BUSCADOR RECOLECTA

[EN] Learning using mobile devices or m-learning is gaining predominance at all educational levels due to its ability to make learning accessible to a wider audience and to its motivational nature, among other reasons. Bringing this learning methodology closer to higher education is essential, especially among those being trained to become a teacher. In turn, the use of educational videos as a teaching resource is increasing at a remarkable rate. Aware of the potential derived from the synergy between this methodology and this teaching resource, this study presents an experience based on learning with mobile devices or m-learning for the design of educational videos about manipulatives for teaching mathematics by primary education student teachers. The results obtained from a questionnaire show a positive influence of the experience on the motivation of primary education student teachers towards the teaching and learning of mathematics and in the development of their teaching competence., Este trabajo se ha realizado en el marco de los Proyectos de Innovación Docente de la Universidad de Oviedo PINN-18-A-0022, PINN-20-A-055 y PINN-20-A-074, y del Proyecto TIN2017-87600-P del Ministerio de Ciencia e Innovación de España. Los autores quieren agradecer a todos los estudiantes para maestro que colaboraron en la experiencia y respondieron al cuestionario.

In this paper some properties of two-determinant pivoting for Neville elimination are presented. In particular, we consider a zero-increasing property and we show an optimal normwise growth factor. Comparisons with other pivoting strategies for Neville elimination and with Gaussian elimination with partial pivoting of almost strictly sign regular matrices are performed. Numerical examples are included.

The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II staircase. We prove that, under an irreducibility condition, the pattern of zero and nonzero entries of an ASSR matrix is preserved by the corresponding combined matrix. Without the irreducibility condition, it is proved that type-I and type-II staircases are still preserved. Illustrative numerical examples are included.

Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices of maximal rank and analyze their QR factorization.

The concept of depth of an almost strictly sign regular matrix is introduced and used to simplify some algorithmic characterizations of these matrices.

The present paper focuses on the study of the conditions under which the covariance matrix of a multivariate Gaussian distribution is totally positive, paying particular attention to multivariate Gaussian distributions that are Gaussian Markov Random Fields. More specifically, it is proven that, if the graph over which the Gaussian Markov Random Field is defined consists of path graphs and the covariances between adjacent variables on the graph are non-negative, then there always exists a reordering of the variables that renders the resulting covariance matrix totally positive. Moreover, this reordering is identified and some cases for which the conditions for the covariance matrix of a multivariate Gaussian distribution to be totally positive are necessary and sufficient are provided.