An algorithm for linearly constrained nonlinear programming problems

In this paper an algorithm for solving a linearly constrained nonlinear programming problem is developed. Given a feasible point, a correction vector is computed by solving a least distance programming problem over a polyhedral cone defined in terms of the gradients of the “almost” binding constraints. Mukai's approximate scheme for computing the step size is generalized to handle the constraints. This scheme provides an estimate for the step size based on a quadratic approximation of the function. This estimate is used in conjunction with Armijo line search to calculate a new point. It is shown that each accumulation point is a Kuhn-Tucker point to a slight perturbation of the original problem. Furthermore, under suitable second order optimality conditions, it is shown that eventually only one trial is needed to compute the step size.     

The use of kinetic methods for the determination of ultra-trace amount of iodide in water

A new method for the determination of ultra-trace amounts of iodide ion w as developed. The proposed method employs ABTS, (2.2′-azinobis(3-ethylbenzothiazoline-6-sulphonic acid)), as the chromogenic reagent, and made full use of the advantages of stopped-flow methodology. This method was found to be selective and sensitive. The method was based on the monitoring of the alteration in the rate of formation of the cation radical of ABTS by oxidation with chloramine-T using a stopped-flow system. Traces of iodide markedly increases the rate of the reaction. The alteration is proportional to the concentration of the iodide which can be determined over the range 0–50 ppb with an RSD of less than 0.5% over this range.     

Kinetics and mechanism of oxidation of N,N-bis(salicylaldehyde-1,2-diaminoethane) cobalt(II) by N-bromosuccinimide in aqueous acidic medium

The kinetics of oxidation of N,N-bis(salicylaldehyde-1,2-diaminoethane) cobalt(II) complex by N-bromosuccinimide (NBS) in aqueous acid and H₂O–MeOH solvent mixtures were studied spectrophotometrically over the 20–40 °C range, 0.1–0.5 mol dm^?3 ionic strength, 2.2–2.8 pH range and 0–40 wt% MeOH–H₂O solvent mixtures for a range of NBS and complex concentrations. The rate shows first-order dependence on both [NBS] and [complex] and decreases with pH over the range studied. The protonated form of N-bromosuccinimide was identified as the main reactive species. An inner-sphere mechanism involving free radicals is proposed.     

Malayanines A and B, two novel limonoids from Chisocheton erythrocarpus Hiern

Two structurally interesting novel limonoids, malayanine A and malayanine B, were isolated from the bark of Chisocheton erythrocarpus Hiern. The structures were fully characterized through spectroscopic methods.     

Experimental determination and prediction of (solid + liquid) phase equilibria for binary mixtures of heavy alkanes and fatty acids methyl esters

Solid–liquid equilibria for three binary mixtures of {n-eicosane (1) + methyl palmitate (2)}, {n-tetracosane (1) + methyl stearate (2)} and {n-octacosane (1) + methyl stearate (2)} were measured using differential scanning calorimeter. Simple eutectic behaviours for these systems were observed. The experimental results were correlated by means of the modified UNIFAC (Larsen and Gmehling versions), UNIQUAC and ideal models. The root-mean-square deviations of the solubility temperatures for all measured data vary from 0.21 K (for UNIQUAC model) to 1.07 K (for Ideal model) and depend on the particular model used. The best solubility correlation was obtained with UNIQUAC model.     

Gas-phase reactivity of 2,7-dimethyl-[1,2,4]-triazepine thio derivatives toward Cu+ cation: a DFT study

The gas-phase interactions of 2,7-dimethyl-[1,2,4]-triazepine and its thio derivatives with Cu+ were studied through the use of high-level density functional theory (DFT) calculations. The structure of all possible tautomers and their conformers was optimized at the B3LYP/6-31G(d) level of theory. Final energies were obtained at the B3LYP/6-311+G(2df,2p) level. It has been found that the direct association of Cu+ occurs at the oxygen atom attached to position 3 in the case of the dioxo derivative and at the sulfur atom in all other cases. For the dithio derivatives, the global minimum of the PES corresponds to the structure in which the metal ion bridges between the heteroatom at position 3 and the nitrogen atom at position 4 of the corresponding enolic tautomer, forming a four-membered ring structure; for the dioxo derivative, this conformer competes with the ketone tautomer. Moreover, the isomerization processes leading from the most stable adduct to the other stable conformers were investigated. Among all the considered compounds, the 3,5-dithiotriazepines-Cu+ is found to be the one that associates Cu+ more tightly in the gas phase. The calculated Cu+ binding energies show a good correlation with the experimental proton affinities.     

An acceleration scheme for cyclic subgradient projections method

An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis (tese de Doutoramento), Instituto de Matemática da UFRJ, Cidade Universitária, Rio de Janeiro, Brasil, 1981), which is designed for simultaneous algorithms, is used in the algorithm to speed up the fully sequential cyclic subgradient projections method. A convergence proof is presented. The advantage of using this strategy is demonstrated with some examples.     

Uniform and weak stability of Bresse system with two infinite memories

In this paper, we consider one-dimensional linear Bresse systems in a bounded open domain under Dirichlet–Neumann–Neumann boundary conditions with two infinite memories acting only on two equations. First, we establish the well-posedness in the sense of semigroup theory. Then, we prove two (uniform and weak) decay estimates depending on the speeds of wave propagations, the smoothness of initial data and the arbitrarily growth at infinity of the two relaxation functions.