name
Sergeev Alexander Eduardovich
Scholastic degree
•
Academic rank
associated professor
Honorary rank
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Organization, job position
• Kuban State University
кафедра высшей алгебры и геометрии
Доцент
Research interests
теория Галуа над различными полями и её приложения (спектры многочленов, критерии нахождения групп Галуа над полями характеристики два, группы Галуа триномов, генерирующие многочлены)
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TOP5 co-authors
Articles count: 23
Сформировать список работ, опубликованных в Научном журнале КубГАУ
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Description
Sommelier evaluates the quality of wine on the basis of their subjective feelings. At the same time, what the sommelier says when evaluating wine, it is difficult or impossible to rationally understand for the uninitiated to this art. The process of assessing the quality of wine by sommelier can not be formalized and is carried out entirely at the sensual level. Sometimes, different sommeliers differently evaluate the same wine poured from the same barrel into bottles of different prestige, with stickers differing in the number of stars. This raises at least two legitimate and natural questions. The first question is whether any subjective sommelier evaluations of the quality of wine are connected with its objective physical and chemical properties? The second question arises in the case of a positive answer to the first one: is it possible to analyze the objective methods of physical and chemical properties of wine to predict its subjective assessment by various sommeliers or some "generalized sommelier", generalizing many such subjective assessments? This article is devoted to obtaining reasoned answers to these questions. The purpose of this work, which is of great scientific and practical interest, is to create a model that provides an automated assessment of the quality of wine based on the analysis of its objective physical and chemical properties, coinciding with its sommelier-evaluation. To achieve this goal, we use Automated system-cognitive analysis (ASC-analysis) and its software tools – the intelligent system called "Eidos". A detailed numerical example based on 1599 real-world examples of sommelier evaluation of wine quality with known physical and chemical properties is considered. In addition to the answer to the two questions in the article, there is a study of the created system-cognitive model
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Description
At present, databases of 27-year observations of various adverse weather conditions and dangerous hydrometeorological phenomena leading to social and economic losses on the territory of Russia are in full open free access. Some of these natural hazards also cause significant damage to agriculture, especially crop production, horticulture and viticulture. Therefore, a great scientific and practical interest is the intellectual analysis of these data, which will create more favorable conditions for the prediction of such adverse events and decision-making, taking into account their possible negative impact on human activity. To achieve this goal, it is necessary to solve the following tasks, which are obtained by decomposition of the goal and are the stages of its achievement: Task 1: cognitive structuring of the subject area. Task 2: preparation of initial data and formalization of the subject area. Task 3: synthesis and verification of statistical and system-cognitive models and selection of the most reliable model. Task 4: solving problems in the most reliable model: - subtask 4.1. Forecasting (diagnostics, classification, recognition, identification); - subtask 4.2. Support decision-making; - sub-task 4.3. Study of the simulated subject area by studying its model (cognitive diagrams of classes and values of factors, agglomerative cognitive clustering of classes and values of factors, nonlocal neurons and neural networks, 3d-integral cognitive maps, cognitive functions). It is proposed to use automated system-cognitive analysis (ASC-analysis) to solve the tasks. The article provides a detailed numerical example illustrating the solution of all these problems
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ON THE NUMERATIONS OF THE FINITE PARTIALLY ORDERED SETS
01.00.00 Physical-mathematical sciences
Description
In this article, we discuss various issues related to the formulas approximating the distribution function of prime numbers pi(x). This question has occupied many scholars, but the exact function is well approximated function pi(x) over the number of positive integers not. Based on certain hypotheses, we present a new function s(x) is very well approximated pi(x). The above article hypotheses are so important that their numerical validation and refinement for the lengths of the segments more in 1014 - one of the main areas related to the problem of approximation of the function pi(x) throughout the series of natural numbers. After analyzing the behaviors and constructs many functions, we are building the basis of the function s(x), which is well approximates the function pi(x) throughout the series of natural numbers. We also present a table of values for x, less or equal 1022 for the difference of s(x) - pi(x)
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01.00.00 Physical-mathematical sciences
Description
The concept of generic polynomial appeared in Saltman’s works at the end of the last century and it is connected with the inverse problem of Galois theory, which is still far from its complete solution. Let G be a finite group and K be a field, the polynomial f(x,t1, … , tn) with coefficients from the field K is generic for the group G, if Galois group of this polynomial over the field K(t1, … , tn) is isomorphic G and if for any Galois extension L/K with Galois group isomorphic G there are such values of parameters ti = ai , i = 1,2, … , n, that the field L is the splitting field of the polynomial f(x,a1, … , an) over K. Generic polynomials over a given field K and a given finite group G do not always exist, and if they exist then it’s not easy to construct them. For example, for a cyclic group of the eight order C8 there is no generic polynomial over the field of rational numbers Q, although there are found specific polynomials with rational coefficients having Galois group isomorphic C8. Therefore, this is of interest to construct generic polynomials for the group G in cases when G is a direct product of groups of lower orders. In this study we show to solve this problem in case when G is a direct product of certain cyclic groups and there is a type of corresponding generic polynomials. Moreover, we give constructions over the fields of characteristic 0 and over the fields of characteristic 2
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GENERIC POLYNOMIALS FOR THE CYCLIC 2-GROUPS OVER FIELDS WITH CHARACTERISTIC TWO
01.00.00 Physical-mathematical sciences
Description
In this article, the generic polynomials for cyclic groups of order 4, 8 and 16 over fields with characteristic two are constructed. With this construction, the generic polynomials for all cyclic 2-groups over fields with characteristic two can be obtained. We also give survey of known results of generic polynomials for the cyclic groups.
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COGNITIVE VETERINARY – DIGITAL SOCIETY VETERINARY: THE DEFINITION OF BASIC CONCEPTS
06.02.00 Veterinary and Husbandry
Description
There are many opinions on the question of what kind of society we live in at the beginning of the XXI century. Previously, it was believed that this is a post-industrial society. There was even an opinion that it would be a society of developed socialism or even a communist society. After that, the opinion on this has changed. First, modern society was called the information society, and then the society based on knowledge. The latest news in this area is that it seems that modern society is a digital society, that is, a society, based on digital technologies, digital communications, digital information processing and transmission technologies, as well as digital artificial intelligence technologies. In a digital society and science people must move to digital intelligent research technologies. In particular, the question arises as to whether veterinary medicine in a digital society should not also become cognitive veterinary medicine. This work is devoted to a detailed and reasoned (according to the authors) answer to this question. The methodology and terminology in this new field is not yet established and is not generally accepted. Therefore, in this work a lot of attention is paid to the logic and methodology of scientific knowledge, terminological issues and definitions of concepts
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06.02.00 Veterinary and Husbandry
Description
A number of authors (Milaeva I. V., Zaitsev S. Yu., Dovzhenko N. A., Tsarkov D. V., Tsarkova M. S., 2015) have proposed a regression model and a method for indirect measurement of fat and protein content in cow's milk by its dynamic surface tension, which has a number of advantages over the traditional approach. The model reflects the objectively existing relations between the content of fat and protein in cow's milk and parameters of centigrams of dynamic surface tension at the interface of the milk/air. These relationships are revealed by the authors of the method wit mathematical processing of 112 empirical samples. For this purpose, they have applied regression and correlation analysis (in MS Excel). Since the content of fat and proteins in milk largely determines its quality, this problem refers to the problems of qualimetry. However, this problem of qualimetry also refers to typical problems of pattern recognition (multi-parameter typing and system identification), and therefore it is possible that the quality of its solution can be improved by the use of artificial intelligence methods, in particular cognitive and information technologies. Moreover, these relationships are quite complex. The use of intelligent technologies also creates additional opportunities for the study of the simulated subject area by studying its model. All this is of great scientific and practical interest for both researchers and practitioners. To solve all these problems in the work we have applied Automated System-Cognitive analysis (ASC-analysis) and its software tool which is an intelligent system called "Eidos". A numerical example based on real data has been considered in detail as well
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08.00.13 Mathematical and instrumental methods of Economics
Description
In the article, we develop the methodology of strategic planning and management of the holding on the theoretical basis of automated system-cognitive analysis (ASC-analysis). This methodology provides scientific research of any holding by creating and researching its model. The methodology includes both the synthesis, adaptation and verification of system-cognitive models of the holding, and the use of these models for strategic planning and decision support for managing the holding, as a complex, multiparametric, nonlinear system. The relevance of the research is due to the special role of holdings and other corporate integrated structures both in Russia as a whole and, in particular, in the Krasnodar region. Despite obvious system advantages, holdings face a wide range of problems related to management efficiency, ensuring their sustainable functioning, etc. The proposed methodology offers ways to solve these problems and can be successfully applied in holdings and other corporate integrated structures of various regions, volumes and areas of activity, which determines the relevance of the research topic. The level of significance and scientific novelty of the Research consists in the development of conceptual and theoretical and methodological provisions aimed at managing the development of holdings. The expected results and their significance are that the methodology developed as a result of the Research can be applied by holding companies and other corporate integrated structures and will significantly improve the quality of their management
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01.00.00 Physical-mathematical sciences
Description
The article obtained the explicit form of root polynomials for cyclic polynomials of degree three over fields of characteristic 2. We also give an overview of known results on the root polynomials over arbitrary fields
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01.00.00 Physical-mathematical sciences
Description
In 1893, the French mathematician J. Adamar raised the question: given a matrix of fixed order with coefficients not exceeding modulo this value, then what is the maximum modulo value can take the determinant of this matrix? Adamar fully decided this question in the case when the coefficients of the matrix are complex numbers and put forward the corresponding hypothesis in the case when the matrix coefficients are real numbers modulo equal to one. Such matrices satisfying the Hadamard conjecture were called Hadamard matrices, their order is four and it is unknown whether this condition is sufficient for their existence. The article examines a natural generalization of the Hadamard matrices over the field of real numbers, they are there for any order. This paper proposes an algorithm for the construction of generalized Hadamard matrices, and it is illustrated by numerical examples. Also introduces the concept of constants for the natural numbers are computed values of this constant for some natural numbers and shown some applications of Hadamard constants for estimates on the top and bottom of the module of the determinant of this order with arbitrary real coefficients, and these estimates are in some cases better than the known estimates of Hadamard. The results of the article are associated with the results of the con on the value of determinants of matrices with real coefficients, not exceeding modulo units
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