Blow-up of the quantum potential for a free particle in one dimension

We derive a non-linear differential equation that must be satisfied by the quantum potential, in the context of the Madelung equations, in one dimension for a particular class of wave functions. In this case, we exhibit explicit conditions leading to the blow-up of the quantum potential of a free particle at the boundary of the compact support of the probability density

A multi-material transport problem and its convex relaxation via rectifiable GG-currents

In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of the transportation depends on the network used to move the masses, as it is common in models studied in branched transportation. The main novelty is that in our model the cost per unit length of the network does not depend only on the total flow, but on the actual quantity of each commodity. This allows to take into account different interactions between the transported goods. We propose an Eulerian formulation of the discrete problem, describing the flow of each commodity through every point of the network. We provide minimal assumptions on the cost, under which existence of solutions can be proved. Moreover, we prove that, under mild additional assumptions, the problem can be rephrased as a mass minimization problem in a class of rectifiable currents with coefficients in a group, allowing to introduce a notion of calibration. The latter result is new even in the well studied framework of the "single-material" branched transportation.Comment: Accepted: SIAM J. Math. Ana

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Education-job (mis)match and interregional migration:Italian university graduates’ transition to work

This paper analyses the micro-level determinants of the education-job (mis)matches of recent university graduates in Italy. As the Italian graduate population has experienced increasing internal migration, we focus in particular on the role of interregional migration in driving education-job match. The methodology takes into account both the endogenous relationship between migration and employment, and the self-selection bias between employment and education-job (mis)match. Using a survey on Italian graduates’ entry into the labour market, we find that whilst migration at the national level is confirmed to have a positive role in both finding a job and decreasing the probability of overeducation, robust differences emerge when looking at the subnational dimension. Indeed, the Northern regions by receiving inflows of Southern graduates that manage to attain a good education-job match in the recipient labour markets, are apparently reaping part of the return to the investment in university education bore in the Sout

Copper(I) complexes from CuX2(X = NO3, BF4, 1 2SO4) and some heterocyclic ligands containing the thioamido group

Complexes of copper(I) CuLnX(n = 2, 3; X = NO3, BF4 1 2SO4) have been obtained by reacting the corresponding copper(II) salts with the following ligands HNCH2·CH2X·C = S (where X = NH, NMe, NEt, S, O and CH2). All the ligands bind the metal through the thioketonic sulphur, as shown by the IR spectroscopy. The copper(I) seems always to realize a trigonal planar geometry both with three molecules of ligands and with two ligands and