Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

Some new nonlinear inequalities and applications to boundary value problems

In this paper, we establish some new nonlinear integral inequalities of the Gronwall–Bellman–Ou-Iang-type in two variables. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of differential equations. We illustrate this by applying our new results to certain boundary value problem.     

O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.     

Ultraviolet photolysis of CH2I2 in methanol: O-H insertion and HI elimination reactions to form a dimethoxymethane product

Ultraviolet photolysis of low concentrations of CH2I2 in methanol solution found that CH2I2 is converted into dimethoxymethane and some H+ and I- products. Picosecond time-resolved resonance Raman (ps-TR3) experiments observed that the isodiiodomethane (CH2I-I) photoproduct decayed faster as the concentration of methanol increases, suggesting that isodiiodomethane is reacting with methanol. Ab initio calculations indicate isodiiodomethane is able to react with methanol via an O-H insertion/HI elimination to form an iodoether (ICH2-O-CH3) and HI products. The iodoether can then further react via another O-H insertion/HI elimination reaction to form the dimethoxymethane (CH3-O-CH2-O-CH3) observed in the photochemistry experiments. A reaction mechanism consistent with these experimental and theoretical observations is proposed.     

Comparison of the dehalogenation of dihalomethanes (CH2XI, where X = Cl, Br, I) following ultraviolet photolysis in aqueous and NaCl saltwater environments

The ultraviolet photolysis of low concentrations of CH(2)XI (X = Cl, Br, I) were investigated in water and saltwater solutions by photochemistry and picosecond time-resolved resonance Raman spectroscopy. Photolysis in both kinds of solutions formed mostly CH(2)(OH)(2) and HI and HX products. However, photolysis of the CH(2)XI molecules in saltwater resulted in production of some CH(2)XCl products not observed in aqueous solutions without salt present. The appearance of these new products in saltwater solutions is accompanied by a decrease in the amount of CH(2)(OH)(2), HI, and HX products compared to photolysis in aqueous solutions without salt present. The possible implications for photolysis of CH(2)XI and other polyhalomethanes in seawater and other salt aqueous environments compared to nonsaltwater solvated environments is briefly discussed.     

Filamentous growth in activated sludge

Applied Biochemistry and Biotechnology - Bulking and foaming in activated sludge have been associated with filamentous overgrowth. FilamentousNocardia amarae and nonfilamentousPseudomonas...