Portuguese Population in France: a snapshot 25 years after their arrival

In year 2000 Portugal is celebrating the 500th anniversary of the arrival to Brazil. The Portuguese overseas adventure is now five centuries old and more than one third of the Portuguese nationals are living outside their homeland; in France they are the largest foreign community. This paper uses the data from the French Employment Survey (Enqujte de l Emploi) 1994 and 1995 to characterise the Portuguese population and to study individual decisions taken by the Portuguese migrants concerning naturalisation, family, residence and education. As a result of the analysis it seems that the decisions of the younger Portuguese are getting closer to the decisions of their French neighbours, increasing the gap with respect to the decisions of their countrymen who stayed in Portugal. In this very sense, we can say that some assimilation by the Portuguese is occurring in France. There is an educational convergence of the Portuguese migrants in France and the French.

Rheology of fractal networks

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in 1, 2 or 3 dimensions, we are able to express the viscoelasticity of the network as an effective generalised Kelvin-Voigt model with a power law spectrum of retardation times, $\cal L\sim\tau^{\alpha}$. We relate the parameter $\alpha$ with the fractal dimension of the gel. In some regimes ($0<\alpha<1$), we recover the weak power law behaviours of the elastic and viscous moduli with the angular frequencies, $G'\sim G''\sim w^\alpha$, that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for $G'$ and $G''$.Comment: 5 pages, 3 figure

Simple thermodynamics of jet engines

We use the first and second laws of thermodynamics to analyze the behavior of an ideal jet engine. Simple analytical expressions for the thermal efficiency, the overall efficiency, and the reduced thrust are derived. We show that the thermal efficiency depends only on the compression ratio r and on the velocity of the aircraft. The other two performance measures depend also on the ratio of the temperature at the turbine to the inlet temperature in the engine, T-3/T-i. An analysis of these expressions shows that it is not possible to choose an optimal set of values of r and T-3/T-i that maximize both the overall efficiency and thrust. We study how irreversibilities in the compressor and the turbine decrease the overall efficiency of jet engines and show that this effect is more pronounced for smaller T-3/T-i

The BTZ black hole as a Lorentz-flat geometry

It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.Comment: 2 page

Generalized inverses of a sum in rings

Documento submetido para revisão pelos pares. A publicar em "Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 82:1 (2010) 156-164.We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1 − ba in terms of generalized inverses of 1 − ab. In our development we prove that the Drazin index of 1 − ba is equal to the Drazin index of 1 − ab.Fundação para a Ciência e a Tecnologia (FCT) através do programa POCTIMinisterio de Educación y Ciencia of Spain - Project MTM2007-6723