In this article we prove a generalization of Selberg’s lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to questions of Long–Reid and the author.

Background: In vivo dosimetry is a method for estimation of overall error in the delivered dose to the patients at the end of radiotherapy process. In this research, two methods for target dose calculation were evaluated on midline and central axis of photon beams in in vivo dosimetry of thorax fields. Materials and Methods: Entrance and exit doses for anterior and lateral fields of thorax were...

This paper proposes the development of an index to assess rural based on a set 25 demographic, economic, environmental, and social welfare indicators previously selected through Delphi approach. Three widely accepted aggregation methods were then tested: mixed arithmetic/geometric mean without weightings for each indicator; weighted arithmetic using weights generated by panel Principal Componen...

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, a steep pressure gradient and great variation of hydraulic conductivity occur across the wetting front during the infiltration of water.  So, the averaging method applied to compute hydraul...