The article presents a mathematical model of the ion transport across phase boundary exchange membrane / solution. The border is considered as an object in space, endowed with all the physical and chemical properties that are inherent physical and chemical phases. It is regarded as a special physical and chemical environment, having a distributed exchange capacity in which there is space charge dissociation of water molecules. The size of this object is estimated in the range of 1-300 nm. The surface morphology of industrial membrane type MK-40, ÐœA-41 and ÐœA-41P was investigated experimentally by scanning electron microscopy (REM). There was analyzed the amplitude of average surface roughness. In this article, the reaction layer is modeled as a region that forms as a relief morphology of the membrane. Membrane properties are due to the properties of the solution and the properties of the membrane. To determine the dependence of Q(x) is proposed procedure for assessing the proportion of solid phase in the total volume of which can be seen in the vertical cross section microprofile on the membrane surface line. Height multivendors determine the reaction layer zone on frame of model. Influence of surface morphology on the V-A characteristics and the sizes of the convective instability of cation-exchange membrane evaluated numerically simulating the hydrodynamic flow conditions using a solution of the Navier-Stokes equations. The transfer of a strong electrolyte such as NaCl ions through the thin layer of the reaction layer is considered. The place of nanomodel in the structure of a three-layer membrane system is showed. The distribution of the concentration of ions in the system, the charge density distribution and the dependence of the integrate charge with extent nanolayer is present. How to change the shape of the space charge and its integral value with one is investigated

The article is devoted to the discussion of the
organization of clinical-statistical studies and
experiments. We have considered the examples of
the application of statistical methods in scientific
medical research. Under the clinical-statistical
research we understand specially organized
collection and analysis of medical data about the
course of disease in patients, research of the
dynamics of objective and subjective indicators of
the state of reaction to these or other therapeutic
effects. We study one, two or more groups of
individuals (patients or healthy), conclusions are
drawn on the whole group, but not for each
individual patient. The purpose of research - to
transfer the conclusions reached for the sample to
the general population, i.e., clinical and statistical
study focused on the production of useful
recommendations concerning those patients who fall
into the field of view of doctors after the end of the
study. There are two main types of research -
prospective and retrospective. The first related to the
analysis of the last patients, the second - to
monitoring the course of their disease in the future.
We have considered typical mistakes in the
organization of clinical-statistical studies. When
planning a research, we usually distinguish the
experimental and control groups, which are identical
or similar in all respects except for the studied
factors (exposure). We discuss the various options
for blind methods and consider the application of
statistical models and methods in scientific medical
research. We have analyzed examples of confidence
estimation of proportion (probability) and the
homogeneity test of probabilities. For statistical
modeling we use the Poisson distribution in the case
of small probability. With its help, we analyze
statistical data on the opisthorchiasis

We consider the methods for estimation of the
effectiveness and quality of the scientific activities
of the researcher, of the organization, of the
magazine. Performance indicators of scientific
activity are used as an important part in the
estimation of higher education institutions, the
innovative capacity of enterprises, etc. To estimate
the effectiveness of scientific activity is natural to
use intellectual tools which are well-established in
other subject areas. This will include, in particular,
the balanced scorecard, based on key performance
indicators (hence the title of this article), as well as
controlling, primarily controlling of research
activities. There are two more developed and
widely used types of tools for estimation the
effectiveness of the scientific activity - the
scientometric indicators and the expert estimators.
Their critical analysis is the subject of this article.
The goal - to choose the most effective tool.
Different versions of manipulating of values of
scientometric indicators in the Russian Federation,
in our estimation, are still relatively rare. Perhaps
this is due to the relatively short period of their use
in the management of science. Since an indicator
such as citation index (the number of citations of
publications) of researcher, allows estimating its
contribution to science, the use of this
scientometric indicator for the management of
science is justified. At the same time, the number
of publications and especially h-index is not
possible to objectively estimate the effectiveness of
research activities, particularly in view of the
properties of the real bibliometric databases. Expert
procedures have several disadvantages. In this
article we discuss the real effectiveness of expert
procedures in the areas of their application, as
conferring academic degrees and elections to the
National Academy of Sciences (primarily in the
Russian Academy of Sciences), as well as
appointments to senior positions. The basic
principles of expertise in these areas remain the
same for the past 70 years. Based on an analysis of
practice it is necessary to ascertain the lack of
efficacy of expert estimators in these areas. Rationale to what has been said is given in the
article

The article deals with numerical solutions of MHD
equations describing turbulent flow of a conducting
fluid in a rectangular cavity in the rotating magnetic
field at large values of the magnetic Taylor number,
and Reynolds number. It is known that there is a
mechanism of turbulent mixing in natural systems,
leading to an increase in the viscosity of the
continuous medium. In this regard, we suggest
methods of regularization of the Navier-Stokes
equations, similar to the natural mechanisms of
mixing. The models based on the properties of
currents of the turbulent environment proposed. A
modification of the continuity equation taking into
account the final magnitude of pressure fluctuations
was considered. It is shown that due to pressure
fluctuation the incompressibility condition can be
violated even for flows with low Mach numbers.
Modification of continuity in the system of NavierStokes
equations by the introduction of turbulent
viscosity allows the regularization of the NavierStokes
equations to solve the problems with rapidly
changing dynamic parameters, for example, in the
case of a conducting fluid flow in a magnetic field
rotating with a high frequency. It was shown that the
modification of the continuity equation taking into
account turbulent fluctuations leads to a system of
nonlinear equations of parabolic type. A numerical
model of turbulent MHD flow in a rectangular cavity
with rapid change in flow parameters was proposed.
In numerical calculations revealed that under the
influence of a rotating magnetic field in a conducting
fluid there are forces occur, causing unsteady vortex
flow, which is consistent with experimental data. We
have discovered a type of large scale instability of the
turbulent flow, connecting with the secondary flow in
a form of vortices

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 the intellectual system called "Eidos", which is a software toolkit for the automated system-cognitive analysis (ASC-analysis), we use initially proposed by its developers measure of the reliability of the models, which is essentially a fuzzy multiclass generalization of the classical F-measure (it is proposed to call it the L-measure). In this article, L-measure is mathematically described and its application is demonstrated on a simple numerical example

This article focuses on the mathematical modeling of
evaluation of financial and economic activities of a
company and on definition (based on this model) of
such balance settings (line F1 and F2) which would
make financial-economic indicators of the activities of
the organization optimal, and the total cumulative
score was the maximum. The knowledge and the use
of the optimal parameters of the balance will allow the
managers to plan strategy for the future development
of the company. The article analyzes the dependencies
of each of the 15 basic indicators (profitability,
turnover, financial stability, liquidity and solvency) of
financial and economic activity of the organization on
the balance parameters. The optimal values of the
parameters of the balance and the main indicators of
financial and economic activities of the organization
have been found. We have also built a mathematical
model of optimal control of financial and economic
indicators in the form of a problem of mathematical
programming. For example, for the company called "Nika" it is shown the possibility of improving
estimation of financial and economic condition of the
organization. Knowledge of the optimal parameters of
the balance will allow the managers to plan strategy
for the future development of the organization. To
solve this problem we have used the method of
generalized reduced gradient implemented in Excel,
with which there was found a maximum of the
objective function for the article restrictions. The
article describes the analysis algorithm of the
optimization problem. A common assessment was
carried out in stages, based on the calculation
algorithm of sequentially improved target functions

This article is a continuation of the previous works of
the authors [The influence of reaction dissociation /
recombination of molecules of water on transportation
of electrolyte 1:1 in the membrane systems in the
diffusion layer. Part 1. Mathematical model //
Scientific journal of Kuban State Agrarian University,
2016. No. 07(121) and The influence of the reaction of
dissociation / recombination of molecules of water on
transportation of electrolyte 1: 1 in membrane systems
in the diffusion layer. Part 2. Asymptotic analysis //
Scientific journal of Kuban State Agrarian University,
2016. â€“ â„–08(122)] and devoted to assessing the
possibility of gravitational convection due to the
recombination of hydrogen and hydroxyl ions. The
article presents the solution of a boundary-value
problem, which is a mathematical model of
electrodiffusion for the four types of ions at the same
time (two ions of salts and hydrogen and hydroxyl
ions) in the diffusion layer in electro-membrane
systems with ideal selective membrane, with the heat
transfer equation and the Navier-Stokes equation. The
article shows the possibility of the emergence of
gravitational convection due to the exothermic reaction
of recombination of water molecules in the depth of
the solution. The article considered the reaction of
recombination of hydrogen ions and hydroxyl,
although the main results can be applied, after appropriate modifications, and to amfolit-containing
solutions, such as wine, juices, dairy products,
microbiological processing of biomass (amino acids,
anions of polybasic carboxylic acids), municipal
effluent (anions of phosphoric acid), etc.

This article discusses an economic game called
"The struggle for markets". We have generated a
mathematical model of quantum realization of this
game. For clarity, the algorithms are derived for
soft and hard quantum games for assessing the
impact of the degree of entanglement to work and
the result of the algorithm. There are step-by-step
instructions for the sequence of actions and
operations to create a quantum model of the game.
The aim is to assess the influence of the degree of
entanglement on work algorithms. Also, we
investigate the influence of quantum entanglement
on the win for two or more players. The article
gives a comparison with classical results

We consider an approach to the transition from
continuous to discrete scale which was defined by
means of step of quantization (i.e. interval of
grouping). Applied purpose is selecting the number
of gradations in sociological questionnaires. In
accordance with the methodology of the general
stability theory, we offer to choose a step so that the
errors, generated by the quantization, were of the
same order as the errors inherent in the answers of
respondents. At a finite length of interval of the
measured value change of the scale this step of
quantization uniquely determines the number of
gradations. It turns out that for many issues gated it
is enough to point 3 - 6 answers gradations (hints).
On the basis of the probabilistic model we have
proved three theorems of quantization. They are
allowed to develop recommendations on the choice
of the number of gradations in sociological
questionnaires. The idea of "quantization" has
applications not only in sociology. We have noted,
that it can be used not only to select the number of
gradations. So, there are two very interesting
applications of the idea of "quantization" in
inventory management theory - in the two-level
model and in the classical Wilson model taking into
account deviations from it (shows that
"quantization" can use as a way to improve
stability). For the two-level inventory management
model we proved three theorems. We have
abandoned the assumption of Poisson demand,
which is rarely carried out in practice, and we give
generally fairly simple formulas for finding the
optimal values of the control parameters,
simultaneously correcting the mistakes of
predecessors. Once again we see the interpenetration
of statistical methods that have arisen to analyze
data from a variety of subject areas, in this case,
from sociology and logistics. We have another proof
that the statistical methods - single scientificpractical
area that is inappropriate to share by areas
of applications

The article begins with the letter of the chief
engineer of chemical plant near Moscow. He
requests to analyze of data by means of modern
statistical methods and give an opinion on the
presence (or absence) of the relationship between
the two methods of determining the viscosity of the
mastic. For each of the batches of mastic It was
presented two numbers - the viscosity measurement
results of the two methods. These numbers form two
paired samples. We want to install, give whether
two specific methods similar results. The true values
of viscosity in different batches are not equal. Their
difference is not allows us to combine the results of
the first measurement method in first sample, the
results of the second method - in the second sample,
as we can do in the case of testing the homogeneity
of two independent samples. For solutions to this
problem we discuss four statistical criterions, based
on a study of the differences between corresponding
values in two paired samples. We test the hypothesis
of equality 0 of median of these differences (sign
test) and of equality 0 of the mathematical
expectation of these differences. Hypothesis of
testing of equality of the distribution functions of
two paired samples is reduced to the hypothesis of
symmetry of the distribution function of these
differences with respect to 0. In the alternative of the
shift is proposed to use the Wilcoxon signed rank
criterion. In the total alternative is proposed to use
criterion of the omega-square type which is
developed by the author of this article