An analysis of the experimental data obtained by the
authors, as well as reference books, allowed to
hypothesize about the essential role of gravitational
convection in electromembrane systems with
ampholytes even in underlimiting current regimes. The
article is devoted to the development of the
mathematical model of ion transport in a flow
elecrtomembrane system during electrodialysis of
ampholyte-containing solutions with taking into
account a possible appearance of gravitational
convection, in particular, due to nonisothermal
protonationâ€“deprotonation reactions of ampholytes.
The article presents the boundary value problem that is
the new mathematical model for diffusion, convection
and electromigration of four components of the
solution (ions of sodium, dihydrogen phosphate and
hydrogen, as well as molecules of orthophosphoric
acid) in a half of an electrodialysis desalination
channel, adjacent to an anion-exchange membrane. The membrane is considered as ideally selective and
homogeneous. The system of partial differential
equations, that is the base of the model, also includes
equations of Navier-Stokes, material balance,
convective heat conduction and the electroneutrality
condition. The system of equations is supplemented by
a number of natural and original boundary conditions.
A distinctive feature of this study is the absence of
assumptions about the equilibrium of chemical
reactions in a diffusion layer. The results of the study
can be used for the development of environmentally
rational and resource saving membrane technologies
for a processing of products of agro-industrial complex

There is a 2D mathematical model of ion transport
binary salt with the main conjugate effects of
concentration polarization in the overlimiting current
mode: the bulk charge and the dissociation/
recombination of water, gravity and electroconvection
and Joule heating the solution in the form of a
boundary value problem for systems of differential
equations with partial derivatives in the article. This
system is presented in a form convenient for numerical
solution. We describe the necessary boundary
conditions. This article presents a theoretical study of
the interaction of forced, gravitational and
electroconvection, the dissociation / recombination of
water molecules, and Joule heating of the solution and
heat transport through membranes. We have
constructed a mathematical model of two-dimensional
non-stationary ion transport binary salt in a smooth
rectangular channel desalting electrodialysis device
using equations Nernst-Planck-Poisson, heat
conduction and Navier-Stokes equations and the
natural boundary conditions. For numerical solution
we use the finite element method, with the splitting of
task at each new time layer into three subtasks:
electrochemical, thermal conductivity, hydrodynamic.
Such approach to the development of numerical
methods is the original and can solve arising in
modeling boundary-value problems for a nonlinear system of partial differential equations

The creation of artificial intelligence systems is one
of important and perspective directions of
development of modern information technology.
Since there are many alternatives of mathematical
models of systems of artificial intelligence, there is a
need to assess the quality of these models, which
requires their comparison. To achieve this goal we
require free access to the source data and
methodology, which allows to convert these data
into a form needed for processing in artificial
intelligence. A good choice for these purposes is a
database of test problems for systems of artificial
intelligence of repository of UCI. In this work we
used the database "Iris Data Set" from the bank's
original task of artificial intelligence â€“ UCI
repository, which solved the problem of
formalization of the subject area (development of
classification and descriptive dials and graduations
and the encoding of the source data, resulting
training sample, essentially representing a
normalized source data), synthesis and verification
statistical and system-cognitive models of the
subject area, identify colors with classes, which
serve varieties of Iris, as well as studies of the
subject area by studying its model. To solve these
problems we used the automated system-cognitive
analysis (ASC-analysis) and its programmatic
Toolkit â€“ intellectual system called "Eidos"

Problem having elementary formulation makes us
look for its easier solution. So the combinatorial
method of positive integerâ€™s factorization is an
attempt to do it. The combinatory method possesses
simple algorithm, leading immediately to finding out
all the factorizations and identification of all prime
numbers on any interval of the positive integers.
Prime numbers donâ€™t carry any information except
their own magnitude. Composite numbers, possessing
divisibility properties provide possibility to discover
the law of their distribution. The achievement of this
purpose also completely solves the problem of
finding out the law of prime numbersâ€™ distribution

Specially formed mixtures of isotopes of chemical
elements have better consumer properties than their
natural counterparts. Therefore, the development of
methods for increasing the efficiency of the known
methods for producing of isotope materials is relevant. It
is known that the chemical bond is formed only in the singlet state of the spins of valence electrons of the
reagents. On the basis of the known representations
about dispersion of spin projections on the coordinate
axes and the molecular-kinetic theory of gases was
obtained an expression for the constant of the chemical
reaction between the radicals occurring in the magnetic
field. This expression allows calculating the reactivity of
the isotopic modifications of radicals. Plasma allows to
transfer many of the compounds in the gas phase. It is
known that a significant part of particles in low
temperature plasma is in a radical form. The equations of
chemical kinetics for describing the process of oxidation
of the carbon isotopes in argon-oxygen plasma occurring
in an external permanent magnetic field were written in
the work. It was shown that the efficiency of plasma
process of isotopes separation can be increased only
under insufficient oxygen relative to the stoichiometric
value. These equations of chemical kinetics of processes
occurring in the plasma process of incomplete oxidation
of carbon isotopes needed to find experimental
conditions that provide the maximum isotope effect in a
magnetic field

In this article we consider the many-body problem in
general relativity in the case of the distribution of N
singularities on the circle. It specifies the exact solution
of the problem for an arbitrary distribution of
singularities. It is shown that the static metric of N
singularities corresponds to Newton's theory of N centers
of gravity, moving around the central body in a circular
orbit in a non-inertial frame of reference, rotating with a
period of bodies revolving. We consider the statement of
the problem of many bodies distributed at the initial time
on the circle. 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 circle. This
is achieved due to relativistic effects, which have no
analogues in Newton's theory of gravitation. Using the
properties of relativistic potentials justified transition
from the relativistic motion of the particles to the
dynamic equations in the classical theory. A system of
non-linear parabolic equations describing the evolution
of the metric in the Ricci flow proposed. The problem of
the calculation of the potentials in the Ricci flow
formulated. The application of the theory to describe the
ring galaxy, planetary rings and the asteroid belt
considered

In this work, we examine the dynamics of relativistic
particles in the ring or spiral galaxy metric in general
relativity. On the basis of the solution of Einstein's
equations we have derived metric having axial
symmetry, comprising N centers of gravity and a
logarithmic singularity. The application received metrics
to describe the motion of particles in a spiral and ring
galaxy. On the basis of Einstein's equations solutions for
vacuum we are explained rotation of matter in spiral
galaxies. An expression for gravitation potential in the
inner region of spiral galaxies in agreement with
experimental data on the rotation of the CO and
hydrogen is described. It is established that in the metric
with N centers of gravity which are distributed on the
circumference, exist as a local motion near the center of
gravity, and motion around N gravity center as well. The
transition from one mode of motion to another is
determined by the initial distance to the circle on which
the distributed centers of gravity. A system of non-linear
parabolic equations describing the evolution of the
metric in the Ricci flow proposed. The boundary
problem for the gravitational potentials in the Ricci flow
was formulated. There are applications of the theory to
describe a spiral and ring galaxy

Adequate and effective assessment of the efficiency, effectiveness and the quality of scientific activities of specific scientists and research teams is crucial for any information society and a 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 his 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. The world has 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 the information about citation of these publications from more than 6,000 Russian journals. There is too much information; it is so-called "Big data". But the problem is how to make sense of these large data, more precisely, to identify the meaning of scientometric indicators) and thus to convert them into great information ("great information"), and then apply this information to achieve the objective of scientometrics, i.e. to transform it into a lot of knowledge ("great knowledge") about the specific scientists and research teams. The solution to this problem is creating a "Scientific smart metering system" based on the use of the automated system-cognitive analysis and its software tools â€“ an intellectual system called "Eidos". The article provides a numerical example of the creation and application of Scientometric intelligent measurement system based on a small amount of real scientific data that are publicly available using free on-line access to the RSCI

This article is devoted to the asymptotic analysis of
boundary value problem for a system of equations of
Nernst-Planck and Poisson for a singularly perturbed
system of ordinary differential equations [1], based on
two parameters. This boundary value problem
simulates electrodiffusion of four kinds of ions at the
same time in the diffusion layer in electro-membrane
systems with perfectly selective membrane, taling into
consideration the reaction of recombination of two
ions. Meanwhile the other two ions represent ions of a
binary salt. As a simple example, we consider the
transport of ions sodium, chlorine, hydrogen and
hydroxide, moreover, hydrogen and hydroxyl ions
recombine in the diffusion layer. A more complex case
is the transfer of the products of dissociation of the
dihydrogen phosphate of sodium, namely, ions of
sodium and dihydrogen phosphate, the latter dissociate at the interface, in turn, hydrogen ions and hydrogen
phosphate. Thus, in the solution can simultaneously
store three different types of ions: sodium, hydrogen,
phosphate. During the transfer, hydrogen ions and ions
of hydrogen phosphate recombine to produce
phosphoric acid. The article has revealed the structure
of the Nernst diffusion layer at currents above
Harkatsa current. It is shown, that in the diffusion
layer, there are two types of boundary layers: the inner
(reaction) boundary layer and boundary layer at the
interface solution / membrane

In various applications, it is necessary to analyze
several expert orderings, i.e. clustered rankings
objects of examination. These areas include
technical studies, ecology, management, economics,
sociology, forecasting, etc. The objects can be some
samples of products, technologies, mathematical
models, projects, job applicants and others. In the
construction of the final opinion of the commission
of experts, it is important to find clustered ranking
that averages responses of experts. This article
describes a number of methods for clustered
rankings averaging, among which there is the
method of Kemeny median calculation, based on the
use of Kemeny distance. This article focuses on the
computing side of the final ranking among the
expert opinions problem by means of median
Kemeny calculation. There are currently no exact
algorithms for finding the set of all Kemeny
medians for a given number of permutations
(rankings without connections), only exhaustive
search. However, there are various approaches to
search for a part or all medians, which are analyzed
in this study. Zhikharev's heuristic algorithms serve
as a good tool to study the set of all Kemeny
medians: identifying any connections in mutual
locations of the medians in relation to the
aggregated expert opinions set (a variety of expert
answers permutations). Litvak offers one precise
and one heuristic approaches to calculate the median
among all possible sets of solutions. This article
introduces the necessary concepts, analyzes the
advantages of median Kemeny among other possible searches of expert orderings. It identifies
the comparative strengths and weaknesses of
examined computational ways