01.00.00 Physical-mathematical sciences
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01.00.00 Physical-mathematical sciences
DescriptionIn this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed
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GENERIC POLYNOMIALS FOR THE CYCLIC 2-GROUPS OVER FIELDS WITH CHARACTERISTIC TWO
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the generic polynomials for cyclic groups of order 4, 8 and 16 over fields with characteristic two are constructed. With this construction, the generic polynomials for all cyclic 2-groups over fields with characteristic two can be obtained. We also give survey of known results of generic polynomials for the cyclic groups.
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01.00.00 Physical-mathematical sciences
DescriptionThe concept of generic polynomial appeared in Saltman’s works at the end of the last century and it is connected with the inverse problem of Galois theory, which is still far from its complete solution. Let G be a finite group and K be a field, the polynomial f(x,t1, … , tn) with coefficients from the field K is generic for the group G, if Galois group of this polynomial over the field K(t1, … , tn) is isomorphic G and if for any Galois extension L/K with Galois group isomorphic G there are such values of parameters ti = ai , i = 1,2, … , n, that the field L is the splitting field of the polynomial f(x,a1, … , an) over K. Generic polynomials over a given field K and a given finite group G do not always exist, and if they exist then it’s not easy to construct them. For example, for a cyclic group of the eight order C8 there is no generic polynomial over the field of rational numbers Q, although there are found specific polynomials with rational coefficients having Galois group isomorphic C8. Therefore, this is of interest to construct generic polynomials for the group G in cases when G is a direct product of groups of lower orders. In this study we show to solve this problem in case when G is a direct product of certain cyclic groups and there is a type of corresponding generic polynomials. Moreover, we give constructions over the fields of characteristic 0 and over the fields of characteristic 2
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01.00.00 Physical-mathematical sciences
DescriptionSpecially formed mixtures of isotopes of chemical elements have better consumer properties than their natural counterparts. Therefore, the development of methods for increasing the efficiency of the known methods for producing of isotope materials is relevant. It is known that the chemical bond is formed only in the singlet state of the spins of valence electrons of the reagents. On the basis of the known representations about dispersion of spin projections on the coordinate axes and the molecular-kinetic theory of gases was obtained an expression for the constant of the chemical reaction between the radicals occurring in the magnetic field. This expression allows calculating the reactivity of the isotopic modifications of radicals. Plasma allows to transfer many of the compounds in the gas phase. It is known that a significant part of particles in low temperature plasma is in a radical form. The equations of chemical kinetics for describing the process of oxidation of the carbon isotopes in argon-oxygen plasma occurring in an external permanent magnetic field were written in the work. It was shown that the efficiency of plasma process of isotopes separation can be increased only under insufficient oxygen relative to the stoichiometric value. These equations of chemical kinetics of processes occurring in the plasma process of incomplete oxidation of carbon isotopes needed to find experimental conditions that provide the maximum isotope effect in a magnetic field
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RENEWAL DEPENDENCE METHOD OF LEAST SQUARES BASED NONPARAMETRIC MODEL WITH PERIODIC COMPONENT
01.00.00 Physical-mathematical sciences
DescriptionWe consider the nonparametric problem of reneval dependence, which is described by the sum of a linear trend and periodic function with a known period. We obtain the asymptotic distribution of the parameter estimates and the trend component. The methods of estimating the periodic component and designing in-terval forecast. In the model of the points of observa-tion, natural for applications, justified by the condi-tions of use. In particular, we prove an asymptotically unbiased estimate of the coefficient of the linear term
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01.00.00 Physical-mathematical sciences
DescriptionThis article is devoted to the asymptotic analysis of boundary value problem for a system of equations of Nernst-Planck and Poisson for a singularly perturbed system of ordinary differential equations [1], based on two parameters. This boundary value problem simulates electrodiffusion of four kinds of ions at the same time in the diffusion layer in electro-membrane systems with perfectly selective membrane, taling into consideration the reaction of recombination of two ions. Meanwhile the other two ions represent ions of a binary salt. As a simple example, we consider the transport of ions sodium, chlorine, hydrogen and hydroxide, moreover, hydrogen and hydroxyl ions recombine in the diffusion layer. A more complex case is the transfer of the products of dissociation of the dihydrogen phosphate of sodium, namely, ions of sodium and dihydrogen phosphate, the latter dissociate at the interface, in turn, hydrogen ions and hydrogen phosphate. Thus, in the solution can simultaneously store three different types of ions: sodium, hydrogen, phosphate. During the transfer, hydrogen ions and ions of hydrogen phosphate recombine to produce phosphoric acid. The article has revealed the structure of the Nernst diffusion layer at currents above Harkatsa current. It is shown, that in the diffusion layer, there are two types of boundary layers: the inner (reaction) boundary layer and boundary layer at the interface solution / membrane
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01.00.00 Physical-mathematical sciences
DescriptionThis article is a continuation of the previous works of the authors [The influence of reaction dissociation / recombination of molecules of water on transportation of electrolyte 1:1 in the membrane systems in the diffusion layer. Part 1. Mathematical model // Scientific journal of Kuban State Agrarian University, 2016. No. 07(121) and The influence of the reaction of dissociation / recombination of molecules of water on transportation of electrolyte 1: 1 in membrane systems in the diffusion layer. Part 2. Asymptotic analysis // Scientific journal of Kuban State Agrarian University, 2016. – №08(122)] and devoted to assessing the possibility of gravitational convection due to the recombination of hydrogen and hydroxyl ions. The article presents the solution of a boundary-value problem, which is a mathematical model of electrodiffusion for the four types of ions at the same time (two ions of salts and hydrogen and hydroxyl ions) in the diffusion layer in electro-membrane systems with ideal selective membrane, with the heat transfer equation and the Navier-Stokes equation. The article shows the possibility of the emergence of gravitational convection due to the exothermic reaction of recombination of water molecules in the depth of the solution. The article considered the reaction of recombination of hydrogen ions and hydroxyl, although the main results can be applied, after appropriate modifications, and to amfolit-containing solutions, such as wine, juices, dairy products, microbiological processing of biomass (amino acids, anions of polybasic carboxylic acids), municipal effluent (anions of phosphoric acid), etc.
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01.00.00 Physical-mathematical sciences
DescriptionThe influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the space-charge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work
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01.00.00 Physical-mathematical sciences
DescriptionA model is developed for stress-dependent surface generation and recombination of point defects in silicon. Using the model, such phenomena as stacking fault growth and stress-mediated dopant diffusion in silicon are simulated
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VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physical-mathematical sciences
DescriptionIn this work, we consider two types of vortex currents-cyclones and anticyclones in the Northern and Southern Hemispheres. Numerical modeling of turbulent flows of these types uses the model of the planetary boundary layer developed by the author. The purpose of the study is to test hypotheses about the influence of the Coriolis force on the formation of cyclones and anticyclones in the northern and southern latitudes. The first hypothesis on the direction of circulation in cyclones was verified in the case of axisymmetric radially converging and vertically rising turbulent flows with a natural Coriolis parameter and viscosity. From the obtained data of numerical experiments, it follows that the current in the northern latitudes circulates in a counter clockwise direction, and in the south - in a clockwise direction, in full accordance with the observational data. Thus, we have shown that a cyclonic flow is formed in a turbulent radially converging flow under the influence of the Coriolis force. The second hypothesis on the formation of anticyclones was verified in the case of radially divergent and vertically descending turbulent flows. Because of numerical experiments, it was established that in this case, the current in the northern latitudes circulates clockwise, and in the south - in a counter clockwise direction, which corresponds to observations for anticyclones. To test the effect of the cyclone (anticyclone) center velocity on circulation, a nonstationary 3D model of turbulent flow was developed. Within the framework of this model, flows in cyclones and anticyclones moving at a constant speed, as well as in shear flow, are studied. Some types of loop protuberances on the Sun are explained by the presence of a vortex turbulent flow starting in the bowels of the Sun and encompassing the chromosphere