The article presents the model of the large-scale clustering
of the matter in the universe. The base for mathematical
calculations is interval mathematics
Particle dynamics in metrics with logarithmic potential
The work considers the problem of modeling the
motion of particles in a unified field theory to 6D, in
theory, supergravity in the 112D and metric galaxies.
We have investigated a centrally symmetric metric in
the 112-dimensional Riemannian space, which
depends on the radial coordinate, time, and 110 angles.
We present a system of equations describing the
angular movement on a hypersphere of any dimension
N. It is shown that the motion on the hypersphere
depends on the 2 (N-1) of singular points. We have
installed general nature of relativistic motion on a
hypersphere when it is displayed on the plane and in
three-dimensional space. It is shown that the motion
determined by the reflection from the singular points
that of motion on the plane in some cases leads to
thickening of the trajectories in the neighborhood of
sides of the rectangle. The 6D investigated metric
describing the case of motion with two centers of
symmetry. It is shown that in such a metric exists a
class of exact solutions, logarithmically dependent on
the gravity centers of origin. It is found that in this
system there is a motion with condensation paths
around the sides of the rectangle, due to scattering of
test particles gravity sources. We set the general nature
of angular motion on a hypersphere and radial
movements in 6D in the metric of a logarithmic
potential. It is proved that similar solutions with
logarithmic potential exist in galaxies metric in the
metric of Einstein's theory of gravity. The article also
describes the connection of the solutions to the
nonlinear electrodynamics, and with a theory of quark
interactions and Yang-Mills theory
The article discusses various examples of dynamical
systems in which the motion is determined by the
logarithmic law - quark systems, hydrodynamic
systems, galaxies. Set the general nature of angular
motion on a hypersphere in a space of arbitrary
dimension and radial movement 6D in the metric of a
logarithmic potential. We investigate the 6D metric
describing the case of motion with two centers of
symmetry. It is shown that in such a metric exists a
class of exact solutions, logarithmically dependent on
the gravity center coordinates. It was established that
in spiral galaxies the orbital motion is due to the
logarithmic potential, which is the exact solution of the
field equations of Einstein's theory of gravity. The
most well-known and widespread in nature case is
turbulent flow over a smooth or rough surface, in
which the mean velocity depends logarithmically on
the distance from the wall. We derivate the logarithmic
velocity profile in turbulent flow from the NavierStokes
equations. An analogy of the logarithmic
velocity profile and the logarithmic law in the case of
erosion of materials under impacts been proposed. In
electrodynamics, Ampere's law, which describes the
interaction of current-carrying conductors, is a
consequence of the logarithmic dependence of the
vector potential of the distance from the conductor
axis. There is, however, an alternative derivation of
Ampere law of the Riemann hypothesis about the
currents due to the motion of charges
In the article, we describe and illustrate a method of
mathematical modeling in relation to process of decision-making
in the conditions of risk and uncertainty
on the example of building of agricultural object
The work discusses various examples of physical
systems which state is determined by the logarithmic
law - quantum and classical statistical systems and
relativistic motion in multidimensional spaces. It was
established that the Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann
distribution could be
described by a single equation, which follows from
Einstein's equations for systems with central
symmetry. We have built the rate of emergence of
classical and quantum systems. The interrelation
between statistical and dynamic parameters in
supergravity theory in spaces of arbitrary dimension
was established. It is shown that the description of the
motion of a large number of particles can be reduced
to the problem of motion on a hypersphere. Radial
motion in this model is reduced to the known
distributions of quantum and classical statistics. The
model of angular movement is reduced to a system of
nonlinear equations describing the interaction of a test
particle with sources logarithmic type. The HamiltonJacobi
equation was integrated under the most general
assumptions in the case of centrally-symmetric metric.
The dependence of actions on the system parameters
and metrics was found out. It is shown that in the case
of fermions the action reaches extremum in fourdimensional
space. In the case of bosons there is a
local extremum of action in spaces of any dimension
In the article we present a spatial structure of largescale
transport systems. The model of a transport
network can be presented in the form of a graph, with
a set of the nodes corresponding to elements of a
network and a set of edges – to sections of roads the
connecting these nodes. As the model of a card of
roads, it is offered to use prefractal graphs which
naturally reflect structure of communications when
reviewing a transport network in different scales (the
states, regions, areas). Prefractal graphs allow
describing structural dynamics of the studied system
in the discrete time. One of the most widespread
scenarios of structural dynamics is the growth of
structure. The statement of tasks of the organization
of transport routes contains requirements criteria to
finding of optimal solutions. Often these requirements
and criteria are contradicting each other. It leads to
appearance of a multicriteria problem definition.
The multicriteria problem definition on a class of
prefractal graphs is considered. The optimum
algorithm of separation of the greatest maximum
paths by the given criterion is constructed and
estimates by remaining criteria are given. In operation
computing complexity of the constructed algorithm of
separation of the greatest maximum paths on a
prefractal graph is calculated and advantage of
operation of algorithm on last before algorithm of
separation of the greatest maximum paths on normal
graphs is justified. The constructed algorithm on
prefractal graphs has polynomial complexity
In the USSR higher attestation Commission from
1975 to the collapse of the USSR was subordinated
not to the Ministry of education and science, but to
the Council of Ministers of the USSR directly.
However, since then there is a steady trend of gradual
reduction of the status of the Commission. Today
it is not just included in the Ministry of education,
it is just one of the units of one of its structures:
the Rosobrnadzor. Reduced status of the HAC inevitably
leads to a decline in the status and in the adequacy
of scientific degrees assigned as well as scientific
ranks. This process of devaluation of traditional
academic degrees and titles assigned to the HAC,
has reached the point when a few years ago there
were abolished salary increments for them. Now,
instead of that, every university and research institutes
have developed their local, i.e. non-comparable
with each other scientometric methods of evaluation
of the results of scientific and teaching activities.
Despite the diversity of these techniques, there is a
common thing among all of them, which is the disproportionate
role of the h-index. The value of the
Hirsch index starts to play an important role in the
protection, when considering competitive cases for
positions, as well as in determining the monthly
rewards for the results of scientific and teaching
activities. By itself, this index is well founded, theoretically.
However, in connection with the practice
of its application in our conditions, in the collective
consciousness of the scientific community there was
a kind of mania, which the authors call the "Hirschmania".
This mania is characterized by elevated
unhealthy interest to the value of the Hirsch index,
as well as incorrect manipulation of its value, i.e.
inadequate artificial exaggeration of this value, as
well as a number of negative consequences of that
interest. In this study we have made an attempt to construct a quantitative measure for assessing the
extent of improper manipulation of the value of the
Hirsch index, and offered a science-based modification
of the h-index, insensitive (resistant) to the manipulation.
The article presents a technique for all
the numerical calculations, which is simple enough
for any author to use
We have considered the formation of the Russian
scientific school in the field of econometrics,
obtained its obtained scientific results, the
possibilities of their use in solving problems of the
economy, the organization of production and
controlling of industrial companies and
organizations, as well as in teaching. As
econometrics we consider a scientific and an
academic discipline devoted to the development and
application of statistical methods to study economic
phenomena and processes, in short, statistical
methods in economics. Therefore, we can say that a
lot of domestic books and articles, in particular, the
works by the author of this publication from the
beginning of the 70s, are the parts of econometrics.
However, in this article we consider only the works,
in the titles of which we can see the word of
"econometrics". In our country the term
"econometrics" has become popular since the mid
90s. However, many publications and training
courses are still developed in the western outdated
paradigm. They do not conform to the new paradigm
of mathematical methods of economics, the new
paradigm of applied statistics and mathematical
statistics, mathematical methods of research. Russian
science school in the field of econometrics operates
within the scientific school in the field of probability
theory and mathematical statistics based by A.N.
Kolmogorov. Russian science school is developed in
accordance with the new paradigm of mathematical
methods. It is necessary to examine the main results
of Russian scientific schools in the field of
econometrics. We present the information on the
institutional design of national scientific schools in
econometrics, in particular, on the activities of the
Institute of High Technologies statistics and
econometrics
This work studies the mathematical model of the
object “inverted pendulum” on the example of the
unstable electromechanical devices which is
balancing robot on wheel couple. Unfortunately,
many details of object model are unknown. Logical
and empirical method offers hypotheses about the
difference between the actual object model from its
mathematical approximation based on logical
analysis with subsequent refinement of this model
and testing of the hypothesis with modeling of the
systems with the updated model. As a result, the
amendments to the model have been found
containing nonlinear components. With the help of
these amendments, the dynamic characteristics of
the actuator, filters, friction and the tendency of the
object to fluctuations are better taken into account
We propose an approach to the modeling of stressstrain
state of lithospheric structures near faults by
modeling them as Kirchhoff plates on threedimensional
elastic foundation. We describe an
efficient method of solving problems for plates with
rectilinear fractures, based on the transformation of
the differential operator, which allows us to analyze
the solutions obtained for different contact conditions
in the area of the fracture. The method is presented
on the example of the vibration problem of two
elongated plates on the surface of the elastic layer
under the effect of concentrated surface load. The
results of numerical implementation of the developed
algorithm make it possible to identify the influence of
the substrate properties, characteristics of the plates
and the nature of their border interactions on the
picture of wave process in the test structure. At the
same time obtained configurations of the harmonic
signal passage through the fracture can serve as an
indicator of its type. The proposed approach should
be used to determine the presence and type of
fractures based on measurements of signals from
vibration sources in cases when geophysical
environment can be modeled by the previously
described structure. The problems of studying objects
we reviewed in this paper also occur in various areas
of technology, and, therefore we can apply the
proposed method for their solution