Approach to the Steady State in Kinetic Models with Thermal Reservoirs at Different Temperatures

We continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in Carlen et al. (Braz J Probab Stat 29:372–386, 2015), we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not spatially uniform. Making a further simplification of our models, we then prove non-existence of such NESS and exponential approach to the unique spatially uniform NESS (with a computably boundable rate). The method of proof relies on refined Doeblin estimates and other probabilistic techniques, and is quite different form the analysis in Carlen et al. (Braz J Probab Stat 29:372–386, 2015) that was based on contraction mapping methods.     

Singular Hartree equation in fractional perturbed Sobolev spaces

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.     

On the Role of Spin in Quantum Mechanics

From the invariance properties of the Schrödinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an external motion, which can be interpreted as the motion of the centre of mass, and an internal one, whose presence disappears in the classical limit. The latter is caused by the spin of the particle, whatever is its actual value (different from zero). The quantum potential in the Schrödinger equation, which is responsible of the quantum effects of the system, is then completely determined from the properties of the internal motion, and its unusual properties have a simple and physical explanation in the present context. From the impossibility to fix the initial conditions relevant for the internal motion follows, finally, the need of a probabilistic interpretation of quantum mechanics.     

Molecular insights into azumamide e histone deacetylases inhibitory activity

Azumamide E, a cyclotetrapeptide isolated from the sponge Mycale izuensis, is the most powerful carboxylic acid containing natural histone deacetylase (HDAC) inhibitor known to date. In this paper, we describe design and synthesis of two stereochemical variants of the natural product. These compounds have allowed us to clarify the influence of side chain topology on the HDAC-inhibitory activity. The present contribution also reveals the identity of the recognition pattern between azumamides and the histone deacetylase-like protein (HDLP) model receptor and reports the azumamide E unprecedented isoform selectivity on histone deacetylases class subtypes. From the present studies, a plausible model for the interaction of azumamides with the receptor binding pocket is derived, providing a framework for the rational design of new cyclotetrapeptide-based HDAC inhibitors as antitumor agents.     

Doped SiO x emitter layer in amorphous/crystalline silicon heterojunction solar cell

In this work we propose to replace the emitter layer of the n-type doped a-Si:H/p-type doped crystalline silicon heterojunction solar cell, with an n-type doped SiO _x amorphous oxide layer. The n-type doped SiO _x :H shows a lower activation energy and higher carrier mobility value with respect to the n-type doped a-Si:H. Moreover, higher transmission, below 500 nm of wavelength, and higher conductivity are measured. The relevance of transparency of the (n) a-SiO _x :H has been studied using that film in solar cells. The electrical parameters revealed a solar cell efficiency of 15.8 %. Moreover, the effect of TCO as a front side cell electrode is considered and discussed on the base of its workfunction when applied on top of the n-type doped SiO _x emitter layer using also numerical simulations.     

A global existence and uniqueness result for a class of hyperbolic operators

In this paper a global existence and uniqueness theorem for the Cauchy problem related to the class of hyperbolic operators with double characteristics \(P=D^2_{t} - D^2_{x_1} - (t+ \lambda - \alpha (x_1))^2 D^2_{x_2},\) depending on the parameter \(\lambda \) in the half-space \(\Omega = \mathbb {R}^2 \times ]0, + \infty [\) is proved. In the first part of the paper, a priori estimates in Sobolev spaces \(W^{r,2}\), with \(r\) negative, have been established. Then, the regularity is studied by using these spaces and by constructing a Green’s function in the half-plane for the operator of the waves.     

New Developments and Results for Mathematical Models in Environment Evaluations

A new mathematical model capable to provide a detailed evaluation of the ecological state of an environmental system is here presented. The mathematical model consists in a set of ordinary differential equations. The state variable of the system is the so-called Biological Territorial Capacity. The analysis is performed at the scale of each biotope that is the patch of land cover with homogeneous vegetation. Since the model consists in a very large number of ODE, in order to implement numerical computations with a fast algorithm, an approximated solution procedure is proposed. Finally a study case with comparisons between different designs and plans of the territory under investigation is performed.     

The effects of thermal annealing on the structure and the electrical transport properties of ultrathin gadolinia-doped ceria films grown by pulsed laser deposition

Ultrathin crystalline films of 10 mol% gadolinia-doped ceria (CGO10) are grown on MgO (100) substrates by pulsed laser deposition at a moderate temperature of 400°C. As-deposited CGO10 layers of approximately 4 nm, 14 nm, and 22 nm thickness consist of fine grains with dimensions ≤∼11 nm. The films show high density within the thickness probed in the X-ray reflectivity experiments. Thermally activated grain growth, density decrease, and film surface roughening, which may result in the formation of incoherent CGO10 islands by dewetting below a critical film thickness, are observed upon heat treatment at 400°C and 800°C. The effect of the grain coarsening on the electrical characteristics of the layers is investigated and discussed in the context of a variation of the number density of grain boundaries. The results are evaluated with regard to the use of ultrathin CGO10 films as seeding templates for the moderate temperature growth of thick solid electrolyte films with improved oxygen transport properties.     

A characterization of the circle group via uniqueness of roots

It was shown in Bíró et al. (2001) [7] that every cyclic subgroup C of the circle group T admits a characterizing sequence (un) of integers in the sense that unx→0 for some x∈T iff x∈C. More generally, for a subgroup H of a topological (abelian) group G one can define:

(a)

g(H) to be the set of all elements x of G such that unx→0 in G for all sequences (un) of integers such that unh→0 in G for all h∈H;

(b)

H to be g-closed if H=g(H).

We show then that an infinite compact abelian group G has all its cyclic subgroups g-closed iff G≅T.