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

Kinematic study of planetary nebulae in NGC 6822

By measuring precise radial velocities of planetary nebulae (which belong to the intermediate age population), H II regions, and A-type supergiant stars (which are members of the young population) in NGC 6822, we aim to determine if both types of population share the kinematics of the disk of H I found in this galaxy. Spectroscopic data for four planetary nebulae were obtained with the high spectral resolution spectrograph Magellan Inamori Kyocera Echelle (MIKE) on the Magellan telescope at Las Campanas Observatory. Data for other three PNe and one H II region were obtained from the SPM Catalog of Extragalactic Planetary Nebulae which employed the Manchester Echelle Spectrometer attached to the 2.1m telescope at the Observatorio Astron\'omico Nacional, M\'exico. In the wavelength calibrated spectra, the heliocentric radial velocities were measured with a precision better than 5-6 km s$^{-1}$. Data for three additional H II regions and a couple of A-type supergiant stars were collected from the literature. The heliocentric radial velocities of the different objects were compared to the velocities of the H i disk at the same position. From the analysis of radial velocities it is found that H II regions and A-type supergiants do share the kinematics of the H I disk at the same position, as expected for these young objects. On the contrary, planetary nebula velocities differ significantly from that of the H I at the same position. The kinematics of planetary nebulae is independent from the young population kinematics and it is closer to the behavior shown by carbon stars, which are intermediate-age members of the stellar spheroid existing in this galaxy. Our results are confirming that there are at least two very different kinematical systems in NGC 6822

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