In some works, the feasibility of the use of fixed and
variable electromagnetic fields of different frequencies
and tension in the production technology of sunflower
oil are shown, but there is no theoretical justification.
The possibility of electromagnetic effects is associated
with the presence of polar molecules specific to organic
systems. Without prejudice to the role of polar groups
of terrestrial circuits, this work tries to address this
challenge more comprehensively. The reason for this is
the distinctive feature of the behavior of sunflower
during its flowering. This characteristic is that the
sunflower hat during the day changes its direction in
accordance with the direction of movement of the Sun
across the sky; so called "magnetism" of their
attraction. To justify this effect, we have analyzed the
essence of emitted photons, the Sun chemical
composition and structure arrangement of seeds in a
sunflower hat. Particles of light from the Sun represent
a stream of photons - a wide range of electromagnetic
waves of frequencies that exhibit and magnetic
properties. The article shows principal macro- and
micronutrients of sunflower raw materials and divides
them into groups of para- , dia- , and ferromagnetic
materials. In sunflower seeds, there are chemical
elements: diamagnetism-C, H, N, P, S, B, Cu, Zn, J;
paramagnetism-O, K, Ca, Mg, Mo, As and
ferromagnetic-iron (Fe). As there is resultant force of
the magnetic attraction between the sunflower hat and
magnetic flow of photons from the Sun, this effect
dominates the action of paramagnetics K2O ( -28.4
24.5%), CaO (7.6-17.0)%, MgO (12.3-17.9%),
magnetized in an external magnetic field in the
direction of the field. The presence of evident effect
demonstrates that it is possible to improve a number of
technological operations in the manufacture of
sunflower oil using electrical, magnetic or
electromagnetic fields

In this work, a model is developed that describes the
formation of a stepped lightning leader in a conducting
medium. To describe the contribution of the conductivity
currents, we modified the standard electrostatic equation
taking into account the vortex component of the electric
field. As a result of this generalization, a system of
parabolic-type nonlinear equations is formulated that
describes the formation of streamers and the lightning
channel. Numerical simulation of the propagation of
ionization waves in a region with a ratio of 1/100, 1/200
allows us to identify two types of stepped streamers in
the form of waves of compression and rarefaction,
respectively. It was previously established that there are
three streamer branching mechanisms. The first
mechanism is related to the instability of the front, which
leads to the separation of the head of the streamer into
two parts. The second mechanism is associated with the
instability of the streamer in the base region, which leads
to the branching of the streamer with the formation of a
large number of lateral streamers closing the main
channel of the streamer to the cathode. In numerical
experiments, the third branching mechanism observed in
experiments connected with closing the space charge to
the anode through the streamer system was observed.
These branching mechanisms are also revealed when the
leader is propagated. The obtained results, as well as the
data of numerical experiments confirm the hypothesis of
the universality of the minimal model of the streamer, as
well as its expansion in the form proposed by the author.
Known phenomena of nature associated with the
electrical discharge - streamer, plasmoid, ball lightning
and stepped leader can be described within the
framework of the minimal model

Nonparametric estimates of the probability
distribution density in spaces of arbitrary nature are
one of the main tools of non-numerical statistics.
Their particular cases are considered - kernel density
estimates in spaces of arbitrary nature, histogram
estimations and Fix-Hodges-type estimates. The
purpose of this article is the completion of a series
of papers devoted to the mathematical study of the
asymptotic properties of various types of
nonparametric estimates of the probability
distribution density in spaces of general nature.
Thus, a mathematical foundation is applied to the
application of such estimates in non-numerical
statistics. We begin by considering the mean square
error of the kernel density estimate and, in order to
maximize the order of its decrease, the choice of the
kernel function and the sequence of the blur
indicators. The basic concepts are the circular
distribution function and the circular density. The
order of convergence in the general case is the same
as in estimating the density of a numerical random
variable, but the main conditions are imposed not on
the density of a random variable, but on the circular
density. Next, we consider other types of
nonparametric density estimates - histogram
estimates and Fix-Hodges-type estimates. Then we
study nonparametric regression estimates and their
application to solve discriminant analysis problems
in a general nature space

It is known that not every finite group can be
realized over the field of rational numbers as a
Galois group of some binomial. In this connection,
a more general question arises: suppose that there
is given a finite transitive subgroup G of the
symmetric group S on n symbols; Can this group G
be realized as a Galois group of some trinomial of
degree n over the field of rational numbers? In this
paper we prove that every transitive subgroup of
the group S can be realized in the form of the
Galois group of a certain trinomial of the degree n,
for the values n = 2, 3, 4. For n = 5 , 6 we give
examples that realize concrete Galois groups. In the
case n = 7, all the transitive subgroups of the group
S are realized, except possibly one group of the
isomorphic dihedral group D. Further calculations
will be directed to the realization of specific Galois
groups for n = 8, 9 ..., however, the number of
transitive subgroups of the group S for n = 8, 9 ...
grows very fast, so the larger the value of n, the
more difficult it is to realize not just everything but
the specific subgroup of the group S in the form of
a trinomial over Q

In this work, a model is developed to describe the
formation of streamers, plasmoid, and ball lightning in a
conducting medium. To describe the contribution of the
conductivity currents, we modified the standard
electrostatic equation taking into account the vortex
component of the electric field. As a result of this
generalization, a system of parabolic-type nonlinear
equations is formulated that describes the formation of
streamers, plasma long-lived formations and ball
lightning. As is known, in laboratories it is possible to
create a plasmoid with a lifetime of 300-500 ms and a
diameter of 10-20 cm, which is interpreted as a ball
lightning. With high-speed photography, a complex
structure is detected, consisting of a plasmoid and
surrounding streamers. Within the framework of the
proposed model, problems are posed about the formation
of a plasmoid and the propagation of streamers in an
external electric field. In this model, the plasmoid is
considered to be a long-lived streamer. The range of
parameters in which a plasmoid of spherical shape is
formed is indicated. It is established that there are three
streamer branching mechanisms. The first mechanism is
related to the instability of the front, which leads to the
separation of the head of the streamer into two parts. The
second mechanism is associated with the instability of
the streamer in the base region, which leads to the
branching of the streamer with the formation of a large
number of lateral streamers closing the main channel of
the streamer to the cathode. In numerical experiments,
the third branching mechanism observed in experiments
connected with the branching of the plasmoid in the
cathode region with the closure of the space charge to
the anode through the streamer system was observed.
The results of modeling the evolution of globular
clusters in a scale of hundreds of milliseconds are given.
Plasma exchange recharge modes leading to the
formation of a positive or negative charge of the system
are found

The inverse matrix for the square matrix A of order n
with coefficients of some field exists, as it is known
then and only then, when its determinant is not equal to
zero. If the matrix A has a certain type (certain
structure), then an inverse matrix A-1 should not have
exactly the same structure. Therefore, it is interesting
to describe such square matrices A, which have an
inverse matrix A-1, having the same structure as the
matrix A, under certain conditions. For example, a
subdiagonal matrix with nonzero elements on the main
diagonal has an inverse matrix over a field of
characteristic zero, having also the form of subdiagonal
matrix. Similarly, an inverse matrix towards
symmetrical or skew-symmetric matrix is also
symmetric or skew-symmetric accordingly. Also, the
matrix inverse to non-degenerate (nonsingular)
circulant will be a circulant itself, and finally, the
matrix inverse to nonsingular quasdiagonal matrix D
will be quasdiagonal itself, and will have the same
partitioned structure as D. Thus, there is a problem of
determining these types of nonsingular matrices that
have an inverse matrix of the same type as a given
matrix. In line with this problem in the present study it
is determined such type of matrices for which an
inverse matrix has the same type, at that the conditions
are identified in explicit form, ensuring the
nonsingularity of the matrix. The matrices of three
orders are shown in detail. These results allow
determining the characteristics of fields over which
there are inverse matrices of the considered types

Partially ordered set is a basic concept of modern settheoretic
mathematics. The problem of linear set
ordering with given binary relations is well-known.
Every partial order over a finite set can be linearly
ordered, but not every binary relation over this set can
be linearly ordered as well. Up to now, there is no
known formula for calculating the number of partial
orders over a given finite set. It appears that there is a
formula for calculating linearly ordered binary
relations over a finite set. This article is concerned
with derivation of this formula. The fact from work of
G.N. Titov [9] that a binary relation over a finite set is
linearly ordered if and only if any diagonal block,
derived from the binary relation matrix as a result of
setting main diagonal elements to zero, contains at
least one zero row (diagonal block of matrix means
any matrix composed of elements at the crossings of
rows and columns of a given matrix with the same
numbers), plays a key role in process of corroboration.
The main conclusion of the article is a theorem that
allows to find the number of linearly ordered binary
relations over a set of n elements using the formula. A
recurrence formula for the number of linearly ordered
(irreflexive) binary relations over a finite set of n
elements, provided in the lemma, was derived as well

In this article, we have proposed a forecast of labor
resources by sectors of the labor market of the Russian
Federation until 2018 inclusive. The probabilistic
parameters of the dynamics of labor resources were
calculated using the considered model (articles [1-4]).
Further, these probabilities were used to estimate and
parameterize the trends of employed and unemployed
(with a known last place of employment) specialists in
each industry. For each sector of the Russian economy,
the type of trend that best approximates the long-term
(more than three years) dynamics of labor resources in
this sector was selected. It is shown that the forecast
error for 1 year is less than 1% using the selected trend
models. Further, identified long-term trends were used
in forecasting. Based on the results of the forecast of
the number of people employed in the sectors of the
Russian economy, the sectors were divided into two
groups. The first group contains sectors with a
significant change in the number of employed in. The
second group contains sectors, changes in employed in
which were insignificant. At the end of the article, an
example of an analysis of two sectors from the first
group is given. Causes of changes in the dynamics of
labor resources in the researched sectors of the
economy were identified. Ones of the main sectors of
the economy were considered in this example:
"Manufacturing industries" and "Financial activities,
real estate transactions, leasing and provision of
services"

In this work, a model is developed that describes the
formation of a plasmoid and streamers in a conducting
medium. To describe the contribution of the conductivity
currents, we modified the standard electrostatic equation
taking into account the vortex component of the electric
field. As a result of this generalization, the streamer
model is formulated in the form of a system of parabolictype
nonlinear equations. As is known, in laboratories it
is possible to create a plasmoid with a lifetime of 300-
500 ms and a diameter of 10-20 cm, which is interpreted
as a ball lightning. With high-speed photography, a
complex structure is detected, consisting of a plasmoid
and surrounding streamers. Within the framework of the
proposed model, problems are posed about the formation
of a plasmoid and the propagation of streamers in an
external electric field. In this model, the plasmoid is
considered to be a long-lived streamer. The range of
parameters in which a plasmoid of spherical shape is
formed is indicated. It is established that there are three
streamer branching mechanisms. The first mechanism is
related to the instability of the front, which leads to the
separation of the head of the streamer into two parts. The
second mechanism is associated with the instability of
the streamer in the base region, which leads to the
branching of the streamer with the formation of a large
number of lateral streamers closing the main channel of
the streamer to the cathode. In numerical experiments,
the third branching mechanism observed in experiments
connected with the branching of the plasmoid in the
cathode region with the closure of the space charge to
the anode through the streamer system was observed.
The similarity of ball lightning and plasmoid is
discussed. If this similarity is confirmed, then the
number of theoretical hypotheses concerning the nature
of ball lightning, currently more than 200, can be
drastically reduced to one described in this article

Statistical methods are widely used in domestic
feasibility studies. However, for most managers,
economists and engineers, they are exotic. This is
due to the fact that modern statistical methods are
not taught in the universities. We discuss the
situation, focusing on the statistical methods for
economic and feasibility studies, ie, econometrics.
In the world of science, econometrics has a rightful
place. There are scientific journals in econometrics,
Nobel Prizes in Economics are given to series of
researches in econometrics. The situation in the field
of scientific and practical work and especially the
teaching of econometrics in Russia is disadvantaged.
Often, individual particular constructions replace
econometrics in general, such as those related to
regression analysis. The article is devoted to
econometrics as an academic discipline. Our course
begins with a discussion of the structure of modern
econometrics, the connections between applied
statistics and econometric methods. We consider
sample researches (analysis of surveys results), the
elements of econometrics numbers, and methods of
testing of statistical hypothesis about homogeneity.
We have given the concepts of regression analysis,
econometric classification methods, modern
measurement theory. The important places are
occupied by the statistics of non-numerical data
(including fuzzy sets and their links with random
sets) and the statistics of interval data. The problem
of the stability of statistical procedures with respect
to the tolerances of input data and model
prerequisites is discussed. The representations of the
econometric methods of expert research and quality
control, analysis and forecasting of time series,
econometrics of forecasting and risks are given