Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

SDP diagonalizations and perspective cuts for a class of nonseparable MIQP

We present a new approach, requiring the solution of a SemiDefinite Program, for decomposing the Hessian of a nonseparable mixed-integer quadratic problem to permit using perspective cuts to improve its continuous relaxation bound. The new method favorably compares with a previously proposed one requiring a minimum eigenvalue computation.     

Promotion by phosphorus compounds of ruthenium-catalyzed methyl formate homologation

Trivalent phosphorus compounds are promoters for methyl formate homologation to ethanol and ethyl formate catalyzed by ruthenium compounds in the presence of iodide at 220°C and 27 MPa of synthesis gas. Under these conditions the phosphines are quaternized, but decomposition of phosphonium salts occurs during the reaction. Promotion is also observed for methyltriphenyl-phosphonium bromide and triphenylphosphine sulfide, but benzyltrimethyl-ammonium bromide, triphenylarsine, and triphenylantimony are not effective. The major ruthenium species present is Ru(CO)₃I₃^- but with triphenylantimony a trimethylantimony complex, Ru(CO)₂(Sb(CH₃)₃)₂I₂, can be isolated in high yield.     

Nouveaux exemples d'acétonides d'aldéhydosucres furanniques

Further examples of O-isopropylidenaldehydosugars in the furanose series Formyl-bearing furanose derivatives 1–3 (α-D -xylo or α-D -erythro configurations) and 5–8 (configurations α-D -ribo, α-D -lyxo, β-L -threo and D -arabino) have been prepared by classical synthetic steps and their properties mainly spectroscopic, reported. The coupling constant between the formyl and the vicinal proton is always small. Like other members of the series, these new aldehydosugars constitute very useful and flexible synthetic intermediates.     

The reactivity of the A-CH=N-NR-CX-B system. 1,3,4-Oxadiazoles and 2,3,4,5-tetrahydro-1,2,4-triazin-3-ones through the 1–5 and 1–6 cyclization reactions of α-thienylglyoxal monosemicarbazones

The factors influencing the reactivity of α-thienylglyoxal monosemicarbazones when treated with cyclizing reagents (bromine/sodium acetate and hydrobromic acid in acetic acid) were investigated. Depending on the experimental conditions, on the position of the substituent on the semicarbazide residue, and on the cyclizing agent, the substrates 1a-e give the semicarbazone bromides 2a-b, 5 , the 1,3,4-oxadiazoles 3a-c , the 1,2,4-triazine 11 and the 2,3,4,5-tetrahydro-1,2,4-triazine-3-ones 6, 8 and 9 . Compound 6 by thermolysis undergoes ring contraction in the Δ²-1,3,4-oxadiazoline 12 , while treatment with base involves the conversion of 6 into 1,2,4-triazol-5-one 13 . Ir, nmr and mass spectra support the reported structures.     

The use of chiral interaction reagents in the separation of D(−)-and L(+)-ascorbic acid by ion interaction reversed-phase HPLC

Summary An HPLC reversed-phase ion interaction reagent method is presented, which makes use of chiral compounds as the interaction reagents. By employing the optical isomeric forms of malic, tartaric and mandelic acids as the interaction reagents, a good separation of D(−) and L(+) ascorbic acid has been achieved. The method has also been applied to the identification of vitamin C in some medical formulations. The separation of te enantiomeric forms of DL malic acid has been attempted and a shor discussion is presented about the elution sequence in chromatographic separation of D- and L-enantiomers.     

Optimization by experimental design and artificial neural networks of the ion-interaction reversed-phase liquid chromatographic separation of twenty cosmetic preservatives

Particular attention are recently receiving antimicrobial agents added as preservatives in hygiene and cosmetics commercial products, since some of them are suspected to be harmful to the human health. The preservatives used belong to different classes of chemical species and are generally used in their mixtures. Multi-component methods able to simultaneously determinate species with different chemical structure are therefore highly required in quality control analysis. This paper presents an ion interaction RP-HPLC method for the simultaneous separation of the 20 typical antimicrobial agents most used in cosmetics and hygiene products, that are: benzoic acid, salicylic acid, 4-hydroxybenzoic acid, methyl-, ethyl-, propyl-, butyl-, benzyl-benzoate, methyl-, ethyl-, propyl-, butyl-, benzyl-paraben, o-phenyl-phenol, 4-chloro-m-cresol, triclocarban, dehydroacetic acid, bronopol, sodium pyrithione and chlorhexidine. For the development of the method and the optimization of the chromatographic conditions, an experimental design was planned and models were built by the use of artificial neural network to correlate the retention time of each analyte to the variables and their interactions. The neuronal models developed showed good predictive ability and were used, by a grid search algorithm, to optimize the chromatographic conditions for the separation of the mixture.