On the classification of complete area-stationary and stable surfaces in the sub-Riemannian Sol manifold

We study the classification of area-stationary and stable $C^2$ regular surfaces in the space of the rigid motions of the Minkowski plane E(1,1), equipped with its sub-Riemannian structure. We construct examples of area-stationary surfaces that are not foliated by sub-Riemannian geodesics. We also prove that there exist an infinite number of $C^2$ area-stationary surfaces with a singular curve. Finally we show the stability of $C^2$ area-stationary surfaces foliated by sub-Riemannian geodesics

Salt marsh harvest mouse abundance and site use in a managed marsh

The salt marsh harvest mouse (Reithrodontomys raviventris) is a federal and California listed endangered mammal endemic to the San Francisco Bay. The objectives of this research were to determine habitat use of endangered salt marsh harvest mice in a managed marsh in Fremont California, and to evaluate whether managed flooding of the marsh provides favorable habitat conditions for the mice. In addition, this research explores the effectiveness of using mark-recapture model selection analysis to estimate capture probability, survival, and population growth rate for salt marsh harvest mice. Mice were captured for four nights per month between May and August, 2008. Thirty-six unique salt marsh harvest mice were captured for a catch per 100 nights of trap effort of 1.9. The sex ratio of male to female mice was skewed towards males with a sex of 2.3:1. Salt marsh harvest mice were distributed randomly throughout the marsh and no relationships were found between mice distribution and pickleweed salinity, pickleweed height, distance to levees, distance to dry or filled water bodies, percent cover of vegetation, or sympatric rodents. The findings of this study indicate that catch-per-trap-effort, the current standard method to estimate salt marsh harvest mice populations, may not be accurate. The results of this study can be used by managers of salt marsh harvest mice habitat to manage and estimate mouse populations

Clusters of galaxies and variation of the fine structure constant

We propose a new method to probe for variations in the fine structure constant alpha using clusters of galaxies, opening up a window on a new redshift range for such constraints. Hot clusters shine in the X-ray mainly due to bremsstrahlung, while they leave an imprint on the CMB frequency spectrum through the Sunyaev-Zel'dovich effect. These two physical processes can be characterized by the integrated Comptonization parameter Y_SZ DA^2 and its X-ray counterpart, the Y_X parameter. The ratio of these two quantities is expected to be constant from numerical simulations and current observations. We show that this fact can be exploited to constrain alpha, as the ratio of the two parameters depends on the fine structure constant as alpha^{3.5}. We determine current constraints from a combination of Planck SZ and XMM-Newton data, testing different models of variation of alpha. When fitting for a constant value of alpha, we find that current constraints are at the 1% level, comparable with current CMB constraints. We discuss strategies for further improving these constraints by almost an order of magnitude.Comment: 7 pages, 3 figure