## Mathematical Structures and Modeling ¹1(49)

 Mathematical Structures and Modeling. - Omsk : OmSU, 2019. ¹1(49), 129 p. ISSN (print): 2222-8772 ISSN (online): 2222-8799 For researchers, post-graduate students and senior students. Journal issue in one file

The Fundamental Mathematics and Physics

Group theoretical description of Seaborg table (an eight-periodic extension of the Mendeleev table) is considered in the framework of the Rumer-Fet model. The mass formula, which allows one to provide a termwise mass splitting of the basic representation of the Rumer-Fet group, is introduced. Masses of elements of the Seaborg table, beginning from atomic number $$Z=121$$ and finishing by $$Z=220$$, are calculated. A continuation of the Seaborg homology between lanthanides and actinides is establihed up to superactinide group.
Keywords: Seaborg table, Rumer-Fet group, unitary quantum system, mass formulas, homological series

The necessary and sufficient conditions for the validity of the local limit theorem for functions of dependent random variables is obtained. These conditions contain so-called minimal conditions of weak dependence.
Keywords: local limit theorem, symmetric functions of random variables, minimal conditions of weak dependence

The article investigates various essential spectra of minimum, maximal and intermediate ordinary differential operators in Lebesgue spaces of $$L^{p}$$ that are received by rather small indignations of differential operators with constant coefficients. These results allow to prove analogs of the classical theorem of Weyl.
Keywords: perturbation theory of operators, essential spectra, ordinary differential operators

Any program of mathematical justification comprises rational and irrational assumptions. Philosophical and methodological problems of modern mathematical formation of different severity level allow rational justification or an explanation of mathematical statements.
Keywords: mathematical education, the problem of substantiation of mathematics, rationality in mathematics

Applied Mathematics and Modeling

R.Yu. Galimov, A.M. Akhtyamov
Identification general boundary conditions of the diffusion operator

The problems of identification of both general and separated boundary conditions of the diffusion operator by its eigenvalues are investigated. For general boundary conditions it is shown that if at least one of the coefficients in the differential equation is asymmetric function, then the problem of identifying boundary conditions by all eigenvalues has two solutions, and if both of the coefficients are symmetric functions, then the problem of identifying the boundary conditions over all there are infinitely many solutions to the eigenvalues. It is also proved that if at least one of the coefficients in the differential equation is an asymmetric function, then two solutions can be obtained by four eigenvalues, if the rank of some matrix is four. For separated boundary conditions it is shown that if at least one of the coefficients in the differential equation is an asymmetric function, then the problem of identifying boundary conditions by all eigenvalues has a unique solution, and if both of the coefficients are symmetric functions, then the problem of identifying boundary conditions has two solutions. It is also shown that under certain conditions a unique solution can be obtained from three eigenvalues, and two solutions by two eigenvalues. Appropriate examples are considered.
Keywords: Diffusion operator, identification of boundary conditions, inverse eigenvalue problem, eigenvalue problems

An algorithm for filling data gaps on the basis of restoring the vector of object indices from the factorial data structure, calculated with penalty method, is developed. Data gaps and the corresponding factor model equations for individual objects were not taken into account in the optimization criterion for residuals of the factor model equations. That allows to reliably estimate the values of data gaps. A numerical experiment confirming the operability of the algorithm is carried out and a program with an interface that allows the user to upload new data is created.
Keywords: factor analysis, penalty method, hypertension

Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Detecting At-Risk Students: Empirical Results and Their Theoretical Explanation

In teaching, it is very important to identify, as early as possible, students who may be at risk of failure. Traditionally, two natural criteria are used for this identification: poor grades in previous classes, and poor grades on the first assignments in the current class. Our empirical results show that these criteria do not always work: sometimes a students deemed at-risk by one of these criteria consistently succeeds, and sometimes a student who is not considered at-risk frequently fails. In this paper, we provide a theoretical explanation of our quantitative empirical results, and we use these results to provide recommendations on how to better detect at-risk students.
Keywords: teaching, detecting at-risk students, predicting student grades

Computer Science

Proposed model of synchronous processes in which mathematical formulas and ratios that allow calculations of optimum ratio of Exchange processors and channel light amounts of computations, solve Xia task of minimizing time unproductive downtime CPUs and channels, optimizing the number of blocks and Exchange accounts, where the minimum value of the total execution time of all processes is reached. This, in turn, is the starting point when designing the system and applications.
Keywords: multiprocessor systems, processors, peering, synchronous processes, optimization problems

Information Security

N.F. Bogachenko, A.V. Filippova
Ranking of Permissions on the Basis of Analysis of Roles Hierarchy in Access Control Models

The term "severity level of permissions"\ is introduced for the probability estimation of the permissions leakage in the role-based access control policy. The postulates which define the dependence of severity levels of permissions on the structure of the role hierarchy are formulated. The technique (method and algorithm) of automatic calculation of severity levels of permissions is suggested, using analytic hierarchy process. The computing experiment which reveals the dependence of severity level of permission on the algorithm's parameter is made. The algorithm's parameter allows regulating the influence of postulates on results of calculations.
Keywords: roles, permissions, redundancy, severity level, analytic hierarchy process

The article deals with the method of formation of the structure of the functions of an automated information security management system. The essence of the technique is to build a model of information security problems Z, reflecting their dynamics and the relationship between the tasks of information security, as well as the situation of coincidence of tasks on the whole set of tasks of information security, and on this basis, the structure of the functions of the automated control system by setting in accordance with each task of information security and each pair (set) of matching tasks of information security corresponding to them functions of the automated control system.
Keywords: significant objects of critical information infrastructure of the Russian Federation, information security system, frames, growing pyramid networks

A.K. Guts, O.V. Matushina
The Program That Simulates Network Attacks on Computers

The purpose of the article is to present a computer program that simulates the operation of a computer network, and also demonstrates the results of using some network vulnerabilities by an unfair user.
Keywords: computer network, network attacks, network vulnerabilities, network attack imitation