Complete families of commuting functions for coisotropic Hamiltonian actions

Let G be an algebraic group over a field F of characteristic zero, with Lie algebra g=Lie(G). The dual space g^* equipped with the Kirillov bracket is a Poisson variety and each irreducible G-invariant subvariety X\subset g^* carries the induced Poisson structure. We prove that there is a family of algebraically independent polynomial functions {f_1,...f_l} on X, which pairwise commute with respect to the Poisson bracket and such that l=(dim X+tr.deg F(X)^G)/2. We also discuss several applications of this result to complete integrability of Hamiltonian systems on symplectic Hamiltonian G-varieties of corank zero and 2.Comment: Changed presentatio

Evidence for Extremely High Dust Polarization Efficiency in NGC 3184

Recent studies have found the Type II-plateau supernova (SN) 1999gi to be highly polarized (p_max = 5.8%, where p_max is the highest degree of polarization measured in the optical bandpass; Leonard & Filippenko 2001) and minimally reddened (E[B-V] = 0.21 +/- 0.09 mag; Leonard et al. 2002). From multiple lines of evidence, including the convincing fit of a ``Serkowski'' interstellar polarization (ISP) curve to the continuum polarization shape, we conclude that the bulk of the observed polarization is likely due to dust along the line of sight (l-o-s), and is not intrinsic to SN 1999gi. We present new spectropolarimetric observations of four distant Galactic stars close to the l-o-s to SN 1999gi (two are within 0.02 degrees), and find that all are null to within 0.2%, effectively eliminating Galactic dust as the cause of the high polarization. The high ISP coupled with the low reddening implies an extraordinarily high polarization efficiency for the dust along this l-o-s in NGC 3184: ISP / E(B-V) = 31^{+22}_{-9} % mag^{-1}. This is inconsistent with the empirical Galactic limit (ISP / E[B-V] < 9% mag^{-1}), and represents the highest polarization efficiency yet confirmed for a single sight line in either the Milky Way or an external galaxy.Comment: 27 pages, accepted for publication by the Astronomical Journa

Study of a quasi-microscope design for planetary landers

The Viking Lander fascimile camera, in its present form, provides for a minimum object distance of 1.9 meters, at which distance its resolution of 0.0007 radian provides an object resolution of 1.33 millimeters. It was deemed desirable, especially for follow-on Viking missions, to provide means for examing Martian terrain at resolutions considerably higher than that now provided. This led to the concept of quasi-microscope, an attachment to be used in conjunction with the fascimile camera to convert it to a low power microscope. The results are reported of an investigation to consider alternate optical configurations for the quasi-microscope and to develop optical designs for the selected system or systems. Initial requirements included consideration of object resolutions in the range of 2 to 50 micrometers, an available field of view of the order of 500 pixels, and no significant modifications to the fascimile camera

Spin-orbit coupled cold exciton condensates

We analyze theoretically the dynamics of degenerate condensate of cold indirect excitons. We account for both linear spin dependent terms arising from spin-orbit interaction of Rashba and Dresselhaus types and non-linear terms transforming a pair of bright excitons into a pair of dark ones. We show that both terms should lead to the qualitative changes in the dynamics of cold exciton droplets in the real space and time.Comment: 14 pages, 7 figure

Global Solar Radiation Annual Profile, Causes and Seasonal Effects, at Ilorin, Nigeria

The data of short-wave global (total) solar radiation of 4 years (1995-1998) at Ilorin (8˚ 34′ N, 4˚ 34′ E), Nigeria was used to study the characteristic behavior of SW- global solar radiation in the tropics. To do this, its weekly average was plotted and analyzed with respect to the atmospheric constituents responsible for the behavior. On the profile obtained, two “Wells” of unequal size and depth were identified; a “hill” and a “plateau” representing the potentials of the radiation were also identified in a 52 - week year. These features were associated with seasons of the year and the radiation potentials obtainable in the region. The size of the Wells indicates the time prevalence of the atmospheric constituents causing the Wells and the length of the respective season, while the depth indicates the amount and severity of the constituents. The “Wells” and the “Plateau” constitute 3 seasons in a 52- week year