Markoff-Rosenberger triples in geometric progression

Solutions of the Markoff-Rosenberger equation ax^2+by^2+cz^2 = dxyz such that their coordinates belong to the ring of integers of a number field and form a geometric progression are studied.Comment: To appear in Acta Mathematica Hungaric

Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio

Lagrangians for Massive Dirac Chiral Superfields

A variant for the superspin one-half massive superparticle in $4D$, $\mathcal{N}=1$, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the supermultiplet are those of the lowest mass dimensions possible: scalar, Dirac and vector fields. Besides the supersymmetric chiral condition, the Dirac superfields are not further constrained, allowing a very straightforward implementation of the path-integral method. The corresponding superpropagators are presented. In addition, an interaction super Yukawa potential, formed by Dirac and scalar chiral superfields, is given in terms of their component fields. The model is first presented for the case of two superspin one-half superparticles related by the charged conjugation operator, but in order to treat the case of neutral superparticles, the Majorana condition on the Dirac superfields is also studied. We compare our proposal with the known models of spinor superfields for the one-half superparticle and show that it is equivalent to them.Comment: 22 pages. Matches published versio

What determines large scale galaxy clustering: halo mass or local density?

Using dark matter simulations we show how halo bias is determined by local density and not by halo mass. This is not totally surprising, as according to the peak-background split model, local density is the property that constraints bias at large scales. Massive haloes have a high clustering because they reside in high density regions. Small haloes can be found in a wide range of environments which determine their clustering amplitudes differently. This contradicts the assumption of standard Halo Occupation Distribution (HOD) models that the bias and occupation of haloes is determined solely by their mass. We show that the bias of central galaxies from semi-analytic models of galaxy formation as a function of luminosity and colour is not correctly predicted by the standard HOD model. Using local density instead of halo mass the HOD model correctly predicts galaxy bias. These results indicate the need to include information about local density and not only mass in order to correctly apply HOD analysis in these galaxy samples. This new model can be readily applied to observations and has the advantage that the galaxy density can be directly observed, in contrast with the dark matter halo mass.Comment: 11 pages, 9 figure

A simulation model for public bike-sharing systems

Urban areas are in need of efficient and sustainable mobility services. Public bicycle sharing systems stand out as a promising alternative and many cities have invested in their deployment. This has led to a continuous and fast implementation of these systems around the world, while at the same time, research works devoted to understand the system dynamics and deriving optimal designs are being developed. In spite of this, many promoting agencies have faced the impossibility of evaluating a system design in advance, increasing the uncertainty on its performance and the risks of failure. This paper describes the development of an agent-based simulation model to emulate a bike-sharing system. The goal is to obtain a tool to evaluate and compare different alternatives for the system design before their implementation. This tool will support the decision-making process in all the stages of implementation, from the strategical planning to the daily operation. The main behavioral patterns and schemes for all agents involved are designed and implemented into a Matlab programming code. The model is validated against real data compiled from the Barcelona’s Bicing system showing good accuracy.Postprint (published version

Prácticas realizadas en el Departamento de Medio Ambiente de SGS TECNOS S.A.

Una vez finalizados y superados los créditos doctrinales, he realizado una estancia de seis semanas en la empresa de SGS TECNOS S.A. En el presente trabajo Fin de Máster se describen los trabajos realizados durante ese período, respetando la confidencialidad y los cumplimientos éticos establecidos.Departamento de Ingeniería Química y Tecnología del Medio AmbienteMáster en Gestión de la Prevención de Riesgos Laborales, Calidad y Medio Ambient

La responsabilidad de los servidores públicos en un estado de derecho (The responsibility of the civil employees in a lawful state)

El Estado de Derecho se está perfeccionando en México con la redefinición de la responsabilidad de los funcionarios en los tres niveles de gobierno. Este ensayo intenta explicar los casos principales de esa responsabilidad para que la sociedad pueda reclamar a sus gobernantes una actuación verdaderamente profesional. The State of Right is being perfected in Mexico with the redefinition of the responsibility of the civil employees in the three levels of government. This test tries to explain the main cases of that responsibility so that the society can demand to its governors a truly professional performance