01.00.00 Physical-mathematical sciences
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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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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
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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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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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
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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GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory
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GEOMETRIC TURBULENCE AND QUANTUM THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe parabolic equation describing the evolution of the gravitational field is derived from Einstein equation. The instability of metric leads to a geometric pattern of turbulence. Microscopic turbulent pulsations generate two kinds of matter with positive and negative energy density, respectively. It is shown that in the case of negative energy density parabolic equation leads to an equation of Schrödinger type
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GEOMETRIC TURBULENCE AND STELLAR EVOLUTION
01.00.00 Physical-mathematical sciences
DescriptionIn this article we consider Einstein's theory of gravity in relation to the Yang-Mills theory. It is shown that in Einstein's theory there exists a metric together with the Yang-Mills theory, in which the field equations are reduced to the Liouville equation describing the evolution of stars. The mechanism of generation of stellar energy of dark energy in the processes of geometric turbulence is discussed
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GRAVITY FIELD IN THE VICINITY OF STARS AND GEOMETRIC TURBULENCE
01.00.00 Physical-mathematical sciences
DescriptionIn this article, the solutions of Einstein's equations for empty space, describing the gravitational field near the Sunlike star have been investigated. We have accounted the own field of the star, the motion of the star around the galactic center, the motion of the galaxy relative to the center of the local supercluster and the expansion of the Universe. The resulting gravitational field near the star has a complex structure, which leads to large-scale geometric turbulence linking large and small scales in this problem