Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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abstract 1301706071 issue 130 pp. 975 – 981 30.06.2017 ru 593
The inverse matrix for the square matrix A of order n with coefficients of some field exists, as it is known then and only then, when its determinant is not equal to zero. If the matrix A has a certain type (certain structure), then an inverse matrix A-1 should not have exactly the same structure. Therefore, it is interesting to describe such square matrices A, which have an inverse matrix A-1, having the same structure as the matrix A, under certain conditions. For example, a subdiagonal matrix with nonzero elements on the main diagonal has an inverse matrix over a field of characteristic zero, having also the form of subdiagonal matrix. Similarly, an inverse matrix towards symmetrical or skew-symmetric matrix is also symmetric or skew-symmetric accordingly. Also, the matrix inverse to non-degenerate (nonsingular) circulant will be a circulant itself, and finally, the matrix inverse to nonsingular quasdiagonal matrix D will be quasdiagonal itself, and will have the same partitioned structure as D. Thus, there is a problem of determining these types of nonsingular matrices that have an inverse matrix of the same type as a given matrix. In line with this problem in the present study it is determined such type of matrices for which an inverse matrix has the same type, at that the conditions are identified in explicit form, ensuring the nonsingularity of the matrix. The matrices of three orders are shown in detail. These results allow determining the characteristics of fields over which there are inverse matrices of the considered types
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abstract 1291705014 issue 129 pp. 170 – 184 31.05.2017 ru 651
Partially ordered set is a basic concept of modern settheoretic mathematics. The problem of linear set ordering with given binary relations is well-known. Every partial order over a finite set can be linearly ordered, but not every binary relation over this set can be linearly ordered as well. Up to now, there is no known formula for calculating the number of partial orders over a given finite set. It appears that there is a formula for calculating linearly ordered binary relations over a finite set. This article is concerned with derivation of this formula. The fact from work of G.N. Titov [9] that a binary relation over a finite set is linearly ordered if and only if any diagonal block, derived from the binary relation matrix as a result of setting main diagonal elements to zero, contains at least one zero row (diagonal block of matrix means any matrix composed of elements at the crossings of rows and columns of a given matrix with the same numbers), plays a key role in process of corroboration. The main conclusion of the article is a theorem that allows to find the number of linearly ordered binary relations over a set of n elements using the formula. A recurrence formula for the number of linearly ordered (irreflexive) binary relations over a finite set of n elements, provided in the lemma, was derived as well
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abstract 1291705037 issue 129 pp. 420 – 431 31.05.2017 ru 1268
In this article, we have proposed a forecast of labor resources by sectors of the labor market of the Russian Federation until 2018 inclusive. The probabilistic parameters of the dynamics of labor resources were calculated using the considered model (articles [1-4]). Further, these probabilities were used to estimate and parameterize the trends of employed and unemployed (with a known last place of employment) specialists in each industry. For each sector of the Russian economy, the type of trend that best approximates the long-term (more than three years) dynamics of labor resources in this sector was selected. It is shown that the forecast error for 1 year is less than 1% using the selected trend models. Further, identified long-term trends were used in forecasting. Based on the results of the forecast of the number of people employed in the sectors of the Russian economy, the sectors were divided into two groups. The first group contains sectors with a significant change in the number of employed in. The second group contains sectors, changes in employed in which were insignificant. At the end of the article, an example of an analysis of two sectors from the first group is given. Causes of changes in the dynamics of labor resources in the researched sectors of the economy were identified. Ones of the main sectors of the economy were considered in this example: "Manufacturing industries" and "Financial activities, real estate transactions, leasing and provision of services"
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abstract 1291705041 issue 129 pp. 471 – 497 31.05.2017 ru 424
In this work, a model is developed that describes the formation of a plasmoid and streamers 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, the streamer model is formulated in the form of a system of parabolictype nonlinear equations. 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 similarity of ball lightning and plasmoid is discussed. If this similarity is confirmed, then the number of theoretical hypotheses concerning the nature of ball lightning, currently more than 200, can be drastically reduced to one described in this article
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abstract 1281704050 issue 128 pp. 678 – 708 28.04.2017 ru 531
Statistical methods are widely used in domestic feasibility studies. However, for most managers, economists and engineers, they are exotic. This is due to the fact that modern statistical methods are not taught in the universities. We discuss the situation, focusing on the statistical methods for economic and feasibility studies, ie, econometrics. In the world of science, econometrics has a rightful place. There are scientific journals in econometrics, Nobel Prizes in Economics are given to series of researches in econometrics. The situation in the field of scientific and practical work and especially the teaching of econometrics in Russia is disadvantaged. Often, individual particular constructions replace econometrics in general, such as those related to regression analysis. The article is devoted to econometrics as an academic discipline. Our course begins with a discussion of the structure of modern econometrics, the connections between applied statistics and econometric methods. We consider sample researches (analysis of surveys results), the elements of econometrics numbers, and methods of testing of statistical hypothesis about homogeneity. We have given the concepts of regression analysis, econometric classification methods, modern measurement theory. The important places are occupied by the statistics of non-numerical data (including fuzzy sets and their links with random sets) and the statistics of interval data. The problem of the stability of statistical procedures with respect to the tolerances of input data and model prerequisites is discussed. The representations of the econometric methods of expert research and quality control, analysis and forecasting of time series, econometrics of forecasting and risks are given
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abstract 1281704080 issue 128 pp. 1148 – 1169 28.04.2017 ru 577
In this work, we develop a model describing the propagation and branching of a streamer in a conducting medium in external electric field. 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, the streamer model is formulated in the form of nonlinear equations of parabolic type. In the framework of the proposed model, the problem of the propagation of a streamer in the form of a traveling wave is considered, which leads to the emergence of SaffmanTaylor streamers. For streamers of this type, the branching problem is formulated, which has a unique solution. The dependence of the branch point on the parameters of the problem-the speed of the streamer, the diffusion coefficient of the electrons and the strength of the external electric field, is found. The branching mechanism of the streamer head by dividing it into two parts has been well studied and several alternative models have been formulated for its description. The novelty of the problem in question is that the streamer splits into two three-dimensional channels that are symmetric with respect to the given plane. Numerical experiments also revealed the mechanism of branching of the streamer in the cathode region, connected with the separation of the main channel into several lateral branches. It is noted, that in nature both branching mechanisms are realized, whereas in theory the instability of the surface of the streamer head is investigated
469 kb


abstract 1271703004 issue 127 pp. 113 – 125 31.03.2017 ru 752
The Euler function is very important in number theory and in Mathematics, however, the range of its values in the natural numbers has not been written off. The greatest value of the Euler function reaches on Prime numbers, furthermore, it is multiplicative. The value of the Euler function is closely associated with the values of the Moebius function and the function values of the sum of the divisors of the given natural number. The Euler function is linked with systems of public key encryption. The individual values of the Euler function behave irregularly because of the irregular distribution of primes in the natural numbers. This tract is illustrated in the article with charts; summatory function for the Euler function and its average value are more predictable. We prove the formula of Martinga and, based on it, we study the approximation accuracy of the average value of the Euler function with corresponding quadratic polynomial. There is a new feature associated with the average value of the Euler function and calculate intervals of its values. We also introduce the concept of density values of the Euler function and calculate its value on the interval of the natural numbers. It can be noted that the results of the behavior of the Euler function are followed by the results in the behavior of functions of sums of divisors of natural numbers and vice versa. We have also given the results of A.Z.Valfish and A.N.Saltykov on this subject
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abstract 1271703006 issue 127 pp. 138 – 149 31.03.2017 ru 639
There is a discussion about the question of the mechanism of the action of the magnetic field of the Earth and the Sun on the human body. It is noted that in the 21st century an international conference on the subject "Man and electromagnetic fields" is regularly held, as well as the international congress "Weak and superweak fields and radiation in biology and medicine". This indicates the importance of studying the effect of electromagnetic fields on the human body. Participants in these conferences and congresses give a lot of experimental data on the influence of various factors on various biological objects. However, there is no theoretical justification for the influence of these fields on the human body. In this connection, in order to solve this problem, the article analyzes the atomic composition of the human body. It is shown that the human body more than 60% consists of hydrogen atoms. On the example of a hydrogen atom, the interaction of the magnetic moment of an electron of an atom with an external magnetic field is considered. This leads to a precession motion of the electron's orbit. Taking into account the fact that photons rotate around electrons in atoms and the temperature is determined by the bulk density of photon energy, the appearance of precessional electron motion will lead to an increase in the frequency of oscillation of photons and, consequently, to an increase in their energy and body temperature. This is confirmed by the fact that the body temperature changes during the day, and, it is minimal in the morning and increases by the evening. The chemical elements of the human body, related to different groups of magnets, are analyzed. It is noted that the external magnetic field has the greatest influence on the state of the human body through a ferromagnet - iron. It is concentrated in the blood, up to 60% in hemoglobin. It is a complex iron-containing blood protein, an integral part of erythrocyte - red blood cells, oxygen carriers. Under conditions of an increase in the intensity of the external magnetic field or the immobile state of the body, the orientation of the individual erythrocytes will increase due to their iron atoms in the direction of the external field. This will lead to the pooling of erythrocytes into clusters, that is, to the formation of unique magnetic domains with a significant increase in the viscosity of the blood and a decrease in its circulatory ability. The last is confirmed by the fact that in people suffering from cardiovascular diseases, heart attacks and strokes most often occur in the early morning especially during periods of solar magnetic storms
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abstract 1271703007 issue 127 pp. 150 – 163 31.03.2017 ru 566
The article continues the cycle of their studies associated with the formulation and development of methods of construction of nonnegative solutions of inverse problems for dynamic systems. In practice, we have developed and tested mathematical models of dynamic systems. The basis of these models was based on the apparatus of linear algebra, mathematical analysis, mathematical programming, differential equations, optimization methods, optimal control theory, probability theory, stochastic processes, operations research, game theory, statistical analysis. The inverse problem in various models of mathematical Economics was considered rare. These tasks were sufficiently well investigated in the study of physical processes. As shown by the analysis of the theoretical and applied studies of economic processes they represent considerable interest for practice. Therefore, the article considered the inverse problem of the mathematical model, as shown already introduced the results of other mathematical models, are of considerable interest in applied and theoretical research. In this article the authors formulated and investigated the inverse problem for dynamical systems zero-order and the model of Keynes. For their solution, the authors propose to build a system of algebraic equations, then, using methods of quadratic programming, to find the best average of mean square estimation of the model parameter, which are defined in MS Excel
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abstract 1271703047 issue 127 pp. 693 – 712 31.03.2017 ru 387
It was shown before [1,2], that variants of intensity of γ-quantas of axion origin, induced by the variants of the magnetic field in the the tacho wedge through the termomagnetic Ettinshausen-Nernst effect, cause variations of solar luminance and ultimately characterise the changes of active and calm state of the Sun. It is shown in the article in which way the areas of sunspots are generated by the action of global dynamo in the convective zone, or in other words, which fundamental processes connect the sunspots and solar cycles with the large-scaled magnetic field of the Sun