№ 134(10), December, 2017
Public date: 29.12.2017
Archive of journal: Articles count 112, 287 kb

01.00.00 Physicalmathematical sciences
THE ASSESSMENT OF COMPLEXITY OF COMBINATORY METHOD OF NUMBERS’ FACTORIZATION
01.00.00 Physicalmathematical sciences
DescriptionThis article is devoted to the assessment of the calculating complexity of combinatory method of numbers’ 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 graphs’ structure allows to state that it’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 it’s stated that the assessment of complexity of combinatory method as well other present methods of numbers’factorization is exponential. In this aspect the combinatory method doesn’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

01.00.00 Physicalmathematical 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

FRACTAL AND PREEFACTAL GRAPHS, BASIC DEFINITIONS AND SYMBOLS
01.00.00 Physicalmathematical 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

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

01.00.00 Physicalmathematical sciences
DescriptionThe timeoptimal 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 timeoptimal 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 timeoptimal 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

CHARACTERIZATION OF AVERAGE VALUES BY MEANS OF MEASUREMENT SCALES
01.00.00 Physicalmathematical 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

01.00.00 Physicalmathematical 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 x3a . More general reciprocity laws solve the formulated problem for some classes of polynomials, for example, with Abelian Galois group, but for polynomials with nonAbelian 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 x32. Specific examples are given, for instance, for the polynomial x3x  I, also conditions arc formulated for which a quadratic field is immersed in nonAbelian Galois extension of degree 6. Also, conditions are given under which a Diophantine equation: а12a224a224a13a3 27a32+18a1a2a3=D has a solution for integer values of D

VORTEX TURBULENT FLOWS IN ATMOSPHERES OF PLANETS AND ON THE SUN
01.00.00 Physicalmathematical sciences
DescriptionIn this work, we consider two types of vortex currentscyclones 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

Description
Studying natural phenomena in all their diversity, humanity worked experienced in every field of science the model of perceiving the world and methods of obtaining information. The development of science currently cannot be imagined without research on the intersection of its regions. This article presents the results of the automated systemcognitive analysis of the size of atoms from the main characteristics that are of research at the interface of General chemistry elements and intelligent systems. Dependence of nuclear radius, mass and of the atom and the charge number are identical in shape and size, which is probably connected with the linear increase of these parameters in the Periodic system of chemical elements. There is also a similar form of the dependences of radii of atoms from the factors ex and x, because these factors are interrelated. The obtained results of the ask analysis have confirmed the theoretical assumptions and the formulae of the dependence of main characteristics of the atom

PREPARATION OF GRAPHENE MATERIAL WITH BENZIMIDAZOLE FRAGMENTS
DescriptionThe new benzimidazolefunctionalized graphene material based on graphene oxide (GO) and 3,3',4,4' tetraaminodiphenyl oxide (TADPO) was obtained under onestep hydrothermal synthesis conditions. According to IR spectroscopy and elemental analysis, as a result of the reaction, benzimidazole (BI) rings are formed, and the mass content of nitrogen is 12.3%. The new graphene material is characterized by excellent electrochemical efficiency in a threeelectrode supercapacitor. As a result of the redox activity of BI cycles the specific capacitance reaches 286 F/g at the scan rate of 2 mV/s, which is substantially higher than the reduced graphene oxide (RGO) sample obtained under similar conditions without using TADPO (159 F/g at 2 mV/s)