Subsolutions to the least area problem and the «minimal hull» of a bounded set inR n

Summary We discuss some properties of Caccioppoli sets, whose boundaries minimize the area with respect to all compact perturbations which increase the sets. In particular, the stability under countable intersection enables us to give a precise meaning to the concept of ?minimal hull? of a bounded set.

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Riassunto Vengono studiate alcune proprietà degli insiemi di Caccioppoli, aventi frontiere di area minima rispetto a modificazioni che aumentano gli insiemi stessi. In particolare, la stabilità rispetto all'intersezione numerabile permette di definire il concetto di ?inviluppo minimale? di un dato insieme limitato.

     

Semiclassical Propagation of Coherent States for the Hartree Equation

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in L ² by C ?{e}{C \sqrt {\varepsilon}} , e{\varepsilon} being the Planck constant. Finally we present a full formal asymptotic expansion.     

Bacteriostatic Behavior of PLA-BaTiO3 Composite Fibers Synthesized by Centrifugal Spinning and Subjected to Aging Test

The present work investigated the effect of Polylactic acid (PLA) fibers produced by centrifugal spinning with incorporated BaTiO₃ particles to improve their bacteriostatic behavior. The PLA matrix and three composites, presenting three different amounts of fillers, were subjected to UV/O₃ treatment monitoring the possible modifications that occurred over time. The morphological and physical properties of the surfaces were characterized by different microscopic techniques, contact angle, and surface potential measurements. Subsequently, the samples were tested in vitro with human dermal fibroblasts (HDF) to verify the cytotoxicity of the substrates. No significant differences between the PLA matrix and composites emerged; the high hydrophobicity of the fibers, derived by the polymer structure, represented an obstacle limiting the fibroblast attachment. Samples underwent bacterial exposure (Staphylococcus epidermidis) for 12 and 24 h. Increasing the concentration of BT, the number of living bacteria and their distribution decreased in comparison with the PLA matrix suggesting an effect of the inorganic filler, which generates a neutralization effect leading to reactive oxygen species (ROS) generation and subsequently to bacterial damages. These results suggest that the barium titanate (BT) fillers clearly improve the antibacterial properties of PLA fibers after aging tests made before bacterial exposure, representing a potential candidate in the creation of composites for medical applications.     

Stress dependence of optically active diamagnetic point defects in silicon oxynitride

The cathodoluminescence (CL) spectrum arising from diamagnetic point defects of silicon oxynitride lattice was analyzed to extract quantitative information on local stress fields stored on the surface of a silicon nitride polycrystal. A calibration procedure was preliminarily made to obtain a relationship between CL spectral shift and applied stress, according to the piezo-spectroscopic effect. In this calibration procedure, we used the uniaxial stress field developed in a rectangular bar loaded in a four-point flexural jig. Stress dependence was clearly detected for the most intense spectral band of a doublet arising from diamagnetic ([triple bond]Si-Si[triple bond]) defects, which was located at around 340 nm. The shallow nature of the electron probe enabled the characterization of surface stress fields with sub-micrometer-order spatial resolution. As applications of the PS technique, the CL emission from [triple bond]Si-Si[triple bond] defects was used as a stress probe for visualizing the residual stress fields stored at grain-boundary regions and at the tip of a surface crack propagated in polycrystalline silicon nitride.     

Acidity predictions in an electron propagator approach

An alternative way to calculate vertical ionization potentials (VIP) and vertical electron affinity (VEA) is the application of Koopman's theorem, using the electron propagator theory. In the present work, the results of the application of this theorem using the electron propagator formalism have been compared with the experiment in order to validate different basis set. Using the basis set with the best performance, the acidity tendencies in some substituted acetic acid molecules have been analyzed by correlating the proton affinity (PA) with molecular electronegativity (χ) and hardness (η); these last indexes were obtained from the calculated VIP and VEA considering the finite difference approximation. The above correlations were compared with equivalent correlations using the energy of the frontier Hartree–Fock orbitals and the corresponding Kohn–Sham orbitals, which were calculated with the B3LYP‐DFT procedure. The results indicate that the electron propagator theory could be an interesting alternative to evaluate reactivity indexes, since this theory gives reliable values of VIP and VEA. It was also found that (i) the VIP values are very close to experiment, with only a 0.38% of error; (ii) acceptable results are inferred for VEA; (iii) a triple zeta quality function works quite well in these calculations, and particularly the 6‐311G(d,p) basis set is the best, as it had been reported; and (iv) using the depronation energy (DPE), good results were obtained in the correlations δDPE‐VEA and δDPE‐χ. The results tested that P3 approximation in the electron propagator approach can be a new and interesting alternative in predicting VIP, VEA, and some reactivity indexes, such as χ and η, at least for the compounds studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Variational problems of least area type with constraints

Summary We establish a new regularity result for boundaries of sets minimizing the area functional perturbed by a curvature term, and subject to a mass constraint of the type , with a fixed, strictly positive integrable functiong(x). The existence of Lagrange parameters is also considered. A preliminary version of the paper was presented at the meeting on “Partial Differential Equations”, Ferrara (Italy), October 13–16, 1986. Work partially supported by the Italian M.P.I.