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

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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 O2_2 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