01.00.00 Physical-mathematical sciences
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MAGNETIC PARTICLES` FORMATION IN CONDITIONS OF THE LOW-TEMPERATURE PLASMA AND MAGNETIC FIELD
01.00.00 Physical-mathematical sciences
DescriptionChemical 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
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01.00.00 Physical-mathematical sciences
DescriptionIn this article, the properties of prefractal graphs generated by a seed representing a tree are investigated. To determine the phenomenon of the object under investigation with a fractal structure, we present a concept which is the degree of fractalization. The degree of fractalization will allow us to evaluate the structure relative to its belonging to the prefractal graphs
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FRACTAL AND PREEFACTAL GRAPHS, BASIC DEFINITIONS AND SYMBOLS
01.00.00 Physical-mathematical sciences
DescriptionThe fractal and prefractal graph are described in the article. The basic definitions and notation are proposed, the procedure for constructing prefractal graph, the operation of replacement vertex by seed is given
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FUNDAMENTAL INTERACTIONS IN KALUZA-KLEIN THEORY
01.00.00 Physical-mathematical sciences
DescriptionThe fundamental interaction model is developed on the basis of Kaluza-Klein theory in 5-dimension space
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CHAOS AND ORDER OF DISCRETE SYSTEMS IN LIGHT OF SYNERGETIC INFORMATION THEORY
01.00.00 Physical-mathematical sciences
DescriptionEstimation of chaos and order in structure of electronic systems of atoms, protein molecules, webs of spiders, poetic products is done with the help of synergetic information theory. Existence of statistical rule of structural organization in nature is expected. This rule directs evolution of discrete system towards balance of chaos and order.
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CHAOS AND PHASE TRANSITION IN ATOMIC NUCLEI
01.00.00 Physical-mathematical sciences
DescriptionThe model of chaotic behavior of nucleons in nuclei, based on the model of nuclear interactions and the Fermi-Dirac statistics is discussed
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CHARACTERIZATION OF AVERAGE VALUES BY MEANS OF MEASUREMENT SCALES
01.00.00 Physical-mathematical sciences
DescriptionAccording to measurement theory, statistical data are measured in various scales. The most widely used ordinal scale, scales of intervals and relations. Statistical methods of data analysis should correspond to the scales in which the data is measured. The term "correspondence" is specified with the help of the concepts of an adequate function and an allowable scale transformation. The main content of the article is a description of the average values that can be used to analyze data measured in the ordinal scale, interval and relationship scales, and some others. The main attention is paid to the means for Cauchy and the means for Kolmogorov. In addition to the mean, from this point of view, polynomials and correlation indices are also analyzed. Detailed mathematical proofs of characterization theorems are given for the first time in scientific periodicals. It is shown that in the ordinal scale there are exactly n average values, that can be used, namely, n order statistics. The proof is represented as a chain of 9 lemmas. In the scale of intervals from all Kolmogorov means, only the arithmetic mean can be used. In the scale of relations from all the Kolmogorov means, only the power means and the geometric mean are permissible. The kind of adequate polynomials in the relationship scale is indicated
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01.00.00 Physical-mathematical sciences
DescriptionRecently, the process of monetization of the evaluation of scientific activity was initiated, and there is a need for quantitative methods and comparable assessment of the effectiveness and quality of work of a scientist. There are numerous methods to reward for these results. What is common to all these techniques covered is the role of the Hirsch index or h-index. By itself, this index is well founded. However, in connection with the practice of application of h-index in our environment in the minds of the scientific community it has started some kind of mania, which the author proposes to call "Hirsch-mania". This mania is characterized by elevated unhealthy interest to the value of the Hirsch index, especially inadequate artificial exaggeration of this value, as well as a number of negative implications of this interest. In this article we have made an attempt to briefly describe some of the negative effects of this new mental infection that hit the public consciousness of the scientific community. And also we want to identify ways of overcoming at least some of their causes. This is the problem solved in this work. To solve the formulated problem, we propose to apply multi-criteria approach based on information theory, namely those options, which are implemented in an automated system-cognitive analysis (ASC-analysis) and its software tools - intelligent system called "Eidos
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SPECIAL CASES OF INVERSE MATRICES
01.00.00 Physical-mathematical sciences
DescriptionThe 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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A NUMERICAL ALGORITHM IN THE PROBLEM OF SELF-ORGANIZATION OF LABOR RESOURCES
01.00.00 Physical-mathematical sciences
DescriptionIn this article, there is a numerical method of solving the problem of self-organization of the labor resources. The problem deals with finding probabilities of hiring and the layoffs of specialists from the sectors of the labor market. A mathematical model of labor resources dynamics is used to solve this problem. The initial problem is incorrect, because number of equations of the descriptive system is less than number of unknown variables. A special algorithm is designed for guaranteed finding the normal solution in finite number of iterations. The algorithm is separated into two key stages. Initially, unconditional normal solution of the problem is found by applying the modified method of Gauss for underdetermined systems. Later, this solution is projected in the subspace of permissible values. After that, the normal solution of the problem with consideration of non-negativity of the desired values is being found by using the gradient projection method. The proposed algorithm has been successfully used to develop application in programming environment C++. This application is focused on solving of the problem of selforganization of the labor resources. Comparative analysis of speed of the application and add-ins MS Excel "Solver" showed that the same problem is solved much faster in the application designed by the author than in a table processor MS Excel when using the add-in "Solver". This demonstrates the high efficiency of the proposed method