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Physics, mathematics, and technology

Mathematics and computer science

Strongly associated threefold distributions of projective space

Abstract

Construction of a general theory of a special class (SH -distribution) of the regular threefold distributions (H -distribution) of the projective space Pn consisting of a basic distribution of the 1st kind of r-dimensional planes  r are equipped with the distribution of the 1st kind of m-dimensional planes Mm (m  r) and equip distribution 1st the first kind of hyperplane elements (hyperplanes) Hn-1 with the ratio of the incidence of the corresponding elements in the common center X: X    M  H is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the SH -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements (n  1)-dimensional linear elements and hyperband distribution. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately. Research was carried out by G. F. Laptev method. Determinations of the H -distributionand existence theorems are given in the frame of zero order. Requiring that Λ-, L-, E-distribution were mutually associated we introduce a special class of threefold distributions, which we call strongly associated distributions or SH -distribution. Definition of SH -distribution is given in the frame of the 1st order and the existence theorem is proved.

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Use of the Z-scheme in an Rayleigh-Taylor instability model

Abstract

A nonlinear finite-differential scheme for solution of convection-diffusion equation in the field of models of Rayleigh-Taylor instability in the equatorial region of Earth ionosphere is considered. For test tasks monotony of the constructed scheme is in number confirmed. Experimental value of an order of approximation of the offered method of nonlinear correction of the finitedifferential scheme is received.

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A mathematical model of conversion of GaAs substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate

Abstract

A mathematical model of conversion of GaAS substrate into thin GaNxAs1-x films obtained by nitridation of porous GaAs substrate are presented. The technologic conditions influence on GaNxAs1-x parameters are discussed. The comparative analysis of both experimental and theoretic data was applied for optimization nitridation conditions in order to obtain «soft» substrates for GaN growth. The results will help to decrease mechanical strains in GaN/GaAs semiconductors structures. For solving and analysis of the presented system of differential equation was used mathematical package for partial differential equation FlexPDE.

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Theoretical and experimental physics

The calculation of the spectrum of nuclear quadrupole resonance deuterium replaced methyl group

Abstract

Values for quadrupole energy levels of CD3 molecule are obtained. Besides the energy values stationary states of this system is marked by total spin projection on the molecular symmetry axis. Nuclear selection rule for radiative transitions is M  1. The radiative transition frequencies are calculated and it is obtained, that spectrum have a dublet and triplet structure.

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A method for reducing phase noise in oscillator with variable-capacitance diode

Abstract

A method for reducing phase noise in voltage-controlled oscillator by introducing negative feedback noise circuit, offsetting the effect of fluctuations in the amplitude on the variable-capacitance diode capacity is proposed. The relationship between the level of the amplitude fluctuations and the amount of compensation of the bias is defined.

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The transmitting antenna system of moving object

Abstract

Presents the development of the transmitting antenna system has advantages when used in a ship: the constancy of the antenna current is independent of the operating frequency, reduced size and weight, reduce the impact of radiation on the electromagnetic environment of the ship, simplifying the coordination of feeder to the antenna; increase in the radiation power transmitting system.

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Formalization and solving optimal control technological complexes

Abstract

Results of development of mathematical methods and statement of problems of optimum control of a set of the interconnected trajectories–technologies of continuous technological processes and creations of numerical methods of their decision are given.

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Mechanics