Associative nil-algebras over finite fields

The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.Comment: 12 page

The Freiheitssatz for generic Poisson algebras

We prove the Freiheitssatz for the variety of generic Poisson algebras

Method of modeling distortions in summetric differential line based on prior measurements

Настоящая статья посвящена описанию методики моделирования искажении в симметричных линии передач, используемых в системах связи построенных на основе стандарта ГОСТ Р 52070-2003 на основе проведенных измерении. Приведена методика моделирования искажении в программной среде NI AWR Design Environment. Производится разбор этапов построения модели.This article is dedicated to the describe method of modeling of signal distortion in symmetric transmission lines in systems build upon standard GOST R 52070-2003 based on prior measurements. Method of modeling distortions in NI AWR Design Environment been presented. An extensive explanation of modeling process is given

Towards the azimuthal characteristics of ionospheric and seismic effects of "Chelyabinsk" meteorite fall according to the data from coherent radar, GPS and seismic networks

We present the results of a study of the azimuthal characteristics of ionospheric and seismic effects of the meteorite 'Chelyabinsk', based on the data from the network of GPS receivers, coherent decameter radar EKB SuperDARN and network of seismic stations. It is shown, that 6-14 minutes after the bolide explosion, GPS network observed the cone-shaped wavefront of TIDs that is interpreted as a ballistic acoustic wave. The typical TIDs propagation velocity were observed 661+/-256m/s, which corresponds to the expected acoustic wave speed for 240km height. 14 minutes after the bolide explosion, at distances of 200km we observed the emergence and propagation of a TID with spherical wavefront, that is interpreted as gravitational mode of internal acoustic waves. The propagation velocity of this TID was 337+/-89m/s which corresponds to the propagation velocity of these waves in similar situations. At EKB SuperDARN radar, we observed TIDs in the sector of azimuthal angles close to the perpendicular to the meteorite trajectory. The observed TID velocity (400 m/s) and azimuthal properties correlate well with the model of ballistic wave propagating at 120-140km altitude. It is shown, that the azimuthal distribution of the amplitude of vertical seismic oscillations can be described qualitatively by the model of vertical strike-slip rupture, propagating at 1km/s along the meteorite fall trajectory to distance of about 40km. These parameters correspond to the direction and velocity of propagation of the ballistic wave peak by the ground. It is shown, that the model of ballistic wave caused by supersonic motion and burning of the meteorite in the upper atmosphere can satisfactorily explain the various azimuthal ionospheric effects, observed by the coherent decameter radar EKB SuperDARN, GPS-receivers network, as well as the azimuthal characteristics of seismic waves at large distances.Comment: 25 pages, 8 figures. To be submitted to JG