The Brezis-Nirenberg problem near criticality in dimension 3

We consider the problem of finding positive solutions of Δu+λu+u^q=0 in a bounded, smooth domain Ω in , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<λ<λ₁. We analyze the role of Green's function of Δ+λ in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or λ are regarded as parameters. As a special case of our results, we find that if , where λ∗ is the Brezis-Nirenberg number, i.e., the smallest value of λ for which least energy solutions for q=5 exist, then this problem is solvable if q>5 and q−5 is sufficiently small.     

Classification of ancient Roman glazed ceramics using the neural network of Self-Organizing Maps

Artificial neural networks with unsupervised learning strategy known as Self-Organizing Maps were applied to classify ancient Roman glazed ceramics. Their clay ceramic bodies were analyzed by Inductively Coupled Plasma-Atomic Emission Spectroscopy and the chemical composition obtained was processed by this neural algorithm. The results obtained provide two types of information: firstly, classification of ceramic samples with identification of several groups and secondly, differentiation between the elemental chemical information. It was found that there are certain chemical elements which can be considered as principal and which can serve to differentiate between ceramics, whereas other elements give redundant information and do not contribute to sample differentiation. Seven chemical elements were considered principal and provide the necessary information. Two types of element were identified: 1 – a group formed by common elements, such as: Ca, Fe, Mg, Mn and 2 – another formed by optional elements: K or Na and Ba or Sr and Al or Ti.     

Sulphur content estimation of Venezuelan heavy oil by fast neutron and gamma transmission technique

A compact and modern equipment for implementing the fast neutron and γ-ray transmission technique (FNGT) has been developed in order to estimate the sulphur content of crude oil. FNGT is employed for non- destructive analysis of different kinds of samples. The compact system presented in this work represents an improvement of our previous experimental set-up [1, 2]. It makes use of a ²⁵²Cf source, an EJ-301 liquid scintillator detector (2″ × 2″) with excellent n/γ discrimination capabilities, and modern nuclear electronics based on fast digitizers. The fast neutron and gamma transmission technique was employed to study a system for on-line sulphur concentration measurement in Venezuelan heavy sour oil. The range of sulphur concentrations investigated is between 0.1 and 6.5 wt%. The equipment performances and limitations are compared with those predicted by a Monte Carlo model built in GEANT4 v10.01. The results show the possibility to implement a compact unit for on-line determination of sulphur concentration in crude oil.

     

Metric-based mesh adaptation for 2D Lagrangian compressible flows

In this paper, we present a method to compute compressible flows in 2D. It uses two steps: a Lagrangian step and a metric-based triangular mesh adaptation step. Computational mesh is locally adapted according to some metric field that depends on physical or geometrical data. This mesh adaptation step embeds a conservative remapping procedure to satisfy consistency with Euler equations. The whole method is no more Lagrangian.After describing mesh adaptation patterns, we recall the metric formalism. Then, we detail an appropriate remapping procedure which is first-order and relies on exact intersections.We give some hints about the parallel implementation. Finally, we present various numerical experiments which demonstrate the good properties of the algorithm.     

Reconstitution of aluminium and iron core in horse spleen apoferritin

This study investigates the uptake of iron and aluminium by apoferritin. In particular, we provide the first evidence that apoferritin is able to bind in vitro the physiological form of aluminium, Al(OH)₄ ^?, to reach an Al/Fe atomic ratio of about 0.15. Mass spectrometry analysis shows that the Al content increases linearly as a function of Al concentration in solution. These findings provide a better understanding of the Al uptake in vivo, confirming that the metal content of ferritin depends on the metal bio-availability.     

Use of ionic liquid aggregates of 1-hexadecyl-3-butyl imidazolium bromide in a focused-microwave assisted extraction method followed by high-performance liquid chromatography with ultraviolet and fluorescence detection to determine the 15+1 EU priority PAHs in toasted cereals ("gofios")

A focused-microwave assisted extraction method using aggregates of the ionic liquid (IL) 1-hexadecyl-3-butylimidazolium bromide (HDBIm-Br) followed by high-performance liquid chromatography (HPLC) with ultraviolet (UV) detection and single-channel fluorescence detection (FLD) has been developed for the determination of polycyclic aromatic hydrocarbons (PAHs) in toasted cereals (“gofios”) of different nature (wheat, barley, rye, and maize corn) from the Canary Islands, Spain. The optimized HPLC-UV-vis/single-channel FLD method takes 40 min for the chromatographic run with limits of detection varying between 0.02 and 4.01 ng mL⁻¹ for the fluorescent PAHs from the European Union (EU) priority list in foods, and 20.5 ng mL⁻¹ for the non-fluorescent PAH cyclopenta[c,d]pyrene (CPP). The optimized microwave step presented extractions recoveries ranging from 70.1 to 109% and precision values lower than 12.6% (as relative standard deviation), using an extraction time of 14 min. The extraction method also utilizes low amounts of sample (0.1 g), and low amounts of IL (77 mg), avoiding completely the use of organic solvents.     

Developing qualitative extraction profiles of coffee aromas utilizing polymeric ionic liquid sorbent coatings in headspace solid-phase microextraction gas chromatography-mass spectrometry

Two solid-phase microextraction (SPME) sorbent coatings based on polymeric ionic liquids (PILs) have been utilized for the analysis of complex coffee aroma samples. The PIL-based SPME coatings examined, namely, poly(1-(4-vinylbenzyl)-3-hexadecylimidazolium bis[(trifluoromethyl)sulfonyl]imide) [poly(VBHDIm⁺ NTf₂⁻)], with ∼14-μm thickness, and poly(1-vinyl-3-hexylimidazolium chloride) [poly(ViHIm⁺ Cl⁻)], with ∼8-μm thickness, were employed for the headspace determination of up to 49 analytes from four different coffee beans: two French roast coffees of different brands, Sumatra coffee, and decaffeinated Sumatra coffee. The analysis was conducted using gas chromatography coupled to mass spectrometry. For comparative purposes, the commercial polyacrylate (PA, 85-μm film thickness) SPME coating was utilized under the same extraction conditions. The three SPME coatings tested behaved quite differently as a function of the families of compounds extracted. Thus, the poly(VBHDIm⁺ NTf₂⁻) coating was extremely selective for aldehydes while also exhibiting good extraction efficiencies for acids. The poly-(ViHIm⁺ Cl⁻) coating exhibited superior performance for aromatic alcohols, and the PA coating worked better for heterocyclic aromatics. Both PIL-based SPME sorbent coatings demonstrated exceptional selectivity and extraction efficiency when dealing with complex coffee aromas in spite of their small film thicknesses.