Orderings of coherent systems with randomized dependent components

Consider a general coherent system with independent or dependent components, and assume that the components are randomly chosen from two different stocks, with the components of the first stock having better reliability than the others. Then here we provide sufficient conditions on the component’s lifetimes and on the random numbers of components chosen from the two stocks in order to improve the reliability of the whole system according to different stochastic orders. We also discuss several examples in which such conditions are satisfied and an application to the study of the optimal random allocation of components in series and parallel systems. As a novelty, our study includes the case of coherent systems with dependent components by using basic mathematical tools (and copula theory).     

Infinite-Dimensional Calculus Under Weak Spatial Regularity of the Processes

Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus.     

Effects of flavonoid derivatives on human microvascular endothelial cells

Some natural compounds, including flavonoids, are active in vasculature re-growth during hair follicle disruption, but their effects have not been yet evaluated directly on microvascular endothelial cells. Skin vascularisation regulates the physiological blood supply required for hair growth and its dysregulation is the basis of several human diseases. Follicle-derived vascular endothelial growth factor (VEGF) release from follicular keratinocytes promotes perifollicular vascularisation and increases follicle and hair size, while blockade of VEGF-mediated angiogenesis leads to impaired hair growth. Here, we tested three flavonoids, namely visnadin (VSD), hesperidin (HSP) and baicalin (BC), on cultured human microvascular endothelial cells (HMEC), comparing their effects with minoxidil (MXD), a synthetic drug broadly used in the treatment of androgenetic alopecia. The response to these compounds was assayed in terms of endothelial survival, proliferation, tubulogenesis and proangiogenic signalling. We show that BC promotes HMEC proliferation, while both VSD and MXD enhance tubulogenesis. Interestingly, only HSP increases VEGFR-2 phosphorylation.     

Evidence for cation-π interactions in calixcrown·KPic complexes from X-ray crystal structure analysis and energy calculations

Abstract

The crystal and molecular structures of the 1,3-diisopropoxy-p-tertbutyl calix[4]arene crown-5 fixed in the partial cone conformation and that of its potassium picrate salt have been determined by single crystal X-ray diffraction studies. Energy calculations have been performed to gain more insight on the stabilizing cation…ligand interactions. The calculation of the total potential energy indicates that the contribution which comes from the electrostatic polarization induced by the electric field of the cation on the rotated nucleus gives a net stabilizing contribution of almost 6 kcal/mol. A comparison between the molecular geometry of some partial cone 1,3-disubstituted-p-tertbutylcalix[4]arene derivatives is reported and discussed in view of the preorganization principle.     

An analytical method for the optimum thermal design of convective longitudinal fin arrays

The paper analyzes the problem of the optimum thermal design of free and forced convection fin arrays composed of longitudinal fins with constant thickness. Two different optimization problems have been considered: the minimization of the weight for a given heat flow and the maximization of the heat flow for a given weight. Two different geometrical configurations of the fin array have been considered: closed array and open array. The procedure for the optimization is provided in a general case and a complete analytical solution of the problem, for the case with the tip approximated as being insulated, is developed. The paper contains several illustrative examples of the application of the proposed optimization procedure.     

Positive fixed points and fourth-order equations

This work presents sufficient conditions for the existence ofat least one positive solution for a nonlinear fourth-orderbeam equation under Lidstone boundary conditions. The main toolused is a fixed point theorem that essentially combines themonotone iterative technique with fixed point theorems of coneexpansion or compression type. The last section contains twoexamples that complement some related results existent in theliterature.