Aggiornamento CV
Da oggi nella sezione Info del presente Blog si può trovare il mio Curriculum Vitae aggiornato. Per dimostrare, se ce ne fosse ancora bisogno, la versatilità del plugin WP LaTeX, voglio presentarvi l’equazione integro-differenziale di Amoroso
![U(\boldsymbol{z})=\frac{(n-2)!}{2\pi^n}\int_{\partial\Omega}\left[U(\boldsymbol{\zeta})\frac{\partial}{\partial\nu_{\boldsymbol{\zeta}}}\frac{1}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n-2}} - \mathscr{D}U(\boldsymbol{\zeta }) \frac{1}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n-2}}\right]\mathrm{d}\sigma_{\boldsymbol{\zeta }}](http://s.wordpress.com/latex.php?latex=U%28%5Cboldsymbol%7Bz%7D%29%3D%5Cfrac%7B%28n-2%29%21%7D%7B2%5Cpi%5En%7D%5Cint_%7B%5Cpartial%5COmega%7D%5Cleft%5BU%28%5Cboldsymbol%7B%5Czeta%7D%29%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%5Cnu_%7B%5Cboldsymbol%7B%5Czeta%7D%7D%7D%5Cfrac%7B1%7D%7B%7C%5Cboldsymbol%7Bz%7D-%5Cboldsymbol%7B%5Czeta%7D%7C%5E%7B2n-2%7D%7D%20-%20%5Cmathscr%7BD%7DU%28%5Cboldsymbol%7B%5Czeta%20%7D%29%20%5Cfrac%7B1%7D%7B%7C%5Cboldsymbol%7Bz%7D-%5Cboldsymbol%7B%5Czeta%7D%7C%5E%7B2n-2%7D%7D%5Cright%5D%5Cmathrm%7Bd%7D%5Csigma_%7B%5Cboldsymbol%7B%5Czeta%20%7D%7D&bg=ffffff&fg=000000&s=1 "U(\boldsymbol{z})=\frac{(n-2)!}{2\pi^n}\int_{\partial\Omega}\left[U(\boldsymbol{\zeta})\frac{\partial}{\partial\nu_{\boldsymbol{\zeta}}}\frac{1}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n-2}} - \mathscr{D}U(\boldsymbol{\zeta }) \frac{1}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n-2}}\right]\mathrm{d}\sigma_{\boldsymbol{\zeta }}")
dove
con
è un dominio limitato nello spazio vettoriale complesso a dimensione finita e
è la sua frontiera, che assumiamo di classe
e
sono punti della frontiera
è il versore normale a
(che nelle ipotesi fatte esiste sempre)
è la funzione incognita
è un particolare operatore differenziale tangenziale, univocamente determinato solo se
.
E per rilassarci, vi propongo ancora i Watchtower
Watchtower – The Fall of reason
Date: 1 novembre 2009
Categories: Cronaca, Matematica
è una parte della sua frontiera 
è un punto della frontiera
è la ![{\mu(\boldsymbol{z},\bar{\boldsymbol{z}})}= \sum_{k=2}^n\sum_{h=1}^{k-1}{f_{hk}(\boldsymbol{z},\bar{\boldsymbol{z}})}\mathrm{d}\bar{\boldsymbol{z}}[h][k]](http://s.wordpress.com/latex.php?latex=%7B%5Cmu%28%5Cboldsymbol%7Bz%7D%2C%5Cbar%7B%5Cboldsymbol%7Bz%7D%7D%29%7D%3D%20%5Csum_%7Bk%3D2%7D%5En%5Csum_%7Bh%3D1%7D%5E%7Bk-1%7D%7Bf_%7Bhk%7D%28%5Cboldsymbol%7Bz%7D%2C%5Cbar%7B%5Cboldsymbol%7Bz%7D%7D%29%7D%5Cmathrm%7Bd%7D%5Cbar%7B%5Cboldsymbol%7Bz%7D%7D%5Bh%5D%5Bk%5D&bg=ffffff&fg=000000&s=1 "{\mu(\boldsymbol{z},\bar{\boldsymbol{z}})}= \sum_{k=2}^n\sum_{h=1}^{k-1}{f_{hk}(\boldsymbol{z},\bar{\boldsymbol{z}})}\mathrm{d}\bar{\boldsymbol{z}}[h][k]")
![\mathrm{d}\bar{\boldsymbol{z}}[h][k] = \mathrm{d}\bar{z}_1\wedge\cdots \wedge\mathrm{d}\bar{z}_{h-1}\wedge \mathrm{d}\bar{z}_{h+1}\wedge\cdots\wedge\mathrm{d}\bar{z}_{k-1}\wedge \mathrm{d}\bar{z}_{k+1}\wedge\cdots\wedge \mathrm{d}\bar{z}_n](http://s.wordpress.com/latex.php?latex=%5Cmathrm%7Bd%7D%5Cbar%7B%5Cboldsymbol%7Bz%7D%7D%5Bh%5D%5Bk%5D%20%3D%20%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_1%5Cwedge%5Ccdots%20%5Cwedge%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_%7Bh-1%7D%5Cwedge%20%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_%7Bh%2B1%7D%5Cwedge%5Ccdots%5Cwedge%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_%7Bk-1%7D%5Cwedge%20%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_%7Bk%2B1%7D%5Cwedge%5Ccdots%5Cwedge%20%5Cmathrm%7Bd%7D%5Cbar%7Bz%7D_n&bg=ffffff&fg=000000&s=0 "\mathrm{d}\bar{\boldsymbol{z}}[h][k] = \mathrm{d}\bar{z}_1\wedge\cdots \wedge\mathrm{d}\bar{z}_{h-1}\wedge \mathrm{d}\bar{z}_{h+1}\wedge\cdots\wedge\mathrm{d}\bar{z}_{k-1}\wedge \mathrm{d}\bar{z}_{k+1}\wedge\cdots\wedge \mathrm{d}\bar{z}_n")
e 
è un 
è una funzione continua del punto 
.
mentre 
è la ![U(\boldsymbol{z}-\boldsymbol{\zeta})=-\frac{(n-1)!}{(2\pi i)^n} \sum_{k=1}^n (-1)^{k-1}\frac{\bar{\zeta}_k-\bar{z}_k}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n}}\mathrm{d}\bar{\boldsymbol{\zeta}}[k]\wedge\mathrm{d}\boldsymbol{\zeta}](http://s.wordpress.com/latex.php?latex=U%28%5Cboldsymbol%7Bz%7D-%5Cboldsymbol%7B%5Czeta%7D%29%3D-%5Cfrac%7B%28n-1%29%21%7D%7B%282%5Cpi%20i%29%5En%7D%20%5Csum_%7Bk%3D1%7D%5En%20%28-1%29%5E%7Bk-1%7D%5Cfrac%7B%5Cbar%7B%5Czeta%7D_k-%5Cbar%7Bz%7D_k%7D%7B%7C%5Cboldsymbol%7Bz%7D-%5Cboldsymbol%7B%5Czeta%7D%7C%5E%7B2n%7D%7D%5Cmathrm%7Bd%7D%5Cbar%7B%5Cboldsymbol%7B%5Czeta%7D%7D%5Bk%5D%5Cwedge%5Cmathrm%7Bd%7D%5Cboldsymbol%7B%5Czeta%7D&bg=ffffff&fg=000000&s=1 "U(\boldsymbol{z}-\boldsymbol{\zeta})=-\frac{(n-1)!}{(2\pi i)^n} \sum_{k=1}^n (-1)^{k-1}\frac{\bar{\zeta}_k-\bar{z}_k}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n}}\mathrm{d}\bar{\boldsymbol{\zeta}}[k]\wedge\mathrm{d}\boldsymbol{\zeta}")
![\mathrm{d}\bar{\boldsymbol{\zeta}}[k] = \mathrm{d}\bar{\zeta}_1\wedge\cdots \wedge\mathrm{d}\bar{\zeta}_{k-1}\wedge \mathrm{d}\bar{\zeta}_{k+1}\wedge\cdots\wedge \mathrm{d}\bar{\zeta}_n](http://s.wordpress.com/latex.php?latex=%5Cmathrm%7Bd%7D%5Cbar%7B%5Cboldsymbol%7B%5Czeta%7D%7D%5Bk%5D%20%3D%20%5Cmathrm%7Bd%7D%5Cbar%7B%5Czeta%7D_1%5Cwedge%5Ccdots%20%5Cwedge%5Cmathrm%7Bd%7D%5Cbar%7B%5Czeta%7D_%7Bk-1%7D%5Cwedge%20%5Cmathrm%7Bd%7D%5Cbar%7B%5Czeta%7D_%7Bk%2B1%7D%5Cwedge%5Ccdots%5Cwedge%20%5Cmathrm%7Bd%7D%5Cbar%7B%5Czeta%7D_n&bg=ffffff&fg=000000&s=0 "\mathrm{d}\bar{\boldsymbol{\zeta}}[k] = \mathrm{d}\bar{\zeta}_1\wedge\cdots \wedge\mathrm{d}\bar{\zeta}_{k-1}\wedge \mathrm{d}\bar{\zeta}_{k+1}\wedge\cdots\wedge \mathrm{d}\bar{\zeta}_n")
.
è una funzione continua del punto 
è il versore coniugato
è la funzione
. Ed ora ascoltiamo ancora 
