Torsion of rational elliptic curves over quadratic fields

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)_tors and the torsion subgroup E(K)_tors, where K is a quadratic number field

Circumnuclear structure and kinematics in the active galaxy NGC 6951

A study is presented of the central structure and kinematics of the galaxy NGC 6951, by means of broad band B'IJK images and high resolution high dispersion longslit spectroscopy, together with archival HST WFPC2 V and NICMOS2 J and H images. We find that there is evidence of two modes of star formation, in bursts and continuously. The equivalent width of the CaII triplet absorption lines show that, in the metal rich central region, the continuum is dominated by a population of red supergiants. The gaseous and stellar kinematics along three slit position angles, suggest the existence of a hierarchy of disks within disks, whose dynamics are decoupled at the two ILRs, that we find at 180 pc and at 1100 pc. This is supported by the structure seen in the high resolution HST images. The nucleus is spatially resolved within a radius of 1.5 arcsec, just inside the innermost ILR. Outside the iILR, the stellar CaT velocity profile is resolved into two components, associated with the bar and the disk. Several results indicate that this is a dynamically old system. It is thus possible that a nuclear bar has existed in NGC 6951 that drove the gas towards the nucleus, as in the bars within bars scenario, but that this bar has already dissolved by the gas accumulated within the circumnuclear region. We discuss the possibility that the kinematical component inside the iILR could be due to a nuclear outflow produced by the combined effects of SN and SN remnants, or to a nuclear disk, as in the disk within disk scenario that we propose for the fueling of the AGN in NGC 6951.Comment: 14 pages, 16 figures. Accepted for publication in Astronomy and Astrophysics. High resolution images in http://www.iaa.es/~eperez/research/degas.htm

Players Indifferent to Cooperate and Characterizations of the Shapley Value

n this paper we provide new axiomatizations of the Shapley value for TU-games using axioms that are based on relational aspects in the interactions among players. Some of these relational aspects, in particular the economic or social interest of each player in cooperating with each other, can be found embedded in the characteristic function. We define a particular relation among the players that it is based on mutual indifference. The first new axiom expresses that the payoffs of two players who are not indifferent to each other are affected in the same way if they become enemies and do not cooperate with each other anymore. The second new axiom expresses that the payoff of a player is not affected if players to whom it is indifferent leave the game. We show that the Shapley value is characterized by these two axioms together with the well-known efficiency axiom. Further, we show that another axiomatization of the Shapley value is obtained if we replace t he second axiom and efficiency by the axiom which applies the efficiency condition to every class of indifferent players. Finally, we extend the previous results to the case of weighted Shapley values

Science with an ngVLA: Resolved Substructures in Protoplanetary Disks

Terrestrial planets and the cores of giant planets are thought to be built by the collisional agglomeration of solids spanning over 20 orders of magnitude in size within a few million years. However, there is tension between this basic picture of planet formation and standard theoretical assumptions associated with the migration of "pebbles" ($\sim$mm/cm-sized particles) in gas-rich disks and the presumably much longer timescales necessary to assemble ($\sim$km-scale) "planetesimals". To confront these potential theoretical discrepancies with observational constraints, the ideal tracer of the solids concentrated in protoplanetary disk substructures is the 30-100 GHz continuum, which strikes the best balance in sensitivity (emission still bright), optical depth (low enough to reliably estimate densities), and angular resolution (high enough to resolve fine-scale features at disk radii as small as 1 au). With its combination of sensitivity, frequency coverage, and angular resolution, the next-generation VLA will be the only facility that has the capabilities to open up this new window into the physics of planetesimal formation.Comment: To be published in the ASP Monograph Series, Science with a Next-Generation VLA, ed. E. J. Murphy (ASP, San Francisco, CA

Desarrollo de una placa de osteosíntesis personalizada como técnica de fijación y posicionamiento simultáneo del maxilar superior en osteotomías tipo Lefort I en cirugía ortognática

En este estudio se desarrolla una técnica de posicionamiento y fijación para osteotomías tipo Lefort I en cirugía ortognática. En concreto, se lleva a cabo una prueba de concepto de diseño de una placa de osteosíntesis multifunción customizada. Inicialmente se han analizado parámetros influyentes en la morfología y situación de la placa, según lo cual se ha diseñado la placa. Este diseño se ha validado mediante la impresión 3D de prototipos plásticos y ha sido validado por un cirujano maxilofacial especialista en cirugía ortognática. El resultado del diseño CAD (Computer-Aided Design) de la placa de osteosíntesis ha sido exitoso y se ha completado en un tiempo aceptable para una cirugía electiva. Gracias a las características de la placa se prevé que aumente la precisión del procedimiento y que, por tanto, se obtengan mejores resultados clínicos