APPLIED MATHEMATICS
AND CONTROL SCIENCES

The production of any multilayer structure begins with the development of technological documentation, which describes, among other things, the temperature regimes during their manufacture. Conventionally, the temperature process of polymerization can be divided into three stages: preheating, temperature stabilization and cooling. The paper presents the results of a numerical calculation of temperature fields in a multilayer composite structure with a honeycomb filler during its manufacture by autoclave molding at the preheating stage. This method of manufacturing composite structures makes it possible to mold parts of varying complexity and dimensions, the demand for which is growing in such industries as mechanical engineering, aircraft building, and shipbuilding. The requirements for the quality of such products are increasing, which is greatly influenced by compliance with the temperature regime during molding. Conducting direct experiments requires large energy costs, therefore, to solve the problem of controlling heat exchange processes inside the structure, mathematical models were developed that describe these processes. A non-stationary heat conduction problem is formulated for a multilayer unbounded plate with a constant initial distribution, boundary conditions of the third kind on the outer boundaries, and boundary conditions of the fourth kind on the contact surfaces of the layers. Using the finite element method, the problem is reduced to three-point difference equations, the solution of which is found by the sweep method. The determination of the sweep coefficients is shown taking into account the thermal characteristics of the layers. The results of a numerical calculation of the temperature distribution for a nine-layer composite structure with a honeycomb core are presented. The numerical calculation was carried out using the developed program in the BorlandDelphi 7.0 object-oriented programming environment. The results obtained are presented in the form of graphic dependences of the temperature over the thickness of the sample at different points in time, as well as the dependence of temperature on time at various nodes of the sample in comparison with the theoretical curve. An analysis of these dependences was carried out, which showed that the heating of the sample occurs unevenly over its thickness. The deviation from the theoretical temperature values is observed in the layers located closer to the honeycomb layer. This can adversely affect the course of the polymerization step, which is characterized by the conversion of the binder into a polymer, and occurs at certain temperatures. Therefore, achieving the desired temperature values at the stage of heating the structure is important for the manufacture of reliable and durable structures that can withstand extreme operating conditions. The obtained temperature distributions make it possible to correct the technological process of manufacturing various multilayer structures at the stage of its development, which will reduce the economic costs of production.

Scoliosis is the most common orthopedic disease in children, which most often leads to disability. An urgent task of the current stage of the development of spinal deformity diagnostics is the search and introduction of new available methods of non-invasive safe diagnosis of spinal deformity at early stages, since existing diagnostic methods can detect spinal column deformity in three planes during the development of scoliosis, however, they have a number of limitations for use, since either X-ray radiation or diagnostic installations are used for their implementation, requiring complex installation in a separate room and training of operating personnel. In this regard, there is an urgent need to develop digital tools for the diagnosis of spinal deformity, which would neutralize these difficulties in clinical practice. The aim of the study was to develop a mathematical algorithm for identifying the deformation of the spinal column in the horizontal plane according to the photogrammetric evaluation of a three-dimensional model of the surface of the human back, which was obtained from the results of the operation of the original software for a personal telecommunications device. The algorithm for assessing spinal column deformity is a sequence of four stages: reposition of the coordinate system, stratification of the spine line into segments, calculation of the rotation of V-segments, separation of the V-segment ratios to the physiological bends of the spine and visualization of spinal deformity in the horizontal plane. The developed algorithm has a number of advantages compared to those developed earlier: it allows to identify the rotation of individual vertebrae and torsion of the spine as a whole, is implemented in relation to all vertebrae of the thoracic and lumbar spine, thereby providing the possibility of differentiated diagnosis of forms of spinal deformity - from posture disorders to scoliosis. The described algorithm is a separate part for modular software that allows diagnostics of spinal column deformity using a personal telecommunication device. This algorithm can be used in a comprehensive assessment of posture disorders and scoliosis, monitoring the dynamics of spinal column deformity in the rehabilitation process.

The article considers the problem of forming an integral indicator for evaluating the effectiveness of management in terms of ranking factors by their informativeness based on mathematical methods of pattern recognition. Since in the modern realities of the crisis, pandemic and other socio-political challenges, medical issues are becoming more and more relevant, it is proposed to take a more qualitative approach to assessing the effectiveness of management in this area. Assumptions are made about an integrated approach to the development of such an assessment that would cover the entire pool of necessary indicators. However, there are difficulties on this path, because in this case there will be many factors; with such a volume of data, calculations are difficult even with the available computing power. It is assumed that some of the parameters can be discarded, but the question arises: which are really less important, and which are simply necessary. To do this, it is proposed to use an algorithm to identify the most informative factors, as well as to use an integral evaluation indicator. The whole procedure for constructing an integral indicator for evaluating the effectiveness of management is divided into several parts. The most important part is the choice of informative factors. It is proposed to consider factors as some vector, with a priori weights found in a certain way. From a mathematical point of view, informativeness is proposed to be understood as the average distance between certain quantities. Then, with the help of the majority committee, the problem of pattern recognition is directly solved. At the same time, a question arises regarding the construction of the majority committee itself, and the main drawback of this approach is also indicated. The Seniority Committee is not considered in this case because of its inefficiency. To eliminate all the vulnerabilities, it is proposed to solve the problem of constructing a separating majority committee for sets by modifying the N. Nilson linear correction algorithm, which is the novelty of this method. This modification makes it possible to build the necessary dividing majority committee for the set, which subsequently leads to the choice of informative factors. The algorithm for selecting the most informative indicators is carried out for each enlarged group of factors. After its implementation, we get a certain number of indicators, much smaller than they were at the beginning, while the question of assigning weight to each factor remains open. To solve this problem, the authors propose the use of expert assessments. Thus, within each enlarged group of indicators, we get the sum of indicators with weighting coefficients, from which an integral indicator of the effectiveness of the management of a medical organization is already obtained.

Constant changes in the number of inspectors of the supervisory activity units of the Ministry of the Russian Federation for Civil Defence, Emergencies and Elimination of Consequences of Natural Disasters, both by reducing and increasing, have led to the need to search for and assess the significance of factors affecting the staffing structure of the units. In addition, for personnel decisions, it is necessary to conduct a retrospective analysis of changes in the number of staff units of the supervisory activity units of the Ministry of Emergency Situations of Russia, as well as the level of correlation (Pearson correlation) of the number of units with the main indicators of the activities of supervisory authorities: the number of inspections, objects of supervision, fires, the number of people killed and injured in fires. Aim of the study: to identify statistically significant factors influencing the regulation of the staffing of the supervisory activity units of the Ministry of Emergency Situations of Russia, to determine the level of correlation between these parameters, as well as: the number of objects of supervision and the number of actually conducted scheduled inspections; between the optimal number of inspections and the number of actually conducted scheduled inspections. Research method: the assessment of the level of influence of factors was carried out by the method of correlation analysis of statistical data on the main indicators of the EMERCOM of Russia in the period from 2011 to 2021. Results: the calculation of the optimal (evenly distributed over the years) number of inspections was made; the conclusion was made that there was no statistically significant relationship between the main performance indicators and the number of inspectors; the level of correlation between: the number of objects of supervision and the number of actually conducted scheduled inspections; between the optimal number of inspections and the number of actually conducted scheduled inspections. Practical significance: the results can be used to study the personnel potential and develop a methodology for calculating the optimal number of inspections for a specific department of supervisory activities of the Ministry of Emergency Situations of Russia.

In line with the fundamental reform of the Russia administrative legislation, this article discusses the synthesis of a geoinformation system for preventive management of the full cycle of production on affairs about administrative offenses. According to the Anokhin - Sudakov's theory of functional systems, the tasks of forming a structural image and synthesizing a mathematical model to manage the administrative process stages, as well as the tasks of substantiating the mathematical criterion and its structural and functional implementation to prevent violations of a reasonable time in production on affairs about administrative offenses, were set. According to the law of management object integrity preservation, it is obtained that the opposing side of the administrative conflict counteracts by the joint use of protective (geoinformation), target (enforcement) and providing (geolocation) management subsystems, each of which generates a different contribution to efficiency at the next stage of the administrative process. To create a mathematical model for making a managerial decision, adequately formalized for each stage of the administrative process, a natural-scientific approach to the synthesis of management in conditions of limited resources was used. An analytical dependence is determined, that integrates the functioning regularities of law enforcement, geoinformation and geolocation components of the management system at the stage of administrative practice. When concretizing it, the possibility of representing administrative production by Poisson transitions of the affairs flow about administrative offenses between the states of the administrative process stages in a continuous Markov chain is used. Through modeling a Markov chain by the Kolmogorov - Chapman's equations system the criterion of preemptive management existence of the administrative process stages complex is revealed, allowing under proper efficiency of administrative production to optimize the intensity of identification and neutralization of threats to ensure a reasonable time in the target, protective or providing subsystems of management. The structure and functionality of probabilistic transitions of the affairs flow about administrative offenses, including management procedures, in a Markov chain of administrative production are established by their network modelling based on accumulated observations of administrative statistics. Numerical studies of a synthesized model of preemptive management of administrative production have clarified the effects of disruption of transition processes between states of administrative practice on its efficiency.