Differentiation operator and series of Dirichlet type

New results are obtained concerning the representation of analytic functions by means of Dirichlet series by using the spectral properties of a boundary problem for a differentiation operator.Translated from Matematicheskie Zametki, Vol. 6, No. 6, pp. 759–766, December, 1969.In concluding, the author wishes to thank A. F. Leont'ev for a helpful discussion of the results of this paper.     

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu,FeMn, FeNi,and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ? 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.     

Investigation of bound diffusion of ultrafine particles of FeIII,hydroxide in a polymeric sorbent by Mössbauer spectroscopy

Bound diffusion of ultrafine particles of Fe^III hydroxide in the pores of a solvated polymeric sorbent has been discovered and investigated by Mössbauer spectroscopy. Particles with diameters of 30 Å <-d <- 90 Å were precipitated from an aqueous solution in the pores of the poly(divinylbenzene-ethylstyrene) Porolas A sorbent. The Mössbauer spectra obtained atyT > 250 K (i.e., above the crystallization and glass transition points of the liquid in the pores,viz., water or glycerol) were found to assume the shape of a superposition of broadened and nonbroadened components, which is characteristic of bound diffusion. Experimental data were treated in terms of two alternative models of bound diffusion,viz., in harmonic (Brownian overdamped oscillator) and rectangular potentials. The following values for the parameters of bound diffusion (diffusion coefficientD and diffusion displacementr) at room temperature were found: for glycerol,D = 0.3 · 10^–9; 0.5 · 10^–9 cm² s^–1 andr = 0.14; 0.38 Å for water,D > 2 × 10^–8 cm² s^–1 andr = 0.22; 0.45 Å. Unlimited diffusion of particles in the solvated sorbent was not observed. No diffusion of the particles was observed in the dry sorbent.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 886–895, April, 1996.     

Inversion of integral operators with kernels discontinuous on the diagonal

Conditions implying the invertibility of the integral operator

Pressing a rigid plastic surface by a wedge-shaped stamp under the Coulomb-Mohr yield condition

The problem of treating a surface with a wedge-shaped stamp is considered using the model of an ideal rigid plastic body. The strain fields in the vicinity of singularities of the displacement velocity field (on the discontinuity lines of the displacement velocities and at the center of the fan of characteristics) are investigated taking into account irreversible compressibility.     

A Study of the Near-Wall Plasma of the Globus-M Tokamak Using an Array of Divertor Langmuir Probes

Technical Physics - An array of ten built-in divertor probes was installed on the lower dome of the Globus-M spherical tokamak. It was used to measure the profiles of the floating potential,...     

Effect of the dimension of the phonon spectrum on the stability of condensed media states

The effect of dimension index d _f of the phonon spectrum, which is a structural characteristic in continual models, on the stability of states of condensed media is considered in the Einstein and Debye approximations. The estimate of the phase state stability is based on the Lindemann criterion generalized to arbitrary values of 0 ≤ d _f ≤ ∞. The problem of variation of physical characteristic of a substance by controlling the structure of its phonon spectrum is considered by analyzing the possibility of obtaining molecular hydrogen in the superfluid state. The Einstein and Debye models as applied to the problem on the dynamics of atomic oscillations are compared, and the divergence of the latter model for fractal dimensions d _f < 2 of the phonon spectrum is demonstrated, as well as the incompatibility of the Debye model at high temperatures and the model of a classical oscillator for all dimensions except d _f → ∞.