Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement

The transformations of functions acting on sublevel sets that satisfy a P\'olya-Szeg\H{o} inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.Comment: 9 page

Efficient and Robust Segmentations Based on Eikonal and Diffusion PDEs

In this paper, we present efficient and simple image segmentations based on the solution of two separate Eikonal equations, each originating from a different region. Distance functions from the interior and exterior regions are computed, and final segmentation labels are determined by a competition criterion between the distance functions. We also consider applying a diffusion partial differential equation (PDE) based method to propagate information in a manner inspired by the information propagation feature of the Eikonal equation. Experimental results are presented in a particular medical image segmentation application, and demonstrate the proposed methods

Production of Gaseous Carriers Via Biomass Gasification for Energy Purposes

AbstractIt is under development a biomass gasification plant based on a 1 MWth bubbling fluidized bed (BFB) reactor with internal recirculation. Compared to conventional BFB design, the mechanism of internal circulation of solids can give beneficial effect to the process in terms of biomass conversion efficiency into gaseous product and gas quality. A model describing the process of biomass gasification in the two reaction chambers was developed. Expected results were preliminarily validated by experimental results obtained at a bench scale facility working on the same gasification concept

Fetal nutrition : a review

Knowledge of fetal nutrient supply has greatly increased in the last decade due to the availability of fetal blood samples obtained under relatively steady-state conditions. These studies, together with studies utilizing stable isotope methodologies, have clarified some aspects of the supply of the major nutrients for the fetus such as glucose, amino acids and fatty acids. At the same time, the relevance of intrauterine growth has been recognized not only for the well-being of the neonate and child, but also for later health in adulthood. The major determinants of fetal nutrient availability are maternal nutrition and metabolism together with placental function and metabolism. The regulation of the rate of intrauterine growth is the result of complex interactions between genetic inheritance, endocrine environment and availability of nutrients to the fetus

Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Diffeomorphism-invariant properties for quasi-linear elliptic operators

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and non-degenerate coerciveness.Comment: 16 page