(Created page with "'''''MathJax''''' is an open source Ajax-based framework to display mathematical notations in web browsers. It renders the input, entered as LaTeX or MathML expre...") |
|||
| Line 1: | Line 1: | ||
| + | = MathJax = | ||
| + | |||
'''''MathJax''''' is an [[open source]] [[Ajax]]-based framework to display mathematical notations in web browsers. It renders the input, entered as [[LaTeX]] or [[MathML]] expressions, as high-quality display in MathML or [[HTML]] with CSS and integrates well with text-based content, both in display mode and inline. | '''''MathJax''''' is an [[open source]] [[Ajax]]-based framework to display mathematical notations in web browsers. It renders the input, entered as [[LaTeX]] or [[MathML]] expressions, as high-quality display in MathML or [[HTML]] with CSS and integrates well with text-based content, both in display mode and inline. | ||
| − | = Examples = | + | == Examples == |
An identity from Ramanujan: | An identity from Ramanujan: | ||
| Line 8: | Line 10: | ||
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = | \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = | ||
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} | 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} | ||
| − | {1+\frac{e^{-8\pi}} {1+\ldots} } } } | + | {1+\frac{e^{-8\pi}} {1+\ldots} } } }\,. |
\] | \] | ||
| − | A result from | + | A result from [[Elena]]: |
| + | <wz tip="Mollow triplet under incoherent excitation.">\begin{multline} | ||
| + | \label{eq:elena} | ||
| + | S_\mathrm{inc}(\omega)=\Big(\frac{2P_\sigma}{\kappa_\sigma+\Gamma_\sigma}-\frac{\Gamma_\sigma}{\kappa_\sigma}\Big) | ||
| + | \delta(\omega)+\frac{\frac{1}{2\pi}\frac{\Gamma_\sigma}{2}}{\big(\frac{\Gamma_\sigma}{2}\big)^2+\omega^2}+\\ | ||
| + | \frac{(P_\sigma-\gamma_\sigma)\Big(3\Gamma_\sigma^3-(P_\sigma-5\gamma_\sigma)\Gamma_\sigma\kappa_\sigma+2\gamma_\sigma | ||
| + | \kappa_\sigma^2\Big)-\Big(\Gamma_\sigma^2-(3P_\sigma-\gamma_\sigma)\kappa_\sigma\Big)\omega^2}{\pi(\kappa_\sigma+\Gamma_\sigma)\Big(9\Gamma_\sigma^2\omega^2+[2\omega^2-\kappa_\sigma(P_\sigma-\gamma_\sigma)]^2\Big)}\,, | ||
| + | \end{multline}</wz> | ||
| + | |||
| + | A result from [[Fabrice|me]]: | ||
| + | |||
| + | <wz tip="An exact picture of Bose-Einstein condensation."> | ||
\[ | \[ | ||
| − | \label{eq: | + | \label{eq:fabrice} |
p(n_0,\Sigma) | p(n_0,\Sigma) | ||
= | = | ||
| − | \frac{(1-\theta_0)(1-\theta)^M\theta^{n_0+\Sigma}{M+n_0+\Sigma-1\choose M-1}{}_2F_1(1,-n_0+\Sigma,-M-n_0+\Sigma+1,\frac{\theta_0}{\theta})}{\left(\frac{\xi}{\xi-1}\right)^M-\frac1{\xi^{n_0+1}}{M+\Sigma+n_0\choose M-1}{}_2F_1(1,M+\Sigma+n_0+1,\Sigma+n_0+2,\frac{1}{\xi})}\, | + | \frac{(1-\theta_0)(1-\theta)^M\theta^{n_0+\Sigma}{M+n_0+\Sigma-1\choose M-1}{}_2F_1(1,-n_0+\Sigma,-M-n_0+\Sigma+1,\frac{\theta_0}{\theta})}{\left(\frac{\xi}{\xi-1}\right)^M-\frac1{\xi^{n_0+1}}{M+\Sigma+n_0\choose M-1}{}_2F_1(1,M+\Sigma+n_0+1,\Sigma+n_0+2,\frac{1}{\xi})}\,. |
| − | + | ||
\] | \] | ||
| + | </wz> | ||
| − | + | The beauty of it beyond perfect typesetting and integration in the flow of the text is that you can even label them. Equation \eqref{eq:elena} is the lineshape for the incoherent Mollow triplet or the luminescence spectrum of a two-level emitter in strong-coupling with a cavity which it brought in the lasing regime [http://dx.doi.org/10.1103/PhysRevLett.105.23360]. Equation \eqref{eq:fabrice} is the exact solution of quantum Boltzmann master equation which provide an analytical description of Bose-Einstein condensation. | |
| − | + | ||
| − | \ | + | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | \ | + | |
| − | + | And just when you thought you could not be impressed further, you have to get a look at inline display, like, Euler's formula <math>e^{i\pi}-1=0</math> displayed idiotically to feature all the fundamental numbers, $e$, $i$, $\pi$, $0$ and $1$ (even a $-$). See the [[Knuth]]ian quality of the insert of math in the text? I'm doing that merely putting $\TeX$'s dollar signs, I'm feeling at home on the web! What an age we live in! | |
| − | = Links = | + | == Links == |
* http://www.mathjax.org Webpage of the project. | * http://www.mathjax.org Webpage of the project. | ||
* http://sourceforge.net/projects/mathjax [[Sourceforge]] page of the project. | * http://sourceforge.net/projects/mathjax [[Sourceforge]] page of the project. | ||
* http://www.mediawiki.org/wiki/Extension:MathJax [[MediaWiki]] extension (thanks to [http://people.cs.kuleuven.be/~dirk.nuyens/ Dirk Nuyens]). | * http://www.mediawiki.org/wiki/Extension:MathJax [[MediaWiki]] extension (thanks to [http://people.cs.kuleuven.be/~dirk.nuyens/ Dirk Nuyens]). | ||
MathJax is an open source Ajax-based framework to display mathematical notations in web browsers. It renders the input, entered as LaTeX or MathML expressions, as high-quality display in MathML or HTML with CSS and integrates well with text-based content, both in display mode and inline.
An identity from Ramanujan:
\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } }\,. \]
A result from Elena:
\begin{multline} \tag{1} S_\mathrm{inc}(\omega)=\Big(\frac{2P_\sigma}{\kappa_\sigma+\Gamma_\sigma}-\frac{\Gamma_\sigma}{\kappa_\sigma}\Big) \delta(\omega)+\frac{\frac{1}{2\pi}\frac{\Gamma_\sigma}{2}}{\big(\frac{\Gamma_\sigma}{2}\big)^2+\omega^2}+\\ \frac{(P_\sigma-\gamma_\sigma)\Big(3\Gamma_\sigma^3-(P_\sigma-5\gamma_\sigma)\Gamma_\sigma\kappa_\sigma+2\gamma_\sigma \kappa_\sigma^2\Big)-\Big(\Gamma_\sigma^2-(3P_\sigma-\gamma_\sigma)\kappa_\sigma\Big)\omega^2}{\pi(\kappa_\sigma+\Gamma_\sigma)\Big(9\Gamma_\sigma^2\omega^2+[2\omega^2-\kappa_\sigma(P_\sigma-\gamma_\sigma)]^2\Big)}\,, \end{multline}
A result from me:
\[ \tag{1} p(n_0,\Sigma) = \frac{(1-\theta_0)(1-\theta)^M\theta^{n_0+\Sigma}{M+n_0+\Sigma-1\choose M-1}{}_2F_1(1,-n_0+\Sigma,-M-n_0+\Sigma+1,\frac{\theta_0}{\theta})}{\left(\frac{\xi}{\xi-1}\right)^M-\frac1{\xi^{n_0+1}}{M+\Sigma+n_0\choose M-1}{}_2F_1(1,M+\Sigma+n_0+1,\Sigma+n_0+2,\frac{1}{\xi})}\,. \]
The beauty of it beyond perfect typesetting and integration in the flow of the text is that you can even label them. Equation (1) is the lineshape for the incoherent Mollow triplet or the luminescence spectrum of a two-level emitter in strong-coupling with a cavity which it brought in the lasing regime [1]. Equation (1) is the exact solution of quantum Boltzmann master equation which provide an analytical description of Bose-Einstein condensation.
And just when you thought you could not be impressed further, you have to get a look at inline display, like, Euler's formula \(e^{i\pi}-1=0\) displayed idiotically to feature all the fundamental numbers, $e$, $i$, $\pi$, $0$ and $1$ (even a $-$). See the Knuthian quality of the insert of math in the text? I'm doing that merely putting $\TeX$'s dollar signs, I'm feeling at home on the web! What an age we live in!