The isotropic correlation function of plane figures: the triangle case

The knowledge of the isotropic correlation function of a plane figure is useful to determine the correlation function of the cylinders having the plane figure as right-section and a given height as well as to analyze the out of plane intensity collected in grazing incidence small-angle scattering from a film formed by a particulate collection of these cylinders. The correlation function of plane polygons can always be determined in closed algebraic form. Here we report its analytic expression for the case of a triangle. The expressions take four different forms that depend on the relative order among the sides and the heights of the triangle.Comment: 11 pages, 2 figure

Conjugacy theorems for loop reductive group schemes and Lie algebras

The conjugacy of split Cartan subalgebras in the finite dimensional simple case (Chevalley) and in the symmetrizable Kac-Moody case (Peterson-Kac) are fundamental results of the theory of Lie algebras. Among the Kac-Moody Lie algebras the affine algebras stand out. This paper deals with the problem of conjugacy for a class of algebras --extended affine Lie algebras-- that are in a precise sense higher nullity analogues of the affine algebras. Unlike the methods used by Peterson-Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of reductive group schemes developed by Demazure and Grothendieck, and on the work of J. Tits on buildingsComment: Publi\'e dans Bulletin of Mathematical Sciences 4 (2014), 281-32

Study of Hg vacancies in (Hg,Cd)Te after THM growth and post-growth annealing by positron annihilation

Positron lifetime measurements have been performed to study vacancy defects in Hg0.78Cd0.22Te. Post-growth annealing under various Hg vapour pressure conditions have been used to create a well-defined number of Hg vacancies. The sensitivity range of the positron annihilation method was found to be 1015 < cHgvac<1018 cm-3. The obtained experience has been used to investigate THM-grown single crystals. The measured longitudinal and radial dependence of the vacancy concentration can be explained by the temperature profile in the grown (Hg,Cd)Te ingots

Revised reference model for nitric acid

A nearly global set of data on the nitric acid distribution was obtained for seven months by the Limb Infrared Monitor of the Stratosphere (LIMS) experiment on the Nimbus 7 spacecraft. The evaluation of the accuracy, precision, and resolution of these data is described, and a description of the major features of the nitric acid distributions is presented. The zonal mean for nitric acid is distributed in a stratospheric layer that peaks near 30 mb, with the largest mixing ratios occurring in polar regions, especially in winter

Quaternion algebras with the same subfields

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F /K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields

A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

Spectrometry: Report of panel

Spectroscopic measurements are required to define the spectral background and provide the detailed spectral information that is essential for the design of species-specific systems and the analysis of data obtained from them. This function of spectroscopic measurements is expected to be an important part of any tropospheric remote-sensing program, and both emission and absorption spectroscopy are relevant in this context. The data from such observations are of value to tropospheric science in their own right, during the initial phases while species-specific techniques and instruments are under development. In addition, there are a number of unresolved problems in tropospheric radiative transfer and spectroscopy which presently limit the accuracy and reliability of all remote sensing methods. Only through a supporting program of spectroscopic measurements can progress be made in improving the understanding of these aspects of radiative transfer and ultimately reaching the desired confidence in the accuracy to species-specific monitoring techniques