On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.     

Mineral salts removal and lithium traces determination in highly concentrated solutions and natural brines

The usual methods, of lithium traces determination, refer in particular to the aqueous solutions whose dry residues do not exceed 7 g L⁻¹. Flame spectrometry or atomic absorption is used for the determination of the considered element.In the case of natural brines, the total dissolved salt ranges from 250 to 350 g L⁻¹. Consequently the determination of lithium traces in this kind of solutions, by the above mentioned spectroscopic methods, may be disturbed due to interferences phenomena. So, a preparatory processing step of the samples is needed.In order to prevent the mentioned phenomena, the total or partial removal of mineral salts, by adding appropriate organic solvent, is carried out. Accordingly, it is significant to make sure that the total quantity of lithium remains in the solution.Therefore, the experimental conditions (sulfate ion removal, solvent ratio and solid-liquid contact time) are optimized. After that the different experimental steps are arranged to make sure the lithium determination, by flame spectrometry, practicable.Finally, the established method is applied firstly to determine Li⁺ in some natural brines and secondly to estimate the lithium reserves in the Tunisian natural brines deposits.     

Nonlinear Degenerate Anisotropic Elliptic Equations with Variable Exponents and L1 Data

This paper is devoted to the study of a nonlinear anisotropic elliptic equation with degenerate coercivity, lower order term and L¹ datum in appropriate anisotropic variable exponents Sobolev spaces. We obtain the existence of distributional solutions.     

1,2,4-trihydroxynaphthalene-2-O-β-D-glucopyranoside: A new powerful antioxidant and inhibitor of Aβ42 aggregation isolated from the leaves of Lawsonia inermis

Mounting evidence indicates free radicals as toxic species causing damage to human cells leading to the pathogenesis of many diseases such as neurodegenerative disease. Plant derived antioxidants are considered as promising strategy to prevent free radical toxicity. In this study, the crude extract (CE), 50%MeOH, Petroleum Ether (PE) and Ethyl acetate (EA) fractions of Lawsonia inermis leaves were investigated for their antioxidant activity and their ability to counteract amyloid-β₄₂ (Aβ₄₂) aggregation. Elution of the most bioactive fraction (EA) on silica gel column chromatography led to six sub-fractions. The most active sub-fraction (1) was further resolved on silica gel column chromatography. A new compound with powerful antioxidant and anti-Aβ₄₂ aggregation properties was purified and characterised by spectroscopic methods as 1,2,4-trihydroxynaphthalene-2-O-β-D-glucopyranoside (THNG). This finding suggests that the antioxidant and anti-Aβ₄₂ aggregation activities of L. inermis leaves are strongly correlated to this compound.     

Extended Hardy-Littlewood inequalities and some applications

We establish conditions under which the extended Hardy-Little- wood inequality

where each is non-negative and denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on such that equality occurs in the above inequality if and only if each is Schwarz symmetric. We end this paper with some applications of our results in the calculus of variations and partial differential equations.

     

Flavonol triglycosides from the leaves of Hammada scoparia (POMEL) ILJIN

A new flavonol triglycoside, isorhamnetin 3-O-beta-D-xylopyranosyl-(1"-->3)-alpha-L-rhamnopyranosyl-(1'-->6")-beta-D-galactopyranoside, has been isolated from the leaves of Hammada scoparia together with two known compounds, isorhamnetin 3-O-beta-D-apiofuranosyl-(1'-->2")[alpha-L-rhamnopyranosyl-(1"-->6")]-beta-D-galactopyranoside and isorhamnetin 3-O-alpha-L-rhamnopyranosyl-(1'-->2")[alpha-L-rhamnopyranosyl-(1"-->6")]-beta-D-galactopyranoside. The structures were determined by spectroscopic methods.     

Synthesis,characterization, and application of sol gel derived Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> powder

This paper reports a successful preparation of a pure forsterite Mg₂SiO₄ using the sol–gel approach and its application for the removal of impurities from a Tunisian frying oil. Magnesium nitrate hexahydrate and tetraethylortho-silicate were used as magnesium and silicon precursors, respectively. The synthesis was held at different calcination temperatures for 30?min. The annealed samples were characterized by X-ray diffraction, Fourier transform infrared, scanning electron microscopy, and laser diffraction. The results revealed that the sample calcined at 500?°C was forsterite with unimodal particle size distribution (PSD) centered at 122.8?±?0.3?μm. The dispersion index I (indicator of particle size uniformity) was 1.84. With the temperature increase, well crystallized compounds were obtained. Their PSDs remain unimodal and shift towards smaller particles. A decrease of the dispersion index was also noted, indicating the formation of Mg₂SiO₄ with more uniform particle size. This study showed that 900?°C could be selected as energy saving temperature suitable for the preparation of a pure and well crystallized Mg₂SiO₄ within just 30?min of annealing time. The obtained silicate exhibited promoting results for the purification of waste frying oils.

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Pure and fine Mg₂SiO₄ powder with unimodal particle size distribution was prepared by sol gel route under energy saving conditions. The obtained magnesium orthosilicate showed excellent results for waste frying oil purification

     

Orthorhombic and monoclinic ferroelectric phases investigated by Raman spectroscopy in PZN-4.5%PT and PZN-9%PT crystals

Polarized Raman spectra measurements have been performed on orientated single crystals of Pb[(Zn_1/3Nb_2/3)_0.955Ti_0.045]O₃ (PZN-4.5%PT) and Pb[(Zn_1/3Nb_2/3)_0.91Ti_0.09]O₃ (PZN-9%PT) poled by an electric field along the pseudo-cubic direction in order to determine the nature of the induced ferroelectric phases. Under field-cooled (FC) conditions the ferrolectric phase transition sequence, tetragonal-orthorhombic-rhombohedral, was observed in PZN-4.5%PT. Comparison between the phase transitions induced in PZN-9%PT and PZN-4.5%PT crystals in FC shows that the low- temperature ferroelectric phase in PZN-9%PT cannot be orthorhombic and it can be attributed to the monoclinic phase. The characteristic temperatures found by Raman spectroscopy correspond to those obtained by dielectric measurements and by X-ray diffraction reported previously.     

Copper(I)-doped Wyoming’s montmorillonite for the synthesis of disubstituted 1,2,3-triazoles

A new catalytic system based on copper(I)-doped Wyoming’s montmorillonite was elaborated. This system was studied and was found to catalyze the formation of 1,4-disubstituted 1,2,3-triazoles when starting from azides and alkynes. It was used for the synthesis of a few triazole derivatives to show its usefulness.