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

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

Waves in flexural beams with nonlinear adhesive interaction

The paper studies the well posedness of the initial boundary value problem related to the evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachement-detachement of the material during adhesion phenomena. The existence of solutions in energy space and various counterexamples to uniqueness are detailed and suitable numerical simulations are provided

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

Spanish internal migration: is there anything new to say?

Abstract Spanish internal migration has long been resistant to traditional economic explanations. However, this paper examines the data for the period 1999–2006 after considerable changes in the Spanish economy. Moreover, it examines migration at the disaggregated level of Spanish provinces rather than regions, the usual unit of measurement. Using a spatial error model as well as a spatial autoregression model it finds the differentials in wages and unemployment between provinces to be significant explanatory variables. House prices are also important in accounting for the dynamics of internal migration. Les migrations internes en Espagne: qu'y a-t-il de nouveau? Les migrations internes en Espagne résistent, depuis toujours, à des explications économiques traditionnelles. Cependant, la présente communication examine les données relatives à la période 1999–2006, dans le sillage des changements considérables qui sont survenus dans l’économie espagnole. Elle se penche également sur la migration au niveau désagrégé de provinces espagnoles plutôt que de régions, unité de mesure traditionnelle. En utilisant un modèle d'erreur spatiale ainsi qu'un modèle à autorégression spatiale, elle en conclut que les différences sur le plan des salaires et du chômage entre les différentes provinces constituent des variables explicatives significatives. En outre, le prix de l'immobilier résidentiel joue également un rôle important dans l'examen de la dynamique des migrations internes. Migracin interior espaola: Queda algo nuevo por decir? La migración interior española lleva mucho tiempo resistiéndose a las explicaciones económicas tradicionales. No obstante, este artículo examina los datos de 1999–2006, después de considerables cambios en la economía española. Asimismo, examina la migración al nivel desagregado de provincias españolas, en lugar de regiones, que representa la unidad típica de medida. Utilizando un modelo de error espacial, así como un modelo de autorregresión espacial, se descubre que los diferenciales en salarios y empleo entre las provincias son importantes variables explicativas. Los precios de la vivienda también son importantes a la hora de comprender la dinámica de la migración interior.Internal migration, Spain, spatial error model, J61, O15, R23,

The Fabulous Destiny of Richard Dedekind

By using the preliminary results given in [11], we present here a concise and self contained introduction to the construction of the real field as the unique, up to increasing isomorphisms, Dedekind complete totally ordered field. Moreover, we also show the equivalence between the Dedekind completeness property on totally ordered fields and some meaningful well{known notions present in the literature, such as the Cauchy completeness on totally ordered Archimedean fields. This characterization result allows us to correctly encode the Dedekind completeness for totally ordered fields in the general abstract setting of metric spaces. We believe that the essential parts of the paper can be easily accessed by anyone with some experience in abstract mathematical thinking. The paper completes the lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018