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
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
Some estimators of the probability density function
in spaces of arbitrary nature are used for various
tasks in statistics of non-numerical data. Systematic
exposition of the theory of such estimators has been
started in our articles [3, 4]. This article is a direct
continuation of these works [3, 4]. We will regularly
use references to conditions and theorems of the
articles [3, 4], in which introduced several types of
nonparametric estimators of the probability density.
We have studied linear estimators. In this article, we
consider particular cases - kernel density estimates in
discrete spaces. When estimating the density of the
one-dimensional random variable, kernel estimators
become the Parzen-Rosenblatt estimators. Under
different conditions, we prove the consistency and
asymptotic normality of kernel density estimators.
We have introduced the concept of "preferred rate
differences" and are studied nuclear density
estimators based on it. We have introduced and
studied natural affinity measures which are used in
the analysis of the asymptotic behavior of kernel
density estimators. Kernel density estimates are
considered for sequences of spaces with measures.
We give the conditions under which the difference
between the densities of probability distributions and
of the mathematical expectations of their nuclear
estimates uniformly tends to 0. Is established the
uniform convergence of the variances. We find the
conditions on the kernel functions, in which take
place these theorems about uniform convergence. As
examples, there are considered the spaces of fuzzy
subsets of finite sets and the spaces of all subsets of
finite sets. We give the condition to support the use
of kernel density estimation in finite spaces. We
discuss the counterexample of space of rankings in
which the application of kernel density estimators
can not be correct
In this article, we investigate the problem of creation of
matter in the collision of particles, presented by
singularities of the gravitational field. A system of nonlinear
parabolic equations describing the evolution of the
axially symmetric metrics in the Ricci flow derived. A
model describing the creation of matter in the collision
and merger of the particles in the Ricci flow proposed. It
is shown that the theory that describes the Ricci flow in
the collision of black holes is consistent with EinsteinInfeld
theory, which describes the dynamics of the
material particles provided by the singularities of the
gravitational field. As an example, we consider the
metric having axial symmetry and which contains two
singularities simulating particles of finite mass. It is
shown that the static metric with two singularities
corresponding to in Newton's theory of gravity two
particles moving around the center of mass in circular
orbits in a non-inertial frame of reference, rotating with a
period of two-body system rotation. We have
numerically investigated the change of the metric in the
collision of particles with subsequent expansion. In
numerical experiments, we have determined that the
collision of the particles in the Ricci flow leads to the
formation of two types of matter with positive and
negative energy density, respectively. When moving
singularities towards each other in the area between the
particles the matter is formed with negative energy
density, and in the region behind the particles - with
positive density. In the recession of the singularities, the
matter with positive energy density is formed in the area
between the particles. The question of the nature of
baryonic matter in the expanding universe is discussed
In this article, the restricted problem of three and more
bodies in the Ricci flow in the general theory of
relativity considered. A system of non-linear parabolic
equations describing the evolution of the axially
symmetric metrics in the Ricci flow proposed. A model
describing the motion of particles in the Ricci flow
derived. It is shown that the theory describing the Ricci
flow in the many-body problem is consistent with the
Einstein-Infeld theory, which describes the dynamics of
the material particles provided by the singularities of the
gravitational field. As an example, consider the metric
having axial symmetry and contains two singularities
simulating particles of finite mass. It is shown that the
static metric with two singularities corresponds to
Newton's theory of the two centers of gravity, moving
around the center of mass in circular orbits in a noninertial
frame of reference, rotating with a period of
bodies. We consider the statement of the problem of
many bodies distributed at the initial time on the axis of
symmetry of the system. 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
axis of the system. This is achieved due to relativistic
effects, which have no analogues in Newton's theory of
gravitation. Using the properties of relativistic potentials
we have justified transition from the relativistic motion
of the particles to the dynamic equations in the classic
theory
In this article, we investigate the restricted problem of
many bodies with a logarithmic potential in the general
theory of relativity. We consider the metric having
axial symmetry and containing a logarithmic
singularity. 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 axis of the
system. This is achieved due to relativistic effects,
which have no analogues in Newton's theory of
gravitation. The motion of relativistic particles in a
logarithmic potential sources distributed on the surface
of a torus simulated. It is shown that the trajectory of
the particles in these systems form a torus covered with
needles. It was found, that the Ricci flow in the general
theory of relativity could be born three kinds of matter -
positive and negative energy density, as well as the
color of matter, the gravitational potential of which is
complex. It has been shown that this type of material is
associated with the manifestation of the quantummechanical
properties, which is consistent with the
hypothesis of the origin of Schrodinger quantum
mechanics. It is assumed that the most likely candidate
for the role of the color of matter is the system of
quarks as to describe the dynamics of quarks using the
logarithmic potential, and the quarks themselves are not
observed in the free state
To develop the novel herbicide antidotes for the
sunflower vegetative plants, the group of chemical
compounds, belonging to the derivatives of
isoxalopyrazolopyridines was synthesized and their
antidote activity both in the laboratory and field
experiments was studied. The compounds with a high
antidote effect were found
For the conservation of biodiversity, this study of
patterns of biological processes and phases in the
development of Convallaria majalis L. that are
repeated annually becomes actual. In the article, we
have presented an analysis of five years of
observations of the rhythm of the development of
Convallaria majalis L. in the conditions of the middle
Don. There were allocated phenological phases of lily
of the valley: vegetative (beginning of sprout growth,
deploying of leaves), bud formation, flowering
(disclosure of the first flower, mass blossoming, the
withering of separate flowers, the ending of
flowering), fruitage (the beginning of fruit setting,
mass of fruit setting, mass ripening of fruits), the end
of the vegetation (appearance of the first changes in
color of leaves, the complete drying). We have defined
daily average temperature and the appropriate amount
of positive temperatures for the passage of various
phases of development Convallaria majalis L. By the
results of two growing seasons, the optimal daily
average temperature for the flowering period is 14,3 °
C (the sum of average daily temperatures 161,3-204,
0С) - until 9-15 days. At higher daily air temperatures
flowering begins at lower amount of positive and
effective temperatures after 40-45 days after the start
of the vegetation. At lower daily air temperatures
flowering is longer than at higher. In the conditions of
the middle Don there were allocated some examples of
Convallaria majalis L. which bloom two years in a
row
The article discusses the formation of the collection
that includes the most numerous genus Pelargonium
(L.Herit.) from the family Geraniaceae Juss, as well as
its importance, and the prospects for replenishing and
use. There is also analysis of the publications for the
recent years, clarifying approaches and principles in
classifying the representatives of this species. The
collection of Russian Research Institute of Floriculture
and Subtropical Crops is described, taking into account
new palynological and cytogenetic criteria in
pelargoniums section division. It is represented by
more than 120 species, cultivars, as well as
intravarietal and interspecific hybrids and is divided
into three branches (A, B, C2), three subgenus
(Pelargonium. Parvulipetala, Paucisignata) and five
sections (Pelargonium, Otidia, Peristera., Reniformia
Ciconium). Collection samples are included to the
breeding research, as sources of economic features
when creating highly-ornamental hybrids and
cultivars. The work also studies possible using of the
most adapted species, cultivars and hybrids in urban
landscaping on the Black Sea coast
The isolation of E.coli phages from samples of natural
and waste water obtained during expeditions in the
different regions of Russian Federation was carried
out. The obtained phages (286 isolates) were tested for
their ability to lyse the pathogenic strains of E. coli –
pathogenic agents of pig colibacteriosis in Krasnodar
region. The study was conducted of their ability to
phage transduction, the molecular-genetic
characterization and biotechnological parameters of
selected bacteriophages. For first experimental design
of veterinary drugs was selected 5 coliphages having no ability of plasmids transduction. It has been shown
that all the investigated phages are representatives of
T4-type phages of family Myoviridae. The reported
study was partially supported by RFBR, research
projects No. 08-04-99111, 09-04-10132, 16-44-
230855