IKBFU's Vestnik

2017 Issue №02

The derivation formulas and equations for an affine space structure from the point of view of smooth manifolds

Abstract

Using the derivation formulas of Akivis and the Laptev structure equations for smooth manifolds, two methods yield corresponding formulas and equations for an affine space are received. The hierarchy of smooth manifolds and a principal bundle of linear coframes over a smooth manifold are used.

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About fields of geometrical objects of the H -distribution of the affine space

Abstract

A creation of geometric objects of the hyperband distribution (H -distribution) of affine space An in the differential 1–3rd orders neighborhoods is continued. As a result a number of new normalization in Norden's sense of the main structural subbundles of this H -distribution are constructed (are found) internally invariantly.

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Differential comparisons for the components of the curvature object of affine connection of the second order

Abstract

Differential comparisons for the components of the curvature object of affine connection of the second order are received. These comparisons show that, in the general case, the second-order curvature object forms a geometric object only in conjunction with the first-order curvature object and the second-order connectivity object.

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A modeling the interaction of a oxygen plasma with a positively charged microsatellite with the molecular dynamics modeling method

Abstract

The results of modeling the interaction of a single-ion thermal ionospheric plasma consisting of oxygen ions and electrons with a charged microsatellite are presented. The molecular dynamics modeling method was used. It is shown that behind the satellite there is a so-called ionic shadow with a low ionic concentration.

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About one algorithm of calculation of inverses in finite fields

Abstract

In work are two algorithms of calculation of inverses in a finite field qn F developed, where q is power of the prime number. They are received by generalisation of algorithm of Wong for a field F2n with use of the main idea for fast algorithm of calculation of inverses in the field 2 F n .

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An elementary solving of cubic Diophantine equations

Abstract

An elementaryAn elementary approach to solving of the cubic Diophantine equations y 2  x 3  2 2s, depending on one natural parameter s is presented. The full solving for all values s is received. approach to solving of the cubic Diophantine equations y 2  x 3  2 2s, depending on one natural parameter s is presented. The full solving for all values s is received.

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