Extremum Problem for Periodic Functions Supported in a Ball

We consider the Turan n-dimensional extremum problem of finding the value of A_n(hB ⁿ ) which is equal to the maximum zero Fourier coefficient of periodic functions f supported in the Euclidean ball hB ⁿ of radius h, having nonnegative Fourier coefficients, and satisfying the condition f(0)= 1. This problem originates from applications to number theory. The case of A₁([–h,h]) was studied by S. B. Stechkin. For A_n(hB ⁿ we obtain an asymptotic series as h 0 whose leading term is found by solving an n-dimensional extremum problem for entire functions of exponential type.     

Development of tools for real-time betatron tune measurements at the Nuclotron

A betatron tune measurement system was developed and tested at the Nuclotron. A white noise and chirp signals were used for transverse beam motion excitation. A custom FlexRIO digitizer module was developed which provides excitation signal generation for kicker electrodes and real-time signal acquisition from pickup electrodes. A high resolution FFT algorithm was implemented inside a NI PXI FPGA module, connected to digitizer. The measurement system is integrated with the NICA control system based on the TANGO Controls. Results and tests performed with the Nuclotron beam are presented.     

The thermometry system of superconducting magnets test bench for the Nica accelerator complex

Precise temperature control in various parts of the magnet and thermostat is one of the vital problems during cryogenic tests. The report describes design of the thermometry system, developed at LHEP JINR. This system is the operational prototype for the NICA thermometry system. Besides, the report describes generic software tools, developed for the TANGO-based control system web client software design.     

Gas-turbine power stations on associated gas by Motor Sich OJSC

Wide introduction of gas-turbine power stations working on associated oil gas is topical for Russia. Designing and operational characteristics of PAES-2500 (2.5 MW) and EG-6000 (6.0 MW) gas-turbine power stations on associated oil gas manufactured by Motor Sich Company are presented.     

Determination of activity of <Superscript>51</Superscript>Cr on gamma radiation measurements

A method of determining the activity of intensive distributed -sources on the measurement of the continuous spectrum of radiation, for example the internal bremsstrahlung, is developed. The recurrent formula for reconstructing of a continuous spectrum, registered in a Ge detector, at distorting it in the detector. The method of precise measurements of the spectrum of ⁵¹Cr internal bremsstrahlung using two point sources of low activity is described.     

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.