Level Zero Core Curriculum and Entrance Examination: An Italian Experience

In this paper the mathematical part of the entrance examinations at the Politecnico di Torino is considered; the topics covered are compared with the SEFI Mathematical Working Group Level Zero Core Curriculum. The structure of the examinations is described, and the global results of the examination, in particular Algebra and Trigonometry, are analysed

L'uso della piattaforma Moodle al Politecnico di Torino

La piattaforma Moodle è in uso presso il Politecnico di Torino da almeno 5 anni, con finalità tra di loro molto diverse che spaziano dal Test di Ammissione per tutti i corsi nell'area dell'Ingegneria, ai test di livello per l'inserimento negli insegnamenti della Lingua Inglese, alla verifica della conoscenza della Lingua Italiana per gli studenti stranieri, sino all'utilizzo che sotto descriveremo a titolo di esempio, come parte dell'esame di un insegnamento curricular

BMO spaces on weighted homogeneous trees

We consider an infinite homogeneous tree $\mathcal V$ endowed with the usual metric $d$ defined on graphs and a weighted measure $\mu$. The metric measure space $(\mathcal V,d,\mu)$ is nondoubling and of exponential growth, hence the classical theory of Hardy and $BMO$ spaces does not apply in this setting. We introduce a space $BMO(\mu)$ on $(\mathcal V,d,\mu)$ and investigate some of its properties. We prove in particular that $BMO(\mu)$ can be identified with the dual of a Hardy space $H^1(\mu)$ introduced in a previous work and we investigate the sharp maximal function related with $BMO(\mu)$.Comment: 14 page

Schr\"odinger type propagators, pseudodifferential operators and modulation spaces

We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schr\"odinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents $p,q,r_1,r_2,t_1,t_2 \in [1,\infty]$ of modulation spaces such that a symbol in $M^{p,q}(\mathbb R^{2d})$ gives a pseudodifferential operator that is continuous from $M^{r_1,r_2}(\mathbb R^d)$ into $M^{t_1,t_2}(\mathbb R^d)$.Comment: 25 pages, 2 figures, to appear in J. London Math. So