Resolvent estimates for 2 dimensional perturbations of plane Couette Flow

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the L_2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that the problem can be reduced to estimating the solution of a homogeneous ordinary differential equation with non-homogeneous boundary conditions. Numerical approximations indicate that the norm of the resolvent is proportional to R in the whole region of interest.Comment: 16 pages, 4 figures. A mistake in the proof of Theorem 1 was corrected. The presentation was changed a little, and typos were correcte

A mass transportation approach for Sobolev inequalities in variable exponent spaces

In this paper we provide a proof of the Sobolev-Poincar\'e inequality for variable exponent spaces by means of mass transportation methods. The importance of this approach is that the method is exible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result obtained by Fan.Comment: 12 page

Facultades, funciones y atribuiciones de los miembros del H. ayuntamiento municipal

El presente ensayo tiene como finalidad analizar el sentido histórico del Municipio el marco jurídico de las funciones, facultades y atribuciones de los integrantes del Ayuntamiento Municipal, y la Ley Orgánica Municipal del Estado de México así como el Bando Municipal de los Ayuntamientos, dentro de los cuales se encuentran uno a uno marcadas las facultades de los servidores públicos, tan es así que no se nos debe olvidar que los gobiernos por medio de las personas que en su momento los representan, deben de hacer valer lo que al pie de la letra dicen las leyes, sin que exista dolo o vicio alguno en su aplicación