# mathematical model

## CONSTRUCTION OF A MATHEMATICAL MODEL OFAN UNBALANCED VIBRATING SEPARATOR ON A SPRING SUSPENSION

In the article, a mathematical model of the oscillating motion of a vibrating separator is constructed. The methods of nonlinear mechanics and the calculation scheme of the vibration separator with an eccentric and a spring suspension, which is presented in the form of a flat mechanical system with four degrees of freedom, were used for its construction. The amplitude of oscillations of the vibration separator capacities in the vertical plane is greater than the amplitude of its oscillations in the horizontal plane.

## Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment

In this article, we propose a discrete mathematical model which describes the propagation of the drug phenomenon in a human population.  The population is unscrewed in five compartments: "$S$" People likely to become drug addicts, "$M$" Moderate drug addicts, "$H$" Heavy drug addicts, "$T$" People receiving drug addiction treatment, "$R$" The recovered people who have completely abstained from drug addiction.  Our goal is to find a better strategy to reduce the number of heavy addicts and to maximize the number of people receiving full treatment.  The tools of optimal c

## Optimal control strategy for the administration of the third vaccine dose in the treatment of pandemic COVID-19

In this paper, we propose a mathematical model of COVID-19 infection, taking into account the division of the population according to vaccination criteria.  Our goal is to demonstrate the positive effect of receiving the third dose of the Corona vaccine.  We proposed two strategies to limit the spread of the COVID-19 pandemic respectively awareness programs on the importance of the third dose of the vaccine and the delivery of treatment to infected individuals who have health problems.  Pontryagin's maximum principle is applied in order to characterize the optimal contr

## Determination of parameters of magnetically coupled coils based on mathematical models of their magnetic circuits

Calculation of electromagnetic parameters of static and dynamic magnetically coupled inductors based on mathematical models of their magnetic circuits is proposed. The inductance and mutual inductance of such coils are determined using the geometric dimensions of the coils themselves, their relative location, and the physical parameters of the environment.

## Mathematical modeling of the efficiency indicator of the functioning of the transport and production system in the conditions of the quarry of a metallurgical enterprise

The study of the operation of quarry vehicles made it possible to form the target function of the study, taking into account the criterion of the efficiency of all processes of the system, which provides for the reduction of costs for the operation of the transport and production system of the quarry of a metallurgical enterprise, namely, the subsystems: “Incoming raw materials”, “Processing of raw materials”, “Sales of raw materials”. Factors influencing the cost indicator are highlighted.

## Organization of passenger rail transportation on the section with the combined track Nyzhankovychi- Starzhava

Passenger transportation by rail is an important component of ensuring cross-border cooperation between our country and neighboring EU countries. Transport transformations are being carried out on both sides of the border, and directives are being developed and implemented to establish uniform rules and standards for the successful operation of transport and passenger movement. At the same time, the organization of traffic is being improved, taking into account the features of the infrastructure, as well as changes in traffic flows, in particular passenger flows at border areas.

## Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage.  The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated.  By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained.  Also, we propose an optimal strategy to implement the optim

## Mathematical model of magnetic state of single-phase commutator motor

Single-phase commutator motors (SPCM) with sequential excitation have a simple design and low cost, and therefore promising for use in the drive of household appliances and electric hand tools. This necessitates the creation of mathematical models of SPCM, which would allow both the development of new and modernization of existing models of such motors. The aim of the article is to create an engineering mathematical model of the magnetic state of SPCM using circular methods.

## Development of a Mathematical Model for Obtaining Energy Characteristics of the Turbine Unit with the K-325-23.5 Steam Turbine

The results of mathematical modelling of the turbine unit with the K-325-23.5 steam turbine are presented. The mathematical model of the turbine is a system of equations for the components of the heat-balance diagram and the main dependencies of its operating characteristics obtained through the thermal full-scale tests. The developed mathematical model allows adjusting the results of the full-scale tests, creating normative characteristics and conducting research of the intermediate modes of the turbine operation.

## The use of cellular automata in the simulation of wood drying processes in a wood drying chamber of periodic action

In this work, research the essence of the wood drying process in a periodic wood drying chamber. This paper provides a mathematical model of a wood drying chamber, which describes the general essence of physical drying processes using the equipment available in the wood drying chamber. This approach allows to take into account the physical parameters of the necessary equipment, such as heaters, fans, humidifying nozzles or other. This approach also allows to ignore some design characteristics that may differ depending on the type of wood drying chamber.