Chemical processes are often connected with use or
formation of condensed dispersed phase (CDP).
Dispersed particles can change mobility of charges, as
well as other parameters of the low-temperature plasma.
The aim of this work is to study the effect of magnetic
field on the processes of dispersed particles formation in
argon-oxygen plasma containing iron and carbon atoms
at atmospheric pressure. The equilibrium composition of
iron and carbon atoms containing mixture simulated at
temperatures of 1000-5000K for optimization of the
plasma-forming gas composition. It is shown that in case
of oxygen excess, the CDP particles contain only iron
oxides. The literature data about the phase transition
processes in a low-temperature plasma, as well as the
data about the processes with participation of
ferromagnetic particles in a constant magnetic field
analyzed. The results of investigations of the dispersed
particles forming in argon-oxygen plasma of arc
discharge in the presence and in the absence of the
magnetic field are shown. The formed disperse phase
was deposited on the substrates and studied by the
electron microscopy and X-ray methods. It was found
that with the lack of oxygen the size of the iron-oxide
particles created in the arc discharge containing iron and
carbon is affected by magnetic field: in a magnetic field
of 10 mT the particles are larger than in its absence

In the present article, we investigate the metric of the
crystal space in the general theory of relativity and in the
Yang-Mills theory. It is shown that the presence of a
lattice of gravitational ether has observable macroscopic
consequences. Earlier, the influence of the gravity of the
celestial bodies of the solar system on the electrical
conductivity, inductance, the rate of radioactive decay of
atomic nuclei, on seismic activity, the magnetic field and
the motion of the pole of our planet, and on the rate of
biochemical reactions was established. In all cases, a
similar behavior of the physicochemical characteristics
of materials and processes is observed, depending on the
universal parameters characterizing the seasonal
variations of the gravitational field of the solar system.
The relationship between lattice parameters and the
properties of materials, elements, atomic nuclei, and
elementary particles is discussed. Possible metrics of the
crystal space are constructed: a metric that depends on
the Weierstrass function, derived in the Yang-Mills
theory and analogous metrics found in Einstein's theory.
Such metrics, which have a central symmetry, can be
used to justify the structure of elementary particles, the
properties of atomic nuclei, atoms and matter. Periodic
metrics are constructed that admit an electromagnetic
field, as well as metrics associated with the assumed
structure of the crystal space. These metrics are of
particular interest, since the properties of the substance
are related to the metric parameters. We proposed the
model of electron beam as a streamer of preons

Classic quantitative measure of the reliability of the models: F-measure by van Rijsbergen is based on counting the total number of correctly and incorrectly classified and not classified objects in the training sample. In multiclass classification systems, the facility can simultaneously apply to multiple classes. Accordingly, when the synthesis of the model description is used for formation of generalized images of many of the classes it belongs to. When using the model for classification, it is determined by the degree of similarity or divergence of the object with all classes, and a true-positive decision may be the membership of the object to several classes. The result of this classification may be that the object is not just rightly or wrongly relates or does not relate to different classes, both in the classical F-measure, but rightly or wrongly relates or does not relate to them in varying degrees. However, the classic F-measure does not count the fact that the object may in fact simultaneously belongs to multiple classes (multicrossover) and the fact that the classification result can be obtained with a different degree of similarity-differences of object classes (blurring). In the numerical example, the author states that with true-positive and true-negative decisions, the module similarities-differences of the object classes are much higher than for false-positive and false-negative decisions. It would therefore be rational to the extent that the reliability of the model to take into account not just the fact of true or false positive or negative decisions, but also to take into account the degree of confidence of the classifier in these decisions. In classifying big data we have revealed a large number of false-positive decisions with a low level of similarity, which, however, in total, contribute to reducing the reliability of the model. To overcome this problem, we propose a L2-measure, in which instead of the sum of levels of similarity we use the average similarity by different classifications. Thus, this work offers measures of the reliability of the models, called L1-measure and the L2 measure, mitigating and overcoming the shortcomings of the F-measures; these measures are described mathematically and their application is demonstrated on a simple numerical example. In the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we have implemented all these measures of the reliability of the models: F, L1 and L2

In 1893, the French mathematician J. Adamar
raised the question: given a matrix of fixed order
with coefficients not exceeding modulo this value,
then what is the maximum modulo value can take
the determinant of this matrix? Adamar fully
decided this question in the case when the
coefficients of the matrix are complex numbers and
put forward the corresponding hypothesis in the
case when the matrix coefficients are real numbers
modulo equal to one. Such matrices satisfying the
Hadamard conjecture were called Hadamard
matrices, their order is four and it is unknown
whether this condition is sufficient for their
existence. The article examines a natural
generalization of the Hadamard matrices over the
field of real numbers, they are there for any order.
This paper proposes an algorithm for the
construction of generalized Hadamard matrices,
and it is illustrated by numerical examples. Also
introduces the concept of constants for the natural
numbers are computed values of this constant for
some natural numbers and shown some
applications of Hadamard constants for estimates
on the top and bottom of the module of the
determinant of this order with arbitrary real
coefficients, and these estimates are in some cases
better than the known estimates of Hadamard. The
results of the article are associated with the results
of the con on the value of determinants of matrices
with real coefficients, not exceeding modulo units

In the article we investigate the multicriteria task
arising at the organization of distributed calculations
in a corporate network. As a mathematical tool to
solve the problem we use prefractal graphs, which
naturally reflect the structure of relationships in
global and corporate networks. The corporate network
with the distributed computing system at the solution
of a particular task has to be reliable, quickly and
qualitatively to make decisions. And every computer
in the network should be a part in the solution of the
problem, since it is fixed for a certain function. The
problem is reduced to cover the prefractal graphs with
disjoint simple paths along the edges and vertices.
On the set of all admissible coverings we constructed
a vector-target function with specific criteria. All
these criteria have a specific meaningful
interpretation, allowing organizing the calculation of
maximum reliability, with minimum time information
processing and loading balancing between the
network elements. In the article we constructed
polynomial algorithms for finding optimal solutions
according to specific criteria. For the criteria which
are not optimizing the allocated coverings, estimates
of the lower and upper bounds are given. For all the
algorithms we constructed and substantiated
estimation of computational complexity, confirming
the advantage of using algorithms on prefractal
graphs to classical algorithms on graphs

The article continues the cycle of their studies
associated with the formulation and development of
methods of construction of nonnegative solutions of
inverse problems for dynamic systems. In this article
the authors formulated and investigated inverse
problems for dynamic systems: model of Samuelssonâ€“
Hicks. The technique of constructing non-negative
solutions of the studied inverse problems. This method
is based on the following scheme of the solution. First,
we have to identify the formulation of the direct
problem, then the formulation of the inverse. This
work investigates how correct the mathematical
models describing the dynamic economic system are.
Further, in the specified tabular solutions of the direct
problem, we have built a system of algebraic equations
containing the unknown estimated parameters of the
studied model. Then posed inverse problem is reduced
to solution of a problem of quadratic programming, the
solutions of which are defined in MS Excel. The
theoretical material is accompanied by the specific
example

Atmospheric currents on Jupiter and Saturn are
characterized by turbulence and complex vortex
structure, which is caused by a large angular speed of
the gas giants. In this paper we consider two types of
eddy currents - for hexagonal in the northern polar
region of Saturn and the Great Red Spot in the
equatorial region of Jupiter. For the numerical
simulation of turbulent flows of this type the model of
the planetary boundary layer was developed by the
author. In both cases, the main strengthening
mechanism is associated with geostrophic flow of
small amplitude interacting with the planetary
turbulent boundary layer. For hexagonal Saturn with
its characteristic length scales and speed - 120 m / s
and 14,500 km, respectively, there are more than 35
years data of observation. We have found that a small
axial symmetry violation geostrophic flow in the
shear causes the development of a hexagonal pattern
in a turbulent boundary layer. In addition, under the
influence of the Coriolis force and the eddy viscosity
gradient in the turbulent boundary layer there is the
jet formed, pressed against the lower edge of the
layer. Great Red Spot on Jupiter has the characteristic
velocity and length scales - 150 m / s, 14,000 km
from north to south and 24000-40000 km from west
to east, there are already more than 350 years data. It
identified another mechanism of formation of vortex
flow, coupled with the strengthening of small
amplitude zonal flow in a turbulent boundary layer
with the eddy viscosity gradient and the volume
turbulent viscosity on a rotating planet. Both
mechanisms are confirmed by numerical calculations
of non-stationary planetary boundary
layer

Adequate and effective assessment of the efficiency, effectiveness and quality of scientific activities of specific scientists and research teams is crucial for the information society and society based on knowledge. The solution to this problem is the subject of scientometrics and its purpose. The current stage of development scientometrics differs greatly from its previous appearance in the open as well as paid on-line access to huge amount of detailed data on a large number of indicators on individual authors and on scientific organizations and universities. In the world, there are well-known bibliographic databases: Web of Science, Scopus, Astrophysics Data System, PubMed, MathSciNet, zbMATH, Chemical Abstracts, Springer, Agris, or GeoRef. In Russia, it is primarily the Russian scientific citing index (RSCI). RSCI is a national information-analytical system, accumulating more than 9 million publications of Russian scientists, as well as information about citation of these publications from more than 6,000 Russian journals. There is a lot of data, so-called "Big data". The main primary scientometric indicator (based on which we build all the rest, such as the h-index) is the number of citations of the author's works, placed in the bibliographic database. This number of citations is determined by the software of RSCI using so-called "binding" which is a grammatical analysis and search in databases for works of the author, for relevant links from references in the works of various authors. However, the problem is, as experience shows, that authors make a very large number of simply incorrect and incomplete references in the reference lists, very far from standard. Currently, the software that RSCI uses does not automatically bind these invalid references, and this requires human intervention. But, centrally, to do this is not possible by experts of RSCI because of the huge amount of work, and distributed work for a large number of specialists in the field still requires a centralized moderation. As a result, the work for binding references to the literary sources is very slow and a huge amount of links is unbound. This leads to an underestimation of nanomatrices indicators of both individual authors and research teams that cannot be considered acceptable. The solution to this problem is offered by applying the automated system-cognitive analysis (ASC-analysis) and its programmatic Toolkit â€“ intellectual system called "Eidos". This work provides a numerical example of the intellectual anchor of the real incorrect references to the works of the author on the basis of a small amount of real scientific data that are publicly available free on-line access to the RSCI

In the article we build a mathematical model of elec-tro-diffusion of ions in the diffusion layer of a mem-brane system complicated by the occurrence of the previous slow homogeneous chemical reaction with the condition of electrical neutrality of the solution. We have set a two-point boundary value problem and developed a method to solve it; we have given an algorithm and a numerical method for solving it in Comsol 3.5 environment. The formula for limiting kinetic current was derived. Some of the modelâ€™s capabilities to describe the properties of the system are given

As we know, currently, around the north pole of Saturn there is a large-scale hexagonal flow, with characteristic scales of length and speed - 120 m / s and 14,500 km respectively. This trend observed for more than 35 years, is the subject of many experimental and theoretical studies. In this study, we propose a model and discuss the numerical solutions of the equations describing turbulent flow in the planetary boundary layer around the north pole of Saturn. It has been shown that a small violation of the axial symmetry in geostrophic shear leads to the development of hexagonal patterns in a turbulent boundary layer. In addition, under the influence of Coriolis forces and turbulent eddy viscosity gradient in a turbulent boundary layer formed jet pressed to the bottom edge of the layer. These results are used to simulate the observed hexagonal flow around the north pole of Saturn. It is assumed that the small amplitude geostrophic flow is described by a sum of zero and the sixth current harmonic functions, which leads to the excitation current at the upper boundary of the planetary boundary layer. It is found that such excitation enhanced in the boundary layer and reaches a maximum in the jet pressed to the bottom border. This jet, circulating on the hexagon coincides with the region of origin of the cloud cover, which is registered in the experiments. This excitation mechanism hexagonal flow around the north pole of Saturn is confirmed by numerical calculations of three-dimensional non-stationary planetary boundary layer