Skip to content


Exemples d’équations avec le plugin wp-latex dans WordPress…

Introduction :

Exemples....

\alpha+\beta\geq\gamma

dU_i = d \left( \frac{\partial X_i}{ \partial x_j} \right).u_j + \frac{\partial X_i}{ \partial x_j}.du_j = \frac{\partial^2 X_i}{\partial x_k \partial x_j}.dx_k.u_j + \frac{\partial X_i}{ \partial x_j}.du_j = \frac{\partial X_i}{ \partial x_j}. \left( \frac{ \partial x_j}{\partial X_l}.\frac{\partial^2 X_l}{\partial x_k \partial x_m} .dx_k.u_m + du_j \right)

Il peut être intéressant pour certains d'entre nous de pouvoir écrire ou formuler des équations dans nos petits articles...
Pour cela il existe un plugins pour wordpress sur le site suivant : http://wordpress.org/extend/plugins/wp-latex/
Cliquez sur "Download" en haut à droite..

A quoi cela peut-il servir ? Et bien j'ai quelques idées d'articles sur la physique qui trainent et j'aimerais bien en traiter quelques un ! 🙂

Voici quelques exemples créés par l'intermédiaire de {{LyX}} puis {{LaTeX}}

Les exemples :

g(x,y)=\frac{\partial F(x,y)}{\partial x}+\frac{\partial F(x,y)}{\partial y}+2.\frac{\partial F(x,y)}{\partial x}.\frac{\partial F(x,y)}{\partial y} \ \ \ \ (eq 1) \mathbb{\underset{\beta\thicksim X}{\mathbb{H}}} \ \ \ \ (eq 2) \underset{i:1\rightarrow5}{\sum}i=1+2+..=15\ \ \ \ (eq 3)

Voir beaucoups plus :
Un exemple des équation de la relativité générale :

dU_i = d \left( \frac{\partial X_i}{ \partial x_j} \right).u_j + \frac{\partial X_i}{ \partial x_j}.du_j = \frac{\partial^2 X_i}{\partial x_k \partial x_j}.dx_k.u_j + \frac{\partial X_i}{ \partial x_j}.du_j = \frac{\partial X_i}{ \partial x_j}. \left( \frac{ \partial x_j}{\partial X_l}.\frac{\partial^2 X_l}{\partial x_k \partial x_m} .dx_k.u_m + du_j \right)
\left[ \nabla^i ; \nabla^j \right] = \frac{\nabla~}{\partial x_i}\frac{\nabla~}{\partial x_j} - \frac{\nabla~}{\partial x_j}\frac{\nabla~}{\partial x_i}
\frac{\nabla~}{\partial x_i} = \nabla^i
G_{ij} = R_{ij}-\frac{1}{2}g_{ij}.R
R_{ij}-\frac{1}{2}g_{ij}.R = \chi T_{ij} \;,
\ \chi = \frac{8 \pi G}{c^4}
R_{ij}-\frac{1}{2}g_{ij}.R = \chi T_{ij} + g_{ij}.\Lambda

Voir : Relativité Générale sur Wikipedia
Voir aussi : {{LaTeX}}

Le code suivant :

dollarLATEX \left[\sum_{n=1}^{+\infty}\frac{1}{n^2}=\frac{\pi^2}{6}\right]$

donne :
\left[\sum_{n=1}^{+\infty}\frac{1}{n^2}=\frac{\pi^2}{6}\right]

Le code des équations précédentes en remplaçant $LATEX par $latex :

$LATEX g(x,y)=\frac{\partial F(x,y)}{\partial x}+\frac{\partial F(x,y)}{\partial y}+2.\frac{\partial F(x,y)}{\partial x}.\frac{\partial F(x,y)}{\partial y} \ \ \ \ (eq 1)$
$LATEX \mathbb{\underset{\beta\thicksim X}{\mathbb{H}}} \ \ \ \ (eq 2)$
$LATEX \underset{i:1\rightarrow5}{\sum}i=1+2+..=15 \ \ \ \ (eq 3)$
$LATEX dU_i = d \left( \frac{\partial X_i}{ \partial x_j} \right).u_j + \frac{\partial X_i}{ \partial x_j}.du_j = \frac{\partial^2 X_i}{\partial x_k \partial x_j}.dx_k.u_j + \frac{\partial X_i}{ \partial x_j}.du_j $
$LATEX dU_i = \frac{\partial X_i}{ \partial x_j}. \left( \frac{ \partial x_j}{\partial X_l}.\frac{\partial^2 X_l}{\partial x_k \partial x_m} .dx_k.u_m + du_j \right)$
$LATEX \left[ \nabla^i ; \nabla^j \right] = \frac{\nabla~}{\partial x_i}\frac{\nabla~}{\partial x_j} - \frac{\nabla~}{\partial x_j}\frac{\nabla~}{\partial x_i} $
$LATEX \frac{\nabla~}{\partial x_i} = \nabla^i$
$LATEX G_{ij} = R_{ij}-\frac{1}{2}g_{ij}.R$
$LATEX R_{ij}-\frac{1}{2}g_{ij}.R = \chi T_{ij} \;,$
$LATEX \ \chi = \frac{8 \pi G}{c^4}$
$LATEX R_{ij}-\frac{1}{2}g_{ij}.R = \chi T_{ij} + g_{ij}.\Lambda$

 Le lagrangien du modèle standard

 L = -\frac{1}{2}\partial_{\nu}g_{\mu}^{a}\partial_{\nu}g_{\mu}^{a}-g_{s}f^{abc}\partial_{\mu}g_{\nu}^{a}g_{\mu}^{b}g_{\nu}^{c}-\frac{1}{4}g_{s}^{2}f^{abc}f^{ade}g_{\mu}^{b}g_{\nu}^{c}g_{\mu}^{d}g_{\nu}^{e}+\frac{1}{2}ig_{s}^{2}(\bar{q}_{i}^{\sigma}\gamma^{\mu}q_{j}^{\sigma})g_{\mu}^{a}+\bar{G}^{a}\partial^{2}G^{a}+g_{s}f^{abc}\partial_{\mu}\bar{G}^{a}G^{b}g_{\mu}^{c}-\partial_{\nu}W_{\mu}^{+}\partial_{\nu}W_{\mu}^{-}-M^{2}W_{\mu}^{+}W_{\mu}^{-}-\frac{1}{2}\partial_{\nu}Z_{\mu}^{0}\partial_{\nu}Z_{\mu}^{0}-\frac{1}{2c_{w}^{2}}M^{2}Z_{\mu}^{0}Z_{\mu}^{0}-\frac{1}{2}\partial_{\mu}A_{\nu}\partial_{\mu}A_{\nu}-\frac{1}{2}\partial_{\mu}H\partial_{\mu}H-\frac{1}{2}m_{h}^{2}H^{2}-\partial_{\mu}\phi^{+}\partial_{\mu}\phi^{-}-M^{2}\phi^{+}\phi^{-}-\frac{1}{2}\partial_{\mu}\phi^{0}\partial_{\mu}\phi^{0}-\frac{1}{2c_{w}^{2}}M\phi^{0}\phi^{0}-\beta_{h}[\frac{2M^{2}}{g^{2}}+\frac{2M}{g}H+\frac{1}{2}(H^{2}+\phi^{0}\phi^{0}+2\phi^{+}\phi^{-%%@<br />
})]+\frac{2M^{4}}{g^{2}}\alpha_{h}-igc_{w}[\partial_{\nu}Z_{\mu}^{0}(W_{\mu}^{+}W_{\nu}^{-}-W_{\nu}^{+}W_{\mu}^{-})-Z_{\nu}^{0}(W_{\mu}^{+}\partial_{\nu}W_{\mu}^{-}-W_{\mu}^{-}\partial_{\nu}W_{\mu}^{+})+Z_{\mu}^{0}(W_{\nu}^{+}\partial_{\nu}W_{\mu}^{-}-W_{\nu}^{-}\partial_{\nu}W_{\mu}^{+})]-igs_{w}[\partial_{\nu}A_{\mu}(W_{\mu}^{+}W_{\nu}^{-}-W_{\nu}^{+}W_{\mu}^{-})-A_{\nu}(W_{\mu}^{+}\partial_{\nu}W_{\mu}^{-}-W_{\mu}^{-}\partial_{\nu}W_{\mu}^{+})+A_{\mu}(W_{\nu}^{+}\partial_{\nu}W_{\mu}^{-}-W_{\nu}^{-}\partial_{\nu}W_{\mu}^{+})]-\frac{1}{2}g^{2}W_{\mu}^{+}W_{\mu}^{-}W_{\nu}^{+}W_{\nu}^{-}+\frac{1}{2}g^{2}W_{\mu}^{+}W_{\nu}^{-}W_{\mu}^{+}W_{\nu}^{-}+g^{2}c_{w}^{2}(Z_{\mu}^{0}W_{\mu}^{+}Z_{\nu}^{0}W_{\nu}^{-}-Z_{\mu}^{0}Z_{\mu}^{0}W_{\nu}^{+}W_{\nu}^{-})+g^{2}s_{w}^{2}(A_{\mu}W_{\mu}^{+}A_{\nu}W_{\nu}^{-}-A_{\mu}A_{\mu}W_{\nu}^{+}W_{\nu}^{-})+g^{2}s_{w}c_{w}[A_{\mu}Z_{\nu}^{0}(W_{\mu}^{+}W_{\nu}^{-}-W_{\nu}^{+}W_{\mu}^{-})-%%@<br />
2A_{\mu}Z_{\mu}^{0}W_{\nu}^{+}W_{\nu}^{-}]-g\alpha[H^{3}+H\phi^{0}\phi^{0}+2H\phi^{+}\phi^{-}]-\frac{1}{8}g^{2}\alpha_{h}[H^{4}+(\phi^{0})^{4}+4(\phi^{+}\phi^{-})^{2}+4(\phi^{0})^{2}\phi^{+}\phi^{-}+4H^{2}\phi^{+}\phi^{-}+2(\phi^{0})^{2}H^{2}]-gMW_{\mu}^{+}W_{\mu}^{-}H-\frac{1}{2}g\frac{M}{c_{w}^{2}}Z_{\mu}^{0}Z_{\mu}^{0}H-\frac{1}{2}ig[W_{\mu}^{+}(\phi^{0}\partial_{\mu}\phi^{-}-\phi^{-}\partial_{\mu}\phi^{0})-W_{\mu}^{-}(\phi^{0}\partial_{\mu}\phi^{+}-\phi^{+}\partial_{\mu}\phi^{0})]+\frac{1}{2}g[W_{\mu}^{+}(H\partial_{\mu}\phi^{-}-\phi^{-}\partial_{\mu}H)-W_{\mu}^{-}(H\partial_{\mu}\phi^{+}-\phi^{+}\partial_{\mu}H)]+\frac{1}{2}g\frac{1}{c_{w}}(Z_{\mu}^{0}(H\partial_{\mu}\phi^{0}-\phi^{0}\partial_{\mu}H)-ig\frac{s_{w}^{2}}{c_{w}}MZ_{\mu}^{0}(W_{\mu}^{+}\phi^{-}-W_{\mu}^{-}\phi^{+})+igs_{w}MA_{\mu}(W_{\mu}^{+}\phi^{-}-W_{\mu}^{-}\phi^{+})-ig\frac{1-2c_{w}^{2}}{2c_{w}}Z_{\mu}^{0}(\phi^{+}\partial_{\mu}\phi^{-}-\phi^{-%%@<br />
}\partial_{\mu}\phi^{+})+igs_{w}A_{\mu}(\phi^{+}\partial_{\mu}\phi^{-}-\phi^{-}\partial_{\mu}\phi^{+})-\frac{1}{4}g^{2}W_{\mu}^{+}W_{\mu}^{-}[H^{2}+(\phi^{0})^{2}+2\phi^{+}\phi^{-}]-\frac{1}{4}g^{2}\frac{1}{c_{w}^{2}}Z_{\mu}^{0}Z_{\mu}^{0}[H^{2}+(\phi^{0})^{2}+2(2s_{w}^{2}-%%@<br />
1)^{2}\phi^{+}\phi^{-}]-\frac{1}{2}g^{2}\frac{s_{w}^{2}}{c_{w}}Z_{\mu}^{0}\phi^{0}(W_{\mu}^{+}\phi^{-}+W_{\mu}^{-%%@<br />
}\phi^{+})-\frac{1}{2}ig^{2}\frac{s_{w}^{2}}{c_{w}}Z_{\mu}^{0}H(W_{\mu}^{+}\phi^{-}-W_{\mu}^{-}\phi^{+})+\frac{1}{2}g^{2}s_{w}A_{\mu}\phi^{0}(W_{\mu}^{+}\phi^{-}+W_{\mu}^{-}\phi^{+})+\frac{1}{2}ig^{2}s_{w}A_{\mu}H(W_{\mu}^{+}\phi^{-}-W_{\mu}^{-}\phi^{+})-g^{2}\frac{s_{w}}{c_{w}}(2c_{w}^{2}-1)Z_{\mu}^{0}A_{\mu}\phi^{+}\phi^{-}-%%@<br />
g^{1}s_{w}^{2}A_{\mu}A_{\mu}\phi^{+}\phi^{-}-\bar{e}^{\lambda}(\gamma\partial+m_{e}^{\lambda})e^{\lambda}-\bar{\nu}^{\lambda}\gamma\partial\nu^{\lambda}-\bar{u}_{j}^{\lambda}(\gamma\partial+m_{u}^{\lambda})u_{j}^{\lambda}-\bar{d}_{j}^{\lambda}(\gamma\partial+m_{d}^{\lambda})d_{j}^{\lambda}+igs_{w}A_{\mu}[-(\bar{e}^{\lambda}\gamma^{\mu}e^{\lambda})+\frac{2}{3}(\bar{u}_{j}^{\lambda}\gamma^{\mu}%%@<br />
u_{j}^{\lambda})-\frac{1}{3}(\bar{d}_{j}^{\lambda}\gamma^{\mu}d_{j}^{\lambda})]+\frac{ig}{4c_{w}}Z_{\mu}^{0}[(\bar{\nu}^{\lambda}\gamma^{\mu}(1+\gamma^{5})\nu^{\lambda})+(\bar{e}^{\lambda}\gamma^{\mu}(4s_{w}^{2}-1-\gamma^{5})e^{\lambda})+(\bar{u}_{j}^{\lambda}\gamma^{\mu}(\frac{4}{3}s_{w}^{2}-1-\gamma^{5})u_{j}^{\lambda})+(\bar{d}_{j}^{\lambda}\gamma^{\mu}(1-\frac{8}{3}s_{w}^{2}-\gamma^{5})d_{j}^{\lambda})]+\frac{ig}{2\sqrt{2}}W_{\mu}^{+}[(\bar{\nu}^{\lambda}\gamma^{\mu}(1+\gamma^{5})e^{\lambda})+(\bar{u}_{j}^{\lambda}\gamma^{\mu}(1+\gamma^{5})C_{\lambda\kappa}d_{j}^{\kappa})]+\frac{ig}{2\sqrt{2}}W_{\mu}^{-}[(\bar{e}^{\lambda}\gamma^{\mu}(1+\gamma^{5})\nu^{\lambda})+(\bar{d}_{j}^{\kappa}C_{\lambda\kappa}^{\dagger}\gamma^{\mu}(1+\gamma^{5})u_{j}^{\lambda})]+\frac{ig}{2\sqrt{2}}\frac{m_{e}^{\lambda}}{M}[-\phi^{+}(\bar{\nu}^{\lambda}(1-\gamma^{5})e^{\lambda})+\phi^{-}(\bar{e}^{\lambda}(1+\gamma^{5})\nu^{\lambda})]-\frac{g}{2}\frac{m_{e}^{\lambda}}{M}[H(\bar{e}^{\lambda}e^{\lambda})+i\phi^{0}(\bar{e}^{\lambda}\gamma^{5}e^{\lambda})]+\frac{ig}{2M\sqrt{2}}\phi^{+}[-m_{d}^{\kappa}(\bar{u}_{j}^{\lambda}C_{\lambda\kappa}(1-\gamma^{5})d_{j}^{\kappa})+m_{u}^{\lambda}(\bar{u}_{j}^{\lambda}C_{\lambda\kappa}(1+\gamma^{5})d_{j}^{\kappa}]+\frac{ig}{2M\sqrt{2}}\phi^{-}[m_{d}^{\lambda}(\bar{d}_{j}^{\lambda}C_{\lambda\kappa}^{\dagger}(1+\gamma^{5})u_{j}^{\kappa})-m_{u}^{\kappa}(\bar{d}_{j}^{\lambda}C_{\lambda\kappa}^{\dagger}(1-\gamma^{5})u_{j}^{\kappa}]-\frac{g}{2}\frac{m_{u}^{\lambda}}{M}H(\bar{u}_{j}^{\lambda}u_{j}^{\lambda})-\frac{g}{2}\frac{m_{d}^{\lambda}}{M}H(\bar{d}_{j}^{\lambda}d_{j}^{\lambda})+\frac{ig}{2}\frac{m_{u}^{\lambda}}{M}\phi^{0}(\bar{u}_{j}^{\lambda}\gamma^{5}u_{j}^{\lambda})-\frac{ig}{2}\frac{m_{d}^{\lambda}}{M}\phi^{0}(\bar{d}_{j}^{\lambda}\gamma^{5}d_{j}^{\lambda})+\bar{X}^{+}(\partial^{2}-M^{2})X^{+}+\bar{X}^{-}(\partial^{2}-M^{2})X^{-}+\bar{X}^{0}(\partial^{2}-\frac{M^{2}}{c_{w}^{2}})X^{0}+\bar{Y}\partial^{2}Y+igc_{w}W_{\mu}^{+}(\partial_{\mu}\bar{X}^{0}X^{-}-\partial_{\mu}\bar{X}^{+}X^{0})+igs_{w}W_{\mu}^{+}(\partial_{\mu}\bar{Y}X^{-}-\partial_{\mu}\bar{X}^{+}Y)+igc_{w}W_{\mu}^{-}(\partial_{\mu}\bar{X}^{-}X^{0}-\partial_{\mu}\bar{X}^{0}X^{+})+igs_{w}W_{\mu}^{-}(\partial_{\mu}\bar{X}^{-}Y-\partial_{\mu}\bar{Y}X^{+})+igc_{w}Z_{\mu}^{0}(\partial_{\mu}\bar{X}^{+}X^{+}-\partial_{\mu}\bar{X}^{-}X^{-})+igs_{w}A_{\mu}(\partial_{\mu}\bar{X}^{+}X^{+}-\partial_{\mu}\bar{X}^{-}X^{-})-\frac{1}{2}gM[\bar{X}^{+}X^{+}H+\bar{X}^{-}X^{-}H+\frac{1}{c_{w}^{2}}\bar{X}^{0}X^{0}H]+\frac{1-2c_{w}^{2}}{2c_{w}}igM[\bar{X}^{+}X^{0}\phi^{+}-\bar{X}^{-}X^{0}\phi^{-}]+\frac{1}{2c_{w}}igM[\bar{X}^{0}X^{-}\phi^{+}-\bar{X}^{0}X^{+}\phi^{-}]+igMs_{w}[\bar{X}^{0}X^{-}\phi^{+}-\bar{X}^{0}X^{+}\phi^{-}]+\frac{1}{2}igM[\bar{X}^{+}X^{+}\phi^{0}-\bar{X}^{-}X^{-}\phi^{0}]

Print Friendly, PDF & Email

Posted in Maths & Phys, Toutes. Tagged with .

0 Responses

Stay in touch with the conversation, subscribe to the RSS feed for comments on this post.

Some HTML is OK

(required)

(required, but never shared)

or, reply to this post via trackback.

Time limit is exhausted. Please reload CAPTCHA.


/* */
Creative Commons License
Cette création par Laurent Besson est mise à disposition selon les termes de la licence Creative Commons Paternité-Partage des Conditions Initiales à l'Identique 2.0 France.