Invariant tori for commuting Hamiltonian PDEs

We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an $r$-parameter family of $r$-dimensional invariant tori. The parameters belong to a Cantor-like set. The proof is based on the Lyapunof-Schmidt decomposition and on the standard implicit function theorem. Some of the persistent tori are resonant. We also give an application to the nonlinear wave equation with periodic boundary conditions on a segment and to a system of coupled beam equations. In the first case we construct 2 dimensional tori, while in the second case we construct 3 dimensional tori

The small molecule specific EphB4 kinase inhibitor NVP-BHG712 inhibits VEGF driven angiogenesis

EphB4 and its cognitive ligand ephrinB2 play an important role in embryonic vessel development and vascular remodeling. In addition, several reports suggest that this receptor ligand pair is also involved in pathologic vessel formation in adults including tumor angiogenesis. Eph/ephrin signaling is a complex phenomena characterized by receptor forward signaling through the tyrosine kinase of the receptor and ephrin reverse signaling through various protein–protein interaction domains and phosphorylation motifs of the ephrin ligands. Therefore, interfering with EphR/ephrin signaling by the means of targeted gene ablation, soluble receptors, dominant negative mutants or antisense molecules often does not allow to discriminate between inhibition of Eph/ephrin forward and reverse signaling. We developed a specific small molecular weight kinase inhibitor of the EphB4 kinase, NVP-BHG712, which inhibits EphB4 kinase activity in the low nanomolar range in cellular assays showed high selectivity for targeting the EphB4 kinase when profiled against other kinases in biochemical as well as in cell based assays. Furthermore, NVP-BHG712 shows excellent pharmacokinetic properties and potently inhibits EphB4 autophosphorylation in tissues after oral administration. In vivo, NVP-BHG712 inhibits VEGF driven vessel formation, while it has only little effects on VEGF receptor (VEGFR) activity in vitro or in cellular assays. The data shown here suggest a close cross talk between the VEGFR and EphR signaling during vessel formation. In addition to its established function in vascular remodeling and endothelial arterio-venous differentiation, EphB4 forward signaling appears to be an important mediator of VEGF induced angiogenesis since inhibition of EphB4 forward signaling is sufficient to inhibit VEGF induced angiogenesis

E-learning in secondary–tertiary transition in mathematics: for what purpose?

Mathematics is a challenging subject for many science freshmen, and failing mathematics exams is a major factor in university dropout rates. Many factors, including metacognitive, affective and linguistic ones, play a role in students’ difficulties in mathematics. Starting from this perspective, we conducted a theoretical exploration of the potential of online environments in helping students counteract the mathematical difficulties they face in the transition from secondary school to university. Although this secondary–tertiary transition and the use of technology are both widely researched issues in mathematics education, the potential of technology in helping students in the “rite of passage” to tertiary education has not yet been researched. This paper reports on the developed theoretical framework and on the preliminary findings from the implementation of an e-learning course that we designed with the aim of supporting students in the critical phase of transition from secondary school to university

The impact of e-learning on mathematics education: some experiences at university level

The aim of this paper is to illustrate a study about the use of some e-learning platforms for the teaching and learning of Mathematics at University level. The development and the spreading of Internet has allowed the access to a great amount of information and resources. The impact on education and training was unavoidable. The e-Learning Programme 0 launched by the European Commission is directed to the development of the potential offered by Internet to reach a greater access to Learning and Training and stresses «the need for innovative pedagogical approaches and for ambitious objectives regarding learning quality and easy access to e-learning resources and services»

FINVALI 2005 - Aree scientifiche: percorsi e risultati

Si presenta l'attività di ricerca del PROGETTO FINALIZZATO “FINVALI 2005”: obiettivi cognitivi, saperi minimi e linguaggi nelle prove nazionali di fine ciclo relativamente all'area matematica e all’area delle scienze sperimentali