Описується математична модель нейронної схеми типу «K-winners-take-all» (KWTA), призначеної для ідентифікації К максимальних серед N невідомих сигналів, де $1≤K<N$. Аналізується обробка моделлю постійних дискретизованих вхідних сигналів. Розглядається випадок рівних між собою вхідних сигналів. Наводяться відповідні результати комп’ютерного моделювання.
The study of transverse oscillations of systems moving along their axis is a very difficult, but at the same time a very important task. Mathematical models of nonlinear transverse oscillations of a beam moving along its axis are analyzed in this paper work, both for non-resonant and resonant cases. The task becomes even more complicated if we additionally take into account the method of fastening the ends of the beam or the perturbation at its ends. We have obtained dependencies that can be used in construction, transport, industry, mechanical engineering and other
This paper presents a new SIRS mathematical model describing the evolution of an infectious disease, assuming that the spatial supports of this infection are also evolutionary and obey a compartmental model. We propose four control strategies to manage the spread of the disease among individuals and regions. The Pontryagin maximum principle is employed to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are conducted to validate the theoretical analysis using MATLAB.
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.
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
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
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.
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.
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.
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