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

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

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

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

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

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

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: Ð°12a22-4a22-4a13a3-
27a32+18a1a2a3=D has a solution for integer values
of D

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

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

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