The completely closed model of wall turbulence was derived directly from the Navier-Stokes equation. The fundamental constants of wall turbulence including the Karman constant have been calculated within a theory. This model has been developed also for the accelerated and non-isothermal turbulent boundary layer flows over rough surface
Numerical solutions of equations system of turbulent transport of admixtures in a surface layer of the atmosphere and for a large scale have been studied
The model of continuous transition from the laminar flow to the turbulent flow is proposed and the theory of the spectral density of turbulent pulsation is given
The completely closed model of wall turbulence was derived directly from the Navier-Stokes equation. The fundamental constants of wall turbulence including the Karman constant have been calculated within a theory. This model has been developed also for the accelerated and non-isothermal turbulent boundary layer flows over rough surface
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: а12a22-4a22-4a13a3-
27a32+18a1a2a3=D has a solution for integer values
of D
The article discusses the question of the essence of radiation of electromagnetic waves of different sources and questioned the reliability of its description by J.Maxwell in the form of alternating electric and magnetic fields. It justifies the formation of an electromagnetic wave in the form of a wave of compression-decompression in surrounding electromagnetic photon field with a flux of photons of different frequencies emitted by different sources or antenna
On the basis of the objective analysis it must be
noted that in the arsenal of managers, especially
foreign ones, there is practically no fundamentally
new methods and tools of controlling. So says the
executive director of Russian Association of
Controllers prof. S. G. Falco. However, promising
mathematical and instrumental methods of
controlling actively developed in our country. It is
necessary to implement them. For example,
managers should be used techniques which
discussed in the book by Orlov AI, Lutsenko EV,
Loikaw VI "Advanced mathematical and
instrumental methods of controlling" (2015). These
methods are based on the modern development of
mathematics as a whole - on the system interval
fuzzy math (see the same named book by Orlov AI
and Lutsenko EV, 2014). Considered methods are
developed in accordance with the new paradigm of
mathematical methods of research. It includes new
paradigms of applied statistics, mathematical
statistics, mathematical methods of economics,
methods of analysis of statistical and expert data in
management and control. In the XXI century there
were more than 10 books issued, developed in
accordance with the new paradigm of mathematical
methods of research. The systems approach to
solving specific applications often requires going
beyond the economy. Very important are the
procedures for the introduction of innovative
methods and tools. In this article we consider the
above research results in their interconnection
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 consumers’ needs
This question is about the speed of wave
propagation in electromagnetic environment.
Electromagnetic environment (field) is the space
that fills the whole Universe, occupied by the
electromagnetic particles-photons. At the heart of
the special relativity theory, the constancy of the
speed of light in vacuum is affirmed. According to
modern concepts, the speed of light in vacuum is the
maximum speed of the particle motion and
propagation of interactions. However, light is the
narrow range of electromagnetic radiation –
(4÷8)·1014 Hz, therefore experimentally measured
speed of light is referred to this frequency range.
The fact that this speed of electromagnetic waves
can theoretically be non permanent – physicists have
pondered for a long time and this question is
periodically excited in the scientific literature. The
author of this article also had an impression that the
speed of light, in which he understands distribution
speed of waves of a wide range of frequencies in the
electromagnetic environment, is not a constant. The
article attempts to prove it. Many photons of
different frequencies move simultaneously in
different directions in a photonic electromagnetic
field in environment. They are involved in the
formation of a wave of compression –
decompression in this field under the influence of
the antenna radiated photons. It is approved that the
speed of photons of different frequencies can change
within a wide range from 1,285·103
m/s (ν = 1024
Hz) to 1,285·1012 m/s (ν = 106 Hz) and, therefore,
the speed of wave propagation in the
electromagnetic environments that are filled by
photons of the same frequency or a narrow
frequency range can change widely from 8,58·102
m/s to 8,58·1011 m/s and be significantly different
from the experimentally discovered speed of light.
Interplanetary space in different parts of the
Universe can be represented by different spectra of
photons and therefore they will have different speed
of propagation of electromagnetic waves
Theorems of the value distribution of the sums of Abelian Group’s characters and short exponentail triginimetric sums are proved in this article. Asymptotic formulas of these sums’ fractional moments are proved