The heart of a convex body

We investigate some basic properties of the {\it heart} $\heartsuit(\mathcal{K})$ of a convex set $\mathcal{K}.$ It is a subset of $\mathcal{K},$ whose definition is based on mirror reflections of euclidean space, and is a non-local object. The main motivation of our interest for $\heartsuit(\mathcal{K})$ is that this gives an estimate of the location of the hot spot in a convex heat conductor with boundary temperature grounded at zero. Here, we investigate on the relation between $\heartsuit(\mathcal{K})$ and the mirror symmetries of $\mathcal{K};$ we show that $\heartsuit(\mathcal{K})$ contains many (geometrically and phisically) relevant points of $\mathcal{K};$ we prove a simple geometrical lower estimate for the diameter of $\heartsuit(\mathcal{K});$ we also prove an upper estimate for the area of $\heartsuit(\mathcal{K}),$ when $\mathcal{K}$ is a triangle.Comment: 15 pages, 3 figures. appears as "Geometric Properties for Parabolic and Elliptic PDE's", Springer INdAM Series Volume 2, 2013, pp 49-6

Modificazioni dell'assetto elettrolitico ed ematochimico nella cavalla nell’ultimo trimestre di gravidanza e nel primo mese di lattazione

ABSTRACT - The electrolyte and biochemical variables were evaluated in 8 healthy mares, aged 4-10 years. Blood samples were taken after the 8th month of gestation, and then, every 30 days, for 3 consecutive months. During the lactation, blood samples were taken in the day 7, 15, 30 post partum. Mares were bled from the jugular vein between 7:30-9:00 AM. The purpose of this study was to determine which physiological changes occur in serum clinical biochemical analytes in pregnant and lactating mares and to determine whether the changes between pregnancy and lactation conditions are significant. Two way RMANOVA showed significant effects of lactation on the changes of all electrolytes and hematochemical variables, with higher levels of Na+, Pi and urea, and lower levels of Na+, Ca++, K+, creatinine, bilirubin and triglycerides in lactation than in pregnancy

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

Characterization and Processability of Blends of Polylactide Acid with a New Biodegradable Medium-Chain-Length Polyhydroxyalkanoate

In this work the processability and the mechanical performance of polylactide acid (PLA) based blends with a sample of a new biodegradable medium-chain-length poly (hydroxyalkanoate) (PHA) were investigated. The two polymers are incompatible with scarce adhesion and with the dispersed PHA particles size increasing with the PHA content. Rheological tests in shear flow indicate that adding PHA improves the processability of the matrix by increasing the content of this second component in the blend, as observed also for the torque curves, due to the very low viscosity of this new sample of PHA. The processability is only slightly worsened in non-isothermal elongational flow as the melt strength decreases, but accompanied by an increase of the melt stretchability that improves the ability of the pure PLA matrix to produce thin films. Mechanical properties put in evidence a brittle–ductile transition adding PHA to PLA matrix. The elongation at break significantly increases when PHA is added, while the elastic modulus is significantly reduced only at higher contents of PHA. This has been interpreted in terms of both plasticization action of the PHA and also in terms of lubricant action of the PHA macromolecules that allows a better sliding of the PLA macromolecules subjected to solid deformation

Multi-sensor data acquisition and integration processes for the study and documentation of the church of Santa Maria degli Angeli in Pizzofalcone in Naples

The paper presents the results of a research carried out on the Church of Santa Maria degli Angeli in Pizzofalcone in Naples, in which multi-sensor surveys have been performed in order to assess the architectonical, geometrical and colorimetric characteristics of the majestic basilica. The use of integrated technologies made it possible to realize 3D digital models that allowed the complete representation of the building, integrating data and filling the gaps of the different previous surveys. The performances of the various reality-based technologies employed have been subjected to critical analysis in order to maximize their potential, optimize survey and data elaboration phases, and obtain the expected results. These latter have been defined through the derived digital re-elaborations and representations. Hence, the objective of the research is to carry out a comparative analysis on the 3D models generated through the different active and passive sensors employed in order to proceed with their integration and achieve an accurate, original and updated methodology of building survey