Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Monitoring of Spirulina Flakes and Powders from Italian Companies

Microalgae and microalgae-derived compounds have great potential as supplements in the human diet and as a source of bioactive products with health benefits. Spirulina (Arthrospira platensis (Nordstedt) Gomont, or Spirulina platensis) belongs to the class of cyanobacteria and has been studied for its numerous health benefits, which include anti-inflammatory properties, among others. This work was aimed at comparing some spirulina products available on the Italian market. The commercial products here analyzed consisted of spirulina cultivated and processed with different approaches. Single-component spirulina products in powder and flake form, free of any type of excipient produced from four different companies operating in the sector, have been analyzed. The macro- and micromorphological examination, and the content of pigments, phycobiliproteins, phenols, and proteins have shown differences regarding the morphology and chemical composition, especially for those classes of particularly unstable compounds such as chlorophylls and carotenoids, suggesting a great influence of both culture conditions and processing methods.     

Rational Design of Fe2(μ-PR2)2(L)6 Coordination Compounds Featuring Tailored Potential Inversion

It was recently discovered that some redox proteins can thermodynamically and spatially split two incoming electrons towards different pathways, resulting in the one-electron reduction of two different substrates, featuring reduction potential respectively higher and lower than the parent reductant. This energy conversion process, referred to as electron bifurcation, is relevant not only from a biochemical perspective, but also for the ground-breaking applications that electron-bifurcating molecular devices could have in the field of energy conversion. Natural electron-bifurcating systems contain a two-electron redox centre featuring potential inversion (PI), i. e. with second reduction easier than the first. With the aim of revealing key factors to tailor the span between first and second redox potentials, we performed a systematic density functional study of a 26-molecule set of models with the general formula Fe₂(μ-PR₂)₂(L)₆. It turned out that specific features such as i) a Fe−Fe antibonding character of the LUMO, ii) presence of electron-donor groups and iii) low steric congestion in the Fe's coordination sphere, are key ingredients for PI. In particular, the synergic effects of i)-iii) can lead to a span between first and second redox potentials larger than 700 mV. More generally, the “molecular recipes” herein described are expected to inspire the synthesis of Fe₂P₂ systems with tailored PI, of primary relevance to the design of electron-bifurcating molecular devices.     

Existence results for semilinear elliptic variational inequalities with changing sign nonlinearities

In this paper we present some existence results for a class of semilinear elliptic variational inequalities, depending on a real parameter λ, with changing sign nonlinearities. The fundamental tool to prove the existence result is a penalization method combined with the Mountain Pass Theorem and the Linking Theorem, respectively in the case λ < λ ₁ and λ ≥ λ ₁, where λ₁ is the first eigenvalue of the uniformly elliptic operator A involved in the variational inequality.     

Recent advances in characterization of CaCu3Ti4O12 thin films by spectroscopic ellipsometric metrology

CaCu3Ti4O12 (CCTO) thin films were successfully grown on LaAlO3(100) and Pt/TiO2/SiO2/Si(100) substrates by a novel MOCVD approach. Epitaxial CCTO(001) thin films have been obtained on LaAlO3(100) substrates, while polycrystalline CCTO films have been grown on Pt/TiO2/SiO2/Si(100) substrates. Surface morphology and grain size of the different nanostructured deposited films were examined by AFM, and spectroscopic ellipsometry has been used to investigate the electronic part of the dielectric constant (epsilon2). Looking at the epsilon2 curves, it can be seen that by increasing the film structural order, a greater dielectric response has been obtained. The measured dielectric properties accounted for the ratio between grain volumes and grain boundary areas, which is very different in the different structured films.     

The second acidic constant of salicylic acid

The second dissociation constant of salicylic acid (H2L) has been determined, at 25 degrees C, in NaCl ionic media by UV spectrophotometric measurements. The investigated ionic strength values were 0.16, 0.25, 0.50, 1.0, 2.0 and 3.0 M. The protolysis constants calculated at the different ionic strengths yielded, with the Specific Interaction Theory, the infinite dilution constant, log beta1(0) = 13.62 +/- 0.03, for the equilibrium L2- + H+ <==> HL-. The interaction coefficient between Na+ and L2-, b(Na+, L2-) = 0.02 +/- 0.07, has been also calculated.     

Volcanic Quartz Growth Zoning Identified by Cathodoluminescence and EPMA Studies

 Quartz is a common phenocryst in acidic volcanic rocks but rarely contributes to the understanding of the magmatic or eruptive processes due to its apparent chemical homogeneity. Cathodoluminescence studies indicate that volcanic quartz is strongly zoned with respect to the trace elements. The determination of this zoning can help to elucidate the crystallisation history of the magmatic rock. Polished thin sections from rhyolitic and dacitic volcanic rocks were examined by cathodoluminescence mounted on an optical microscope and analysed by electron probe microanalysis. X-ray mapping of the trace elements incorporated in the zoned quartz was also performed. The interpretation of the data obtained from these different analytical methods provides useful information on the chemical zoning of single crystals and therefore on the chemico-physical conditions of the melt from which the quartz crystallised. Quartz from dacitic rock shows a complex cathodoluminescence oscillatory zoning, consisting of large red-brown and blue bands concentric to a resorbed core. Quartz from rhyolite shows simpler cathodoluminescence zoning, consisting of dark to bright blue luminescent bands. The EMPA analyses and the X-ray maps combined with the cathodoluminescence images suggest a clear correlation between the concentrations of some trace element (mainly Al and Ti, acting as activators of luminescence) and the cathodoluminescence colours pattern zoning. The incorporation of these trace elements during the growth of the crystals is linked to small variations in the thermo-chemical properties of the magma such as temperature and chemical composition.     

EPMA Major and Trace Element Analysis in Garnet and its Petrological Application

 A comparison between major and trace element concentrations in garnet performed by electron microprobe (EPMA) technique is reported. Quantitative spot analyses and X-ray maps of major elements (Fe, Mg, Mn, Ca) and the trace element yttrium in garnets from metamorphic rocks are presented. The selected garnet samples come from meta-pelitic and meta-basic specimens belonging to the tectonic unit of the Monte Rosa Nappe (Western Alps). In the metapelites, the quantitative Y distribution maps display a prominent increase at the core, the Y abundance varying by over two orders of magnitude, from about 80 ppm (rim) to over 2100 ppm (core). The Y profiles show well defined patterns with sharp features that do not correlate with major element distributions. A roughly comparable pattern can be supposed only with Mn. The Y distribution suggests that the diffusion of Y through the garnet is very slow compared to the major elements, thus the Y results are suitable for geothermometric estimates. In the metabasites, the Y spatial distribution is characterised by an increasing content from the core to the rim, displaying a zoning pattern opposite to the metapelite garnet. Quantitative EPMA analyses range from 1100 ppm at the rim to values lower than the detection limit at the core. Therefore, the Y content in the garnet can be related to several chemical and physical variables such as the bulk rock composition and the phase assemblage. In particular, in the xenotime-bearing metapelitic system the Y distribution seems to be correlated with metamorphic peak temperature.     

Determination of triazines and dinitroanilines in waters by high-performance liquid chromatography after solid-phase extraction

A rapid and selective method for the simultaneous determination of triazines and dinitroanilines in real water matrices is suggested based on a preliminary adsorption on an RP-18 cartridge, an elution step using acetonitrile and HPLC separation with a Lichrosorb RP- Select B column and UV detection. The washing step cartridge is critical for triazines: terbutryn is eluted with quantitative recovery only after washing with an NH₃ solution. The degree of enrichment of the compounds studied has been determined: triazine recoveries are quantitative, while dinitroaniline recoveries are between 66% and 78% at the lowest fortification level. The detection limits for the ten herbicides are in the range 0.03-0.1 μg/l. The analysis time is 2 h.