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.
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.
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.
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.
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 .
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.
An optimization procedure for constructive parameters of the log-periodic C-band antenna developed in the patent No. 2571607 “Microstrip logoperiodic antenna” is investigated. The electrodynamic model of the log-periodic microstrip- type antenna for the C-band has been developed.
Problems of erosion of elements of stationary plasma electric rocket engines are considered. Modern tasks require the engine significant resource characteristics, confirmed by long-term ground tests. In the paper, the possibility of applying accelerated tests for solving the problem of confirming the correspondence of the engine to the required resource characteristics is justified.
Today in creation of mathematical models of the stationary plasma thruster (SPT) a certain advance is noticeable, but all these models are based on empirical laws with a possibility of application to concrete type of the engine. The paper considers the possibility of constructing a mathematical model that takes into account the various physical processes taking place in the engine and based on statistical methods.
The article is devoted to the development and investigation of a modified antenna with an extended frequency range constructed on the basis of a fractal structure of the «Sierpinski triangle» type, which allows to significantly reduce the dimensions of the structure.
The work of analog-to-digital converter and the problems arising in the reduction of the input signal are investigated. A solution to the problem of aperture uncertainty is presented by using a constructive method with an approximate analysis of the reconstructed signal.
The results of the solution of the integral equations of motion numerical method presented in dimensionless form related to the relative inertia of the particles and the relaxation time of the particle. It is found that when the increase in the relative inertia of the particles, decreases the coefficient of turbulent diffusion of the dispersed phase compared to the ratio of the carrier medium. Increase from-wearing leads to an increase of the coefficient of turbulent diffusion of particles. It is shown that the calculation of the coefficient of vertical diffusion of dispersed impurities in watercourses must take into account not only the turbulence characteristics of the carrier medium, but also the relative inertia of the particles.
The outer shell is an important component influencing on the working capacity of roller one-way clutches. The analysis is carried out and recommendations about use of mathematical models for calculation of deformation of outer shell are made. It is established that at change of number of wedged rollers in a range from 3 to 7 there is a nonlinear decrease of value of a radial deformation, and in a range from 7 to 30 its increase.