A study of the effect of molecular and aerosol conditions in the atmosphere on air fluorescence measurements at the Pierre Auger Observatory

The air fluorescence detector of the Pierre Auger Observatory is designed to perforin calorimetric measurements of extensive air showers created by Cosmic rays of above 10(18) eV. To correct these measurements for the effects introduced by atmospheric fluctuations, the Observatory contains a group Of monitoring instruments to record atmospheric conditions across the detector site, ail area exceeding 3000 km(2). The atmospheric data are used extensively in the reconstruction of air showers, and are particularly important for the correct determination of shower energies and the depths of shower maxima. This paper contains a summary of the molecular and aerosol conditions measured at the Pierre Auger Observatory since the start of regular operations in 2004, and includes a discussion of the impact of these measurements oil air shower reconstructions. Between 10(18) and 10(20) eV, the systematic Uncertainties due to all atmospheric effects increase from 4% to 8% in measurements of shower energy, and 4 g cm(-2) to 8 g cm(-2) in measurements of the shower maximum. (C) 2010 Elsevier B.V. All rights reserved.

Lie properties of symmetric elements in group rings

Let * be an involution of a group G extended linearly to the group algebra KG. We prove that if G contains no 2-elements and K is a field of characteristic p, 0 2, then the *-symmetric elements of KG are Lie nilpotent (Lie n-Engel) if and only if KG is Lie nilpotent (Lie n-Engel). (C) 2008 Elsevier Inc. All rights reserved.

Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.