Superregular matrices and applications to convolutional codes

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.

Study and development of UV photodetectors envisaging COMPASS RICH-1 upgrade and applications

COMPASS is an experiment at CERN’s SPS whose goal is to study hadron structure and spectroscopy. The experiment includes a wide acceptance RICH detector, operating since 2001 and subject to a major upgrade of the central region of its photodetectors in 2006. The remaining 75% of the photodetection area are still using MWPCs from the original design, who suffer from limitations in gain due to aging of the photocathodes from ion bombardment and due to ion-induced instabilities. Besides the mentioned limitations, the increased luminosity conditions expected for the upcoming years of the experiment make an upgrade to the remaining detectors pertinent. This upgrade should be accomplished in 2016, using hybrid detectors composed of ThGEMs and MICROMEGAS. This work presents the study, development and characterization of gaseous photon detectors envisaging the foreseen upgrade, and the progress in production and evaluation techniques necessary to reach increasingly larger area detectors with the performances required. It includes reports on the studies performed under particle beam environment of such detectors. MPGD structures can also be used in a variety of other applications, of which nuclear medical imaging is a notorious example. This work includes, additionally, the initial steps in simulating, assembling and characterizing a prototype of a gaseous detector for application as a Compton Camera.

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.