Electrostatic field of a thin, unclosed spherical shell and a torus

The electrostatic problem for a thin, unclosed spherical shell and a torus is reduced to paired summation equations in the Legendre polynomials by means of formulas relating the spherical and toroidal harmonic functions. The paired equations are transformed to a Fredholm integral equation of the second kind. Formulas are obtained for computing the charges of the conductors in the form of a series in a small parameter. The capacitance is computed for certain geometrical parameters of the conductors. Zh. Tekh. Fiz. 68, 1–6 (July 1998)     

An approach to triquinane synthesis using the Pauson-Khand reaction

Tricyclic skeletons have been generated from acyclic enyne precursors by using an intramolecular Pauson-Khand reaction in combination with aldol, Michael and alkylation reactions.     

Invariant Cocycles Have Abelian Ranges

 Let R be a discrete nonsingular equivalence relation on a standard probability space , and let V be an ergodic strongly asymptotically central automorphism of R. We prove that every V-invariant cocycle with values in a Polish group G takes values in an abelian subgroup of G. The hypotheses of this result are satisfied, for example, if A is a finite set, a closed, shift-invariant subset, V is the shift, μ a shift-invariant and ergodic probability measure on X, the two-sided tail-equivalence relation on X, a shift-invariant subrelation which is μ-nonsingular, and a shift-invariant cocycle.     

Solid-phase epitaxy of CaSi2 on Si(1 1 1) and the Schottky-barrier height of CaSi2/Si(1 1 1)

Thin Ca films were evaporated on Si(1 1 1) under UHV conditions and subsequently annealed in the temperature range 200–650 °C. The interdiffusion of Ca and Si was examined by ex situ Auger depth profiling. In situ monitoring of the Si 2p core-level shift by X-ray photoemission spectroscopy (XPS) was employed to study the silicide formation process. The formation temperature of CaSi₂ films on Si(1 1 1) was found to be about 350 °C. Epitaxial growth takes place at T≥400 °C. The morphology of the films, measured by atomic force microscopy (AFM), was correlated with their crystallinity as analyzed by X-ray diffraction (XRD). According to measurements of temperature-dependent I–V characteristics and internal photoemission the Schottky-barrier height of CaSi₂ on Si(1 1 1) amounts to qΦ_Bn=0.25 eV on n-type and to qΦ_Bp=0.82 eV on p-type silicon.     

Systematic investigations of the multi-element preconcentration from copper by precipitation of the matrix as copper(I) oxide and copper(I) thiocyanate

Two methods for multi-element preconcentration from copper by reductive matrix precipitation are presented. In systematic investigations on the coprecipitation behaviour of Ag, Al, Au, Bi, Cd, Co, Cr, Fe, Ga, In, Mn, Mo, NJ, Pb, Sb, Se, Sn, Te and Zn during precipitation of the copper matrix as Cu₂O or CuSCN, the separation parameters were optimized. By combination with a hexamethyleneammonium hexamethylenedithiocarbamate collector precipitation, a concentration of 8 elements (Cu₂O precipitation) or 13 elements (CuSCN precipitation) in a small volume was achieved. The limits of detection of the procedures are, depending on the element, 0.1–5 μg g^?1 for flame atomic absorption spectrometry (AAS) and 0.01–0.1 μg g^?1 for graphite furnace AAS. The relative standard deviations are about 3%. The analytical performance of the procedures is compared with that of an electrolytic copper separation.     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Efficiency of the multiwave method of determination of the ozone content in the atmosphere by UV spectrometry-ozonometry

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 3, pp. 472–477, September, 1991.