On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

An entropy-based uncertainty principle for a locally compact abelian group

We classify all functions on a locally compact, abelian group giving equality in an entropy inequality generalizing the Heisenberg Uncertainty Principle. In particular, for functions on a real line, we proof a conjecture of Hirschman published in 1957.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Some algorithms for hemiequilibrium problems

In this paper, we suggest and analyze a class of iterative methods for solving hemiequilibrium problems using the auxiliary principle technique. We prove that the convergence of these new methods either requires partially relaxed strongly monotonicity or pseudomonotonicity, which is a weaker condition than monotonicity. Results obtained in this paper include several new and known results as special cases.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.     

Vacancy ion-exclusion chromatography of carboxylic acids on a weakly acidic cation-exchange resin

In this preliminary study, a new approach to ion-exclusion chromatography is proposed to overcome the relatively poor conductivity detection response which occurs in ion-exclusion chromatography when acids are added to the eluent in order to improve peak shape. This approach, termed vacancy ion-exclusion chromatography, requires the sample to be used as eluent and a sample of water to be injected onto a weakly acidic cation-exchange column (TSKgel OApak-A). Vacancy peaks for each of the analytes appear at the retention times of these analytes. Highly sensitive conductivity detection is possible and sharp, well-shaped peaks are produced, leading to efficient separations. Retention times were found to be affected by the concentration of the analytes in the eluent, and also by the presence of an organic modifier such as methanol in the eluent. Detection limits for oxalic, formic, acetic, propionic, butyric and valeric acids were 0.1, 0.2, 0.3, 0.3, 0.4 and 0.5 microM, respectively, and linear ranges for some acids extended over two orders of magnitude. Precision values for retention times were 0.21% and for peak areas were <1.90%. The vacancy ion-exclusion chromatography method was found to give detection responses four to 10 times higher than conventional ion-exclusion chromatography using sulfuric acid eluent and two to five times higher than conventional ion-exclusion chromatography using benzoic acid eluent.     

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.     

Ion-exclusion chromatography with conductimetric detection of aliphatic carboxylic acids on a weakly acidic cation-exchange resin by elution with benzoic acid-beta-cyclodextrin

In this study, an aqueous solution consisting of benzoic acid with low background conductivity and beta-cyclodextrin (beta-CD) of hydrophilic nature and the inclusion effect to benzoic acid were used as eluent for the ion-exclusion chromatographic separation of aliphatic carboxylic acids with different pKa values and hydrophobicity on a polymethacrylate-based weakly acidic cation-exchange resin in the H+ form. With increasing concentration of beta-cyclodextrin in the eluent, the retention times of the carboxylic acids decreased due to the increased hydrophilicity of the polymethacrylate-based cation-exchange resin surface from the adsorption of OH groups of beta-cyclodextrin. Moreover, the eluent background conductivity decreased with increasing concentration of beta-cyclodextrin in 1 mM benzoic acid, which could result in higher sensitivity for conductimetric detection. The ion-exclusion chromatographic separation of carboxylic acids with high resolution and sensitivity was accomplished successfully by elution with a 1 mM benzoic acid-10 mM cyclodextrin solution without chemical suppression.     

Selected valence electron split-shell molecular orbital calculations on the diatomic interhalogen molecules

Selected valence electron split-shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split-shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.