Cross-connections of the singular transformation semigroup

Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the cross-connections in the semigroup $Sing(X)$ of all non-invertible transformations on a set $X$. The categories involved are characterized as the powerset category $\mathscr{P}(X)$ and the category of partitions $\Pi(X)$. We describe these categories and show how a permutation on $X$ gives rise to a cross-connection. Further we prove that every cross-connection between them is induced by a permutation and construct the regular semigroups that arise from the cross-connections. We show that each of the cross-connection semigroups arising this way is isomorphic to $Sing(X)$. We also describe the right reductive subsemigroups of $Sing(X)$ with the category of principal left ideals isomorphic to $\mathscr{P}(X)$. This study sheds light into the more general theory of cross-connections and also provides an alternate way of studying the structure of $Sing(X)$

The Brown-dwarf Atmosphere Monitoring (BAM) Project II: Multi-epoch monitoring of extremely cool brown dwarfs

With the discovery of Y dwarfs by the WISE mission, the population of field brown dwarfs now extends to objects with temperatures comparable to those of Solar System planets. To investigate the atmospheres of these newly identified brown dwarfs, we have conducted a pilot study monitoring an initial sample of three late T-dwarfs (T6.5, T8 and T8.5) and one Y-dwarf (Y0) for infrared photometric variability at multiple epochs. With J-band imaging, each target was observed for a period of 1.0h to 4.5h per epoch, which covers a significant fraction of the expected rotational period. These measurements represent the first photometric monitoring for these targets. For three of the four targets (2M1047, Ross 458C and WISE0458), multi-epoch monitoring was performed, with the time span between epochs ranging from a few hours to ~2 years. During the first epoch, the T8.5 target WISE0458 exhibited variations with a remarkable min-to-max amplitude of 13%, while the second epoch light curve taken ~2 years later did not note any variability to a 3% upper limit. With an effective temperature of ~600 K, WISE0458 is the coldest variable brown dwarf published to-date, and combined with its high and variable amplitude makes it a fascinating target for detailed follow-up. The three remaining targets showed no significant variations, with a photometric precision between 0.8% and 20.0%, depending on the target brightness. Combining the new results with previous multi-epoch observations of brown dwarfs with spectral types of T5 or later, the currently identified variables have locations on the colour-colour diagram better matched by theoretical models incorporating cloud opacities rather than cloud-free atmospheres. This preliminary result requires further study to determine if there is a definitive link between variability among late-T dwarfs and their location on the colour-colour diagram.Comment: 9 pages, 6 figures, 3 tables, accepted for publication in MNRA

Near room-temperature colossal magnetodielectricity and multiglass properties in partially-disordered La2NiMnO6

We report magnetic, dielectric and magnetodielectric responses of pure monoclinic bulk phase of partially-disordered La2NiMnO6, exhibiting a spectrum of unusual properties and establish that this system intrinsically is a true multiglass with a large magnetodielectric coupling (8-20%) over a wide range of temperatures (150 - 300 K). Specifically, our results establish a unique way to obtain colossal magnetodielectricity, independent of any striction effects, by engineering the asymmetric hopping contribution to the dielectric constant via the tuning of the relative spin orientations between neighboring magnetic ions in a transition metal oxide system. We discuss the role of anti-site (Ni-Mn) disorder in emergence of these unusual properties.Comment: 5 pages, 4 figures, Slightly revised version of previous article in condmat: arXiv:1202.4319v