Calkin–Wilf tree: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Mate2code
en>D.Lazard
Merger proposal
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
'''[[Gustav Kirchhoff|Kirchhoff]]'s integral theorem''' (sometimes referred to as the Fresnel-Kirchhoff integral theorem)<ref>G. Kirchhoff, Ann. d. Physik. 1883, 2, 18, p663</ref> uses [[Green's identities]] to derive the solution to the homogeneous [[wave equation]] at an arbitrary point '''P''' in terms of the values of the solution of the wave equation and its first order derivative at all points on an arbitrary surface which encloses '''P'''.<ref name = "Born and Wolf">Max Born and Emil Wolf, Principles of Optics, 1999, Cambridge University Press, Cambridge, pp. 417-420</ref>
If you are looking for a specific plugin, then you can just search for the name of the plugin. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. This CMS has great flexibility to adapt various extensions and add-ons. 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>You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. 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.  If you have any sort of questions pertaining to where and ways to make use of [http://miniURL.fouiner.info/backup_plugin_868520 wordpress backup], you could contact us at our own site. You can up your site's rank with the search engines by simply taking a bit of time with your site. 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>This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. 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>Word - Press installation is very easy and hassle free. But the Joomla was created as the CMS over years of hard work. Next you'll go by way of to your simple Word - Press site. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. If your site does well you can get paid professional designer to create a unique Word - Press theme. <br><br>Under Settings &mdash;> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. Word - Press is the most popular personal publishing platform which was launched in 2003. Your topic is going to be the basis of your site's name.
 
==Equation==
 
===Monochromatic waves===
 
The integral has the following form for a [[monochromatic]] wave:<ref name = "Born and Wolf"/>
<ref>Introduction to Fourier Optics J. Goodman sec. 3.3.3</ref>
:<math>U(r)  = \frac {1}{4 \pi} \int_{S} \left[ U \frac {\partial}{\partial n} \left( \frac {e^{iks}}{s} \right) - \frac {e^{iks}}{s} \frac {\partial U}{\partial n} \right]dS </math>
 
where the integration is performed over the whole of the arbitrary surface ''S'', ''s'' is the distance between the point ''r'' and the surface ''S'', and ∂/∂''n'' denotes differentiation along the normal on the surface with direction into the surface.
 
Please note: It may be confusing because most used to normal direction pointing outwards of the surface. In that case the eq. shall be multiplied by minus.
 
===Non-monochromatic waves===
 
A more  general form can be derived for non-monochromatic waves.  The complex amplitude of the wave can be represented by a Fourier integral of the form:
 
:<math> V(r,t)= \frac {1}{\sqrt{2 \pi}} \int U_ \omega(r) e^{-i \omega t}d \omega</math>
 
where, by [[Fourier inversion theorem|Fourier inversion]], we have:
 
:<math> U_\omega (r)= \frac {1}{\sqrt{2 \pi}} \int V(r,t) e^{i \omega t}dt</math>
 
The integral theorem (above) is applied to each Fourier component {{math|U<sub>ω</sub>}}, and the following expression is obtained<ref name = "Born and Wolf"/>
 
:<math>V(r,t)  = \frac {1}{4 \pi} \int_{S}  \left\{[V] \frac {\partial}{\partial n} \left(\frac {1}{s}\right) - \frac {1}{cs} \frac {\partial s}{\partial n} \left[\frac{\partial V}{\partial t}\right] - \frac{1}{s} \left[\frac{\partial V}{\partial n} \right] \right\} dS </math>
 
where the square brackets on ''V'' terms denote retarded values, i.e. the values at time ''t − s/c''.
 
Kirchhoff  showed the above equation can be approximated in many cases to a simpler form, known as the [[Kirchhoff's diffraction formula|Kirchhoff, or Fresnel-Kirchhoff diffraction formula]], which is equivalent to the [[Huygens-Fresnel principle|Huygens-Fresnel equation]], but provides a formula for the inclination factor which is not defined in the latter. The diffraction integral can be applied to a wide range of problems in optics.
 
==See also==
 
*[[Kirchhoff's diffraction formula]]
*[[Vector calculus]]
*[[Integral]]
*[[Huygens–Fresnel principle]]
*[[Wavefront]]
*[[Surface]]
 
== References ==
<references />
 
==Further reading==
* ''The Cambridge Handbook of Physics Formulas'', G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.
* ''Introduction to Electrodynamics (3rd Edition)'', D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ISBN 81-7758-293-3
* ''Light and Matter: Electromagnetism, Optics, Spectroscopy and Lasers'', Y.B. Band, John Wiley & Sons, 2010, ISBN 978-0-471-89931-0
* ''The Light Fantastic – Introduction to Classic and Quantum Optics'', I.R. Kenyon, Oxford University Press, 2008, ISBN 978-0-19-856646-5
* ''Encyclopaedia of Physics (2nd Edition)'', R.G. Lerner, G.L. Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3
* ''McGraw Hill Encyclopaedia of Physics (2nd Edition)'', C.B. Parker, 1994, ISBN 0-07-051400-3
 
[[Category:Diffraction| ]]
[[Category:Optics]]

Latest revision as of 20:10, 16 December 2014

If you are looking for a specific plugin, then you can just search for the name of the plugin. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. This CMS has great flexibility to adapt various extensions and add-ons. 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.

You just download ready made templates to a separate directory and then choose a favorite one in the admin panel. 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. If you have any sort of questions pertaining to where and ways to make use of wordpress backup, you could contact us at our own site. You can up your site's rank with the search engines by simply taking a bit of time with your site. 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.

This gives a clearer picture that online shoppers are familiar with the WP ecommerce system. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. 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.

Word - Press installation is very easy and hassle free. But the Joomla was created as the CMS over years of hard work. Next you'll go by way of to your simple Word - Press site. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. If your site does well you can get paid professional designer to create a unique Word - Press theme.

Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. It can run as plugin and you can still get to that whole database just in circumstance your webhost does not have a c - Panel area. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. Word - Press is the most popular personal publishing platform which was launched in 2003. Your topic is going to be the basis of your site's name.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Calkin–Wilf_tree&oldid=264112"