# mathematical modeling

## Wave processes in the constructions of mechanisms and buildings

In the article a methodology for researching wave processes in weakly nonlinear homogeneous one-dimensional systems – elements of machine and building structures is proposed. It is based on D'Alembert's method  of constructing solutions of wave equations and the asymptotic method of nonlinear mechanics. Resonant and non-resonant cases are considered. In the non-resonant case, the influence of viscoelastic forces and small periodic disturbances on the oscillatory process is taken into account.

## Control of mathematical modeling process of dynamics of harmful substances concentrations on the basis of ontological approach

The problem of building a mathematical model of the dynamics of nitrogen dioxide concentrations at different parts of the city is considered in the paper. The peculiarities of the construction of such models on the basis of periodic measurement of concentrations of harmful substances and identification on the basis of the measurements obtained are considered.

## Study of two species prey–predator model in imprecise environment with harvesting scenario

This study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting.  We study a non-linear model of prey–predator growths in two species.  The proposed model is supported by theoretical and numerical results.  Some numerical descriptions are provided to help our analytical and theoretical conclusions.  For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method).  We also used MATLAB coding to compare our approxi

## Mathematical Modeling of Transition Processes in the High Voltage Transmission Line in Short Circuit Modes

The article analyzes the publications, which shows that two approaches to the analysis of transients in long power lines with distributed parameters are popular today: based on simplified methods of solving the equation of a long line, or equivalent to the known equation of a long line by circuit substitution schemes. In applying the first approach, the authors do not take into account the running resistance, phase and interphase conductivities, calculating the usually mentioned processes by the known methods of D’Alembert and “wandering waves”.

## Mathematical modeling of Leptospirosis spread in Malaysia

Leptospirosis is a zoonotic disease that is caused by the pathogen Leptospira, and it can spread indirectly or directly from infected animals to humans.  According to the official statistics from the Malaysian Ministry of Health, leptospirosis outbreaks appeared to be in the most critical condition in the recent few years.  The Susceptible--Infected--Recovered compartmental model and its extensions have been applied widely in disease modeling.  This paper aims to present a compartmental model for leptospirosis spread in Malaysia.  Using this approach, an epidemiological model is formulated

## Mathematical Modeling of Transients Processes in Three-phase Transmission Line in Two-phase Short Circuit Mode

The article analyzes scientific publications, which showed that for most part of the study transients processes in the long power lines with distributed parameters is carried out by equivalent to the known equation of a long line with distributed parameters by a circular equivalent, or solve this equation using simplified approaches. These approaches require deterministic boundary conditions to the long line equation, which is not always possible when modeling transients processes in electrical networks.

## Application of a Fuzzy Particle Filter to Observe a Dynamical System States in Real Time

One of the key problems in the implementation of closed-loop control systems is to measure all states of a dynamic system, especially, when there are severe environmental conditions. Consequently, the use of certain types of sensors is impossible for technical or economic reasons. Also, in electromechanical systems, there are a lot of values that cannot be directly measured by physical sensors. Thus, mathematical algorithms named as observers and estimators are in use to calculate the states of the dynamic system utilizing math model and available set of sensors.

## Mathematical modeling switching electromagnetic processes in the long power line in the automatic reclosing cycle

The article analyzes scientific publications, who showed that for the most part, the study of switching transients in electrical networks during automatic reclosing cycles of circuit breaker, are carried out without taking into account the influence of electromechanical processes in the mechanisms of circuit breaker contacts, despite the fact that the speed of their course is commensurate with the speed of the electromagnetic processes.

## Real-time Mathematical Modelling of Asynchronous Generator With Voltage Inverter in Rotor Circuit

The mathematical model of an electromechanical system with an asynchronous generator with rotor’s current regulation by frequency converter with an autonomous voltage inverter controlled by current controllers has been described in the article.

## The Scheffe’s method in the study of mathematical model of the polymeric hydrogels composite structures optimization

Mathematical modeling of 2-hydroxyethylmethacrylate with polyvinylpyrrolidone copolymerization process according to technological parameters of the exothermic reaction has been carried out by Scheffe’s simplex-lattice planning method.  Optimization of polymer monomer composition formula has been carried out and the regression equations of the main parameters of exothermic polymerization –– gelation time, the duration of the gel effect area, and the maximum temperature of the exotherm have been obtained.  Using the mathematical model obtained, the content of the initial composition has been