Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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469 kb

ABOUT EULER FUNCTION

abstract 1271703004 issue 127 pp. 113 – 125 31.03.2017 ru 48
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
158 kb

THE MECHANISM OF HUMAN EXPOSURE TO THE MAGNETIC FIELD OF THE EARTH AND THE SUN

abstract 1271703006 issue 127 pp. 138 – 149 31.03.2017 ru 44
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
495 kb

MATHEMATICAL METHODS OF RESEARCH OF INVERSE DYNAMIC ECONOMIC SYSTEMS

abstract 1271703007 issue 127 pp. 150 – 163 31.03.2017 ru 43
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
329 kb

ABOUT RECONNECTION PHENOMENON IN THE LOWER LAYERS OF A MAGNETIC TUBE. THEORY

abstract 1271703047 issue 127 pp. 693 – 712 31.03.2017 ru 5
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
215 kb

MAGNETIC PARTICLES` FORMATION IN CONDITIONS OF THE LOW-TEMPERATURE PLASMA AND MAGNETIC FIELD

abstract 1271703055 issue 127 pp. 791 – 802 31.03.2017 ru 17
Chemical processes are often connected with use or formation of condensed dispersed phase (CDP). Dispersed particles can change mobility of charges, as well as other parameters of the low-temperature plasma. The aim of this work is to study the effect of magnetic field on the processes of dispersed particles formation in argon-oxygen plasma containing iron and carbon atoms at atmospheric pressure. The equilibrium composition of iron and carbon atoms containing mixture simulated at temperatures of 1000-5000K for optimization of the plasma-forming gas composition. It is shown that in case of oxygen excess, the CDP particles contain only iron oxides. The literature data about the phase transition processes in a low-temperature plasma, as well as the data about the processes with participation of ferromagnetic particles in a constant magnetic field analyzed. The results of investigations of the dispersed particles forming in argon-oxygen plasma of arc discharge in the presence and in the absence of the magnetic field are shown. The formed disperse phase was deposited on the substrates and studied by the electron microscopy and X-ray methods. It was found that with the lack of oxygen the size of the iron-oxide particles created in the arc discharge containing iron and carbon is affected by magnetic field: in a magnetic field of 10 mT the particles are larger than in its absence
520 kb

CRYSTALL SPACE METRIC

abstract 1271703072 issue 127 pp. 1010 – 1044 31.03.2017 ru 10
In the present article, we investigate the metric of the crystal space in the general theory of relativity and in the Yang-Mills theory. It is shown that the presence of a lattice of gravitational ether has observable macroscopic consequences. Earlier, the influence of the gravity of the celestial bodies of the solar system on the electrical conductivity, inductance, the rate of radioactive decay of atomic nuclei, on seismic activity, the magnetic field and the motion of the pole of our planet, and on the rate of biochemical reactions was established. In all cases, a similar behavior of the physicochemical characteristics of materials and processes is observed, depending on the universal parameters characterizing the seasonal variations of the gravitational field of the solar system. The relationship between lattice parameters and the properties of materials, elements, atomic nuclei, and elementary particles is discussed. Possible metrics of the crystal space are constructed: a metric that depends on the Weierstrass function, derived in the Yang-Mills theory and analogous metrics found in Einstein's theory. Such metrics, which have a central symmetry, can be used to justify the structure of elementary particles, the properties of atomic nuclei, atoms and matter. Periodic metrics are constructed that admit an electromagnetic field, as well as metrics associated with the assumed structure of the crystal space. These metrics are of particular interest, since the properties of the substance are related to the metric parameters. We proposed the model of electron beam as a streamer of preons
1876 kb

INVARIANT TO VOLUMES OF DATA, A FUZZY MULTICLASS GENERALIZATION OF F-MEASURE OF PLAUSIBILITY IN VAN RIJSBERGEN MODELS IN ASC-ANALYSIS AND IN THE "EIDOS" SYSTEM

abstract 1261702001 issue 126 pp. 1 – 32 28.02.2017 ru 43
Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In classifying big data we have revealed a large number of false-positive decisions with a low level of similarity, which, however, in total, contribute to reducing the reliability of the model. To overcome this problem, we propose a L2-measure, in which instead of the sum of levels of similarity we use the average similarity by different classifications. Thus, this work offers measures of the reliability of the models, called L1-measure and the L2 measure, mitigating and overcoming the shortcomings of the F-measures; these measures are described mathematically and their application is demonstrated on a simple numerical example. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we have implemented all these measures of the reliability of the models: F, L1 and L2
395 kb

HADAMARD MATRICES

abstract 1261702033 issue 126 pp. 471 – 483 28.02.2017 ru 33
In 1893, the French mathematician J. Adamar raised the question: given a matrix of fixed order with coefficients not exceeding modulo this value, then what is the maximum modulo value can take the determinant of this matrix? Adamar fully decided this question in the case when the coefficients of the matrix are complex numbers and put forward the corresponding hypothesis in the case when the matrix coefficients are real numbers modulo equal to one. Such matrices satisfying the Hadamard conjecture were called Hadamard matrices, their order is four and it is unknown whether this condition is sufficient for their existence. The article examines a natural generalization of the Hadamard matrices over the field of real numbers, they are there for any order. This paper proposes an algorithm for the construction of generalized Hadamard matrices, and it is illustrated by numerical examples. Also introduces the concept of constants for the natural numbers are computed values of this constant for some natural numbers and shown some applications of Hadamard constants for estimates on the top and bottom of the module of the determinant of this order with arbitrary real coefficients, and these estimates are in some cases better than the known estimates of Hadamard. The results of the article are associated with the results of the con on the value of determinants of matrices with real coefficients, not exceeding modulo units
430 kb

MATHEMATICAL MODEL OF ORGANIZATION OF DISTRIBUTED CALCULATIONS IN A CORPORATE NETWORK ON PREFRACTAL GRAPHS IN VECTOR FORMULATION

abstract 1261702040 issue 126 pp. 564 – 581 28.02.2017 ru 34
In the article we investigate the multicriteria task arising at the organization of distributed calculations in a corporate network. As a mathematical tool to solve the problem we use prefractal graphs, which naturally reflect the structure of relationships in global and corporate networks. The corporate network with the distributed computing system at the solution of a particular task has to be reliable, quickly and qualitatively to make decisions. And every computer in the network should be a part in the solution of the problem, since it is fixed for a certain function. The problem is reduced to cover the prefractal graphs with disjoint simple paths along the edges and vertices. On the set of all admissible coverings we constructed a vector-target function with specific criteria. All these criteria have a specific meaningful interpretation, allowing organizing the calculation of maximum reliability, with minimum time information processing and loading balancing between the network elements. In the article we constructed polynomial algorithms for finding optimal solutions according to specific criteria. For the criteria which are not optimizing the allocated coverings, estimates of the lower and upper bounds are given. For all the algorithms we constructed and substantiated estimation of computational complexity, confirming the advantage of using algorithms on prefractal graphs to classical algorithms on graphs
368 kb

INVERSE PROBLEM MODELS OF THE SAMUELSON–HICKS

abstract 1261702042 issue 126 pp. 600 – 608 28.02.2017 ru 27
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 this article the authors formulated and investigated inverse problems for dynamic systems: model of Samuelsson– Hicks. The technique of constructing non-negative solutions of the studied inverse problems. This method is based on the following scheme of the solution. First, we have to identify the formulation of the direct problem, then the formulation of the inverse. This work investigates how correct the mathematical models describing the dynamic economic system are. Further, in the specified tabular solutions of the direct problem, we have built a system of algebraic equations containing the unknown estimated parameters of the studied model. Then posed inverse problem is reduced to solution of a problem of quadratic programming, the solutions of which are defined in MS Excel. The theoretical material is accompanied by the specific example
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