In the training courses on the theory of probability and
mathematical statistics there are various parametric
families of distributions of numerical random variables
considered. Namely, we have been studying the
families of normal distributions, log-normal
distributions, exponential distributions, gamma
distributions, Weibull-Gnedenko distributions, etc. All
of them depend on one, two or three parameters.
Therefore, for a complete description of the distribution
it is sufficient to know or estimate one, two or three
numbers. Parametric theory of mathematical statistics is
widely developed, where it is assumed that the
distribution of observations belong to one or another
parametric family of distributions. This tradition comes
from Karl Pearson, who in the early twentieth century
proposed the use of four parametric family of
distributions. The above families of distributions - are
the subsets of a four-parametric family of Pearson.
Unfortunately, parametric families exist only in the
minds of the authors of textbooks on probability theory
and mathematical statistics. In real life, they are not.
Therefore, modern applied statistics and econometrics
mainly use non-parametric methods, in which the
distribution of observations can have arbitrary form.
First, on an example of a normal distribution, we are
discussing the impossibility of practical use of
parametric families of distributions to describe specific
statistical data. We give the results of research of
metrologists and estimation of convergence in limit
theorems. Then we discuss how the parametric methods
can use for reject outlying observations. It is very
unstable the significance levels for a fixed rejection rule
and the parameter of the rejection rules for a fixed level
of significance. Consequently, the rejection of the
classic rules of mathematical statistics is not sciencebased
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
The federal program on essential drugs provision
(EDP) is one of the most significant and socially
important state projects; it is directed to the reduction
of morbidity and mortality together with the
improvement of life quality of the society and its
social climate. In accordance with the federal law “On
social state assistance” from 17.07.1999 №178- FL,
the essence of the program is that medical recipes are
dispensed for preferential medicines to be received by
federal program participants. The medical-economic
control (MEC) of the drugs designation and provision
of federal benefit recipients is performed basing on the
automated registries examination of released drugs.
The number of passed and failed examination recipes
is determined according to the registers processing
results. A certain percentage of the accepted for
payment prescriptions is a subject for MEC. For the
purpose of the recipes selection for testing, the paper
proposes the mathematical models of criteria
application and MEC-planning. The game model of
organization and MEC performance in health care
organizations is build basing on the theory of games.
The considered play model suggests that the health
services quality examination need to be adjusted and
some strategies are to be improved. The solution on
the planning of checked recipes number allows to
perform the inspection of all the health care
organizations, involved in EDP program
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
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 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
Researches of metric characteristics on prefractal graphs
are known tasks. Such tasks arise when determining
estimates of length, of depth, of width of the graph. Also
these questions arise when determining results of
optimization of these tasks of the prefractal graphs.
Properties of metric characteristics depend on a
trajectory of generation of the prefractal graph and on
the characteristic of primings. In this work, metric
characteristics on prefractal weighed graphs are
investigated, dependence of metric characteristics on a
trajectory of a priming and prefractal graphs is revealed.
Estimates are obtained for the diameter and radius of the
weighted prefractal and fractal graphss
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
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. – №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 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