In the paper the problem of constructing a unified field
theory based on the theory of supergravity in the 112D
is discussed. It is assumed that in the 112-dimensional
Riemann space there are 37 three-dimensional worlds
coexist having a single time and associated gravity.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. It is assumed that in the 112D
performed the wave equation of the general form,
describing the dynamics of the scalar field. From this
equation, the wave equation is displayed in the fourdimensional
space-time, containing terms describing
the contribution of extra dimensions. It is shown that
the quantum numbers of the problem allow us to
describe the structure of the atom and the atomic
nucleus on the assumption that given the total mass of
the central body. The problem on the dynamics of the
scalar field in the 112D in a centrally symmetric metric
has been described. Built of field quantization theory
in general, and in the particular case of metrics
depending on the Weierstrass elliptic functions. It is
shown that in this case there are bounded periodic
potentials and corresponding periodic solutions that
depend on the energy and angular momentum
projection, and on the invariants of the Weierstrass
function. It is found that in an excited state with a
sufficiently large magnitude of the angular momentum
of the projection portion of the radial wave function is
periodic in a limited range, while the ground state
allowed waves on all axes of the radial coordinate. The
connection of the solutions to the Yang-Mills theories
discussed
The paper deals with the problem of changing the
polarity of the geomagnetic field as a problem of a
unified field theory and supergravity in the 112D.
Investigated centrally symmetric metric depends on
the radial coordinate in the observable physical space
of one of the worlds. The equation that relates the
magnetic field of the planet with a gravitational field in
5D has been derived. The problem of changing the
polarity of the magnetic field of the Earth discussed.
The rapid change of the geomagnetic field polarity
detected on the basis of paleomagnetic data is modeled
as a movement on a hypersphere in the 112D, which
corresponds to 110 corners. The simplest example of
such a movement in the case of the three angles is the
Euler model that describes the rigid body rotation. In
this model, there are modes with a quick flip of the
body while conservation of the angular momentum. If
the body has a magnetic moment, when such a change
occurs flip of the magnetic field. It is assumed that the
central core of the earth is magnetized and surrounded
by a number of satellites, each of which has a magnetic
moment. Satellites interact with a central core and one
another by means of gravity and through a magnetic
field. The central core may sudden flip, as in the Euler
model. It is shown that the duration of phase with
constant polarity and upheaval time depends on the
magnitude of the disturbance torque and core
asymmetry. We discuss Einstein's hypothesis about the
origin of the magnetic field when rotating the neutral
masses. It is shown that the motion on a hypersphere
in the 112D has the effect of a magnetic field due to
the interaction of nucleons in nuclei. Such magnetic
field is most evident for iron, cobalt and nickel -
elements are consisting of the Earth's core
There is a widely known problem regarding the
ordering of the partially ordered sets (Linear Ordering
Problem). It boils down to finding the numerations of
such sets. The main result of this article is a
generalization of one of the known S. S. Kislitsyn's
results about finding the number of numerations of
finite partially ordered sets
We should have trained staff to implement
innovative strategies. Therefore, it is natural, that a
lot of attention is paid to the staffing of the
management processes of innovative activity at the
enterprises of the rocket and space industry (RCP).
Training and human resources management in
accordance with current legislation should be based
on professional standards. The content of
professional standards should reflect the results of
forecasting scientific and technical progress in the
field, for example, in the RCP. It is necessary to
forecast trends in the use of information and
communication technologies in solving management
problems in the socio-economic sphere in order to
reflect these developments in professional standards.
The approach to solving this problem is the subject
of this article. What should the professional standard
be like in the RCP? The main problem lies in the
fact that although the standard is to be enacted in the
near future, its actual impact on the industry will
start in 5 - 10 years and will continue for at least
another 10 years, ie, until the 2030s. Professional
standards should come from "Education through
Science" concept, ie, knowledge, skills,
competences, provided by a professional standard,
should be based on modern scientific achievements.
For example, mathematical methods of research
should be based on a new paradigm in the area of
knowledge and statistical data analysis methods
must meet high statistical techniques. For the
development of professional standards in the field of
the RCP it is necessary to predict the characteristics
of the qualification (level of knowledge, skills and
experience) required the employee to carry out
professional activities in the RCP in 2020 - 2030.
Modern information and communication
technologies are creating a fundamentally new
situation in the organization of the economy. We
have an ability to manage the work of organizational
units, scattered throughout the world, from a single
center. The requirement of presence in the
workplace is mainly a relic of the past. We have a
lot of advantages in a remote work
In this article, we discuss various issues related to the
formulas approximating the distribution function of
prime numbers pi(x). This question has occupied many
scholars, but the exact function is well approximated
function pi(x) over the number of positive integers not.
Based on certain hypotheses, we present a new
function s(x) is very well approximated pi(x). The
above article hypotheses are so important that their
numerical validation and refinement for the lengths of
the segments more in 1014 - one of the main areas
related to the problem of approximation of the function
pi(x) throughout the series of natural numbers. After
analyzing the behaviors and constructs many
functions, we are building the basis of the function
s(x), which is well approximates the function pi(x)
throughout the series of natural numbers. We also
present a table of values for x, less or equal 1022 for the
difference of s(x) - pi(x)
In this article we discuss a version of the metric theory
of the fundamental interactions in which it is assumed
that the physical constants due to the presence of extra
dimensions of space-time. The estimation of the
number of physical constants based on the theory of
supergravity in 112D is that the minimum number of
constants is equal to 222, and the maximum number -
1404928. At present, the number of parameters that
characterize the elementary particles, isotopes and
chemical elements is about 150920. This number is 9.3
less than the maximum possible number of parameters
that indicate still great potential of modern science.
Functions describing the area and volume of a unit
hypersphere, embedded in a Riemannian space of
arbitrary dimension, were used to find the fundamental
physical constants. A satisfactory agreement with a
relative error of 0.03% calculated and experimental
values of the fine structure constant found out. For the
ratio of the average mass of a nucleon to the electron
mass is obtained coincidence with the experimental
value with an accuracy of 0.002%. The proposed
theory of physical constants different from that Bartini
theory that established the optimal dimension of the
space is a hypersphere 5 and 7, rather than 6 as in
Bartini theory. The problems of the compactification
of extra dimensions in describing the motion in fourdimensional
space-time are discussed
In this article, there is a numerical method of solving
the problem of self-organization of the labor
resources. The problem deals with finding
probabilities of hiring and the layoffs of specialists
from the sectors of the labor market. A mathematical
model of labor resources dynamics is used to solve
this problem. The initial problem is incorrect,
because number of equations of the descriptive
system is less than number of unknown variables. A
special algorithm is designed for guaranteed finding
the normal solution in finite number of iterations.
The algorithm is separated into two key stages.
Initially, unconditional normal solution of the
problem is found by applying the modified method of
Gauss for underdetermined systems. Later, this
solution is projected in the subspace of permissible
values. After that, the normal solution of the problem
with consideration of non-negativity of the desired
values is being found by using the gradient projection
method. The proposed algorithm has been
successfully used to develop application in
programming environment C++. This application is
focused on solving of the problem of selforganization
of the labor resources. Comparative
analysis of speed of the application and add-ins MS
Excel "Solver" showed that the same problem is
solved much faster in the application designed by the
author than in a table processor MS Excel when
using the add-in "Solver". This demonstrates the high
efficiency of the proposed method
The article deals with the solution of the NavierStokes
equations describing turbulent flows over
rough surfaces. It is known, that there is a mechanism
of turbulent mixing in natural systems, leading to an
increase in the viscosity of the continuous medium. In
this regard, we suggest methods of regularization of
the Navier-Stokes equations, similar to the natural
mechanisms of mixing. It is shown, that in threedimensional
flows over a rough surface turbulent
viscosity increases proportionally to the square of the
distance from the wall. The models of the flow,
taking into account the properties of the turbulent
environment are considered. A modification of the
continuity equation taking into account the limiting
magnitude of pressure fluctuations is proposed. It is
shown, that due to the pressure pulsation, the
incompressibility condition may be violated even for
flows with low Mach numbers. Modification of the
continuity equation taking into account turbulent
fluctuations leads to a system of nonlinear equations
of parabolic type. Modification of continuity equation
in the system of Navier-Stokes by the introduction of
turbulent viscosity allows the regularization of the
Navier-Stokes equations to solve the problems with
rapidly changing dynamic parameters. The main
result of which is obtained by numerical simulation of
the modified system of equations is the stability of the
numerical algorithm at a large Reynolds number,
which can be explained, first, a system of parabolic
type, and a large quantity of turbulent viscosity. A
numerical model of flow around plates with the rapid
change in angle of attack has been verified. We have
discovered the type of instability of the turbulent
boundary layer associated with the rapid changes in
dynamic parameters. It is shown, that the fluctuations
of the boundary layer to cause generation of sound at
a frequency of 100 Hz to 1 kHz
Classical combinatorial formula to calculate the number
of combinations from n on m: C(n,m)=n!/(m!(nm)!)
involves the intermediate calculation of factorials,
which is often impossible when n>170, due to limitations
in the capacity of numbers that are used in programming
languages and created through these systems.
However, in some cases it is necessary to calculate
the number of combinations for n and m much
larger than this limit, such as when a value greater than
10000. In such cases, there is a definite problem,
which manifests itself, for example in the fact that
many on-line services meant to calculate the number
of combinations with these parameters do not work
properly. In this article, we present its solution in the
form of an algorithm and software implementation.
The essence of the approach is to first decompose the
factorials into prime factors and reduce them, and then
to produce multiplication. This approach differs from
those cited in the Internet
In the training courses on the theory of probability and
mathematical statistics there are various parametric
families of distributions of numerical random variables
considered. Namely, we have been studying the
families of normal distributions, log-normal
distributions, exponential distributions, gamma
distributions, Weibull-Gnedenko distributions, etc. All
of them depend on one, two or three parameters.
Therefore, for a complete description of the distribution
it is sufficient to know or estimate one, two or three
numbers. Parametric theory of mathematical statistics is
widely developed, where it is assumed that the
distribution of observations belong to one or another
parametric family of distributions. This tradition comes
from Karl Pearson, who in the early twentieth century
proposed the use of four parametric family of
distributions. The above families of distributions - are
the subsets of a four-parametric family of Pearson.
Unfortunately, parametric families exist only in the
minds of the authors of textbooks on probability theory
and mathematical statistics. In real life, they are not.
Therefore, modern applied statistics and econometrics
mainly use non-parametric methods, in which the
distribution of observations can have arbitrary form.
First, on an example of a normal distribution, we are
discussing the impossibility of practical use of
parametric families of distributions to describe specific
statistical data. We give the results of research of
metrologists and estimation of convergence in limit
theorems. Then we discuss how the parametric methods
can use for reject outlying observations. It is very
unstable the significance levels for a fixed rejection rule
and the parameter of the rejection rules for a fixed level
of significance. Consequently, the rejection of the
classic rules of mathematical statistics is not sciencebased