Stochastic perturbations of convex billiards

We consider a strictly convex billiard table with C 2 boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation distribution corresponds to the physical situation where either the scale of the surface irregularities is smaller than but comparable to the diameter of the reflected object, or the billiard ball is not perfectly rigid. We prove that for a large class of such perturbations the resulting Markov chain is uniformly ergodic, although this is not true in general.Fil: Markarian, R.. Universidad de la Republica. Facultad de Ingeniería; UruguayFil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Sidoravicius, V.. Jardim Botânico; BrasilFil: Tal, F. A.. Universidade de Sao Paulo; BrasilFil: Vares, M. E.. Universidade Federal do Rio de Janeiro; Brasi

Relative expression of hypothetical protein-related genes for Bradyrhizobium diazoefficiens CPAC 7.

ABSTRACT: From the proteomic map of Bradyrhizobium diazoefficiens strain CPAC 7 we selected nine hypothetical protein-related genes and evaluated their relative expression by Realtime quantitative PCR (RT-qPCR). The experiment was performed with two treatments (induced or not with 5 µM genistein). Six out of nine protein-related genes were upregulated in the presence genistein