Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Ab-initio molecular dynamics based on non-local density functional procedure with Gaussian basis; study of structural and temperature behaviour of metallic clusters

An ab-initio molecular dynamics procedure without precalculation of the Born-Oppenheimer energy surface based on an iterative non-local density functional method employing Gaussian atomic basis has been developed. Analytical gradients are calculated and used for the propagation of nuclei. Sufficiently long trajectories can be calculated at an acceptable computational cost, allowing for analysis of dynamical behaviour of small metallic clusters. This is illustrated on an example of the Li₈ cluster. Temperature behaviour of different type of isomers has been investigated. Calculated power spectra allow to identify the presence of more than one isomeric forms along the given trajectories.     

Determination of Low Contents of Fenpiverine Bromide by Extraction Spectrophotometry

An ion-pair extraction spectrophotometry method was developed for the determination of fenpiverine bromide in tablets. To determine this substance it was necessary to find experimental conditions that would allow eliminating the influence of other components of the tablets. Attention was paid to the fact that a suitable pH of water phase was necessary to achieve high selectivity.Received December 11, 2002; accepted April 24, 2003 Published online July 28, 2003     

Oxygen adsorption on hydrated gold cluster anions: experiment and theory

The discovery that supported gold clusters act as highly efficient catalysts for low-temperature oxidation reactions has led to a great deal of work aimed at understanding the origins of the catalytic activity. Several studies have shown that the presence of trace moisture is required for the catalysts to function. Using near-atmospheric pressure flow reactor techniques, we have studied humidity and temperature effects on the reactivity of gas-phase gold cluster anions with O2. Near room temperature, the humid source produces abundant gold-hydroxy cluster anions, Au(N)OH(-), and these have a reversed O2 adsorption activity: Nonreactive bare gold clusters become active when in the form Au(N)OH(-), while active bare clusters are inactive when -OH is bound. The binding energies for the stable structures obtained from density functional calculations confirm fully these findings. Moreover, the theory provides evidence that electron-transfer induced by the binding of a OH group enhances the reactivity toward molecular oxygen for odd anionic gold clusters and suppresses the reactivity for the even ones. The temperature dependence of O2 addition to Au(3)OH(-) and Au(4)(-) indicates deviations from equilibrium control at temperatures below room temperature. The effects of humidity on gold cluster adsorption activity support the conclusion drawn for the mechanism of O2 adsorption on "dry" gold cluster anions and provides insight into the possible role of water in the enhanced activity of supported gold cluster catalysts.     

Vibrational analysis of hydroxyacetone

In order to be able to fully understand the vibrational dynamics of monosaccharide sugars, we started with hydroxyacetone CH2OHCOCH3, and glycolaldehyde CH2OHCOH, which are among the smallest molecules that contain hydroxyl and carbonyl group on neighboring carbon atoms. This sterical configuration is characteristic for saccharides and determines their biochemical activity. In this work vibrational analysis of hydroxyacetone was undertaken by performing the normal coordinate analysis for glycolaldehyde first, and transferring these force constants to hydroxyacetone. The observed Raman and infrared bands for 90 wt.% solution of hydroxyacetone in water (acetol) were used as a first approximation for the bands of free hydroxyacetone. The number of observed Raman and infrared bands for acetol exceeds the number of calculated values for the most stable hydroxyacetone conformer with Cs symmetry, which suggests more than one conformer of hydroxyacetone in water solution. In particular, there are two bands both in infrared (1083 and 1057 cm(-1)) and in Raman spectrum (1086.5 and 1053 cm(-1)) that are assigned to the CO stretching mode and this is one of the indicators of several hydroxyacetone conformers in the solution. Additional information was obtained from low temperature Raman spectra: at 240 K a broad asymmetric band centered around 280 cm(-1) appears, suggesting a disorder in the orientation of hydroxyl groups. Glassy state forms at approximately 150K. The broad band at 80 cm(-1) is assigned to frozen torsions of hydroxymethyl groups.     

Relationships for determining the rate constant of the polymerization growth reaction by means of the emulsion polymerization method

Some simple equations for the emulsion polymerization system were derived on the basis of the Smith-Ewart theory. These are used in calculating the molar monomer concentration and rate of polymerization in units of moles per liter per second for the zero-order region with respect to the monomer as well as in calculating the rate constant of the growth reaction.     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.