12,272 research outputs found
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 TecnologĂa
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
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. 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
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 and mass , 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 () 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 , 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
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