2,696 research outputs found
Relaying Simultaneous Multicast Messages
The problem of multicasting multiple messages with the help of a relay, which
may also have an independent message of its own to multicast, is considered. As
a first step to address this general model, referred to as the compound
multiple access channel with a relay (cMACr), the capacity region of the
multiple access channel with a "cognitive" relay is characterized, including
the cases of partial and rate-limited cognition. Achievable rate regions for
the cMACr model are then presented based on decode-and-forward (DF) and
compress-and-forward (CF) relaying strategies. Moreover, an outer bound is
derived for the special case in which each transmitter has a direct link to one
of the receivers while the connection to the other receiver is enabled only
through the relay terminal. Numerical results for the Gaussian channel are also
provided.Comment: This paper was presented at the IEEE Information Theory Workshop,
Volos, Greece, June 200
On Cosmall Abelian Groups
It is a well-known homological fact that every Abelian groupGhas the property that Hom(G,−)com-mutes with direct products. Here we investigate the ‘dual’ property: an Abelian groupGis said to be cosmallif Hom(−,G)commutes with direct products. We show that cosmall groups are cotorsion-free and that nogroup of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a properclass of strongly compact cardinals, then there are no cosmall grou
On Cosmall Abelian Groups
It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups
If the world were a village of 100 people...
Some last-minute statistics to make you think
Radial molecular abundances and gas cooling in starless cores
Aims: We aim to simulate radial profiles of molecular abundances and the gas
temperature in cold and heavily shielded starless cores by combining chemical
and radiative transfer models. Methods: A determination of the dust temperature
in a modified Bonnor-Ebert sphere is used to calculate initial radial molecular
abundance profiles. The abundances of selected cooling molecules corresponding
to two different core ages are then extracted to determine the gas temperature
at two time steps. The calculation is repeated in an iterative process yielding
molecular abundances consistent with the gas temperature. Line emission
profiles for selected substances are calculated using simulated abundance
profiles. Results: The gas temperature is a function of time; the gas heats up
as the core gets older because the cooling molecules are depleted onto grain
surfaces. The contributions of the various cooling molecules to the total
cooling power change with time. Radial chemical abundance profiles are
non-trivial: different species present varying degrees of depletion and in some
cases inward-increasing abundances profiles, even at t > 10^5 years. Line
emission simulations indicate that cores of different ages can present
significantly different line emission profiles, depending on the tracer species
considered. Conclusions: Chemical abundances and the associated line cooling
power change as a function of time. Most chemical species are depleted onto
grain surfaces at densities exceeding ~10^5 cm^-3. Notable exceptions are NH_3
and N2H^+; the latter is largely undepleted even at n_H~10^6 cm-3. On the other
hand, chemical abundances are not significantly developed in regions of low gas
density even at t~10^5 years, revealed by inward-increasing abundance
gradients. The gas temperature can be significantly different from the dust
temperature; this may have implications on core stability.Comment: Accepted for publication in A&A, above abstract shortened to fit
arXiv forma
Searching for O in the SMC:Constraints on Oxygen Chemistry at Low Metallicities
We present a 39 h integration with the Odin satellite on the ground-state
118.75 GHz line of O2 towards the region of strongest molecular emission in the
Small Magellanic Cloud. Our 3sigma upper limit to the O2 integrated intensity
of <0.049 K km/s in a 9'(160 pc) diameter beam corresponds to an upper limit on
the O2/H2 abundance ratio of <1.3E-6. Although a factor of 20 above the best
limit on the O2 abundance obtained for a Galactic source, our result has
interesting implications for understanding oxygen chemistry at sub-solar metal
abundances. We compare our abundance limit to a variety of astrochemical models
and find that, at low metallicities, the low O2 abundance is most likely
produced by the effects of photo-dissociation on molecular cloud structure.
Freeze-out of molecules onto dust grains may also be consistent with the
observed abundance limit, although such models have not yet been run at
sub-solar initial metallicities.Comment: 4 pages, accepted to A&A Letter
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