Friday, 3 of September of 2010
Scienza, Tecnica e il Mondo che ci circonda
Since recently I have worked on biographies of scientists (mainly mathematicians) I have created a web page on the blog containing links to the biographies I have worked to or I am working to: and also I have changed the classical Wordpress theme with new and more freely configurable one.
Snowy landscape (Via Goccianello, Imola)
Date: 29 May 2010
Categories: Chronicle, Mathematics, Sport
Thanks to the migration of the blog to a server implementing less restrictive policies, but mostly thanks to the work and help of my brother, the functionality of this web site is again full …or at least I think so 
: please tell me if you find orphan links or any other problem you’ll find! And now I would like to tell you about what I am doing in this period:
in the euclidean n-dimensional space and a neighbourhood 
of a point 
on the boundary 
of the given compact, the functions 
and 
, 
are respectively called lower barrier and upper barrier at the given point for the solution 
of the elliptic quasilinear partial differential equation
where 
in 
for all 
Now, thanks to the comparison principle (see David Gilbarg, Neil S. Trudinger, “Elliptic Partial Differential Equations of Second Order“, Berlin-Heidelberg-New York: Springer-Verlag (2001)) it is true that
and then, thanks to the second of the three properties which define barriers,
So, for those points of the boundary of 
therefore if I know the barriers I know the magnitude of the electric field at the boundary of the given region.
As for the other business, the activity as a member of the directive council of the ImoLUG goes as usual, and the same is for biking: but I will not tell you about this, since I want to offer you a musical end for this post. I start by saying that WatchTower, my favourite band, has released a new, wonderful track which is rewarding to listen to:
WatchTower – The Size of Matter
And I continue proposing you a tribute to an old band, whose third LP title titles also this post: they are Blue Cheer.
Blue Cheer – Summertime Blues
And I would like to end this post by offering you a song from Alessandra Amoroso and Gianni Morandi:
Alessandra Amoroso Credo nell’amore (nuovo inedito con Gianni Morandi)
Date: 20 May 2010
Categories: Chronicle, Mathematics
A tutti voi, parenti, amici e collaboratori
Buon Natale/Merry Christmas
To you all, relatives, friends and collaborators
Date: 24 December 2009
Categories: Chronicle
As you all can see, the language-switching icon does not appear on the blog page: this is due to the bilingual plugin wich does not works properly with my current installation of Wordpress. I hope to solve soon this problem: to you all I offer my apologies for the inconvenience, and a song of Rino Gaetano.
Rino Gaetano – Ma il cielo è sempre più blu
Date: 7 December 2009
Categories: Chronicle, Informatics
From now on, you can find my Curriculum Vitae in the Info section of this Blog. Then, in order to demonstrate (if there was still any need) the versatility of the WP LaTeX plugin, I would like to introduce you the Amoroso integro-differential equation
![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 }}")
where
with 
is a bounded domain in the finite dimensional complex vector space and 
is its boundary, which we assume of class 
and 
are points belonging to the boundary 
is the unit hypersurface normal to in 
(which always exists in the given hypothesis)
is the unknown function
is a particular tangential differential operator, univocally determined only if 
.And, in order to relax I still would propose you the listening of Watchtower
Watchtower – The Fall of reason
Date: 1 November 2009
Categories: Chronicle, Mathematics
As I recently told you, we are approaching the Linux Day: at present, updated speech lists, locations and other info’s can be found at the ImoLUG refferring page. All the speech are in Italian therefore the event may be of little interest for English speaking readers, but I think it is interesting for everyone to get the feel of what is going on on the Linux side here in Italy, precisely in our LUG. Next, again continuing to explore the power of the WP LaTeX plugin I’ll write down the weak form of the tangential Cauchy-Riemann equation as Gaetano Fichera introduced and studied for the first time:
where
with is a bounded domain in the finite dimensional complex vector space and 
is a part of its boundary , which we assume of class 
is a point belonging to its boundary
is the differential form
with ![\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")
is a continuous function of 
.And now let’s listen to Watchtower :
Watchtower The Eldritch
Date: 11 October 2009
Categories: Chronicle, Linux, Mathematics
As usual for this season of the year, we are approaching the Linux Day: speech lists, roundtables, locations and other info’s can be found at the ImoLUG refferring page. Also, speech proposal can be submitted to the Directive Council of the LUG by e-mail (direttivo AT imolug.org): a list of preferred topics is the following one
The deadline for the submission of the speech proposals is the 30 of September, included, so hurry up!
Next, I would like to write down the Bochner-Martinelli formula in a more standard form:
where
with is a bounded domain in the finite dimensional complex vector space and is its boundary, which we assume being of class is a point belonging to the interior of 
while is a point belonging to its boundary
is the differential form
with ![\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")
is a continuous function of .And now let’s listen to Mina :
Mina – Brava (1966)
Date: 17 September 2009
Categories: Chronicle, Linux, Mathematics
where
with is a bounded domain in the finite dimensional complex vector space and is its boundary, which we assume being of class is a point belonging to the interior of while is a point belonging to its boundary is the unit hypersurface normal to in (which always exists in the given hypothesis), while 
is its complex orthogonal versor
is the function
is a continuous function of 
Date: 2 September 2009
Categories: Chronicle, Informatics, Mathematics
Com Que Voz – Amália Rodrigues
Date: 27 August 2009
Categories: Chronicle
![{\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]")
![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}")