The model of the motion of particles in the SternGerlach
apparatus in the classical and quantum
mechanics was developed. The data simulation of
particle trajectories and distribution of silver atoms on
the surface of the plate in their deposition are
discussed. It was found that for the experimentally
observed distribution of two-dimensional shapes of
the atoms must be assumed that the atoms are not
involved in the precession motion in a magnetic field,
while maintaining the direction of the magnetic
moment, for example, parallel to the induction vector
of the magnetic field during the time of motion in the
apparatus. To obtain a realistic picture of the figure of
the scattering of atoms used a classical model of
movement and expression of forces compatible with
the quantum picture of the motion of particles with
spin ½. The magnetic field is simulated based on the
original Stern-Gerlach data describing the distribution
of the gradient of the induction components related to
the splitting of the beam. Quantum model of particle
motion is based on the Pauli equation in the boundary
layer approximation. It is found that in this model,
depending on the initial polarization of the particle,
beam is split into either two or is deflected towards
the magnet blade or in the opposite direction. It is
shown that if the initial conditions for the task are
reproducing the geometric dimensions and the
magnetic field in the Stern-Gerlach apparatus, the
figure of the scattering particles in the shape of the
outline is similar to the experimentally observed
shape
We have studied the question of the electromagnetic
structure of a relativistic electron in connection with
the Yang-Mills theory. From the Lorentz
electrodynamics equations of and Dirac electron
theory derived an equation describing nonlinear
waves of the scalar potential. It is shown that this
equation is similar to the equation describing the
dynamics of the condensate in the Yang-Mills theory.
There is also the connection to the Schrödinger
equation: the scalar potential is a complex function,
similar to the wave function in the Schrödinger
theory. The model discussed electron is a solitary
wave that occurs in the electromagnetic field. This
wave has the properties of charged particles, able to
interact with the external electric and magnetic field.
An analytical solution describing solitary
electromagnetic waves traveling at a speed less than
the speed of light has been obtained. The existence of
solitary electromagnetic waves consistent with the
Hertz's hypothesis that suggested that cathode rays
are a form of wave motion in an electromagnetic
field. The proposed model of the electromagnetic
structure of the electron thus solves the problem of
duality wave-particle, which historically arose in the
interpretation of experiments with cathode rays.
Numerical modeling of electromagnetic electron
structure shows that the initial state such as a
spherical shell is unstable and disintegrates into a pair
of nonlinear waves that leave the system with the
speed of light. In the decay of the initial state
concentrated in the neighborhood of the origin, waves
of complex part of potential disappear with time, but
a real part of the potential it tends to equilibrium
In the study we consider the problem of determining
the motion and similarity parameter to the system of
worlds in a Riemannian space 112D with a common
field of gravity. Centrally symmetric metric,
depending on the 110 angle coordinates and the radial
coordinate and time was investigated. It is assumed
that there are intelligent beings in every world, striving
for self-knowledge. By virtue of the presence of the
world hierarchy in one of them there is a system of
complete identification of each characteristic of the
individual being with macroparameters his world. If
sentient beings in all the world to create a device to
simulate their own history in the form of a network of
computers using the available material and the
physical laws of his world, and the loss of information
when displaying one world to another is 1%, then 37-
th world played only 68.9449%. For Earthlings, it was
found that the average similarity parameter of
professional group in recognition by using
astronomical parameters is 68.75%. Therefore, we can
assume that the world system, including Earth,
contains 37 "floors." Assuming that each "floor" takes
three space dimensions, and all the "floors" connected
by a single time, we find here that the number of
dimensions of space-time of the whole system is 112.
In the article the angular motion in a Riemannian space
is considered. The effect of the separate worlds on
other worlds is simulated. It has been shown that the
physical laws in all worlds represent a single
movement covering the markers in the form of the
motion of atoms and elementary particles in a
gravitational field in the 112D
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