Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDE) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.Comment: 16 pages, 6 figure

Perfil de la situación de la mujer en las cooperativas de trabajo en España

El artículo analiza los datos de un estudio sobre la situación de la mujer en las cooperativas de trabajo: su vinculación con la cooperativa, categoría profesional, cualificación, conciliación laboral y familiar, en comparación con una investigación realizada en 2004, así como respecto de la mujer en España y UE

The Erdős–Faber–Lovász conjecture for dense hypergraphs

AbstractA hypergraph, having n edges, is linear if no two distinct edges intersect in more than one vertex, and is dense if its minimum degree is greater than n. A well-known conjecture of Erdős, Faber and Lovász states that if a linear hypergraph, H, has n edges, each of size n, then there is a n-vertex colouring of the hypergraph in such a way that each edge contains vertices of all the colours. In this note we present a proof of the conjecture provided the hypergraph obtained from H by deleting the vertices of degree one is dense

Integración de la videoconferencia en la educación a distancia

El objetivo de este trabajo es sugerir, de forma general, cómo puede integrarse la videoconferencia en la enseñanza-aprendizaje a distancia, teniendo en cuenta sus características y las características de la educación a distancia tradicional (UNED).The objetive of this papper is to define a general way to integrate the videoconference in the Teaching-Learning Distance, attending its characteristics and the educational environment itself

Profile of the situation of women in worker's cooperatives in Spain

El artículo analiza los datos de un estudio sobre la situación de la mujer en las cooperativas de trabajo: su vinculación con la cooperativa, categoría profesional, cualificación, conciliación laboral y familiar, en comparación con una investigación realizada en 2004, así como respecto de la mujer en España y UE.The article analyzes data from a study on the situation of women in the cooperative work: its relationship with the cooperative, professional, qualifications, work-life balance, compared to a survey conducted in 2004 and on the Women in Spain and EU