Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

A Cauchy kernel for slice regular functions

In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.     

Secondary ion mass spectrometric investigation of Au-based composites.

The electrodeposition of thick gold layers plays an important role both in traditional and high-tech productions, such as jewelry and microelectronics, respectively. In this work a secondary ion mass spectrometric study will be presented on Au co-deposits with (sub-)micrometric ceramic powders, in order to harden gold. Mass spectra are used to identify the components deposited, providing evidence of the additives and/or eventual contaminants introduced during electrolysis. Furthermore, analysis of ion depth profiles and the intensity distribution of ionic species along the film were studied.     

Functional rearrangement of 3-Cl or 3,3-diCl-γ-lactams bearing a secondary 1-chloroalkyl substituent at C-4

The study of the reaction with MeONa/MeOH of chlorinated γ-lactams, prepared from the atom transfer radical cyclization of N-allyl-α-perchloroamides, has been extended to the case of substrates carrying an exo halogen atom on a branched carbon. Only with secondary exo C-Cl groups, that are not located on a fused ring, does the functional rearrangement follow the typical transformation route, which with trichloro-lactams can proceed further to give 4-alkylidene derivatives. From a practical point of view, the outcome of the reaction with di- or trichloro N-cinnamylamides is synthetically valuable, affording the 5-methoxy-1H-pyrrol-2(5H)-one or 3-benzylidenepyrrolidine-2,5-dione, respectively, in good to excellent yield.     

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.