# mathematical model

## Advanced asymptotic approaches and perturbation theory methods in the study of the mathematical model of single-frequency oscillations of a nonlinear elastic body

A combination of asymptotic methods in nonlinear mechanics with basic techniques of perturbation theory to study a mathematical model of the nonlinear oscillation system is proposed in the paper.  The system under consideration describes the torsional vibrations of an elastic body, where its elastic properties are under the nonlinear law.  The relationships presented as the ordinary differential equations are obtained due to the proposed procedure.  Therefore, the main parameters of the single-frequency oscillations and the resonance conditions can be determined.  There are proposed applica

## Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement.

## Mathematical Modelling of Heat Transfer System of Convective Heating Surfaces of TPP-210А Steam Boiler

A mathematical model and the respective structural scheme of the convective heating surfaces of the TPP-210А steam boiler were developed as a system of interconnected heat exchangers. The interconnected convective heating surfaces are regarded as the convective heat transfer system of the boiler.

## Integral conditions in the inverse problems of heat conduction

Thermal processes of new technological methods of heat treatment (thermocyclic, electropulse) of metals and alloys are considered in the paper.  Mathematical models of the temperature field in a moving tape and a wire with cyclically acting pulsed heat sources are considered.  Based on these models, the formulation of inverse problems for homogeneous and inhomogeneous thermal conductivity equations is proposed.  For each case (internal, external heat source or a combination), the appropriate method for solving the inverse problem is proposed.  The integral condition of heat balance is used

## Mathematical model of electrical activity of biological network areas

In the paper, the mathematical model describing the generation of action potential and propagation of an impulse in the neuron's filaments on the basis of the analysis of parametric electriс circuits with distributed parameters and the mathematical model of synaptic interneuron connections are proposed.

## QUALITY STRUCTURING OF MEDICAL SERVICES BY DECOMPOSITION OF QUALITY FUNCTION

Quality medical care is an important indicator of the economic development of a country. Today, improving the quality of health care services is a priority for both health care institutions and the state as a whole. The development of methods and tools for continuous improvement of the quality of medical services promotes regulation, the perfection of those services, ensures the effective working of all the components together and the consistency and continuity of their provision, as well as help the staff to determine how to achieve the optimal level of care.

## THE IMPACT OF MICROWAVE RADIATION IN THE PROCESSES OF CARBON DIOXIDE ABSORPTION BY CHLOROPHYLL-PRODUCING MICROALGAE

The influence of microwave radiation on the rate of СО2 uptake by chlorophyll-producing microalgae of the Chlorella Vulgaris has been established. Experimental dependencies of greenhouse gases absorption by microalgae depending on the impact of microwave electromagnetic (MEM) field have been obtained. The mathematical model of the dynamics of biomass growth of Chlorella Vulgaris microalgae depending on the time of electromagnetic radiation has been constructed.

## Mathematical modelling and experimental determination of parameters of the guidance system of weaponry complex

The methodological approaches to the improvement of the control system of the vertical guidance mechanism of FM-21 multiple launch missile system to increasing its speed and positioning accuracy are confirmed. The use of the three-circuit positional structure of the control system of the guidance mechanism with a position control loop and a fuzzy corrector is justified. A mathematical model of the guiding package motion has been obtained and its reaction has been calculated.

## Switched Reluctance Motor With Energy Capasity Storage in System With Autonomus Limited Power Suppling

The article substantiates the expediency of using a capacitive storage in the circle of an electronic switch to improve the technical and economic performance of the switched reluctance motor. Such electromechanical converter is maximally simplest by design and construction, chip in technology side. It has good performance compared to simplest motor — induction, and, electric drive on the base of switched reluctance motor according to the regulating properties to drives with DC motors, that have unlimited distribution as know.

## Modeling of Steady-state Modes of the Electrical Network From the Synchronous Electric Drive of Hydraulic Loading

Pumping stations that provide fluid transportation by pipeline are significant consumers of electricity. Energy overruns due to sub-optimal modes of operation of individual high-power units or sub-optimal number of simultaneously operating less powerful units are quite significant and can have a significant impact on overall energy consumption. Energy overruns at pumping stations also lead to significant overruns in electricity grid elements.