Multiplicity of positive solutions for a critical quasilinear elliptic system with concave and convex nonlinearities

In this paper, by using the Lusternik–Schnirelmann category, we obtain a multiplicity result for a quasilinear elliptic system with both concave and convex nonlinearities and critical growth terms in bounded domains.     

A sensor based on silver nanoparticles synthesized on carbon graphite sheets for the electrochemical detection of nitrofurazone: Application: Tap water,commercial milk and human urine

Nitrofurazone is a nitrofuran-family synthetic chemical that has been used to treat bacterial infections since 1993. Silver nanoparticles synthesized by the thermal technique on graphite carbon sheets under optimal conditions were used to develop a highly sensitive electrochemical sensor. The main experimental characteristics are optimized to assure that this sensor functions correctly. Scanning electron microscope, X-ray diffraction, infrared spectroscopy were used to determine the chemical composition and morphology of the prepared pastes. With a maximal reduction peak of La nitrofurazone observed at ?0.57V/Ag-NPs@CPE versus Ag/AgCl, this sensor demonstrated good electrocatalytic activity for the reduction of La nitrofurazone. The influence of phosphate buffer solution pH indicates that the numbers of protons and electrons in the reaction at the surface of our constructed sensor were the same. The LOD and LOQ were calculated to be 1.2 × 10^?8 M and 1.3 × 10^?7 M, respectively. Using the differential pulse voltammetry technique, the calibration curve was established in the concentration range of 10^?4 M to 2 × 10^?7 M. Our Ag-NPs@CPE sensors were evaluated in order to detect nitrofurazone in real contaminated samples tap water, commercial milk, and human urine, in particular. The electroanalysis results show a very high recovery rate of more than 96% on average, permitting us to determine that our sensors are functional under optimum working conditions.     

Experimental and theoretical study on 3,5‐(oxo/thioxo) derivatives of 2,7‐dimethyl‐1,2,4‐triazepines–iodine molecular complexes

Intermolecular charge‐transfer (CT) spectra of 3‐thioxo‐5‐oxo‐, 5‐thioxo‐3‐oxo‐, and 3,5‐dithioxo‐ derivatives of 2,7‐dimethyl‐[1,2,4]‐triazepine 1:1 molecular complexes with molecular iodine were studied in the UV‐visible region. Equilibrium constants and free energy changes of the formed complexes were determined in solution. Ab initio calculations at HF/LANL2DZ* and MP2/LANL2DZ* were carried out to establish the nature of the complexation site, to determine the complex structures, and to examine the basicity of these compounds toward molecular iodine. The 3,5‐dithioxo‐2,7‐dimethyl‐[1,2,4]‐triazepine is the most basic one toward molecular iodine. In all cases, the complexation takes place at the heteroatom attached to position 3 of the triazepine. Hence, although in general, thiocarbonyls are stronger bases than carbonyls in the gas phase, 5‐thioxo‐2,7‐dimethyl‐[1,2,4]‐triazepin‐3‐one behaves as an oxygen base towards I₂. Experimental free energies in solution and gas‐phase computational values are linearly correlated. Copyright © 2009 John Wiley & Sons, Ltd.     

Aggregation of hydrophobically modified polysaccharides in solution and at the air-water interface

The present article focuses on the comparative study of physicochemical properties of two ionic pullulan derivatives modified by 10 or 35 C8 chains per 100 anhydroglucose units, named CMP10C8 and CMP35C8, respectively. In aqueous solutions, these derivatives exhibited an associative behavior as evidenced by pyrene fluorescence spectroscopy. This phenomenon, which stems from intra- and/or intermolecular interactions between the hydrophobic groups grafted on the polymer backbone, results in the formation of more or less condensed aggregates depending on the C8 ratio and the ionic strength of the media. The hydrophobically modified pullulans also displayed surface properties. Their adsorption at the air-solution interface was assessed from surface tension measurements. The results showed that both hydrophobized polymers adsorb in a coil conformation occupying a large interfacial molecular area. The comparison of these molecular areas indicated that CMP35C8 adopts a more shrunken conformation at the interface than CMP10C8, due to stronger intramolecular interactions. The stability of the adsorbed monolayer under bulk dilution was investigated by ellipsometric measurements. Whereas bulk dilution had no effect on the stability of the adsorbed CMP35C8 film, it provoked significant changes in the adsorbed CMP10C8 monolayer. The stability of the CMP35C8 monolayers was attributed to the existence of intermolecular associations between the adsorbed coils.     

Influence of alkyl chains length on the conformation and solubilization properties of amphiphilic carboxymethylpullulans

The existence of inter- and/or intramolecular interactions in aqueous solutions of hydrophobically modified polysaccharides induces specific macromolecular conformations at the air–solution interface and in the bulk, where hydrophobic microdomains may be formed. The present work focuses on the interfacial and solubilizing properties of amphiphilic pullulans (CMP₁₂C₈, CMP₇C₁₄, and CMP₄C₁₆) differing in the length and percentage of alkyl chains grafted to the anhydroglucose units. The surface tension studies of these polymers evidence a marked difference between the interfacial properties of CMP₁₂C₈ on one hand and those of CMP₇C₁₄ and CMP₄C₁₆ on the other hand. Pyrene fluorescence spectroscopy and benzophenone solubilization experiments demonstrate a similar partition. Increasing alkyl chains length from eight up to 14 or 16 carbons improves the solubilization properties of nonpolar molecules, even though at the same time, the average number of grafted chains per 100 anhydroglucose units is decreased from 12 down to seven and four for the three compounds, respectively.     

Opérateurs pseudo-Fredholm dans les espaces de banach

Résumé  Les opérateurs pseudo-Fredholm ont été introduits et étudiés par M. Mbekhta dans le cas des espaces de Hilbert. Dans ce travail on se propose d’étendre l’étude de cette classe au cadre plus général des espaces de Banach. Notamment, nous montrons que cette classe reste stable par des petites perturbations. Ce dernier résultat donne une généralisation à un Théorème de P. Aiena et M. Mbekhta

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