Controllability of the discrete-spectrum Schrödinger equation driven by an external field

We prove approximate controllability of the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.     

Binding properties of mono-(6-deoxy-6-amino)-β-cyclodextrin towards p-nitroaniline derivatives: a polarimetric study

Polarimetry was used in order to investigate the formation of supramolecular complexes between mono-6-amino-β-cyclodextrin and various p-nitroaniline derivatives at two different pH values. Comparison with the behaviour of native β-cyclodextrin gave us the opportunity to consider the effect exerted by the presence of charged groups, having different solvation requirements, on the binding equilibrium. Data offer some support to the hypothesis of ‘dynamic co-inclusion’ of solvent molecules within the host-guest complex.     

Dalgarno–Lewis perturbation theory for scattering states

We apply the method of Dalgarno and Lewis to scattering states and discuss the choice of the unperturbed model in order to have a convergent perturbation series for the phase shift. We show that a recently proposed approach is a particular case of the method of Dalgarno and Lewis.     

Conformational Relaxation of p‐Phenylenevinylene Trimers in Solution Studied by Picosecond Time‐Resolved Fluorescence

Two p‐phenylenevinylene (PV) trimers, containing 3′‐methylbutyloxyl (in MBOPV3) and 2′‐ethylhexyloxyl (in EHOPV3) side chains, are used as model compounds of PV‐based conjugated polymers (PPV) with the purpose of clarifying the origin of fast (picosecond time) components observed in the fluorescence decays of poly[2‐methoxy‐5‐(2′‐ethylhexyloxy)‐p‐phenylenevinylene] (MEH‐PPV). The fluorescence decays of MBOPV3 and EHOPV3 reveal the presence of similar fast components, which are assigned to excited‐state conformational relaxation of the initial population of non‐planar trimer conformers to lower‐energy, more planar conformers. The rate constant of conformational relaxation k_CR is dependent on solvent viscosity and temperature, according to the empirical relationship k_CR=aη_o^?α?exp(?αE_η/RT), where aη_o^?α is the frequency factor, η_o is the pre‐exponential coefficient of viscosity, E_η is the activation energy of viscous flow. The empirical parameter α, relating the solvent microscopic friction involved in the conformational change to the macroscopic solvent friction (α=1), depends on the side chain. The fast component in the fluorescence decays of MEH‐PPV polymers (PPVs), is assigned to resonance energy transfer from short to longer polymer segments. The present results call for revising this assignment/interpretation to account for the occurrence of conformational relaxation, concurrently with energy transfer, in PPVs.     

Navier–Stokes equations: an analysis of a possible gap to achieve the energy equality

The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes equations. arXiv:1904.07641).

     

Differentiation among dairy products by combination of fast field cycling NMR relaxometry data and chemometrics

A set of commercial milk and Sicilian cheeses was analysed by a combination of fast field cycling (FFC) nuclear magnetic resonance (NMR) relaxometry and chemometrics. The NMR dispersion (NMRD) curves were successfully analysed with a mathematical model applied on Parmigiano–Reggiano (PR) cheese. Regression parameters were led back to the molecular components of cheeses (water trapped in casein micelles, proteins and fats) and milk samples (water belonging to hydration shells around dispersed colloidal particles of different sizes and bulk water). The application of chemometric analysis on relaxometric data enabled differentiating milk from cheeses and revealing differences within the two sample groups of either cheeses or milk samples. Marked differences among cheeses were evidenced by statistical analysis of the sole quadrupolar peaks parameters, suggesting that these contain information on the nature of the milk used during cheese production. Hence, combination of FFC NMR and chemometrics represents a powerful tool to investigate alterations in dairy products.     

Kan Extensions are Partial Colimits

Applied Categorical Structures - One way of interpreting a left Kan extension is as taking a kind of “partial colimit”, whereby one replaces parts of a diagram by their colimits. We...     

Evaluation of different light-curing lamps

The aim of this study has been to evaluate light-curing composites polymerization quality carried out by halogen and new-diode lamps through the thermal analysis (TG?CDTA). Samples have been polymerized at 3?C20?C40?C60?s by halogen lamp and 1?C3?C6?C9?s by new-diode lamp. The TG/DTA analysis shows that different light-curing times affect the degree of conversion of the composite, since by increasing the curing time the quantity of the monomer that has not reacted (residual) decreases. The new-diode lamp, according to the manufacturer, can cure composite restorations in few seconds; but at the conditions used in this study, the samples cured by the halogen lamp at the standard times of exposure, compared to the samples cured in few seconds by the new-diode lamp, show a lower mass loss.     

An unified formulation of strong non-local elasticity with fractional order calculus

Meccanica - The research of a formulation to model non-local interactions in the mechanical behavior of matter is currently an open problem. In this context, a strong non-local formulation based on...