A third HI 21-cm absorption system in the sight-line of MG J0414+0534: A redshift for Object X?

We report the detection of a third HI 21-cm absorber in the sight-line towards the z=2.64 quasar MG J0414+0534 (4C +05.19). In addition to the absorption at the host redshift and in the z=0.96 gravitational lens, we find, through a decimetre-wave spectral scan towards this source, strong absorption at z=0.38. We believe this may be associated with "Object X", an additional feature apparent in the field of the lensing galaxy and lensed images, on the basis of its close proximity to the quasar images and the possible detection of the [OIII] doublet in a published optical spectrum. If real, the strength of the [OIII] emission would suggest the presence of an active galactic nucleus, or a gas-rich galaxy undergoing rapid star formation, either of which is consistent with the strong outflows apparent in the 21-cm spectrum. Although this is the strongest intervening 21-cm absorber yet found, simultaneous observations failed to detect any of the 18-cm OH lines at the 21-cm redshift. This suggests that, as for the lensing galaxy, this is not the primary location of the intervening material responsible for the very red colour of MG J0414+0534.Comment: 5 pages, accepted by MNRAS Letter

Rediscovery of Ooline, Cadellia pentastylis, near Gunnedah : notes on the habitat and ecology of this dry rainforest tree

Cadellia pentastylis F.Muell., (family Surianaceae), a dry rainforest tree with a conservation listing of Vulnerable at state and national levels, was first collected from the Gunnedah area by the botanical collector J.L. Boorman in 1907. We report the first record of Cadellia pentastylis from the Gunnedah area (30°58’49’’S, 150°15’15’’E) since 1907, and provide details of the community and habitat where it occurs, on the lower slopes of Black Jack Mountain. Although this population is one of the smallest in New South Wales, it is significant as it is at its southern distributional limit, and is found adjacent to semi-evergreen vine thicket, another type of dry rainforest, on the same hillslope. We list the New South Wales occurrences of this species and discuss aspects of its flowering phenology

Quantum Exchangeable Sequences of Algebras

We extend the notion of quantum exchangeability, introduced by K\"ostler and Speicher in arXiv:0807.0677, to sequences (\rho_1,\rho_2,...c) of homomorphisms from an algebra C into a noncommutative probability space (A,\phi), and prove a free de Finetti theorem: an infinite quantum exchangeable sequence (\rho_1,\rho_2,...c) is freely independent and identically distributed with respect to a conditional expectation. As a corollary we obtain a free analogue of the Hewitt Savage zero-one law. As in the classical case, the theorem fails for finite sequences. We give a characterization of finite quantum exchangeable sequences, which can be viewed as a noncommutative analogue of sampling without replacement. We then give an approximation to how far a finite quantum exchangeable sequence is from being freely independent with amalgamation.Comment: Added comments and reference [8], final version to appear in Indiana Univ. Math. Journa