Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi: 10.1209/0295-5075/95/69902

A test for asymptotic giant branch evolution theories: Planetary Nebulae in the Large Magellanic Cloud

We used a new generation of asymptotic giant branch (AGB) stellar models that include dust formation in the stellar winds to find the links between evolutionary models and the observed properties of a homogeneous sample of Large Magellanic Cloud (LMC) planetary nebulae (PNe). Comparison between the evolutionary yields of elements such as CNO and the corresponding observed chemical abundances is a powerful tool to shed light on evolutionary processes such as hot bottom burning (HBB) and third dredge-up (TDU). We found that the occurrence of HBB is needed to interpret the nitrogen-enriched (log(N/H)+12>8) PNe. In particular, N-rich PNe with the lowest carbon content are nicely reproduced by AGB models of mass M >=6 Mo, whose surface chemistry reflects the pure effects of HBB. PNe with log(N/H)+12<7.5 correspond to ejecta of stars that have not experienced HBB, with initial mass below about 3 Mo. Some of these stars show very large carbon abundances, owing to the many TDU episodes experienced. We found from our LMC PN sample that there is a threshold to the amount of carbon accumulated at AGB surfaces, log(C/H)+12<9. Confirmation of this constraint would indicate that, after the C-star stage is reached,AGBs experience only a few thermal pulses, which suggests a rapid loss of the external mantle, probably owing to the effects of radiation pressure on carbonaceous dust particles present in the circumstellar envelope. The implications of these findings for AGB evolution theories and the need to extend the PN sample currently available are discussed.Comment: 12 pages, 4 figures, 1 table, accepted for publication in MNRAS (2015 July 13; in original form 2015 June 9

Planetary Nebulae in the Small Magellanic Cloud

We analyse the planetary nebulae (PNe) population of the Small Magellanic Cloud (SMC), based on evolutionary models of stars with metallicities in the range $10^{-3} \leq Z \leq 4\times 10^{-3}$ and mass $0.9 M\odot < M < 8M\odot$, evolved through the asymptotic giant branch (AGB) phase. The models used account for dust formation in the circumstellar envelope. To characterise the PNe sample of the SMC, we compare the observed abundances of the various species with the final chemical composition of the AGB models: this study allows us to identify the progenitors of the PNe observed, in terms of mass and chemical composition. According to our interpretation, most of the PNe descend from low-mass ($M < 2 M\odot$) stars, which become carbon rich, after experiencing repeated third dredge-up episodes, during the AGB phase. A fraction of the PNe showing the signature of advanced CNO processing are interpreted as the progeny of massive AGB stars, with mass above $\sim 6 M\odot$, undergoing strong hot bottom burning. The differences with the chemical composition of the PNe population of the Large Magellanic Cloud (LMC) is explained on the basis of the diverse star formation history and age-metallicity relation of the two galaxies. The implications of the present study for some still highly debated points regarding the AGB evolution are also commented.Comment: Accepted for publication in MNRAS, 11 pages, 4 figure

Role of 5 α -dihydrotestosterone in testicular development of gilthead seabream following finasteride administration

In teleosts, spermatogenesis is regulated by pituitary gonadotropins and sex steroids. 5α-dihydrotestosterone (DHT), derived from testosterone (T) through the action of 5α-reductase, has recently been suggested to play a physiologically important role in some fish species. In this study, gilthead seabream, Sparus aurata L., males received an implant of 1μg T/g body mass (bm) or vehicle alone and, 7 days later, 1 mg finasteride (FIN, an inhibitor of 5α-reductase)/kg bm or vehicle. Serum levels of T, 11-ketotestosterone (11KT), DHT and 17β-estradiol (E2), and the mRNA levels of the main enzymes involved in their synthesis, were analysed. T promoted a transient increase in the serum levels of T, 11KT and E2 but a decrease in those of DHT at day 15 following T injection, in accordance with the up-regulation of mRNA levels of the enzymes involved in T transformation to 11KT (coding genes: cyp11b1 and hsd11b) and the down-regulation of mRNA levels of the enzyme responsible for T transformation to DHT (coding gene:srd5a). Interestingly, a similar effect was observed when FIN was in- jected. However, when fish were injected with T and FIN successively (T + FIN), control levels were not re-covered at the end of the experimental period (28 days). DHT seems to regulate E2 serum levels via the down-regulation of mRNA levels of aromatase (coding gene:cyp19a1a), which is needed for the transformation of T into E2. The testis histology, together with the proliferative rates recorded upon T, FIN or T + FIN treatment, suggests that DHT is involved in the onset of the meiotic phase of spermatogenesis.Versión del edito

High resolution spectroscopy of the high velocity hot post-AGB star LS III +52 24 (IRAS 22023+5249)

The first high-resolution (R~50,000) optical spectrum of the B-type star, LS III +52 24, identified as the optical counterpart of the hot post-AGB candidate IRAS 22023+5249 (I22023) is presented. We report the detailed identifications of the observed absorption and emission features in the full wavelength range (4290-9015 A) as well as the atmospheric parameters and photospheric abundances (under the Local Thermodinamic Equilibrium approximation) for the first time. The nebular parameters (Te, Ne) are also derived. We estimate Teff=24,000 K, log g=3.0, xi=7 kms-1 and the derived abundances indicate a slightly metal-deficient evolved star with C/O<1. The observed P-Cygni profiles of hydrogen and helium clearly indicate on-going post-AGB mass loss. The presence of [N II] and [S II] lines and the non-detection of [O III] indicate that photoionisation has just started. The observed spectral features, large heliocentric radial velocity, atmospheric parameters, and chemical composition indicate that I22023 is an evolved post-AGB star belonging to the old disk population. The derived nebular parameters (Te=7000 K, Ne=1.2x104 cm-3) also suggest that I22023 may be evolving into a compact, young low-excitation Planetary Nebula. Our optical spectroscopic analysis together with the recent Spitzer detection of double-dust chemistry (the simultaneous presence of carbonaceous molecules and amorphous silicates) in I22023 and other B-type post-AGB candidates may point to a binary system with a dusty disk as the stellar origin common to the hot post-AGB stars with O-rich central stars.Comment: Accepted for publication in MNRAS (22 pages, 4 figures, and 8 tables). arXiv admin note: substantial text overlap with arXiv:0707.059