# Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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1414 kb

#### THE ASSESSMENT OF COMPLEXITY OF COMBINATORY METHOD OF NUMBERSâ€™ FACTORIZATION

abstract 1341710006 issue 134 pp. 59 – 87 29.12.2017 ru 637
This article is devoted to the assessment of the calculating complexity of combinatory method of numbersâ€™ factorization. The content of combinatory method is explained in the article of the same name published in the journal issued in November 2016. The author supposes that the reader has learnt its content and knows the basic notions of theory of calculating complexity of the algorithms. The following results of the learning of the given task are expounded in this article. The algorithm of combinatory method permits to accomplish the parallel calculations. Graph of any order is the separate structure, because its initial data are determined independently from the other graphs. So, the calculating complexity of the task about the factorization of numbers in the predetermined interval of the positive integers is defined by the complexity of the most laborious graph. The analysis of the graphsâ€™ structure allows to state that itâ€™s the graph of the third order. In any graph both branches of the first level give the separate structures- partitive graphs of the first level with independent input data. So, the calculating complexity of the graph complete is determined by the maximal complexity of the graph of the first level. The givenat random interval of positive integers stays without changes, if we observe the sequence of the adjacent intervals. In the results itâ€™s stated that the assessment of complexity of combinatory method as well other present methods of numbersâ€™factorization is exponential. In this aspect the combinatory method doesnâ€™t compete with other actual methods. However, evaluating the scientific significance of the algorithm, the decisive factor is not the calculating complexity, but its originality, which permits to explain (if not to discover) any properties of the positive integers. In the conclusion of the article the author describes the advantages of combinatory method, permitting to appreciate the degree of its scientific novelty
287 kb

#### FRACTALIZATION OF TREES

abstract 1341710013 issue 134 pp. 155 – 163 29.12.2017 ru 699
In 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
506 kb

#### FRACTAL AND PREEFACTAL GRAPHS, BASIC DEFINITIONS AND SYMBOLS

abstract 1341710015 issue 134 pp. 174 – 188 29.12.2017 ru 821
The 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
192 kb

#### DIAMETER AND RADIUS OF THE WEIGHTED PREFRACTAL GRAPH BY A COMPLETE BIPARTITE SEED

abstract 1341710033 issue 134 pp. 390 – 403 29.12.2017 ru 226
Researches 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
465 kb

#### THE TIME-OPTIMAL DIAGRAM OF MOVEMENT OF THE EXECUTIVE BODY OF THE PRECISION DIRECT CURRENT MOTOR WITH ELASTIC SHAFTING WITH CONSTRAINS OF MAXIMUM CURRENT AND THE FIFTH DERIVATIVE OF THE SPEED

abstract 1341710044 issue 134 pp. 534 – 550 29.12.2017 ru 173
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 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
304 kb

#### CHARACTERIZATION OF AVERAGE VALUES BY MEANS OF MEASUREMENT SCALES

abstract 1341710070 issue 134 pp. 853 – 883 29.12.2017 ru 160
According 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
263 kb

#### TO THE HYPOTHESIS OF VORONOI

abstract 1341710075 issue 134 pp. 937 – 947 29.12.2017 ru 172
The 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: Đ°12a22-4a22-4a13a3- 27a32+18a1a2a3=D has a solution for integer values of D
1362 kb

#### VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN

abstract 1341710109 issue 134 pp. 1387 – 1411 29.12.2017 ru 191
In 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
253 kb

#### TO THE QUESTION OF MATHEMATICAL MODELS OF MATERIAL FLOW MANAGEMENT

abstract 1331709002 issue 133 pp. 8 – 23 30.11.2017 ru 471
The article concentrates on the matters of current interest in the sphere of product flows. The object of research is the relocation of product flows from the supply sphere, represented by supply and sales organizations or other commercial-intermediary agencies, to the sphere of business enterprise. The ultimate goal of the production and economic system modeling is the preparation for managerial decision-making. The choice of the model depends on the purposes of the modeling, management functions, automation manufacturing step, applied mathematical tools technique. The article considers the main characteristics of the flow, which while retaining their individuality at the same time depend on each other and function logically in the economic space. The advantages and disadvantages of the material inventory and flows management in micrologistic intraproductive systems are being analyzed. External and internal environment, taken as a basis for the real logistical process modeling, determine the type of the principal stock regulation system and the type of the corresponding mathematical model. Methods and models of the stock theory, the primary objective of which is to determine the most important incoming product flow parameters of the system, are still in demand and their primary goal is to adapt the manufacturing company to the consumersâ€™ needs
1854 kb

#### AMPLITUDE-FREQUENCY AND AMPLITUDEVELOCITY CHARACTERISTICS OF A RIGID OSCILLATING INCLUSION MOVING WITHIN A TWO-LAYER ISOTROPIC MEDIUM

abstract 1331709035 issue 133 pp. 448 – 466 30.11.2017 ru 419
The article is dedicated to a numerical investigation of a plane problem of the oscillation amplitude of a buried source, depending on the frequency and motion speed in various isotropic media. Three types of the medium are considered: a two-layer package with a rigidly fixed base, a two-layer package with a mechanically free base, a half-space. The source, in the form of a stress jump simulating a rigid inclusion of small dimensions, moves in the interface plane at a constant speed. Homogeneous boundary value problems are considered in a moving coordinate system associated with a source. The solution method is based on the usage of integral Fourier transforms, the method of direct contour integration and algorithms for constructing symbols of Green's matrices. The method of direct contour integration significantly simplifies calculations in comparison with the traditional approaches to the calculation of Fourier integrals. We have presented calculations of nine amplitude-frequency and amplitude-velocity characteristics for different combinations of medium and source types, that give an exhaustive qualitative and quantitative description of the solutions for boundary value problems in a wide range of velocities and frequencies. Comparative analysis of calculations showed a primary influence of the type of an elastic medium on the investigated characteristics, as well as the large influence of the source type. Which, in turn, revealed some substantial connections between the boundary value problems with a moving source and the corresponding problems with a stationary source 