi} u(e^{i\psi}) \operatorname{Re} {e^{i\psi} + z \over e^{i\psi} - z} \, d\psi\text{ for }|z| &amp;lt; 1.&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
By means of conformal maps, the formula can be generalized to any simply connected open set.&lt;br /&gt;
&lt;br /&gt;
== Notes and references ==&lt;br /&gt;
&amp;lt;references /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* [[Lars Ahlfors|Ahlfors, Lars V.]] (1979), &#039;&#039;Complex Analysis&#039;&#039;, Third Edition, McGraw-Hill, ISBN 0-07-085008-9&lt;br /&gt;
* Remmert, Reinhold (1990), &#039;&#039;Theory of Complex Functions&#039;&#039;, Second Edition, Springer, ISBN 0-387-97195-5&lt;br /&gt;
* Saff, E. B., and A. D. Snider (1993), &#039;&#039;Fundamentals of Complex Analysis for Mathematics, Science, and Engineering&#039;&#039;, Second Edition, Prentice Hall, ISBN 0-13-327461-6&lt;br /&gt;
&lt;br /&gt;
[[Category:Complex analysis]]&lt;/div&gt;</summary>
		<author><name>103.21.125.79</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Semblance_analysis&amp;diff=28211</id>
		<title>Semblance analysis</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Semblance_analysis&amp;diff=28211"/>
		<updated>2013-06-01T09:55:45Z</updated>

		<summary type="html">&lt;p&gt;103.21.125.55: /* History */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The &#039;&#039;&#039;open-circuit test&#039;&#039;&#039;, or &amp;quot;no-load test&amp;quot;, is one of the methods used in [[electrical engineering]] to determine the [[Electrical impedance|no-load impedance]] in the excitation branch of a [[transformer]]. &lt;br /&gt;
&lt;br /&gt;
[[File:Open circuit test.png|right|500px|Circuit diagram for open-circuit test]]&lt;br /&gt;
&lt;br /&gt;
==Method==&lt;br /&gt;
&lt;br /&gt;
The secondary of the transformer is left open-circuited. A [[wattmeter]] is connected to the primary. An [[ammeter]] is connected in series with the primary winding. A [[voltmeter]] is optional since the applied voltage is the same as the voltmeter reading. Rated voltage is applied at primary.&lt;br /&gt;
&lt;br /&gt;
If the applied voltage is normal voltage then normal flux will be set up. Since [[iron loss]] is a function of applied voltage, normal iron loss will occur. Hence the iron loss is maximum at rated voltage. This maximum iron loss is measured using the wattmeter. Since the impedance of the [[Series and parallel circuits|series]] winding of the transformer is very small compared to that of the excitation branch, all of the input voltage is [[voltage drop|dropped]] across the excitation branch. Thus the wattmeter measures only the iron loss.  This test only measures the combined iron losses consisting of the [[hysteresis loss]] and the [[eddy current]] loss.  Although the hysteresis loss is less than the eddy current loss, it is not negligible.  The two losses can be separated by driving the transformer from a variable frequency source since the hysteresis loss varies linearly with supply frequency and the eddy current loss varies with the square.&lt;br /&gt;
&lt;br /&gt;
Since the secondary of the transformer is open, the primary draws only no-load current, which will have some copper loss. This no-load current is very small and because the copper loss in the primary is proportional to the square of this current, it is negligible.  There is no copper loss in the secondary because there is no secondary current.  &lt;br /&gt;
&lt;br /&gt;
[[Electric current|Current]], [[voltage]] and [[electric power|power]] are measured at the [[primary winding]] to ascertain the [[admittance]] and [[power factor|power-factor angle]].&lt;br /&gt;
&lt;br /&gt;
Another method of determining the series impedance of a real transformer is the [[short circuit test]].&lt;br /&gt;
&lt;br /&gt;
==Calculations==&lt;br /&gt;
The current &amp;lt;math&amp;gt;\mathbf{I_0}&amp;lt;/math&amp;gt; is very small. &lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;\mathbf{W}&amp;lt;/math&amp;gt; is the wattmeter reading then,&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{W} = \mathbf{V_1} \mathbf{I_0} \cos \phi_0 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
That equation can be rewritten as,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\cos \phi_0 = \frac {\mathbf{W}} {\mathbf{V_1} \mathbf{I_0}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Thus,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{I_m} = \mathbf{I_0} \sin \phi_0 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{I_w} = \mathbf{I_0} \cos \phi_0 &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Impedance===&lt;br /&gt;
&lt;br /&gt;
By using the above equations, &amp;lt;math&amp;gt;\mathbf{X_0}&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;\mathbf{R_0}&amp;lt;/math&amp;gt; can be calculated as,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{X_0} = \frac {\mathbf{V_1}} {\mathbf{I_m}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{R_0} = \frac {\mathbf{V_1}} {\mathbf{I_w}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Thus,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{Z_0} = \sqrt {\mathbf{R_0}^2 +\mathbf{X_0}^2} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
or&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{Z_0} = \mathbf{R_0} + \mathbf{j} \mathbf{X_0} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Admittance===&lt;br /&gt;
&lt;br /&gt;
The admittance is the inverse of impedance. Therefore,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{Y_0} = \frac {1} {\mathbf{Z_0}} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The conductance &amp;lt;math&amp;gt;\mathbf{G_0}&amp;lt;/math&amp;gt; can be calculated as,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{G_0} = \frac {\mathbf{W}} {\mathbf{V_1}^2} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Hence the susceptance,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{B_0} = \sqrt {\mathbf{Y_0}^2 -\mathbf{G_0}^2} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
or&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\mathbf{Y_0} = \mathbf{G_0} + \mathbf{j} \mathbf{B_0} &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Here, &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{W}&amp;lt;/math&amp;gt; is the wattmeter reading &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{V_1}&amp;lt;/math&amp;gt; is the applied rated voltage &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{I_0}&amp;lt;/math&amp;gt; is the no-load current &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{I_m}&amp;lt;/math&amp;gt; is the magnetizing component of no-load current &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{I_w}&amp;lt;/math&amp;gt; is the core loss component of no-load current &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{Z_0}&amp;lt;/math&amp;gt; is the exciting impedance &amp;lt;br&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\mathbf{Y_0}&amp;lt;/math&amp;gt; is the exciting admittance&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
*{{cite book | author=Kosow| title=Electric Machinery and Transformers | publisher=Pearson Education India | year=2007}}&lt;br /&gt;
*{{cite book | author=Smarajit Ghosh| title=Fundamentals of Electrical and Electronics Engineering | publisher=PHI Learning Pvt. Ltd. | year=2004}}&lt;br /&gt;
*{{cite book | author=Wildi, Wildi Theodore| title=Electrical Machines , Drives And Power Systems, 6th edtn.&lt;br /&gt;
  | publisher=Pearson | year=2007}}&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
*[[Short-circuit test]]&lt;br /&gt;
*[[Thévenin&#039;s theorem]]&lt;br /&gt;
*[[Blocked rotor test]]&lt;br /&gt;
*[[Circle diagram]]&lt;br /&gt;
{{DEFAULTSORT:Open Circuit Test}}&lt;br /&gt;
[[Category:Electrical tests]]&lt;br /&gt;
[[Category:Transformers (electrical)]]&lt;/div&gt;</summary>
		<author><name>103.21.125.55</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Unit_propagation&amp;diff=11024</id>
		<title>Unit propagation</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Unit_propagation&amp;diff=11024"/>
		<updated>2013-05-23T21:32:53Z</updated>

		<summary type="html">&lt;p&gt;103.21.126.79: &lt;/p&gt;
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&lt;div&gt;{{Confusing|article|date=February 2009}}&lt;br /&gt;
&lt;br /&gt;
The &#039;&#039;&#039;Davis–Putnam algorithm&#039;&#039;&#039; was developed by [[Martin Davis]] and [[Hilary Putnam]] for checking the validity of a [[first-order logic]] formula using a [[Resolution (logic)|resolution]]-based decision procedure for [[propositional logic]]. Since the set of valid first-order formulas is [[recursively enumerable]] but not [[Recursive set|recursive]], there exists no general algorithm to solve this problem. Therefore, the Davis–Putnam algorithm only terminates on valid formulas. Today, the term &amp;quot;Davis-Putnam algorithm&amp;quot; is often used synonymously with the resolution-based propositional decision procedure that is actually only one of the steps of the original algorithm.&lt;br /&gt;
&lt;br /&gt;
The procedure is based on [[Herbrand&#039;s theorem]], which implies that an [[satisfiable|unsatisfiable]] formula has an unsatisfiable [[ground instance]], and on the fact that a formula is valid if and only if its negation is unsatisfiable. Taken together, these facts imply that to prove the validity of &#039;&#039;φ&#039;&#039; it is enough to prove that a ground instance of &#039;&#039;¬φ&#039;&#039; is unsatisfiable. If &#039;&#039;φ&#039;&#039; is not valid, then the search for an unsatisfiable ground instance will not terminate. &lt;br /&gt;
&lt;br /&gt;
The procedure roughly consists of these three parts:&lt;br /&gt;
* put the formula in [[prenex]] form and eliminate quantifiers &lt;br /&gt;
* generate all propositional ground instances, one by one&lt;br /&gt;
* check if each instance is satisfiable&lt;br /&gt;
&lt;br /&gt;
The last part is probably the most innovative one, and works as follows:&lt;br /&gt;
&lt;br /&gt;
* for every variable in the formula&lt;br /&gt;
** for every clause &amp;lt;math&amp;gt;c&amp;lt;/math&amp;gt; containing the variable and every clause &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; containing the negation of the variable&lt;br /&gt;
*** [[Resolution (logic)|resolve]] &#039;&#039;c&#039;&#039; and &#039;&#039;n&#039;&#039; and add the resolvent to the formula&lt;br /&gt;
** remove all original clauses containing the variable or its negation&lt;br /&gt;
&lt;br /&gt;
At each step, the intermediate formula generated is [[equisatisfiable]] to the original formula, but it does not retain [[Logical equivalence|equivalence]]. The resolution step leads to a worst-case exponential blow-up in the size of the formula. The [[DPLL algorithm]] is a refinement of the propositional satisfiability step of the Davis–Putnam procedure, that requires only a linear amount of memory in the worst case.&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Herbrandization]]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
* {{cite journal&lt;br /&gt;
|last=Davis&lt;br /&gt;
|first=Martin&lt;br /&gt;
| coauthors= Putnam, Hilary&lt;br /&gt;
| title=A Computing Procedure for Quantification Theory&lt;br /&gt;
| journal =[[Journal of the ACM]]&lt;br /&gt;
| volume = 7 &lt;br /&gt;
| issue = 3&lt;br /&gt;
| pages = 201–215&lt;br /&gt;
| year = 1960&lt;br /&gt;
| url = http://portal.acm.org/citation.cfm?coll=GUIDE&amp;amp;dl=GUIDE&amp;amp;id=321034&lt;br /&gt;
| doi=10.1145/321033.321034}}&lt;br /&gt;
*{{cite journal&lt;br /&gt;
| last=Beckford&lt;br /&gt;
| first=Jahbrill &lt;br /&gt;
| coauthors=Logemann, George, and Loveland, Donald&lt;br /&gt;
| title=A Machine Program for Theorem Proving&lt;br /&gt;
| journal =[[Communications of the ACM]]&lt;br /&gt;
| volume=5&lt;br /&gt;
| issue=7&lt;br /&gt;
| pages = 394–397&lt;br /&gt;
| year=1962&lt;br /&gt;
| url=http://portal.acm.org/citation.cfm?doid=368273.368557&lt;br /&gt;
| doi=10.1145/368273.368557}}&lt;br /&gt;
* {{cite conference&lt;br /&gt;
 | author = R. Dechter&lt;br /&gt;
 | coauthors = I. Rish&lt;br /&gt;
 | editor = J. Doyle and E. Sandewall and P. Torasso&lt;br /&gt;
 | year = &lt;br /&gt;
 | title = Directional Resolution: The Davis–Putnam Procedure, Revisited&lt;br /&gt;
 | conference = &lt;br /&gt;
 | booktitle = Principles of Knowledge Representation and Reasoning: Proc. of the Fourth International Conference (KR&#039;94)&lt;br /&gt;
 | pages = 134–145&lt;br /&gt;
 | publisher = Starswager18&lt;br /&gt;
 | url = &lt;br /&gt;
 | conferenceurl = &lt;br /&gt;
 }}&lt;br /&gt;
* {{cite book|author=John Harrison|title=Handbook of practical logic and automated reasoning|year=2009|publisher=Cambridge University Press|isbn=978-0-521-89957-4|pages=79–90}}&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Davis-Putnam algorithm}}&lt;br /&gt;
[[Category:Boolean algebra]]&lt;br /&gt;
[[Category:Constraint programming]]&lt;br /&gt;
[[Category:Automated theorem proving]]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{formalmethods-stub}}&lt;/div&gt;</summary>
		<author><name>103.21.126.79</name></author>
	</entry>
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