01.00.00 Physical-mathematical sciences
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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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DIAMETER AND RADIUS OF THE WEIGHTED PREFRACTAL GRAPH BY A COMPLETE BIPARTITE SEED
01.00.00 Physical-mathematical sciences
DescriptionResearches of metric characteristics on prefractal graphs are known tasks. Such tasks arise when determining estimates of length, of depth, of width of the graph. Also these questions arise when determining results of optimization of these tasks of the prefractal graphs. Properties of metric characteristics depend on a trajectory of generation of the prefractal graph and on the characteristic of primings. In this work, metric characteristics on prefractal weighed graphs are investigated, dependence of metric characteristics on a trajectory of a priming and prefractal graphs is revealed. Estimates are obtained for the diameter and radius of the weighted prefractal and fractal graphss
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01.00.00 Physical-mathematical sciences
DescriptionThe time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been designed. The algorithm has been developed to determine the parameters of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed. The region of existence of the time-optimal diagram of movement of the executive body of the precision DC drive with elastic shafting with constrains of maximum current and the fifth derivative of the speed has been set. According to the results of the numeral experiment, the dependences of the duration of the cycle of movement of the executive body of the drive from prescribed displacement (rotation angle) for different values of the fifth derivative of the speed have been plotted
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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
DescriptionThe problem of establishing of the factorization of irreducible polynomials with integer coefficients on prime modules p has been long of interest to mathematicians. The quadratic and cubic reciprocity laws solve this problem for quadratic polynomials and binomials of the form x3-a . More general reciprocity laws solve the formulated problem for some classes of polynomials, for example, with Abelian Galois group, but for polynomials with non-Abelian Galois group, the problem is far from its complete solution. Our study shows how using the results of Voronov G.F., Hasse H. and Stickelberger L., one can find conditions that must satisfy prime number p. Gauss received a similar result for binomial x3-2. Specific examples are given, for instance, for the polynomial x3-x - I, also conditions arc formulated for which a quadratic field is immersed in non-Abelian Galois extension of degree 6. Also, conditions are given under which a Diophantine equation: а12a22-4a22-4a13a3- 27a32+18a1a2a3=D has a solution for integer values of D
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VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physical-mathematical sciences
DescriptionIn this work, we consider two types of vortex currents-cyclones and anticyclones in the Northern and Southern Hemispheres. Numerical modeling of turbulent flows of these types uses the model of the planetary boundary layer developed by the author. The purpose of the study is to test hypotheses about the influence of the Coriolis force on the formation of cyclones and anticyclones in the northern and southern latitudes. The first hypothesis on the direction of circulation in cyclones was verified in the case of axisymmetric radially converging and vertically rising turbulent flows with a natural Coriolis parameter and viscosity. From the obtained data of numerical experiments, it follows that the current in the northern latitudes circulates in a counter clockwise direction, and in the south - in a clockwise direction, in full accordance with the observational data. Thus, we have shown that a cyclonic flow is formed in a turbulent radially converging flow under the influence of the Coriolis force. The second hypothesis on the formation of anticyclones was verified in the case of radially divergent and vertically descending turbulent flows. Because of numerical experiments, it was established that in this case, the current in the northern latitudes circulates clockwise, and in the south - in a counter clockwise direction, which corresponds to observations for anticyclones. To test the effect of the cyclone (anticyclone) center velocity on circulation, a nonstationary 3D model of turbulent flow was developed. Within the framework of this model, flows in cyclones and anticyclones moving at a constant speed, as well as in shear flow, are studied. Some types of loop protuberances on the Sun are explained by the presence of a vortex turbulent flow starting in the bowels of the Sun and encompassing the chromosphere