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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SPECIAL CASES OF INVERSE MATRICES
01.00.00 Physical-mathematical sciences
DescriptionThe 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
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents the theorem of Chebyshev on the distribution of primes, considering functions that approximated prime numbers. We have also considered a new function, which is quite good for approximation of prime numbers. A review of the known results on distribution of prime numbers is given as well
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STRATEGIC PLANNING AND MANAGEMENT OF A HOLDING BASED ON INFORMATION AND COGNITIVE TECHNOLOGIES
08.00.13 Mathematical and instrumental methods of Economics
DescriptionIn the article, we develop the methodology of strategic planning and management of a 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 the management of 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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SCORING SYSTEM BASED ON INFORMATION-COGNITIVE MODELING
08.00.13 Mathematical and instrumental methods of Economics
DescriptionOne of the key problems facing the credit institution is the late payment of the loan. Firstly, it is a deeper analysis - in order to be carried out “manually” it is not even required several days, but weeks. Secondly, it allows you to work with clients much faster. And most importantly scoring allows you to negate the influence of the human factor. An automated system, no matter how you look, cannot be liked or not. Data analysis is only based on facts. Scoring is beneficial to all. The bank is able to work faster and reduce the risk of loan defaults. Clients, in turn, can apply for a loan on terms that are more favorable
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THE REALIZATION OF GALOIS GROUPS BY TRINOMIALS OVER THE FIELD OF RATIONAL NUMBERS Q
01.00.00 Physical-mathematical sciences
DescriptionIt is known that not every finite group can be realized over the field of rational numbers as a Galois group of some binomial. In this connection, a more general question arises: suppose that there is given a finite transitive subgroup G of the symmetric group S on n symbols; Can this group G be realized as a Galois group of some trinomial of degree n over the field of rational numbers? In this paper we prove that every transitive subgroup of the group S can be realized in the form of the Galois group of a certain trinomial of the degree n, for the values n = 2, 3, 4. For n = 5 , 6 we give examples that realize concrete Galois groups. In the case n = 7, all the transitive subgroups of the group S are realized, except possibly one group of the isomorphic dihedral group D. Further calculations will be directed to the realization of specific Galois groups for n = 8, 9 ..., however, the number of transitive subgroups of the group S for n = 8, 9 ... grows very fast, so the larger the value of n, the more difficult it is to realize not just everything but the specific subgroup of the group S in the form of a trinomial over Q
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06.02.00 Veterinary and Husbandry
DescriptionThis article briefly discusses a new innovation (brought to a level that ensures its practical use) method of artificial intelligence: automated system-cognitive analysis (ASC-analysis) and its programmatic toolkit which is called intellectual system "Eidos". A detailed numerical example of the solution demonstrating the technology of creating a veterinary diagnostic test of gastrointestinal diseases of horses is given. As the source data, we use data from the UCI repository, kindly given by Mary McLeish and Matt Cecile (Department of computer science of University of Guelph, Ontario, Canada N1G 2W1, with the support of a sponsor: Will Taylor. The developed test is used to solve the problems of diagnosis, decision support and examining the simulated subject area by studying its model. The results of the study can be used by anyone, due to the fact that Eidos the universal automated system, which is a tool of ask-analysis, is in full open free access on the author's website at: http://lc.kubagro.ru/aidos/_Aidos-X.htm, and numerical examples of solving veterinary problems with the use of artificial intelligence technologies are placed as a cloud Eidos-application 129
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08.00.13 Mathematical and instrumental methods of Economics
DescriptionTraditionally, control decisions are made by solving repeatedly the forecasting problem for different values of control factors and choosing a combination of them that ensures the transfer of the control object to the target state. However, real control objects are affected by hundreds or thousands of control factors, each of which can have dozens of values. A complete search of all possible combinations of values of control factors leads to the need to solve the problem of forecasting tens or hundreds of thousands or even millions of times to make a single decision, and this is completely unacceptable in practice. Therefore, we need a decision-making method that does not require significant computing resources. Thus, there is a contradiction between the actual and the desired, a contradiction between them, which is the problem to be solved in the work. In this work, we propose a developed algorithm for decision-making by solving the inverse forecasting problem once (automated SWOT analysis), using the results of cluster-constructive analysis of the target states of the control object and the values of factors and a single solution of the forecasting problem. This determines the relevance of the topic. The purpose of the work is to solve the problem. By decomposing the goal, we have formulated the following tasks, which are the stages of achieving the goal: cognitive-target structuring of the subject area; formalization of the subject area (development of classification and descriptive scales and gradations and formation of a training sample); synthesis, verification and increasing the reliability of the model of the control object; forecasting, decision-making and research of the control object by studying its model. The study uses the automated system-cognitive analysis and its software tools (the intelligent system called "Eidos") as a method for solving the set tasks. As a result of the work, we propose a developed decision-making algorithm, which is applicable in intelligent control systems. The main conclusion of the work is that the proposed approach has successfully solved the problem
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05.13.18 Mathematical modeling, numerical methods and software complexes
DescriptionThis work continues the series of works written by the author on the application of modern scientific methods in the study of human consciousness. In 1979-1981, two monographs were written devoted to higher forms of consciousness, the prospects of man, technology and society. One of these monographs was two-volume and was called "Theoretical Foundations of the Synthesis of Quasi-Biological Robots." In these monographs the author proposed: 1) criterial periodic classification of 49 forms of consciousness, including higher forms of consciousness (HFC); 2) based on this classification, there were psychological, microsocial and technological methods of transition between various forms of consciousness, including methods of transition from the usual form of consciousness to the HFC; 3) information-functional theory of the development of technology (including the rule of improving the quality of the basis); 4) information theory of value; 5) 11 functional schemes of technical systems of future forms of society, including remote telekinetic (mental) control systems; 6) the concept of development of society in groups of socio-economic formations; 7) the concept of determining the form of human consciousness by the functional level of the technological environment; 8) mathematical and numerical modeling of the dynamics of the probability density of states of human consciousness in evolution using the theory of Markov’s random processes. In this study, we carry out a complete automated system-cognitive analysis (ASC- analysis) of the periodic criteria classification of forms of consciousness proposed by the author in 1978. To this end, the following tasks are solved in the work: cognitive structuring and formalization of the subject area; synthesis and verification of statistical and system-cognitive models (multi-parameter typification of forms of consciousness); systemic identification of forms of consciousness; their typological analysis; investigations of a simulated domain by examining its model. We have also given a detailed numerical example of solving all these problems
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PARAMETRIC TRINOMIALS WITH ALTERNATING GALOIS GROUPS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we construct polynomials of third, fourth and fifth degrees with Galois groups as and respectively. In addition, we give examples of polynomials different degrees with Galois groups isomorphic transitive subgroup of group , but calculations with help Maple show that Galois groups of this polynomials is . Also Polynomials with as Galois groups are shown
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FUNDAMENTAL THEOREM OF ARITHMETIC AND SOME OF ITS ASPECTS
01.00.00 Physical-mathematical sciences
DescriptionIn this article, we present the fundamental theorem of arithmetic and its role. We consider various rings for its performance