In 2011 – 2015, the scientific community was
represented by a new paradigm of mathematical
methods of research in the field of organizational
and economic modeling, econometrics and statistics.
There was a talk about a new paradigm of applied
statistics, mathematical statistics, mathematical
methods of economics, the analysis of statistical and
expert data in problems of economics and
management. We consider it necessary to develop
organizational and economic support for solving
specific application area, such as the space industry,
start with a new paradigm of mathematical methods.
The same requirements apply to the teaching of the
respective disciplines. In the development of
curricula and working programs, we must be based
on a new paradigm of mathematical methods of
research. In this study, we present the basic
information about a new paradigm of mathematical
methods of research. We start with a brief
formulation of a new paradigm. The presentation in
this article focuses primarily on the scientific field
of "Mathematical and instrumental methods of
economy", including organizational and economic
and economic-mathematical modeling, econometrics
and statistics, and decision theory, systems analysis,
cybernetics, operations research. We discuss the
basic concepts. We talk about the development of a
new paradigm. We carry out a detailed comparison
of the old and the new paradigms of mathematical
methods of research. We give information about the
educational literature, prepared in accordance with
the new paradigm of mathematical methods of
researches
Some estimators of the probability density function
in spaces of arbitrary nature are used for various
tasks in statistics of non-numerical data. Systematic
exposition of the theory of such estimators has been
started in our articles [3, 4]. This article is a direct
continuation of these works [3, 4]. We will regularly
use references to conditions and theorems of the
articles [3, 4], in which introduced several types of
nonparametric estimators of the probability density.
We have studied linear estimators. In this article, we
consider particular cases - kernel density estimates in
discrete spaces. When estimating the density of the
one-dimensional random variable, kernel estimators
become the Parzen-Rosenblatt estimators. Under
different conditions, we prove the consistency and
asymptotic normality of kernel density estimators.
We have introduced the concept of "preferred rate
differences" and are studied nuclear density
estimators based on it. We have introduced and
studied natural affinity measures which are used in
the analysis of the asymptotic behavior of kernel
density estimators. Kernel density estimates are
considered for sequences of spaces with measures.
We give the conditions under which the difference
between the densities of probability distributions and
of the mathematical expectations of their nuclear
estimates uniformly tends to 0. Is established the
uniform convergence of the variances. We find the
conditions on the kernel functions, in which take
place these theorems about uniform convergence. As
examples, there are considered the spaces of fuzzy
subsets of finite sets and the spaces of all subsets of
finite sets. We give the condition to support the use
of kernel density estimation in finite spaces. We
discuss the counterexample of space of rankings in
which the application of kernel density estimators
can not be correct
In this article, we investigate the problem of creation of
matter in the collision of particles, presented by
singularities of the gravitational field. A system of nonlinear
parabolic equations describing the evolution of the
axially symmetric metrics in the Ricci flow derived. A
model describing the creation of matter in the collision
and merger of the particles in the Ricci flow proposed. It
is shown that the theory that describes the Ricci flow in
the collision of black holes is consistent with EinsteinInfeld
theory, which describes the dynamics of the
material particles provided by the singularities of the
gravitational field. As an example, we consider the
metric having axial symmetry and which contains two
singularities simulating particles of finite mass. It is
shown that the static metric with two singularities
corresponding to in Newton's theory of gravity two
particles moving around the center of mass in circular
orbits in a non-inertial frame of reference, rotating with a
period of two-body system rotation. We have
numerically investigated the change of the metric in the
collision of particles with subsequent expansion. In
numerical experiments, we have determined that the
collision of the particles in the Ricci flow leads to the
formation of two types of matter with positive and
negative energy density, respectively. When moving
singularities towards each other in the area between the
particles the matter is formed with negative energy
density, and in the region behind the particles - with
positive density. In the recession of the singularities, the
matter with positive energy density is formed in the area
between the particles. The question of the nature of
baryonic matter in the expanding universe is discussed
In this article, the restricted problem of three and more
bodies in the Ricci flow in the general theory of
relativity considered. A system of non-linear parabolic
equations describing the evolution of the axially
symmetric metrics in the Ricci flow proposed. A model
describing the motion of particles in the Ricci flow
derived. It is shown that the theory describing the Ricci
flow in the many-body problem is consistent with the
Einstein-Infeld theory, which describes the dynamics of
the material particles provided by the singularities of the
gravitational field. As an example, consider the metric
having axial symmetry and contains two singularities
simulating particles of finite mass. It is shown that the
static metric with two singularities corresponds to
Newton's theory of the two centers of gravity, moving
around the center of mass in circular orbits in a noninertial
frame of reference, rotating with a period of
bodies. We consider the statement of the problem of
many bodies distributed at the initial time on the axis of
symmetry of the system. In numerical calculations, we
studied the properties of the gravitational potential in the
problem of establishing a static condition in which
multiple singularities retain the initial position on the
axis of the system. This is achieved due to relativistic
effects, which have no analogues in Newton's theory of
gravitation. Using the properties of relativistic potentials
we have justified transition from the relativistic motion
of the particles to the dynamic equations in the classic
theory
In this article, we investigate the restricted problem of
many bodies with a logarithmic potential in the general
theory of relativity. We consider the metric having
axial symmetry and containing a logarithmic
singularity. In numerical calculations, we studied the
properties of the gravitational potential in the problem
of establishing a static condition in which multiple
singularities retain the initial position on the axis of the
system. This is achieved due to relativistic effects,
which have no analogues in Newton's theory of
gravitation. The motion of relativistic particles in a
logarithmic potential sources distributed on the surface
of a torus simulated. It is shown that the trajectory of
the particles in these systems form a torus covered with
needles. It was found, that the Ricci flow in the general
theory of relativity could be born three kinds of matter -
positive and negative energy density, as well as the
color of matter, the gravitational potential of which is
complex. It has been shown that this type of material is
associated with the manifestation of the quantummechanical
properties, which is consistent with the
hypothesis of the origin of Schrodinger quantum
mechanics. It is assumed that the most likely candidate
for the role of the color of matter is the system of
quarks as to describe the dynamics of quarks using the
logarithmic potential, and the quarks themselves are not
observed in the free state
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
Today, infectious diseases remain a leading cause of
premature deaths in the world. Agent-based
modeling can play an important role in predicting the
spread of disease and to assess the containment
measures. The aim is to construct a multi-agent
simulation model for the formation of epidemic
measures to reduce effectively their incidence. Using
the multi-agent simulation approach to modeling of
epidemics due to the fact that the approach allows us
to consider a number of factors influencing the
epidemic process, makes it possible to carry out
numerical experiments. The processes of the spatial
distribution and temporal variation of these two
groups of epidemics of infectious the author calls
dynamics. Usually hard-implemented spatial
components of the dynamics in the proposed model
can be substituted by predfractal topology of the
graph, which is built up by voluminous graphs -
primers, and the dynamics of compounding
prefractal graph, called its recognition, is responsible
for the timing of the process component. Under the
term of agent, we consider an elementary study
participant. An agent is active; it is in a state that
may change under the influence of factors. The
properties of the agent are attributed characteristics
that form the level of immunity: height, weight,
gender, income, marital status, education, geography