Automatic Deduction in Dynamic Geometry using Sage

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.Comment: In Proceedings THedu'11, arXiv:1202.453

Charge ordering at the interface in (LaMnO3_3)2n_{2n}/(SrMnO3_3)n_n superlattices as the origin of their insulating state

We have performed ab initio calculations within the LDA+U method in the multilayered system (LaMnO$_3$)$_{2n}$ / (SrMnO$_3$)$_n$. Our results suggest a charge-ordered state that alternates Mn$^{3+}$ and Mn$^{4+}$ cations in a checkerboard in-plane pattern is developed at the interfacial layer, leading to a gap opening. Such an interfacial charge-ordered situation would be the energetically favored reconstruction between LaMnO$_3$ and SrMnO$_3$. This helps understanding the insulating behavior observed experimentally in these multilayers at intermediate values of $n$, whose origin is known to be due to some interfacial mechanism.Comment: 5 pages, 4 figure

La evolución del concepto Influencer y su repercusión en los eventos de moda. Tendencias de la comunicación y la creatividad en el S.XXI

Actualmente el fenómeno de los influencers está en auge. Las marcas recurren cada vez más a ellos para dar visibilidad o ampliar el público de determinados eventos en la industria de la moda, en la que centraremos nuestro estudio. Analizaremos el nacimiento del concepto, así como su evolución y su utilidad a nivel empresarial y, más en concreto, en los eventos de moda.Grado en Publicidad y Relaciones Pública