Approximations and the spectral properties of measure-preserving group actions

This paper presents some extensions and applications of the method of approximations of ergodic theory (see [6]). Two notions of approximation are defined which are applicable to arbitrary σ-finite-measure-preserving group actions (see §1). Building upon results of [2], [13] and [6], the speeds of such approximations are related to the questions of spectral multiplicity, spectral type and ergodicity (see §3). For the result on spectral multiplicity, there is first established a general result concerning the spectral decomposition of unitary representations (see §2). The last section is devoted to applications—chiefly to certain classes of cylinder transformations which arise in connection with irregularity of distribution (see [12]). These transformations provide examples (on infinite measure spaces) of approximations of all finite multiplicities. The method of approximations is shown to be a natural tool for the study of their spectral properties.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

The electronic structure of the valence bands of solid NH3 and H2O studied by ultraviolet photoelectron spectroscopy

The results of a photoelectron study using ultraviolet 40.81 eV photons (UPS) of the outermost bands of the molecular solids NH₃ and H₂O are reported. The binding energies, the energy separation, the band widths and the branching ratio of the two outermost bands of solid NH₃ are found not to be significantly different from the 3a_l and 1e molecular orbital states of the gaseous NH₃ UPS spectrum. This implies that hydrogen bonding has not produced any significant change in the electronic structure of the valence bands of solid NH₃. Because of a much smaller intermolecular hydrogen bond length in solid H₂O compared to that in solid NH₃, the hydrogen bond does, however, produce a significant change in the valence bands of H₂O on solidification, and because of the orbital geometry it predominantly affects the 3a_l molecular orbital state.     

The determination of nitrate in sea water

A heterogeneous reduction method is described for the determination of nitrate in sea water. Nitrate is reduced to nitrite with 91% efficiency by passing the water through a column of amalgamated cadmium filings. The nitrite produced is determined spectrophotometrically by the method of BENDSCHNEIDER and ROBINSON. The method has a coefficient of variation of ca. 2% and is free from salt error. Temperature in the range o°–35° has no effect on the reduction. Interference from nitrite is discussed and a method is described for its destruction if necessary. Sulphide does not interfere.     

Microscale functional group analysis of marine and sedimentary humic substances

Methods are described for the microscale analysis of aquatic and sedimentary humic substances for several oxygen-containing functional groups including total acidity, carboxylic and phenolic hydroxyl groups, quinone groups and hydroxamate linkages. Coefficients of variation of the methods range from 4.9 to 12.9%.     

The spectrophotometric determination of microgram amounts of cerium

A spectrophotometric procedure, which has a coefficient of variation of ca. 2%, is described for the determination of up to 80 μg of cerium. Ceric ion formed by oxidation with persulphate, in the presence of catalytic amounts of silver, is reduced to the cerous state by treatment with excess ferrous-phenanthroline reagent. The decrease in optical density of the ferrous-phenan-throline compared with the reagent blank is a measure of the amount of cerium present. The only common cations which cause serious interference are Mn⁺²and Cr⁺³.