Spectral properties of operators of the theory of harmonic potential

We classify the points of the spectrum of the operatorsB andB ^* of the theory of harmonic potential on a smooth closed surfaceS ³. These operators give the direct value onS of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators inL ₂ (S). We prove that the half-interval [–2, 2) is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operatorsB andB ^* on ellipsoidal surfaces.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.This research was partially supported by the Russian Foundation for Basic Research.     

Chromatomembrane Headspace Analysis of Aqueous Solutions at Elevated Temperatures

Both theoretically and experimentally, the effect of temperature has been studied and assessed on analytical characteristics of continuous chromatomembrane gas extraction of volatile organic compounds from aqueous solutions with the aim of their subsequent gas chromatographic determination. It has been found that a rise of temperature up to 80 °C enables reduction of the detection limits of alcohols, ketones, and esters by a factor of 10 to 20. If a water vapor condenser is used in the extractant gas line, then the repeatability of results does not depend on temperature. The conditions have been optimized for the continuous headspace chromatomembrane analysis in combination with gas adsorption (purge and trap) concentration of analytes.

     

Segregation of 57Co Atomic Probes in the Cores of Grain Boundaries in d-Transition Metals

A new method, which has been developed to examine the structure and physical properties of cores of grain boundaries (GB's) (S.M. Klotsman, Sov. Phys. Uspech. 33, 55 (1990); V.N. Kaigorodov and S.M. Klotsman, Phys. Rev. B 49 (1994)), was used to study segregats localized in two discrete regions of polycrystals: cores of GB's and two-dimensional regions of the lattice adjacent to the GB's. This paper reports and discusses results of investigations of segregation of ⁵⁷Co atomic probes in cores of GB's in the d-transition metals Cr, Ta and W. The interaction of ⁵⁷Co AP's with GB's cores in metals is similar to their interaction with vacancies, because GB's cores are characterized, as vacancies in metals, by an excess volume and a negative charge. GB's are enriched with ⁵⁷Co in chromium and tungsten. The activation enthalpy of the ⁵⁷Co atomic probes segregation at GB's in Cr and W is proportional tothe local magnetic moment of ⁵⁷Co atomic probes. GB's cores are found to be depleted of ⁵⁷Co atomic probes in Ta.     

Initial-boundary value problem and integrodifferential equations of electrodynamics for an inhomogeneous conductive body

The initial-boundary value problem of determining the electromagnetic field in an inhomogeneous conducting sample and the surrounding external medium is solved under certain assumptions on the sample, the external medium, and the external current density. The existence of a classical solution to this problem is proved. The electromagnetic field under small variations in the sample’s electric conductivity is computed by applying perturbation theory.     

Positron spectroscopy of rehydrated pyrogeneous silica surface

Positron annihilation method has been used for investigating amorphous nonporous pyrogeneous silica of high purity. The influence of water adsorption on the structure of the silanol surface is shown. The effect of swelling, that is an increase of interglobular free volume at intermediate degrees of silica hydration has been observed.     

One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field

A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field.     

Band structure and thermodynamic potentials

The behavior of different thermodynamic functions of a system of delocalized electrons in a crystal is considered in the single-band strong coupling approximation depending on the degree of energy band filling and temperature. The chemical potential, grand thermodynamic potential, internal energy, free energy, entropy, and heat capacity are numerically calculated. Dependences of these quantities on the electron concentration at high temperatures are investigated. Their limited energy spectrum leads to the special features in the behavior of these quantities in comparison with the free electron gas.