# Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
Search by author's name Search by title
Sort by:
230 kb

#### THE LIMIT THEORY OF THE SOLUTIONS OF EXTREMAL STATISTICAL PROBLEMS

abstract 1331709045 issue 133 pp. 579 – 600 30.11.2017 ru 459
Many procedures of applied mathematical statistics are based on the solution of extreme problems. As examples it is enough to name methods of least squares, maximum likelihood, minimal contrast, main components. In accordance with the new paradigm of applied mathematical statistics, the central part of this scientific and practical discipline is the statistics of non-numerical data (it is also called the statistics of objects of non-numerical nature or non-numeric statistics) in which the empirical and theoretical averages are determined by solving extreme problems. As shown in this paper, the laws of large numbers are valid, according to which empirical averages approach the theoretical ones with increasing sample size. Of great importance are limit theorems describing the asymptotic behavior of solutions of extremal statistical problems. For example, in the method of least squares, selective estimates of the parameters of the dependence approach the theoretical values, the maximum likelihood estimates tend to the estimated parameters, etc. It is quite natural to seek to study the asymptotic behavior of solutions of extremal statistical problems in the general case. The corresponding results can be used in various special cases. This is the theoretical and practical use of the limiting results obtained under the weakest assumptions. The present article is devoted to a series of limit theorems concerning the asymptotics of solutions of extremal statistical problems in the most general formulations. Along with the results of probability theory, the apparatus of general topology is used. The main differences between the results of this article and numerous studies on related topics are: we consider spaces of a general nature; the behavior of solutions is studied for extremal statistical problems of general form; it is possible to weaken ordinary requirements of bicompactness type by introducing conditions of the type of asymptotic uniform divisibility
830 kb

#### BAERâ€™S LAW AND EINSTEINâ€™S VORTEX HYPOTHESES

abstract 1331709048 issue 133 pp. 630 – 652 30.11.2017 ru 443
We consider numerical solutions of the Navier-Stokes equations describing laminar and turbulent flows in channels of various geometries and in the cavity at large Reynolds numbers. An original numerical algorithm for integrating a system of nonlinear partial differential equations is developed, based on the convergence of the sequence of solutions of the Dirichlet problem. Based on this algorithm, a numerical model is created for the fusion of two laminar flows in a T-shaped channel. A new mechanism of meandering is established, which consists in the fact that when the two streams merge, a jet is formed containing the zones of return flow. Vortex motion in a rectangular cavity is studied. It is established that the numerical solution of the problem with discontinuous boundary conditions loses stability at Reynolds number Re> 2340. The trajectories of passive impurity particles in a cylindrical cavity are investigated. An explanation of the behavior of tea leaves in a cup of tea in the formation of a toroidal vortex because of circular stirring is confirmed, which is confirms the wellknown hypothesis of Einstein. A numerical model of flow in an open channel with a bottom incline in a rotating system is developed. It is shown that in both laminar and turbulent flow under certain conditions a secondary vortex flow arises in the channel due to the Coriolis force, which explains the well-known Baer law and confirms the Einstein hypothesis
150 kb

#### PROBABILISTIC MODEL OF THE PROCESS OF REDUCTION OF THE PRICE FOR PLANNED ACTIONS

abstract 1321708026 issue 132 pp. 324 – 334 31.10.2017 ru 383
The soil fertility increase issues are very relevant now. Intensive development of agriculture cannot be made effectively without complex actions for farmlands protection from different types of degradations. On the one hand, it is necessary to ensure the maximum harvest of crops, and to preserve and increase the fertility of the soil and prevent negative anthropogenic impact on the environment on the other. For an extended reproduction of soil fertility, a system of measures is necessary for introduction of mineral and organic fertilizers into the soil, agrotechnical and reclamation methods, stimulation of humus formation processes, and so on. Therefore, methods are important that allow us to estimate the planned measures in advance to improve soil fertility and to eliminate environmental damage. In the article, the estimated parameters are treated by random variables. This allows us to consider the uncertainty in terms of probability distributions. It is offered a probabilistic model of the process of reducing the price of the proposed activity. Mathematical expectation, variance, distribution density of the considered random variable probabilities as the main characteristics of the object state price are calculated. The model can be used to address issues of rational use of land, scientifically based land management organization, when drafting land reclamation project
339 kb

#### GENERIC POLYNOMIALS

abstract 1321708044 issue 132 pp. 549 – 558 31.10.2017 ru 284
The concept of generic polynomial appeared in Saltmanâ€™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, â€¦ , tn) with coefficients from the field K is generic for the group G, if Galois group of this polynomial over the field K(t1, â€¦ , 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, â€¦ , n, that the field L is the splitting field of the polynomial f(x,a1, â€¦ , 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 itâ€™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
852 kb

#### SIMULATION OF A PLASMA CHANNEL AND TRACK IN MOTION OF PLASMA SOURCE IN CONDUCTIVE ENVIRONMENT

abstract 1321708129 issue 132 pp. 1492 – 1516 31.10.2017 ru 374
A model is developed that describes the formation of the plasma channel and the trace when moving in a conducting medium of various objects that are sources of plasma - ball lightning, plasmoids, charged particles, and so on. To describe the contribution of conduction currents, we modified the standard electrostatic equation considering the vortex component of the electric field. As a result of this generalization, a system of parabolictype nonlinear equations is formulated that describes the formation of the plasma channel and the track behind the moving object. In this formulation, the problem of the formation of the lightning channel in weak electric fields, characteristic for atmospheric discharges of cloudearth, is solved. Numerical simulation of the motion of plasma sources in a region with a ratio of the sizes 1/100, 1/200 makes it possible to find the shape of the channel and the total length of the track, as well as the branching regimes. It was previously established that there are three streamer branching mechanisms. The first mechanism is associated with the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is related to the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. The third branching mechanism, observed in experiments, is associated with the closure of the space charge to the anode through the streamer system. These branching mechanisms are also revealed when the leader is spread. Numerical experiments have revealed a new channel branching mechanism and a trace behind a moving plasma object, caused by the conductivity of the medium
148 kb

#### THE RATIONALE FOR THE USE OF ELECTROMAGNETIC FIELD IN THE PRODUCTION OF SUNFLOWER OIL

abstract 1311707026 issue 131 pp. 260 – 270 29.09.2017 ru 519
In some works, the feasibility of the use of fixed and variable electromagnetic fields of different frequencies and tension in the production technology of sunflower oil are shown, but there is no theoretical justification. The possibility of electromagnetic effects is associated with the presence of polar molecules specific to organic systems. Without prejudice to the role of polar groups of terrestrial circuits, this work tries to address this challenge more comprehensively. The reason for this is the distinctive feature of the behavior of sunflower during its flowering. This characteristic is that the sunflower hat during the day changes its direction in accordance with the direction of movement of the Sun across the sky; so called "magnetism" of their attraction. To justify this effect, we have analyzed the essence of emitted photons, the Sun chemical composition and structure arrangement of seeds in a sunflower hat. Particles of light from the Sun represent a stream of photons - a wide range of electromagnetic waves of frequencies that exhibit and magnetic properties. The article shows principal macro- and micronutrients of sunflower raw materials and divides them into groups of para- , dia- , and ferromagnetic materials. In sunflower seeds, there are chemical elements: diamagnetism-C, H, N, P, S, B, Cu, Zn, J; paramagnetism-O, K, Ca, Mg, Mo, As and ferromagnetic-iron (Fe). As there is resultant force of the magnetic attraction between the sunflower hat and magnetic flow of photons from the Sun, this effect dominates the action of paramagnetics K2O ( -28.4 24.5%), CaO (7.6-17.0)%, MgO (12.3-17.9%), magnetized in an external magnetic field in the direction of the field. The presence of evident effect demonstrates that it is possible to improve a number of technological operations in the manufacture of sunflower oil using electrical, magnetic or electromagnetic fields
844 kb

#### SIMULATION OF A STEPPED LIGHTNING LEADER

abstract 1311707063 issue 131 pp. 737 – 761 29.09.2017 ru 610
In this work, a model is developed that describes the formation of a stepped lightning leader in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, a system of parabolic-type nonlinear equations is formulated that describes the formation of streamers and the lightning channel. Numerical simulation of the propagation of ionization waves in a region with a ratio of 1/100, 1/200 allows us to identify two types of stepped streamers in the form of waves of compression and rarefaction, respectively. It was previously established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. In numerical experiments, the third branching mechanism observed in experiments connected with closing the space charge to the anode through the streamer system was observed. These branching mechanisms are also revealed when the leader is propagated. The obtained results, as well as the data of numerical experiments confirm the hypothesis of the universality of the minimal model of the streamer, as well as its expansion in the form proposed by the author. Known phenomena of nature associated with the electrical discharge - streamer, plasmoid, ball lightning and stepped leader can be described within the framework of the minimal model
282 kb

#### ASYMPTOTICS OF ESTIMATES OF PROBABILITY DISTRIBUTION DENSITY

abstract 1311707070 issue 131 pp. 832 – 860 29.09.2017 ru 458
Nonparametric estimates of the probability distribution density in spaces of arbitrary nature are one of the main tools of non-numerical statistics. Their particular cases are considered - kernel density estimates in spaces of arbitrary nature, histogram estimations and Fix-Hodges-type estimates. The purpose of this article is the completion of a series of papers devoted to the mathematical study of the asymptotic properties of various types of nonparametric estimates of the probability distribution density in spaces of general nature. Thus, a mathematical foundation is applied to the application of such estimates in non-numerical statistics. We begin by considering the mean square error of the kernel density estimate and, in order to maximize the order of its decrease, the choice of the kernel function and the sequence of the blur indicators. The basic concepts are the circular distribution function and the circular density. The order of convergence in the general case is the same as in estimating the density of a numerical random variable, but the main conditions are imposed not on the density of a random variable, but on the circular density. Next, we consider other types of nonparametric density estimates - histogram estimates and Fix-Hodges-type estimates. Then we study nonparametric regression estimates and their application to solve discriminant analysis problems in a general nature space
572 kb

#### THE REALIZATION OF GALOIS GROUPS BY TRINOMIALS OVER THE FIELD OF RATIONAL NUMBERS Q

abstract 1311707124 issue 131 pp. 1497 – 1524 29.09.2017 ru 328
It is known that not every finite group can be realized over the field of rational numbers as a Galois group of some binomial. In this connection, a more general question arises: suppose that there is given a finite transitive subgroup G of the symmetric group S on n symbols; Can this group G be realized as a Galois group of some trinomial of degree n over the field of rational numbers? In this paper we prove that every transitive subgroup of the group S can be realized in the form of the Galois group of a certain trinomial of the degree n, for the values n = 2, 3, 4. For n = 5 , 6 we give examples that realize concrete Galois groups. In the case n = 7, all the transitive subgroups of the group S are realized, except possibly one group of the isomorphic dihedral group D. Further calculations will be directed to the realization of specific Galois groups for n = 8, 9 ..., however, the number of transitive subgroups of the group S for n = 8, 9 ... grows very fast, so the larger the value of n, the more difficult it is to realize not just everything but the specific subgroup of the group S in the form of a trinomial over Q
883 kb

#### SIMULATION OF BALL LIGHTNING IN CONDUCTING ENVIRONMENT

abstract 1301706027 issue 130 pp. 348 – 378 30.06.2017 ru 608
In this work, a model is developed to describe the formation of streamers, plasmoid, and ball lightning in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, a system of parabolic-type nonlinear equations is formulated that describes the formation of streamers, plasma long-lived formations and ball lightning. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300-500 ms and a diameter of 10-20 cm, which is interpreted as a ball lightning. With high-speed photography, a complex structure is detected, consisting of a plasmoid and surrounding streamers. Within the framework of the proposed model, problems are posed about the formation of a plasmoid and the propagation of streamers in an external electric field. In this model, the plasmoid is considered to be a long-lived streamer. The range of parameters in which a plasmoid of spherical shape is formed is indicated. It is established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. In numerical experiments, the third branching mechanism observed in experiments connected with the branching of the plasmoid in the cathode region with the closure of the space charge to the anode through the streamer system was observed. The results of modeling the evolution of globular clusters in a scale of hundreds of milliseconds are given. Plasma exchange recharge modes leading to the formation of a positive or negative charge of the system are found 