On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

A PDE model for computing the optical flow

[EN] In this paper we present a new model for optical flow calculation using a variational formulation which preserves discontinuities of the flow much better than classical methods. We study the Euler-Lagrange equations asociated to the variational problem. In the case of quadratic energy, we show the existence and uniqueness of the corresponding evolution problem. Since our method avoid linearization in the optical flow constraint, it can recover large displacement in the scene. We avoid convergence to irrelevant local minima by embedding our method into a linear scale-space framework and using a focusing strategy from coarse to fine scales.

Las ascensión de los Iriarte. A propósito de la relación entre políticos y literatos en la España del absolutismo borbónico

[ES]Al amparo del tío paterno, que llamó a los sobrinos a la corte y supo servirse de sus influencias para situarlos convenientemente, los Iriarte constituyeron un importante núcleo intelectual y político en la España del siglo XVIII. A pesar de su singularidad, la formidable ascensión del clan familiar no ha sido suficientemente explicada, a pesar de que en ella se concitan de manera ejemplar las particulares circunstancias que orientaron las relaciones entre políticos y literatos en la España del absolutismo borbónico.