Linux Day 2009

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Monday, 6 of September of 2010

September 2009
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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

Open Source scientific tools
Basic concepts of the Linux OS
Open Source business models
Programming
Open Souce graphic tools
Virtualization

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:

$w(\boldsymbol{z})=\int_{\partial\Omega}W(\boldsymbol{\zeta})U(\boldsymbol{\zeta }-\boldsymbol{z})$

where

$\Omega\subset\mathbb{C}^n$ with $n>1$ is a bounded domain in the finite dimensional complex vector space and $\partial\Omega$ is its boundary, which we assume being of class $C^1$
$\boldsymbol{z}=(z_1,\dots,z_n)$ is a point belonging to the interior of $\Omega$ while $\boldsymbol{\zeta}\in\partial\Omega$ is a point belonging to its boundary
$U(\boldsymbol{z}-\boldsymbol{\zeta})$ is the differential form

$U(\boldsymbol{z}-\boldsymbol{\zeta})=-\frac{(n-1)!}{(2\pi i)^n} \sum_{k=1}^n (-1)^{k-1}\frac{\bar{\zeta}_k-\bar{z}_k}{|\boldsymbol{z}-\boldsymbol{\zeta}|^{2n}}\mathrm{d}\bar{\boldsymbol{\zeta}}[k]\wedge\mathrm{d}\boldsymbol{\zeta}$

with $\mathrm{d}\bar{\boldsymbol{\zeta}}[k] = \mathrm{d}\bar{\zeta}_1\wedge\cdots \wedge\mathrm{d}\bar{\zeta}_{k-1}\wedge \mathrm{d}\bar{\zeta}_{k+1}\wedge\cdots\wedge \mathrm{d}\bar{\zeta}_n$ .
$W(\boldsymbol{\zeta})$ is a continuous function of $\boldsymbol{\zeta}\in\partial\Omega$ .