Headings of the journal
"Educational Resources and Technologies"

Annotation: The method of modeling combinatorial sequences using special sequences of tables consisting of positive integers is considered. These sequences are called T-models and are constructed recursively using special mappings. For T-models, q-analogues are introduced, which allow modeling the q-analogs of combinatorial sequences corresponding to them. Partially ordered sets and the corresponding T-diagrams are also defined. With the help of these partially ordered sets and T-diagrams, numerous additional properties of the simulated combinatorial sequences are considered. Examples of T-models of sequences of generalized factorials, Catalan numbers and Bell numbers are given. Their q-analogues and T-diagrams are constructed. This makes it possible to investigate also the properties of balloting numbers, Stirling numbers of the second kind and their q-analogues. The structure of T-models of combinatorial sequences makes it possible to use the well-known analytical calculation packages Mathematica and Maple in their modeling. Therefore, T-models can be used in teaching students to separate sections of discrete mathematics and computer science, as well as to obtain with their help combinatorial results.

Annotation: The paper proposes an approach to estimating the unknown constant parameters of the mathematical model of analog signals used in modern measurement systems. Accounting for the physical features of such models leads to equations of state in the form of Lagrange equations of the second kind. Further identification requires the construction of a residual functional, the minimum of which is provided by the actual values of the unknown parameters. The formulated task is the inverse incorrect according to Hadamard. Its solution is reduced to the search for a stationary point at which the minimum of the smoothing functional is provided. For this purpose, an apparatus for asynchronous variation of the trajectory and needle variation of the disturbance is used. The search for minimum conditions by the method of successive approximation to a stationary point, and then the invariant immersion method to a two-point boundary value problem leads to an iterative algorithm for identifying parameters. The effectiveness of the proposed apparatus is confirmed by numerical simulation in the MathCad environment, a comparison of the results obtained by estimating the unknown parameters of the analog signal model with the results of the Kalman filter demonstrates the advantage of this approach.

Annotation: The article analyzes the changes taking place in the world economy at the present stage of development, considers the key features of the fourth industrial revolution. Revealing the content of the main policy documents, the fundamental criteria for analyzing the development of the digital economy in the Russian Federation are formulated. Specific examples demonstrate the possibility of changing the nature of industrial and agricultural production with the proper use of information technology. The results of information analysis become in the new conditions a more valuable commodity than physical objects. The paper reveals the basic principles of closedloop Economics and justifies the need to expand information exchange at all levels of interaction. The stated facts show that information technologies create the Foundation for the construction of a circular economy that allows to solve the problem of improving the environmental safety of human civilization, making a real contribution to the conservation of natural resources, minimizing undesirable consequences of climate change, maintaining a comfortable living environment of the population.

Annotation: In many practical applications, it is not always possible to solve the problem of optimization of technical system characteristics under dynamic loading at a given degree of reliability, especially for the objective function of a large number of variables. When solving this problem for the created small series technical systems at the design stage, there are no data for a priori statistical analysis and, as a rule, it is not possible to determine the entire set of possible disturbing effects (destabilizing factors or loads) that can lead to abnormal situations. Obtaining approximate solutions makes it necessary to conduct additional tests of the technical system to clarify the limit values of the parameters, which is associated with significant costs. Therefore, improving the accuracy of determining the required values of the characteristics of the technical system at the design stage will reduce the number of tests. In this paper we propose a modified method of sthortest descent on the basis of its interface with the method of accelerated search. The proposed approach allows to reduce the number of iterations and, accordingly, the number of tests while maintaining the required accuracy of the technical system parameters and to increase the stability of the solution to the reliability management problem at the development stage.

Annotation: The problem of the efficiency of the recovery cycle management of a complex technical system is considered. In the process of operation of complex technical systems, failures of some elements occur, and the quality of the system as a whole deteriorates. At the same time, the nature of the costs of ensuring and restoring the quality of functioning of systems is antagonistic. For each specific system, it is necessary to study the relationship between the parameters of the recovery cycle and the indicators of the quality of its functioning in relation to the complex indicator of the economic efficiency of the system at all stages of its life cycle. The article deals with the evaluation and effectiveness of management of the recovery cycle of complex technical systems on the example of civil buildings. As it is known, in the housing sector, with constantly growing material expenditures for the technical operation of buildings, the quality level of their functioning changes very slightly. It is proposed to adapt and Supplement the modern efficiency management apparatus with the recovery cycle of complex technical systems, developed for high-tech sectors of the national economy for the operation of civil buildings, taking into account their features as non-productive systems with a very high social status. Priority additions, determining the effectiveness of management of the rehabilitation cycle of civil buildings, proposed to use indicators of frequency (repeatability) of adverse situations in users of buildings and a set of socially significant costs to ensure the quality of the functioning of the building for a long time. The proposed additions provide a theoretical basis for the applied methods of management of the recovery cycle of complex systems based on the probabilistic analysis of the existing methods of technical operation of buildings.