The article discusses the use of automatic systemic-cognitive analysis (ASC-analysis), its mathematical model is a system of information theory and software tools – an intellectual system called "Eidos" for the solution of some problems of ampelography: 1) digitization of scanned images of the leaves and creation of their mathematical models; 2) the formation of mathematical models of specific leaves using the spreading of information theory; 3) the formation of models of generalized images of leaves of various sorts; 4) comparing an image of a specific leaf with a generalized image of the leaf of different varieties and finding a quantitative degree of similarity and differences between them, i.e. the identification of the varieties on the leaf; 5) quantification of the similarities and differences of the varieties, i.e. cluster-constructive analysis of generalized images of the leaves of different varieties. We propose a new approach to digitizing images of leaves, based on using the polar coordinate system, the center of gravity of the image and its external contour. Before scanning images we may use transformation to standardize the position of the still images, their sizes and rotation angle. Therefore, the results of digitization and ASC-analysis of the images might be invariant (independent) relatively to their position, size and rotation. The specific shape of the contour of the leaf is regarded as noise information on the variety, including information about the true shape of the leaf of the class (clean signal) and noise, which distort this true form, originating in a random environment. Software tools of ASC-analysis – intellectual "Eidos" system ensures noise reduction and the selection of the signal about the true shape of the leaf of each variety on the basis of a number of noisy concrete examples of the leaves of this variety. This creates a one way form of a leaf of each class, free from their concrete implementations, i.e., the "Eidos" of these images (in the sense of Plato) is a prototype or archetype (in the Jungian sense) of the images
The article presents the problem of spanning trees with
topological criteria and interval scales. We have
introduced relationship preferences and
incomparability to find the complete set of alternatives
in the case of interval scales. The base for
mathematical calculations is interval mathematics
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 – 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
In this work, a model is developed to describe the
formation of streamers, plasmoid, and ball lightning in a
conducting medium. To describe the contribution of the
conductivity currents, we modified the standard
electrostatic equation taking into account the vortex
component of the electric field. As a result of this
generalization, a system of parabolic-type nonlinear
equations is formulated that describes the formation of
streamers, plasma long-lived formations and ball
lightning. As is known, in laboratories it is possible to
create a plasmoid with a lifetime of 300-500 ms and a
diameter of 10-20 cm, which is interpreted as a ball
lightning. With high-speed photography, a complex
structure is detected, consisting of a plasmoid and
surrounding streamers. Within the framework of the
proposed model, problems are posed about the formation
of a plasmoid and the propagation of streamers in an
external electric field. In this model, the plasmoid is
considered to be a long-lived streamer. The range of
parameters in which a plasmoid of spherical shape is
formed is indicated. It is established that there are three
streamer branching mechanisms. The first mechanism is
related to the instability of the front, which leads to the
separation of the head of the streamer into two parts. The
second mechanism is associated with the instability of
the streamer in the base region, which leads to the
branching of the streamer with the formation of a large
number of lateral streamers closing the main channel of
the streamer to the cathode. In numerical experiments,
the third branching mechanism observed in experiments
connected with the branching of the plasmoid in the
cathode region with the closure of the space charge to
the anode through the streamer system was observed.
The results of modeling the evolution of globular
clusters in a scale of hundreds of milliseconds are given.
Plasma exchange recharge modes leading to the
formation of a positive or negative charge of the system
are found
The inverse matrix for the square matrix A of order n
with coefficients of some field exists, as it is known
then and only then, when its determinant is not equal to
zero. If the matrix A has a certain type (certain
structure), then an inverse matrix A-1 should not have
exactly the same structure. Therefore, it is interesting
to describe such square matrices A, which have an
inverse matrix A-1, having the same structure as the
matrix A, under certain conditions. For example, a
subdiagonal matrix with nonzero elements on the main
diagonal has an inverse matrix over a field of
characteristic zero, having also the form of subdiagonal
matrix. Similarly, an inverse matrix towards
symmetrical or skew-symmetric matrix is also
symmetric or skew-symmetric accordingly. Also, the
matrix inverse to non-degenerate (nonsingular)
circulant will be a circulant itself, and finally, the
matrix inverse to nonsingular quasdiagonal matrix D
will be quasdiagonal itself, and will have the same
partitioned structure as D. Thus, there is a problem of
determining these types of nonsingular matrices that
have an inverse matrix of the same type as a given
matrix. In line with this problem in the present study it
is determined such type of matrices for which an
inverse matrix has the same type, at that the conditions
are identified in explicit form, ensuring the
nonsingularity of the matrix. The matrices of three
orders are shown in detail. These results allow
determining the characteristics of fields over which
there are inverse matrices of the considered types
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
In this article, there is a numerical method of solving
the problem of self-organization of the labor
resources. The problem deals with finding
probabilities of hiring and the layoffs of specialists
from the sectors of the labor market. A mathematical
model of labor resources dynamics is used to solve
this problem. The initial problem is incorrect,
because number of equations of the descriptive
system is less than number of unknown variables. A
special algorithm is designed for guaranteed finding
the normal solution in finite number of iterations.
The algorithm is separated into two key stages.
Initially, unconditional normal solution of the
problem is found by applying the modified method of
Gauss for underdetermined systems. Later, this
solution is projected in the subspace of permissible
values. After that, the normal solution of the problem
with consideration of non-negativity of the desired
values is being found by using the gradient projection
method. The proposed algorithm has been
successfully used to develop application in
programming environment C++. This application is
focused on solving of the problem of selforganization
of the labor resources. Comparative
analysis of speed of the application and add-ins MS
Excel "Solver" showed that the same problem is
solved much faster in the application designed by the
author than in a table processor MS Excel when
using the add-in "Solver". This demonstrates the high
efficiency of the proposed method
The article describes a numerical example of creating intellectual application designed to predict solar flares of different classes on the basis of the history of their development in the environment of "Eidos" system. As the source data, we used the database of
UCI repository
This work studies the mathematical model of the
object “inverted pendulum” on the example of the
unstable electromechanical devices which is
balancing robot on wheel couple. Unfortunately,
many details of object model are unknown. Logical
and empirical method offers hypotheses about the
difference between the actual object model from its
mathematical approximation based on logical
analysis with subsequent refinement of this model
and testing of the hypothesis with modeling of the
systems with the updated model. As a result, the
amendments to the model have been found
containing nonlinear components. With the help of
these amendments, the dynamic characteristics of
the actuator, filters, friction and the tendency of the
object to fluctuations are better taken into account
The article discusses the application of automated system-cognitive
analysis (ASC-analysis), its mathematical
model which is system theory of information and
its software tool, which is intellectual system called
"Eidos" for solving problems related to identification
of types and models of aircraft by their silhouettes on
the ground, to be more precise, their external contours:
1) digitization of scanned images of aircraft and creation
of their mathematical models; 2) formation of
mathematical models of specific aircraft with the use
of the information theory; 3) modeling of the generalized
images of various aircraft types and models and
their graphic visualization; 4) comparing an image of a
particular plane with generalized images of various
aircraft types and models, and quantifying the degree
of similarities and differences between them, i.e., the
identification of the type and model of airplane by its
silhouette (contour) on the ground; 5) quantification of
the similarities and differences of the generalized images
of the planes with each other, i.e., clusterconstructive
analysis of generalized images of various
aircraft types and models. The article gives a new approach
to digitizing images of aircraft, based on the
use of the polar coordinate system, the center of gravity
of the image and its external contour. Before digitizing
images, we may use their transformation, standardizing
the position of the images, their sizes (resolution,
distance) and the angle of rotation (angle) in three dimensions.
Therefore, the results of digitization and
ASC-analysis of the images can be invariant (independent)
relative to their position, dimensions and
turns. The shape of the contour of a particular aircraft
is considered as a noise information on the type and
model of aircraft, including information about the true
shape of the aircraft type and its model (clean signal)
and noise, which distort the real shape, due to noise
influences, both of the means of countering detection
and identification, and environment. Software tool of
ASC-analysis, i.e. Eidos intellectual system, provides
identification of the type and the model of airplane by
its silhouette, as it was shown in a simplified numerical
example