Existence and regularity properties of non-isotropic singular elliptic equations

We establish existence and sharp regularity results for solutions to singular elliptic equations of the order u ^−β , 0 < β < 1, with gradient dependence and involving a forcing term λ f(x, u). Our approach is based on a singularly perturbed technique. We show that if the forcing parameter λ > 0 is large enough, our solution is positive. For λ small solutions vanish on a nontrivial set and therefore they exhibit free boundaries. We also establish regularity results for the free boundary and study the asymptotic behavior of the problem as b\searrow 0{\beta\searrow 0} and b\nearrow 1{\beta\nearrow 1}. In the former, we show that our solutions u _β converge to a C ^1,1 function which is a solution to an obstacle type problem. When b\nearrow 1{\beta\nearrow 1} we recover the Alt-Caffarelli theory.     

Synthesis and application of imprinted polyvinylimidazole-silica hybrid copolymer for Pb determination by flow-injection thermospray flame furnace atomic absorption spectrometry

A novel ion imprinted polyvinylimidazole-silica hybrid copolymer (IIHC) was synthesized and used as a selective solid sorbent for Pb²⁺ ions preconcentration using an on-line solid phase extraction (SPE) system coupled to TS-FF-AAS. The ionic hybrid sorbent was prepared using 1-vinylimidazole and 3-(trimethoxysilyl)propylmethacrylate as monomers, Pb²⁺ ions as template, tetraethoxysilane as reticulating agent and 2,2′-azobis-isobutyronitrile as initiator. The best on-line SPE conditions concerning sorption behavior, including sample pH (6.46), buffer concentration (9.0 mmol L⁻¹), eluent (HNO₃) concentration (0.5 mol L⁻¹) and preconcentration flow rate (4.0 mL min⁻¹), were optimized by means of full factorial design and Doehlert matrix. The analytical curve ranged from 2.5 to 65.0 μg L⁻¹ (r = 0.999) with limit of detection of 0.75 μg L⁻¹; the precision (repeatability) calculated as relative standard deviation (n = 10) was 5.0 and 3.6% for Pb²⁺ concentration of 10.0 and 60.0 μg L⁻¹, respectively. From on-line breakthrough curve, column capacity was 3.5 mg g⁻¹. Preconcentration factor (PF), consumptive index (CI) and concentration efficiency (CE) were 128.0, 0.16 mL and 25.6 min⁻¹, respectively. The selective performance of the sorbent, based on relative selectivity coefficient, was compared to NIC (non imprinted copolymer) for the binary mixture Pb²⁺/Cd²⁺, Pb²⁺/Cu²⁺ and Pb²⁺/Zn²⁺. The results showed that ion imprinted polyvinylimidazole-silica hybrid polymer had higher selectivity for Pb²⁺ than NIC at 64.9, 16.0 and 8.8 folds. The developed method was successfully applied for highly sensitive and selective Pb²⁺ determination in different kinds of water samples, parenteral solutions and urine. Accuracy was also assessed by analyzing certified reference fish protein (DORM-3) and marine sediment (MESS-3 and PACS-2) with satisfactory results.     

Casbane diterpene as a promising natural antimicrobial agent against biofilm-associated infections

Croton nepetaefolius is a native plant from northeastern Brazil that belongs to the Euphorbiaceae family. The biological action of this plant has been extensively explored, being the secondary metabolites responsible for its properties alkaloids, diterpenes, and triterpenes. This study aimed to evaluate the ability of casbane diterpene (CD), isolated from the ethanolic extract of C. nepetaefolius, to inhibit microbial growth and biofilm formation of several clinical relevant species (bacteria and yeasts). It was found that CD possessed biocidal and biostatic activity against the majority of the species screened, with minimal active concentrations ranging between 125 and 500 μg/mL. In addition, it was observed that biofilm formation was inhibited even when the planktonic growth was not significantly affected. In conclusion, CD showed potential to be a natural tool for the treatment of diseases caused by different infectious microorganisms.     

Fatty acids as chemotaxonomic markers of marine macrophytes from Rio de Janeiro state, Brazil

The distribution of fatty acids in 13 species of macroalgae (Chlorophyta, Ochrophyta and Rhodophyta) and 1 seagrass (Spartina sp), collected on the Rio de Janeiro state coast was determined. The results were evaluated in search of correlations between the taxonomic and phylogenetic position of these macrophytes. Statistical analyses showed the effectiveness as taxonomic and phylogenetic markers of the distribution of the methyl fatty acid esters in these macrophytes.     

Lower bounds for the surface energy of two-dimensional foams

The European Physical Journal E - Amongst the two-dimensional cellular patterns that fill a plane, dry foams at stable equilibrium typify a particular subset for which the total perimeter P of cell...     

The formation of intermetallic phases by solid-phase reaction of Fe/Al multilayers

Thin film multilayers of Fe and Al with thicknesses ranging from 10 nm/2 nm to 10 nm/420 nm Fe/Al are used as starting structures to produce intermetallic phases by solid-phase reaction during high-vacuum thermal annealings. By measuring the relative concentrations of the reacting Fe and Al species nearby the growing interfaces and using the recently introduced concept of effective heat of mixing of binary thin-film metallic systems, a method is suggested to predict the phases to be obtained from different combinations of initial multilayer thickness and annealing temperature.     

Synthesis of new allenic prostanoids

New allenic prostanoids 5c, d, 7,9c, and 15b have been prepared by total synthesis. In each case a cuprate-propargylic acetate reaction was used as the key step.     

Solid state reaction crystallization and amorphization on thin film Fe-Zr multilayers

We study in this paper the thin multilayered film of the system Fe _x Zr_1-x using conversion electron Mössbauer spectroscopy (CEMS) as well as Rutherford backscattering spectroscopy (RBS). The solid state reaction (SSR) at 500°C for thex=0.33 andx=0.67 concentrations produces crystalline and amorphous phases. For the concentrationx=0.50 only an amorphous phase is obtained. For reactions at 700°C, besides Fe-Zr phases, another one is observed in the CEMS spectrum. This phase may be associated with some FeSi compound since the RBS profile shows the presence of Si at the surface.This work was supported by CNPq, FINEP and FAPERGS.     

Effect of the interaction of distant neighbors on the thermodynamic properties of anharmonic-crystal surfaces

The unsymmetrized self-consistsnt field method is employed to study the effect of the interaction of distant neighbors on the structure and thermodynamic properties of a simple model of an anharmonic crystal with a surface — the semiinfinite linear chain. Expressions are obtained for the relaxation of the end atoms, the amplitudes of their oscillations, and the free surface energy. The dependence of the relaxation on the form of the interatomic potential is studied. It is pointed out that relaxation decaying nonmonotonically into the chain as well as a change in the sign of the relaxation accompanying a change in the temperature are possible.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 10–14, February, 1988.