The mean-value theorem for elliptic operators on stratified sets

In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principle.     

Measurement of the stepwise excitation constants for the e3σ and b3σ states of CO in a plasma

Measurements have been made on the rate constants for the stepwise excitation SE of the e³ and b³ states of CO from the a³ metastable state of CO. The measurements were made in the positive column of a discharge in a mixture of He + 0.1% CO by the use of a heating pulse superimposed on the decaying plasma. It is shown to be possible to distinguish the direct excitation from the stepwise and to extract information on the SE cross sections for these states.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 88–92, September, 1984.We are indebted to I. V. Kochetov and V. G. Pevgov for calculations on the EED, and to E. E. Ivanov for providing the program for calculating the r centroid and the Frank-Condon factors.     

Maximum principle for subharmonic functions on a stratified set

The strong maximum principle is proved for solutions of the inequality ??u ?? 0 on a stratified set.     

Digital acoustic communication in shallow-water sea for oceanological applications

Results of experiments on slow transmission of digital information using acoustic signals in complex oceanological conditions, i.e., in the presence of multiray propagation and motion of a sound source, are given. Coding with the help of pseudorandom sequences and coherent summation of the signals transmitted along a multiplicity of different rays with different Doppler frequencies and received by different elements of an extended receiving array are performed. The used method provided an opportunity to attain errorless transmission of codes at distances larger than 5 km. A theoretical estimate is given for the probability of an erroneous decision on the value of transmitted codes.     

Diffraction Radiation from a Slot in the Impedance End of a Semi-Infinite Rectangular Waveguide

Using the induced magnetomotive force method, we obtain an approximate analytical solution of the problem of diffraction of the H₁₀ mode by a narrow slot which is cut in the impedance finite-thickness wall on the end of a semi-infinite rectangular waveguide and radiates into free half-space over an infinite, perfectly conducting screen. The scattering-matrix coefficients of a slotted waveguide radiator are studied numerically for the values of the complex surface impedance which correspond to some particular types of a thin-film coating of the waveguide end wall.     

The normal derivative lemma for the Laplacian on a polyhedral set

An analog of the Oleinik-Hopf normal derivative lemma for the Laplace operator on a polyhedral set is considered.