Listening comprehension and strategy use: a longitudinal exploration

This paper examines the development of strategy use over 6 months in two lower-intermediate learners of L2 French in secondary schools in England. These learners were selected from a larger sample on the basis of their scores on a recall protocol completed after listening to short passages at two time points: one was consistently a high scorer; the other one, a low scorer. Qualitative data on these two learners’ strategic behaviour were gathered at the two time points from verbal reports made by learners while they were completing a multiple-choice listening task. Our results show a high degree of stability of strategy use over the time period, with pre-existing differences between the high and low scorer persisting. The theoretical and pedagogical implications of these findings are discussed

Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

Integral representations for a generalized Hermite linear functional

In this paper we find new integral representations for the {\it generalized Hermite linear functional} in the real line and the complex plane. As application, new integral representations for the Euler Gamma function are given.Comment: 4 figure