The Brown Dwarf Kinematics Project (BDKP). III. Parallaxes for 70 Ultracool Dwarfs

We report parallax measurements for 70 ultracool dwarfs (UCDs). Using both literature values and our sample, we report new polynomial relations between spectral type and M$_{JHK}$. Including resolved L/T transition binaries in the relations, we find no reason to differentiate between a "bright" (unresolved binary) and "faint" (single source) sample across the L/T boundary. Isolating early T dwarfs, we find that the brightening of T0-T4 sources is prominent in M$_{J}$ where there is a [1.2 - 1.4] magnitude difference. A similar yet dampened brightening of [0.3 - 0.5] magnitude happens at M$_{H}$ and a plateau or dimming of [-0.2 - -0.3] magnitude is seen in M$_{K}$. Comparing with evolutionary models that vary gravity, metallicity, and cloud thickness we find that a near constant temperature of 1200 $\pm$100 K along a narrow spectral subtype of T0-T4 is required to account for the brightening and color magnitude diagram of the L-dwarf/T-dwarf transition. Furthermore, there is a significant population of both L and T dwarfs which are red or potentially "ultra-cloudy" compared to the models, many of which are known to be young indicating a correlation between enhanced photospheric dust and youth. For the low surface-gravity or young companion L dwarfs we find that 8 out of 10 are at least [0.2-1.0] magnitude underluminous in M$_{JH}$ and/or M$_{K}$ compared to equivalent spectral type objects. We speculate that this is a consequence of increased dust opacity and conclude that low-surface gravity L dwarfs require a completely new spectral-type/absolute magnitude polynomial for analysis.Comment: 65 pages, Accepted for publication to Ap

Competition and Relational Contracts: The Role of Unemployment as a Disciplinary Device

When unemployment prevails, relations with a particular firm are valuable for workers. As a consequence, a worker may adhere to an implicit agreement to provide high effort, even when performance is not third-party enforceable. But can implicit agreements – or relational contracts – also motivate high worker performance when the labor market is tight? We examine this question by implementing an experimental market in which there is an excess demand for labor and the performance of workers is not third-party enforceable. We show that relational contracts emerge in which firms reward performing workers with wages that exceed the going market rate. This motivates workers to provide high effort, even though they could shirk and switch firms. Our results thus suggest that unemployment is not a necessary device to motivate workers. We also discuss how market conditions affect relational contracting by comparing identical labor markets with excess supply and excess demand for labor. Long-term relationships turn out to be less frequent when there is excess demand for labor compared to a market characterized by unemployment. Surprisingly though, this does not compromise market performance.relational contracts, involuntary unemployment

The Quantum Double in Integrable Quantum Field Theory

Various aspects of recent works on affine quantum group symmetry of integrable 2d quantum field theory are reviewed and further clarified. A geometrical meaning is given to the quantum double, and other properties of quantum groups. Multiplicative presentations of the Yangian double are analyzed.Comment: 43 page

Statistics of the occupation time for a class of Gaussian Markov processes

We revisit the work of Dhar and Majumdar [Phys. Rev. E 59, 6413 (1999)] on the limiting distribution of the temporal mean M_{t}=t^{-1}\int_{0}^{t}du \sign y_{u}, for a Gaussian Markovian process $y_{t}$ depending on a parameter $\alpha$, which can be interpreted as Brownian motion in the scale of time $t^{\prime}=t^{2\alpha}$. This quantity, for short the mean `magnetization', is simply related to the occupation time of the process, that is the length of time spent on one side of the origin up to time t. Using the fact that the intervals between sign changes of the process form a renewal process in the time scale t', we determine recursively the moments of the mean magnetization. We also find an integral equation for the distribution of $M_{t}$. This allows a local analysis of this distribution in the persistence region $(M_t\to\pm1)$, as well as its asymptotic analysis in the regime where $\alpha$ is large. We finally put the results thus found in perspective with those obtained by Dhar and Majumdar by another method, based on a formalism due to Kac.Comment: latex, 31 page

Blocks with quaternion defect group over a 2-adic ring: the case \tilde{A}_4

Except for blocks with a cyclic or Klein four defect group, it is not known in general whether the Morita equivalence class of a block algebra over a field of prime characteristic determines that of the corresponding block algebra over a p-adic ring. We prove this to be the case when the defect group is quaternion of order 8 and the block algebra over an algebraically closed field k of characteristic 2 is Morita equivalent to $k\tilde A_4$. The main ingredients are Erdmann's classification of tame blocks and work of Cabanes and Picaronny on perfect isometries between tame blocks