Wave processes in semi-open tubes

A numerical method based on the solution of the complete problem of integration of a system of nonstationary nonlinear Euler equations for an ideal and perfect gas is developed. A special form of the dimensionless equations is obtained and the concept of the asymmetry of the pressure peak at the closed end of the tube is introduced, making it possible, using Godunov's scheme, to obtain a physically explicable solution even on grids with a small number of points. The frequency characteristics of the semi-open tube are obtained on the Strouhal number interval from 0.05 to 1.25. It is shown that at the linear resonance frequencies the conditions are favorable for the formation and amplification of shock waves leading to heating of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 169–171, September–October, 1990.     

Radiation mechanism of generation of geomagnetic signals from underground and contact explosions

A mechanism is proposed for the generation of geomagnetic perturbations by an atmospheric electrical dipole formed by the gamma radiation from contact and underground explosions accompanied by formation of a ground dome and escape of explosion products into the atmosphere. The gyrotropic E-layer of the ionosphere plays a determining role in the generation of geomagnetic fluctuations at long epicentral distances. The amplitude-frequency parameters of a geomagnetic signal at 1000 km from a contact explosion with an energy of 150 ktons are estimated. The possibility of recording such geomagnetic signals from explosions with emission of gamma radiation into the atmosphere is shown. Moscow Engineering-Physical Institute, Moscow 115409. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 21–26, November–December, 1998.     

A Sharp Jackson Inequality in Lp(ℝd) with Dunkl Weight

A sharp Jackson inequality in the space L_p(?^d), 1 ≤ p < 2, with Dunkl weight is proved. The best approximation is realized by entire functions of exponential spherical type. The modulus of continuity is defined by means of a generalized shift operator bounded on L_p, which was constructed earlier by the authors. In the case of the unit weight, this operator coincides with the mean-value operator on the sphere.

     

Micromaser action in atomic clusters

Optical micromaser action is considered in atomic clusters that can be involved in separable and entangled initial correlations. An equation describing the evolution of the Glauber quasi-probability for a light field is constructed in the Fokker-Planck approximation. The statistics of radiation emitted by a cavity is analyzed.     

Energy losses and scattering of fast electrons in a dense plasma

This paper describes an algorithm for the calculation of specific energy losses and multiple scattering of fast electrons in a plasma, taking into account the interaction of the electrons of the beam with the bound and free plasma electrons and with the plasma. Results are presented of calculations for aluminum and lead plasmas with density 0.001-1 of normal and with temperature up to 1 keV for initial electron kinetic energy of 1 MeV. The energy-loss distribution in an aluminum plasma is calculated by the Monte-Carlo method.Tomsk Polytechnic University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 112–116, September, 1993.     

On increasing the stability of noise-intensity estimates using a first order statistic

Scientific-Research Radio-Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 11, pp. 1064–1068, November, 1993.     

Rate of germanium-isotope production by background processes in the SAGE experiment

Data on a direct determination of systematic uncertainties caused by the background production of germanium isotopes in the radiochemical SAGE experiment measuring the solar-neutrino flux are analyzed. The result obtained for the rate of ⁶⁸Ge production is 6.5(1±1.0) times greater than the expected one; the rate of ⁶⁹Ge production does not exceed preliminary estimates. The above result for ⁶⁸Ge corresponds to the systematic uncertainty that is caused by the interaction of cosmic-ray muons and which is equal to 5.8% (4.5 SNU) at a solar-neutrino-capture rate of 77.0 SNU. An experiment is proposed that would test the effect of cosmic-ray muon influence on the SAGE systematic uncertainty and which would be performed at the location of the underground scintillation telescope facilities of the Baksan Neutrino Observatory (Institute for Nuclear Research, Russian Academy of Sciences).     

Approximation in <Emphasis Type="Italic">L</Emphasis> <Subscript>2</Subscript> by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator

For approximations in the space L₂(?₊) by partial integrals of the Fourier transform over the eigenfunctions of the Sturm–Liouville operator, we prove Jackson’s inequality with exact constant and optimal argument in the modulus of continuity. The optimality of the argument in the modulus of continuity is established using the Gauss quadrature formula on the half-line over the zeros of the eigenfunction of the Sturm–Liouville operator.     

Effective properties of a nonuniform beam under torsion

Effective characteristics are considered in the pure torsion problem for a nonuniform beam. The Saint-Venant semi-inverse method is used. A torsion stress function is introduced; this function can be found by solving a cross-sectional boundary value problem for a partial differential equation with variable coefficients. Two special boundary value problems are formulated for such an equation; after solving these problems, some effective characteristics are calculated in the case of torsion. It is shown that these effective characteristics satisfy the conditions of symmetry and positive definiteness. The case of an infinite in-plane layer of nonuniform thickness is discussed.