Existence Results for Critical Semi-linear Equations on Heisenberg Group Domains

Following the work of G. Citti and F. Uguzzoni who studied Yamabe type problems on Heisenberg group domains, we consider here the following critical semi-linear equation on domains of the Heisenberg group ${{\mathbb{H}^1}}$ : $$(P) \left\{\begin{array}{lll}-{\Delta_{H}}u\quad =\quad K{u^{3}}\quad\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad > \quad0\qquad\,\,\,\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad = \quad 0 \quad\quad\,\,\,{\rm on}\,\partial \Omega, \end{array}\right. $$ where Δ _H is the sublaplacian on ${{\mathbb{H}^1}}$ and K is a C ³ positive function defined on Ω. Using a version of the Morse Lemma at infinity, we give necessary conditions on K to insure the existence of solutions for (P).     

Cytotoxicity of new secondary metabolites,fatty acids and tocols composition of seeds of Ducrosia anethifolia (DC.) Boiss

Two new monoterpene Ducrosin A (1) and sesquiterpene Ducrosin B (2) were isolated along with three known compounds, stigmasterol (3) and two furanocoumarins (4 and 5), from the dichloromethane extract of the seeds of Ducrosia anethifolia (DC.) Boiss. Their structures were determined using extensive 1D and 2D NMR, (ES)-HRMS and IR spectroscopic analyses and by comparison with literature data. Gas chromatography analysis of the fatty acids (FAs) of D. anethifolia seed oils (DAOs) showed high percentages of elaidic acid (C18:1 Δ9t) 65% and oleic acid (C18:1 Δ9c) 15%. The total tocopherol (tocols) content in DAOs was found to be 164 mg/100 g. The cytotoxic effect of the isolates was also evaluated using the MTT assay against the HCT-116 and SKOV-3 cell lines. The results showed that compound 2 was the most cytotoxic agent followed by compounds 1 and 4, which has an epoxide moiety that most likely contributes to its activity.     

Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a Péclet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation.     

The Impact of Apple Variety and the Production Methods on the Antibacterial Activity of Vinegar Samples

Apple vinegar is a natural product widely used in food and traditional medicine as it contains many bioactive compounds. The apple variety and production methods are two factors that play a major role in determining the quality of vinegar. Therefore, this study aims to determine the quality of apple vinegar samples from different varieties (Red Delicious, Gala, Golden Delicious, and Starking Delicious) prepared by three methods using small apple pieces, apple juice, and crushed apple, through determining the physicochemical properties and antibacterial activity of these samples. The antibacterial activity was studied against five pathogenic bacteria: Staphylococcus aureus, Klebsiella pneumonia, Escherichia coli (ATB: 57), Escherichia coli (ATB: 97), and Pseudomonas aeruginosa, using two methods, disk diffusion and microdilution, for determining the minimum inhibitory concentrations and the minimum bactericidal concentrations. The results of this study showed that the lowest pH value was 3.6 for Stark Delicious, obtained by liquid fermentation, and the highest acetic acid values were 4.7 and 4% for the vinegar of Red Delicious and Golden Delicious, prepared by solid fermentation, respectively. The results of the antibacterial activity showed considerable activity of apple vinegar on the tested strains. Generally, the Staphylococcus aureus strain appears less sensitive and Pseudomonas aeruginosa seems to be very sensitive against all samples, while the other strains have distinct sensitivities depending on the variety studied and the method used. A higher antibacterial activity was found in vinegar obtained by the apple pieces method and the Red Delicious variety, with a low MIC and MBC recorded, at 1.95 and 3.90 µL/mL, respectively. This study has shown that the choice of both apple variety and production method is therefore an essential step in determining and aiming for the desired quality of apple vinegar.     

ab-initio investigations of electronic and magnetic properties of the tetragonal chalcopyrite BeTiTe2 compound: DFT + U study

The spin-polarised structural, electronic, and magnetic properties of the chalcopyrite BeTiTe₂ compound in tetragonal structure (Be_0.50Ti_0.50Te) have been studied by employing first-principles full-potential linearised augmented plane wave plus local orbitals (FP-L/APW?+?lo) method within the density functional theory (DFT) and implemented in WIEN2k code. The exchange and correlation energy are described in two frameworks of GGA (generalised gradient approximation) and GGA?+?U (U is the Hubbard term). The structural analysis confirms that the ferromagnetic phase of the tetragonal BeTiTe₂ compound (Be_0.50Ti_0.50Te) is energetically more favourable; also different equilibrium lattice parameters, such as lattice constants (a₀ and c₀), bulk modulus (B₀), and its first-pressure derivative (B?) have been evaluated in both paramagnetic and ferromagnetic phases. The electronic results of the tetragonal BeTiTe₂ compound show a complete half-metallic behaviour. Moreover, the computed total magnetic moment of this compound is close to 4 μ_B, confirming its half-metallic ferromagnetic nature.     

Application of Mie theory and fractal models to determine the optical and surface roughness of Ag–Cu thin films

Thin films of Ag/Cu were deposited by reactive DC magnetron sputtering on (001)-oriented Si and glass substrates for various deposition times (4–24 min). These films were characterized by atomic force microscopy (AFM), and a power law scaling was performed on the obtained micrographs to investigate the self-affine nature of the sample morphology, which is indicative of a fractal structure. We applied the Higuchi’s algorithm to the AFM data to determine the fractal dimension of each sample, and the Hurst exponents were computed. The deposition time dependences of these parameters and the grain size distributions estimated from the UV–visible spectra using the Mie theory, allowed us to describe a particle formation mechanism during the deposition process, in which the length of continuous paths of conductive particles increases as the deposition time is increased. In agreement with this explanation, the electrical resistance decreased with the increment of the deposition time.     

Mesoscopic tube model of fluids composed of worm-like micelles

Rheological model of fluids involving Brownian relaxation, reptation, diffusion, and scission–recombination processes as relaxation mechanisms is formulated. Numerical solution of a particular example of the model displays the S-shape form of the shear rate versus shear stress curves observed in worm-like micellar solutions.     

The window layers effect on the hardness improvement of space solar cells exposed to the 1 MeV electron irradiations

Because of their state of art technology, GaAs solar cells are generally preferred for spatial applications. Exposure to proton and electron irradiations, solar cells suffer significant degradation in their performance such as short circuit current and open circuit voltage. Adding a window layer helps in effectively reducing the surface recombination at the emitter surface of the solar cell without absorbing the useful light required for the device. It remains to study the physics of the window-emitter hetero-interface in order to understand how the window layer presence increases the minority carrier lifetime of the solar cell exposed to particles irradiation. In this work Numerical simulation has been used to study the AlxGa1-xAs window composition effect on the current–voltage characteristics of a GaAs solar cell under AM0 illumination and exposed to 1 MeV electron irradiation. To predict the effect of window layers on solar cells degradation, the current voltage characteristic are evaluated for different electron irradiation fluences. The findings are supported by experimental data. They lead us to get to know how the window layer improves resistance to electron irradiation through its own parameters.     

Signal-levelling agents for eliminating the interferences of iron,aluminium, barium and calcium in the determination of lead by flame atomic absorption spectrometry

The interferences of iron, aluminium, barium and calcium on the determination of lead by flame atomic absorption spectrometry are discussed; a titration procedure was used. Ascorbic acid, citric acid, EDTA and nitric acid were used successfully for levelling the interfering effects from the cations.