A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers

Recently obtained recurrence formulae for relativistic hydrogenic radial matrix elements are cast in a simpler and perhaps more useful form. This is achieved with the help of a new relation between the $r^a$ and the $\beta r^b$ terms ($\beta$ is a $4\times 4$ Dirac matrix and $a, b$ are constants) in the atomic matrix elements.Comment: 7 pages, no figure

NGC 6705 a young α\alpha-enhanced Open Cluster from OCCASO data

The stellar [$\alpha$/Fe] abundance is sometimes used as a proxy for stellar age, following standard chemical evolution models for the Galaxy, as seen by different observational results. In this work we show that the Open Cluster NGC6705/M11 has a significant $\alpha$-enhancement [$\alpha$/Fe]$>0.1$ dex, despite its young age ($\sim$300 Myr), challenging the current paradigm. We use high resolution (R$>65,000$) high signal-to-noise ($\sim$70) spectra of 8 Red Clump stars, acquired within the OCCASO survey. We determine very accurate chemical abundances of several $\alpha$ elements, using an equivalent width methodology (Si, Ca and Ti), and spectral synthesis fits (Mg and O). We obtain [Si/Fe]=$0.13\pm0.05$, [Mg/Fe]=$0.14\pm0.07$, [O/Fe]=$0.17\pm0.07$, [Ca/Fe]=$0.06\pm0.05$ and [Ti/Fe]=$0.03\pm0.03$. Our results place these cluster within the group of young [$\alpha$/Fe]-enhanced field stars recently found by several authors in the literature. The ages of our stars have an uncertainty of around 50 Myr, much more precise than for field stars. By integrating the cluster's orbit in several non-axisymmetric Galactic potentials, we establish the M11's most likely birth radius to lie between 6.8-7.5 kpc from the Galactic center, not far from its current position. With the robust Open Cluster age scale, our results prove that a moderate [$\alpha$/Fe]-enhancement is no guarantee for a star to be old, and that not all $\alpha$-enhanced stars can be explained with an evolved blue straggler scenario. Based on our orbit calculations, we further argue against a Galactic bar origin of M11.Comment: 10 pages, 6 figures, accepted in A&

Relativistic quantum mechanics of a Dirac oscillator

The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in quantum chromodynamics. These considerations should be enough for demonstrating that the Dirac oscillator can be an excellent example in relativistic quantum mechanics. In this paper we offer a solution to the problem and discuss some of its properties. We also discuss a physical picture for the Dirac oscillator's non-standard interaction, showing how it arises on describing the behaviour of a neutral particle carrying an anomalous magnetic moment and moving inside an uniformly charged sphere.Comment: 19 pages, 1 figur

From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Simulador de negocios CAPSTONE: Análisis de la empresa Digby

El primer capítulo de este trabajo presenta el marco teóric,o que permite explicar la definición de estrategia y su importancia en el desarrollo de las empresas; se ejemplifica a través de análisis de casos las principales teorías y herramientas para la aplicación de esta. El capítulo dos, es una explicación detallada de la competencia de CAPSTONE, en las que se discutirán las estrategias genéricas, desarrollo de toma de decisiones, preferencias de mercado y accesibilidad con los clientes. Además, se definirá la estrategia a seguir por parte de la compañía Digby para los siguientes ocho años de operación. En los capítulos tres al seis se detallará un análisis de los resultados y las condiciones del mercado de la industria de los sensores, así como las oportunidades de mejorar de la estrategia establecida por los ejecutivos para ser una empresa líder en el mercado. Por último, en el capítulo siete, se realizan las conclusiones del simulador, análisis del curso y reflexión del posgrado

Exposición de curvas y superficies: una experiencia extraacadémica universitaria

En este artículo se comenta una experiencia extraacadémica realizada por un grupo de alumnos universitarios de Matemáticas, juntamente con su profesor, en el marco de la Semana de las Matemáticas organizada por la Facultad de Matemáticas de Sevilla para conmemorar el Año Mundial de las Matemáticas (Año 2000). La citada experiencia consistió en la realización y montaje de una Exposición de Curvas y Superficies, cuyos objetivos generales, desarrollo y conclusiones finales constituyen la base de este trabajo