Local energy as an indicator of the accuracy of wave functions and probability densities for helium

The local energy is examined as an indicator of the accuracy of approximate wave functions for the ground state of helium. It is observed that at a given point (1) an inaccurate local energy may or may not correspond to an inaccurate value of the wave function or probability density, but (2) a value of the local energy within 0.1 a.u. of the ground-state energy corresponds to a value of the approximate wave function or probability density within about 10% of that for the ground-state wave function.     

Polarographisehe Bestimmung von Zink in Gold

Ohne Zusammenfassung     

Raman and luminescence studies of alkali borate tungstate glasses

Raman and luminescence spectroscopy were used to determine the structure of alkali borate tungstate glasses: M₂O(B₂O₃)₂·xWO₃, M = Li or Na (0 < x < 1). Raman scattering results showed the dominant tungstate species in these photochromic glasses to be tetrahedral WO₄⁼. At high concentrations of WO₃, WO₃·H₂O, and W₂O₇⁼ are also present. Luminescence measurements provided evidence for an octahedral WO₃ structure not identified by the Raman results. The results also revealed a possible change in the structure of the glasses similar to that observed in alkali borate glasses and associated with the “borate anomaly”. In addition, preliminary measurements are reported on the variation of the band gap, density, index of refraction, and the elastic coefficient C₁₁ determined by Brillouin scattering with composition.     

Optical techniques for active integratedantenna circuits

This paper reviews some of the recent efforts in the area of microwave–optical interactions applied to active integrated antennas and arrays. Two optical–microwave techniques and examples of their application are presented. First, antenna remoting via optical means is discussed. Second, optical control of microwave devices in active antenna circuits is demonstrated.     

Ternary phase equilibria in the Ga-As-Cr system and its relevance to diffusion and solubility studies

The phase equilibria in the Ga-As-Cr system were determined for As ? 50 a/o from room temperature to 1300°C by calorimetric and x-ray examination of appropriately prepared samples. Several corrections were made in the literature values for properties of Cr-As binary compounds. The ternary diagram shows that GaAs is not a dominant compound in the system and GaAs and Cr cannot coexist under equilibrium conditions. From one ternary tie triangle region and a solid plus liquid region, appropriate solubility and diffusion sources for Cr in GaAs for most temperatures can be obtained.     

Perturbation theory with an approximate perturbation: The effect of charge overlap on interatomic interactions

The evaluation of interatomic interactions at large separations (R) typically involves neglecting electron exchange, treating the Coulomb interaction between atoms as a perturbation, neglecting third- and higher-order energy contributions, and approximating the Coulomb interaction by a short expansion in spherical harmonics and, usually, powers of R^?1. This last approximation, using an approximate perturbing Hamiltonian to evaluate a second-order perturbed energy, is examined here; error bounds and a simple correction are introduced. Three illustrative applications to the H? H⁺ interaction are given: the error incurred by truncating the spherical-harmonic expansion is bounded, the R^?1 expansion is corrected for the overlap of the “atomic” charge distributions, and the R^?1 expansion is analyzed to see why it works as well as it does.     

Characterization of partially transesterified poly(beta-hydroxyalkanoate)s using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) was used for the characterization of a partially transesterified poly(beta-hydroxyalkanoate), PHA, polymer produced by the bacterial strain Alcaligenes eutrophus using saponified vegetable oils as the sole carbon sources. The transesterification was carried out separately under acidic and basic conditions to obtain PHA oligomers weighing less than 10 kDa. The intact oligomers were detected in their cationized [M + Na](+) and [M + K](+) forms by MALDI-TOFMS. A composition analysis, using the MALDI-TOF spectra, indicate that the oligomers obtained via acid catalysis were terminated with a methyl 3-hydroxybutyrate end group, and those obtained by base catalysis had a methyl crotonate (olefinic) termination. In addition to HB (hydroxy butyrate), the oligomers were found to contain a small percentage of HV (hydroxy valerate). This was independently confirmed using gas chromatography/mass spectrometry (GC/MS). In comparison, the analysis of a commercial PHA polymer, transesterified under identical conditions, only showed the presence of HB, i.e. a pure PHB homopolymer. Copyright 1999 John Wiley & Sons, Ltd.     

A Look at Project AIMS

Project AIMS (Activities that Integrate Mathematics and Science) began in 1981 as a National Science Foundation grant. Twelve years later it is a flourishing program which relies on materials developed and written by teachers, and one which uses inexpensive, easily acquired equipment and materials. It is particularly noteworthy that the focus of AIMS-integration through hands-on mathematics and science-supports such recent initiatives as the NCTM Standards and Project 2061 of the AAAS, even though it predates both of them.     

Effect of silicon surface cleaning procedures on oxidation kinetics and surface chemistry

The effect of surface cleaning procedures on the kinetics of thermal oxide growth on silicon is presented. The goal is to relate the properties of the cleaned surface (composition, chemistry, impurity content) to the changes in oxide growth mechanisms. Experimentally, silicon (100) wafers were given different variations of an RCA clean, and then oxidized in dry O₂ at 900°C producing oxides with thicknesses between 170 and 3900 Å. The results, in general agreement with earlier studies, show that the percentage difference in thickness is strongly dependent on oxide thickness. The data, which are explained in terms of the predictions of a linear-parabolic and a parallel oxidation model, suggest that the surface cleans do not alter the diffusion of molecular oxygen in the oxide. Auger analysis of the surfaces shows that there is a substantial carbon contamination on the HF stripped wafer which is considerably reduced after a 5 min N₂ anneal.