On the generalized Feng-Rao numbers of numerical semigroups generated by intervals

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $r^{th}$ Feng-Rao number is obtained.Comment: 23 pages, 6 figure

Summability Properties for Multiplication Operators on Banach Function Spaces

Consider a couple of Banach function spaces X and Y over the same measure space and the space XY of multiplication operators from X into Y . In this paper we develop the setting for characterizing certain summability properties satisfied by the elements of XY . At this end, using the “generalized K¨othe duality” for Banach function spaces, we introduce a new class of norms for spaces consisting of infinite sums of products of the type xy with x ∈ X and y ∈ Y .Universitat Politécnica de Valencia PAID-06-08 Ref. 3093Ministerio de Educación y Ciencia MTM2006-13000-C03-0

Experimental scheme for unambiguous discrimination of linearly independent symmetric states

We propose an optimal discrimination scheme for a case of four linearly independent nonorthogonal symmetric quantum states, based on linear optics only. The probability of discrimination is in agreement with the optimal probability for unambiguous discrimination among N symmetric states [Phys. Lett. A \textbf{250}, 223 (1998)]. The experimental setup can be extended for the case of discrimination among $2^M$ nonorthogonal symmetric quantum states

Carbon and oxygen abundances from recombination lines in low-metallicity star-forming galaxies. Implications for chemical evolution

We present deep echelle spectrophotometry of the brightest emission-line knots of the star-forming galaxies He 2-10, Mkn 1271, NGC 3125, NGC 5408, POX 4, SDSS J1253-0312, Tol 1457-262, Tol 1924-416 and the HII region Hubble V in the Local Group dwarf irregular galaxy NGC 6822. The data have been taken with the Very Large Telescope Ultraviolet-Visual Echelle Spectrograph in the 3100-10420 {\AA} range. We determine electron densities and temperatures of the ionized gas from several emission-line intensity ratios for all the objects. We derive the ionic abundances of C$^{2+}$ and/or O$^{2+}$ from faint pure recombination lines (RLs) in several of the objects, permitting to derive their C/H and C/O ratios. We have explored the chemical evolution at low metallicities analysing the C/O vs. O/H, C/O vs. N/O and C/N vs. O/H relations for Galactic and extragalactic HII regions and comparing with results for halo stars and DLAs. We find that HII regions in star-forming dwarf galaxies occupy a different locus in the C/O vs. O/H diagram than those belonging to the inner discs of spiral galaxies, indicating their different chemical evolution histories, and that the bulk of C in the most metal-poor extragalactic HII regions should have the same origin than in halo stars. The comparison between the C/O ratios in HII regions and in stars of the Galactic thick and thin discs seems to give arguments to support the merging scenario for the origin of the Galactic thick disc. Finally, we find an apparent coupling between C and N enrichment at the usual metallicities determined for HII regions and that this coupling breaks in very low-metallicity objects.Comment: 27 pages, 12 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Quantum tomography via equidistant states

We study the possibility of performing quantum state tomography via equidistant states. This class of states allows us to propose a non-symmetric informationally complete POVM based tomographic scheme. The scheme is defined for odd dimensions and involves an inversion which can be analytically carried out by Fourier transform