A. V. Mikhalev | Searcharxiv

arXiv2018

Theoretic--model Properties of Regular Polygons

This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete class of regular polygons which satisfy the additional conditions. We study the monoids, whose regular core is presented as a union of the finite number of principal right ideals, all regular polygons over which have the stable and superstable theory. We prove the stability of the axiomatizable model complete class of regular polygons and we also describe the monoids with the superstable and $ω$--stable class of regular polygons when this class is axiomatizable and model complete.

math.LO↗

arXiv2006

Elementary Equivalence of Endomorphism Rings of Abelian p-Groups

In this paper we study a relationship between elementary equivalence of endomorphism rings of Abelian p-groups and second order equivalence of the corresponding Abelian p-groups.

math.GR↗

arXiv2006

Elementary Equivalence of Categories of Modules over Rings, Endomorphism Rings, and Automorphism Groups of Modules

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of submodules of modules, and automorphism groups of modules.

math.RA↗

arXiv2001

Radio and optical observations of large-scale traveling ionospheric disturbances during a strong geomagnetic storm of 6-8 April 2000

Basic properties of the mid-latitude large-scale traveling ionospheric disturbances (LS TIDs) during the maximum phase of a strong magnetic storm of 6-8 April 2000 are shown. Total electron content (TEC) variations were studied by using data from GPS receivers located in Russia and Central Asia. The nightglow response to this storm at mesopause and termospheric altitudes was also measured by optical instruments FENIX located at the observatory of the Institute of Solar-Terrestrial Physics, (51.9 deg. N, 103.0 deg. E) and MORTI located at the observatory of the Institute of Ionosphere (43.2 deg. N, 77.0 deg. E). Observations of the O (557.7 nm, 630.0 nm, 360-410 nm, and 720-830 nm) emissions originating from atmospheric layers centered at altitudes of 90 km, 97 km, and 250 km were carried out at Irkutsk and of the O_2 (866.5 nm) emission originating from an atmospheric layer centered at altitude of 95 km was carried out at Almaty. Variations of the f_0F2 and virtual altitude of the F2 layer were measured at Almaty as well. An analysis of data was performed for the time interval 17.00-21.00 UT comprising a maximum of the Dst derivative. Results have shown that the storm-induced solitary large-scale wave with duration of 1 hour and with the front width of 5000 km moved equatorward with the velocity of 200 ms-1 to a distance of no less than 1000 km. The TEC disturbance, basically displaying an electron content depression in the maximum of the F2 region, reveals a good correlation with growing nightglow emission, the temporal shift between the TEC and emission variation maxima being different for different altitudes.

physics.geo-ph↗