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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05.13.10 Management in social and economic systems
DescriptionOne of the key problems facing medicine is the correct diagnosis given in a timely manner. For all the existence of medicine, humanity has accumulated a lot of knowledge in this area. According to this knowledge, new specialists are trained. But there is so much information that it is sometimes impossible to find the right information in it in time, and this can cost the person who came to see a doctor very expensive. In this specialist comes to the rescue computer. Information technologies, training in information bases perfectly cope with the task of identifying the disease and providing the most appropriate information
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01.00.00 Physical-mathematical sciences
DescriptionThe Euler function is very important in number theory and in Mathematics, however, the range of its values in the natural numbers has not been written off. The greatest value of the Euler function reaches on Prime numbers, furthermore, it is multiplicative. The value of the Euler function is closely associated with the values of the Moebius function and the function values of the sum of the divisors of the given natural number. The Euler function is linked with systems of public key encryption. The individual values of the Euler function behave irregularly because of the irregular distribution of primes in the natural numbers. This tract is illustrated in the article with charts; summatory function for the Euler function and its average value are more predictable. We prove the formula of Martinga and, based on it, we study the approximation accuracy of the average value of the Euler function with corresponding quadratic polynomial. There is a new feature associated with the average value of the Euler function and calculate intervals of its values. We also introduce the concept of density values of the Euler function and calculate its value on the interval of the natural numbers. It can be noted that the results of the behavior of the Euler function are followed by the results in the behavior of functions of sums of divisors of natural numbers and vice versa. We have also given the results of A.Z.Valfish and A.N.Saltykov on this subject
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01.00.00 Physical-mathematical sciences
DescriptionThe problem of establishing of the factorization of irreducible polynomials with integer coefficients on prime modules p has been long of interest to mathematicians. The quadratic and cubic reciprocity laws solve this problem for quadratic polynomials and binomials of the form x3-a . More general reciprocity laws solve the formulated problem for some classes of polynomials, for example, with Abelian Galois group, but for polynomials with non-Abelian Galois group, the problem is far from its complete solution. Our study shows how using the results of Voronov G.F., Hasse H. and Stickelberger L., one can find conditions that must satisfy prime number p. Gauss received a similar result for binomial x3-2. Specific examples are given, for instance, for the polynomial x3-x - I, also conditions arc formulated for which a quadratic field is immersed in non-Abelian Galois extension of degree 6. Also, conditions are given under which a Diophantine equation: а12a22-4a22-4a13a3- 27a32+18a1a2a3=D has a solution for integer values of D
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01.00.00 Physical-mathematical sciences
DescriptionIn 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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01.00.00 Physical-mathematical sciences
DescriptionThe 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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08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn 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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06.02.00 Veterinary and Husbandry
DescriptionA 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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COGNITIVE VETERINARY – DIGITAL SOCIETY VETERINARY: THE DEFINITION OF BASIC CONCEPTS
06.02.00 Veterinary and Husbandry
DescriptionThere 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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GENERIC POLYNOMIALS FOR THE CYCLIC 2-GROUPS OVER FIELDS WITH CHARACTERISTIC TWO
01.00.00 Physical-mathematical sciences
DescriptionIn 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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01.00.00 Physical-mathematical sciences
DescriptionThe 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