Ambiguities and paradoxes in a competence-based approach to vocational education and training in France

This article aims to show the effects of the prevalence of the competence regime within several sectors of vocational education and training in France. The first part of the article outlines the origin of the concept of competence and the evolution of its meaning. Later, the underlying theoretical and epistemological foundations are examined and two different paradigms are distinguished. The second part of the article focuses on ambiguities and paradoxes of effect of competence approaches, in specific educational programmes in the healthcare professions and social work in France. This study is based on the analysis of a corpus of documents concerning French vocational education and training that use a competence-based approach. (DIPF/Orig.

The geometrical quantity in damped wave equations on a square

The energy in a square membrane $\Omega$ subject to constant viscous damping on a subset $\omega\subset \Omega$ decays exponentially in time as soon as $\omega$ satisfies a geometrical condition known as the "Bardos-Lebeau-Rauch" condition. The rate $\tau(\omega)$ of this decay satisfies $\tau(\omega)= 2 \min(-\mu(\omega), g(\omega))$ (see Lebeau [Math. Phys. Stud. 19 (1996) 73-109]). Here $\mu(\omega)$ denotes the spectral abscissa of the damped wave equation operator and $g(\omega)$ is a number called the geometrical quantity of $\omega$ and defined as follows. A ray in $\Omega$ is the trajectory generated by the free motion of a mass-point in $\Omega$ subject to elastic reflections on the boundary. These reflections obey the law of geometrical optics. The geometrical quantity $g(\omega)$ is then defined as the upper limit (large time asymptotics) of the average trajectory length. We give here an algorithm to compute explicitly $g(\omega)$ when $\omega$ is a finite union of squares

Detecting the spin-orbit misalignment of the super-Earth 55 Cnc e

We present time-resolved spectroscopy of transits of the super-Earth 55 Cnc e using HARPS-N observations. We devised an empirical correction for the "color effect" affecting the radial velocity residuals from the Keplerian fit, which significantly improves their dispersion with respect to the HARPS-N pipeline standard data-reduction. Using our correction, we were able to detect the smallest Rossiter-McLaughlin anomaly amplitude of an exoplanet so far (~60 cm/s). The super-Earth 55 Cnc e is also the smallest exoplanet with a Rossiter-McLaughlin anomaly detection. We measured the sky-projected obliquity lambda = 72.4 (+12.7 -11.5 deg), indicating that the planet orbit is prograde, highly misaligned and nearly polar compared to the stellar equator. The entire 55 Cancri system may have been highly tilted by the presence of a stellar companion.Comment: 11 pages, 7 figure

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of exponential decay of a damped membrane and an approximate controllability result for the bilinear Schr\"odinger equation