Positive Solutions to Singular Semilinear Elliptic Problems

We obtain a characterization of all locally bounded functions p ≥ 0 for which the equation (E) Δu +p(x)ψ(u) = 0 has a positive solution in Ω vanishing on the boundary, where Ω is a domain of ℝ^N and ψ > 0 is a nonincreasing continuous function on ]0,∞[. In particular, for Ω = ℝ^N with N ≥ 3, it is shown that (E) has a (unique) positive solution in ℝ^N which decays to zero at infinity if and only if the set {p > 0} has positive Lebesgue measure and This condition can be replaced by if p is radial.     

Pterin chemistry. 45. A new and clear synthesis of isomer-free pteroyl-gamma-L-glutamyl-L-glutamic acid

A new and unequivocal synthesis of pteroyl-λ-L-glutamyl-L-glutamic acid free of isomers is described. A melt of N(2′)-acetyl-6-formylpterine and trimethyl-N-(p-amino-benzoyl)-λ-L-glutamyl-L-glutamate was quantitatively converted to 6-azomethin-pterine-trimethylester XI. NaBH₄-reduction followed by basic hydrolysis of acetyl and methyl ester groups gives pure pteroyl-λ-glutamyl-glutamic acid in good yield.     

Calderon’s Reproducing Formula Related to the Dunkl Operator on the Real Line

 We consider a generalized convolution , , on the real line generated by the Dunkl operator

Calderon’s Reproducing Formula Related to the Dunkl Operator on the Real Line

 We consider a generalized convolution , , on the real line generated by the Dunkl operator

Applications involving the iodide ion: VII. Determination of small amounts of cerium(IV) and analysis of its mixtures with some metal ions

A simple, rapid, and reliable method for cerium(IV) alone; in presence of a variety of cations involving rare earths and iron (III); or in binary, ternary, and quaternary mixtures is given. By its aid 10^?3 down to 1.5 × 10^?5 mole of cerium(IV) were determined with requisite accuracy and precision. The potential breaks detecting the end points ranged from a maximum of 410 to a minimum of 100 mV/0.1 ml of 0.05 or 10^?4M titrant, respectively. Analysis of 15 mixtures using the present method together with other recommended procedures was always much less tedious or time-consuming than reported methods.     

Redox properties of cobalt(III) mixed ligand complexes. II. Redox titration of some organic and inorganic substances potentiometrically

A stable solution of (cobalt(III)(salen))₂O₂ was prepared under optimum conditions for its use for the potentiometric determination of xylenols, hydroquinone, sodium thiosulfate, and sodium metabisulfite, by iodide reduction of unreacted cobalt(III) complex and back titrating excess iodide with mercury(II) using silver amalgum and SCE combination. The possible schemes for the course of the redox reactions were suggested. The procedure was also evaluated in comparison with those mentioned in the literature.     

Application of Fast Grey RA to the spectrophotometric determination of copper in soft tissues of Egyptian camels

Copper in different organs of Egyptian camels was successfully determined spectrophotometrically using Fast Grey RA. Its values amounted to: 200.8 ± 11.4, 155.8 ± 16.1, 142 ± 6.8, 128.3 ± 6.9, 117.6 ± 5.1, 113.0 ± 5.3, 86.3 ± 3.2, 79.0 ± 5.2, 76.3 ± 3.7, 66.3 ± 4.3, 59.8 ± 1.7, 57.6 ± 3.0, 53.0 ± 2.2, 36.3 ± 2.3 and 3.03 ± 0.32 μg/g dry matter of hair, liver, spleen, lung, heart, integument, muscle, brain, lymph gland, small intestine, large intestine, kidney, adrenal, fourth stomach, and hump, respectively, while 1 ml citrated blood contained 6.97 ± 0.64 μg. Of 16 elements mentioned, only vanadium interferes with the determination of copper in hair by the present method.     

On the reaction between iodide and mercury(II)

A survey on the iodide-mercury(II) reaction and its analytical uses is given. Titrations of iodide with mercury(II) in various acidities, using nitrate, acetate, and chloride as titrants and silver or platinum amalgam as the indicator electrode, showed that mercury(II) nitrate is the best titrant giving 0.46 V/0.1 ml potential break in comparison with 0.14 V/0.1 ml of mercury(II) chloride and 0.35V/0.1 ml of mercury(II) acetate, all titrants being 0.05 M in mercury(II).     

Radiation effects on polymers—IV: Straight radiation vulcanization of styrene-butadiene rubber mixes

Vulcanization of styrene-butadiene rubbers was carried out by gamma radiation in air. For unloaded unextracted rubbers, the dose required for optimum cross-linking was about 40 megaroentgens (MR). Elimination of foreign materials and stabilizers and also incorporation of filler affected the vulcanization. Loaded samples gave vulcanizates with best complex physico-mechanical properties for filler content of 50 (phr) and a dose of 30 MR. Evaluation of various fillers has shown that the best properties were obtained with HAF among the black fillers and silica in the case of white fillers.     

Extraction of Eu(III) by dinonylnaphthalenesulfonic acid and synergistic effects of crown ethers and trioctylphosphine oxide

The extraction of Eu(III) by dinonylnaphthalenesulfonic acid (HDNNS) in benzene from nitrate and perchlorate solutions has been investigated. For nitrate solutions the ionic strength of the aqueous phase was kept constant at 0.1M using NaNO₃–HNO₃ mixtures. The Eu distribution was measured at different temperatures. The following stoichiometric formulae for the Eu species in benzene were derived: Eu(NO₃) (H_n–1 (DNNS)_n)₂ and Eu(H_n–1 (DNNS)_n)₃, from the nitrate and perchlorate medium respectively (n being a small number, e.g. 1, 2 or 3). The equilibrium constants were calculated and the thermodynamic parameters of the system were determined. When adding dibenzo-24-crown-8, dicyclohexyl-18-crown-6 or trioctylphosphine oxide, no synergism, but rather antagonism was observed.