Cone characterizations of positive semidefinite operators on a Hilbert space

We extend finite dimensional results of Han and Mangasarian characterizing positive semidefinite matrices. We solve a linear complementarity problem for an operator defined on a Hilbert space, and state a generalization of Moreau's theorem.     

Mechanism of positive iodine reactions: Kinetics of oxidation of semicarbazide by iodamine-T, iodine monochloride and iodine

Kinetics of oxidation of semicarbazide (SC) by iodamine-T (IAT), iodine monochloride and aqueous iodine has been studied in aqueous perchloric acid medium. The rate laws followed by the oxidation of SC were determined. The rates decreased slightly with increase in ionic strength of the medium in IAT and ICI oxidations, while the reverse trend was observed with I₂. Decrease in dielectric constant of the medium increased the rates with IAT and ICI, while it decreased the rate in I₂ oxidations. Addition of the reduced product,p-toluene-sulphonamide had no effect on the rate with IAT. Addition of I⁻ had slight negative and positive effects on the rates of oxidations with IAT and ICI, respectively, but the negative effect was considerable in I₂ oxidations. Mechanisms consistent with the observed rate laws have been proposed and discussed. Rate determining steps have been identified and their coefficients calculated. These constants were used to predict the rate constants from the deduced rate laws as [SC], [H⁺] and [I⁻] varied. Reasonable agreement between the calculated constants and experimental values provide support for the suggested mechanisms.     

N-substituted phenothiazines as indicators in titrations with chloramine-T

Trifluoperazine dihydrochloride, butaperazine dimaleate, promethazine hydrochloride, diethazine hydrochloride, prochlorperazine maleate and chlorpromazine hydrochloride have been studied as redox indicators in titrations of hydroquinone, metol and ascorbic acid with chloramine-T. The end-points obtained are sharper than with conventional indicators. The molar absorptivities of the oxidized indicators are reported. Simple but accurate methods for the determination of hydroquinone and metol are described.     

Effect of substituents on the rate of oxidation of anilines with peroxomonosulfate monoanion (HOOSO−3) in aqueous acetonitrile: A mechanistic study

Mechanistic studies on the oxidation of 18 meta‐, para‐, and ortho‐substituted anilines (Ans) by HOOSO⁻₃ in aqueous acetonitrile medium have been performed. The reaction can be characterized by the experimental rate equation, The addition of p‐toluenesulfonic acid (TsOH) retards the reaction. The increase in the reactivity of anilines as the medium is made more aqueous is interpreted. The reaction is enhanced by electron‐donating groups on the amine in the series consistent with the rate‐limiting nucleophilic attack of the amine on the persulfate oxygen. The proposed mechanism involves the conversion of phenylhydroxylamine to nitrosobenzene in a fast step. The ESR study reveals the absence of free radicals in the reaction. Various attempts have been made to analyze the experimental rate constants in terms of LFER plots. Improved correlations are obtained with σ⁻ values and the σ⁻ form of the Yukawa–Tsuno equation. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 649–657, 2005     

Generalized linear complementarity problems

It has been shown by Lemke that if a matrix is copositive plus on ⁿ , then feasibility of the corresponding linear complementarity problem implies solvability. In this article we show, under suitable conditions, that feasibility of ageneralized linear complementarity problem (i.e., defined over a more general closed convex cone in a real Hilbert space) implies solvability whenever the operator is copositive plus on that cone. We show that among all closed convex cones in a finite dimensional real Hilbert Space, polyhedral cones are theonly ones with the property that every copositive plus, feasible GLCP is solvable. We also prove a perturbation result for generalized linear complementarity problems.This research has been partially supported by the Air Force Office of Scientific Research under grants #AFOSR-82-0271 and #AFOSR-87-0350.     

Energetics and structure of the hydrated gaseous halide anions

Energetics and geometries for the hydrated gaseous halide anions have been computed from a simple model in which the molecular dipole of water was composed of two parts, one due to a lone pair on oxygen (60%) and the rest to formal charges on the nuclei. The calculations were made for both the symmetric and nonsymmetric structures. A variety of structures were used to compute potential energies and distances with up to six water molecules. The total energy consisted of a sum of electrostatic, polarization, dispersion, and repulsion terms. Various sets of repulsive potential parameters, ranging from those determined from molecular beam experiments to those determined using experimental ion–water distances or energies, have been employed to compute repulsive interaction energies. It was found that the range parameters play a significant role in deciding the magnitudes of the distances and energies, as the latter are most sensitive to them. It was also shown that with a simple correlation scheme the consistency of the experimental energies and distances can be tested separately without using repulsive potential parameters from other sources. It also suggests that a range of parameters can be used to compute repulsion energies. Despite the fact that the model is greatly simplified, the agreement of both the predicted ion-oxygen distances and energies with both experiment and other calculations is excellent. A detailed analysis of our calculation suggests that the negative ion clusters with one to three water molecules contain symmetric orientation of water molecules, while those with more than three may contain asymmetric orientations of water molecules or a mixture of both. From the log–log plots of hydration energies versus (R + radius of water molecule), we have proposed empirical expressions of the type ΔE_n?1,n = 10·0^x (R + 1.38)^?y with both Pauling's and Ladd's radii for univalent ions with which stepwise hydration energies of the latter can be predicted if we know thier radii. The values predicted for the alkali cations are in excellent agreement with the experimental and theoretical values, indicating the consistency of the simple model.     

Prochlorperazine bismethanesulfonate as a new reagent for the spectrophotometric determination of palladium

A simple, rapid, and selective method for the determination of palladium is described. The orange-red palladium(II)-prochlorperazine bismethanesulfonate complex in the presence of hydrochloric acid-sodium acetate buffer exhibits maximum absorbance at 480 nm with a molar absorptivity of 4.32 × 10³ liters mol^?1 cm^?1. The sensitivity of the reaction is 24.62 ng cm^?2. The system obeys Beer's law over the concentration range 0.4–20 ppm of palladium with an optimum concentration range of 1–19 ppm. The apparent stability constant of the complex is found to be log K = 5.3 ± 0.1 at 27 °C. The effects of pH, time, temperature, order of addition of reactants, reagent concentration, and interferences from various ions are reported. The proposed method offers the opportunity to carry out the determination at room temperature without the need for an extraction step. The method is also found to be suitable for the determination of palladium in jewelry alloy.