## Modeling the estimate of the volume of recreational fishing based on the Bayesian approach

Mathematical Modeling, Vol. 6 (2022), Issue 3, pg(s) 92-95

In this paper we consider the task of estimating the volume of recreational fish catch yield in a water body. We design mathematical models for the tasks varying in complexity and generality and demonstrate how they can be solved using Bayesian approach. A Markov Chain Monte Carlo (MCMC)-based Bayesian approach is widely used as a solution for stochastic models. To solve the simplest case of a proposed model we have used the PyMC library. The proposed models were later used to estimate the recreational fishing capacity of the water bodies in Qazaqstan.

## Theoretical investigation of the removal of halfrums from sugar beet root heads

Removal of the haulm from the heads of sugar beet to the roots during their harvesting (cutting the main mass) or separation of its residues (when finishing the heads) is a complex technological process associated with either a significant loss of sugar-bearing mass (low cut), or not complete removal of residues (high cut), which significantly degrades the quality of root crops. Therefore, ways to find a complete removal of haulm and its residues from the heads of root crops require research and development of such devices capable of performing this process qualitatively. However, first it is necessary to determine theoretically and experimentally the basic initial conditions under which high quality indicators will be achieved, and losses of sugar-bearing mass during cutting the haulm will be minimal, with the remaining haulm being as small as possible (or they will be absent at all). This paper theoretically and experimentally investigates and determines the loss of sugar mass and remnants of the bud on the heads of sugar beet roots during the separation of the bud and its remnants. It is established that in the interval of working heights of a cut which is equal to 20 … 60 mm deviation of theoretical calculations from experimental does not exceed on the average 1%.

## Features of modeling of ultralow power electric fields

Mathematical Modeling, Vol. 5 (2021), Issue 1, pg(s) 31-35

The article presents the results of modeling quasi-stationary ultralow power electric fields (the order of tens of nanowatts) and establishes ranges of rational values of parameters (average density of electric voltage, specific potential) of these fields. As a result of mathematical modeling (based on a system of Gaussian equations) and subsequent numerical experiment, it is shown that an instantaneous increase in the average electric density of a quasi-static electric field in 2 times in one part of the field leads to an increase in charge redistribution time from 34 ns (at an initial density of electric tension of 17 nN/Ku.μm 3) to 189 ns (at a density of electric tension of 145 nN/Ku.μm3). This redistribution allows us to determine the range of rational values of the specific potential, which is 1.1… 9 nV/μm 2. In this case, the maximum specific power that can occur in such a field is 0.5… 0.77 nW/μm 2.

## On the question of the rational distribution of power between the hydrostatic and hydrodynamic branches of the complex steering mechanism for the tracked vehicle

Mathematical Modeling, Vol. 5 (2021), Issue 1, pg(s) 17-20

The article presents a description of the mathematical model of the curvilinear movement of a tracked vehicle with a complex steering mechanism, which contains a control hydrostatic branch and an additional hydrodynamic branch for unloading the first. The adequacy of the presented mathematical model was verified by calculating the characteristics of the turn in place of the Leop ard-2 tank. The resulting tool can become the basis for parametric optimization of similar steering mechanisms for tracked vehicles.

## Construction of a new calculation mathematical model of the vibration process of excavation of the root body from the soil, taking into account its elastic damping properties

The equation of shock interaction of the vibrating digging working body with the body of the sugar beet root, fixed in the soil, which occurs in the process of vibratory digging of the roots, is made. Based on the shock interaction equation, the shock pulse and the maximum shock force that occur during this interaction were determined, which allowed to further assess the degree of damage and knocking out of root heads in the process of vibration digging of sugar beet. From the conditions of non-damage of root crops the expression for definition of admissible frequency of fluctuations of the vibrating digging working body taking into account its design parameters and translational speed of movement of the beet harvester is received. Based on the obtained equations describing this process, the optimal values of the kinematic and structural parameters of the working plow for vibration digging of sugar beets are found.

## Synthesis and design of hyperboloid gear drives: Methodology and aspects

Machines. Technologies. Materials., Vol. 13 (2019), Issue 7, pg(s) 285-290

The high current requirements for the characteristics determining the accuracy, reliability and efficient manufacturing of modern machines, apparatus and devices applicable in various fields of industry and transport in a big extend dictate the applied scientific methodology to the technological synthesis, design and production of gears. In the processes of synthesis and design of the different types of gear transmissions, the designer faces an extremely complex set of questions to solve, which together define the desired optimal construction.
In this case, an optimal design means a gear transmission that is capable of delivering preliminary defined kinematic and / or strength requirements at minimum design, production and operation costs (including the repair costs during their exploitation). This work presents a review of the methodology, developed by the authors, oriented towards the synthesis and design of spatial gear mechanisms (hyperboloid gear drives), realizing rotations transformation between crossed shafts. The main principles, on which the construction of adequate software programs are based for the synthesis of treated transmissions, are presented.

## Research on characteristics of failures flow according to the maintenance and repair strategy

In the practice of repairing the machines in agriculture, the following strategies are mainly applied: forced repairs; conducting repairs in plan order and a combined strategy with elements of both strategies.
An investigation was carried out and analytical dependencies were obtained to determine the function of the recovery (characteristic of the failure flow) of the machine components in the forced repairs (after failure), to carry out repairs in a planned order and a combined strategy with elements of the first two strategies to calculate the required pool of spare parts to maintain machine performance.

• ## On a mathematical model of land-use change

Mathematical Modeling, Vol. 2 (2018), Issue 4, pg(s) 153-155

The paper is devoted to a mathematical model of land-use change proposed by Dobson et. al. We formulate and investigate some quantitative properties of the corresponding Cauchy problem. We construct a numerical algorithm for approximate solution of the problem and present some of the numerical results. Their meaning is explained and discussed.

• ## Development of methods for calculating the nonequilibrium phase transformations during the condensation of supercooled steam in the turbine flow path

Methods for calculating the nonequilibrium phase transformations during the condensation of supercooled steam in the turbine flow path are developed. In the process of realization, the development of the classical Zel’dovich-Frenckel’s theory for the case of nonstationary nucleation of a new phase with fast extensions of supercooled steam is considered. A numerical-analytical method for calculating condensation was designed and implemented in the form of a software package, which consistently takes into account the nonstationarity of the process. Numerical studies have shown high efficiency and accuracy of the method.

## A SOLID BODY SURFACING MATHEMATICAL MODEL IN STRATIFIED INCOMPRESSIBLE FLUID UNDER THE ACTION OF BUOYANCY FORCE AND LIMITED MOTION CONTROL

Industry 4.0, Vol. 3 (2018), Issue 3, pg(s) 109-111

This paper results are based on the mathematical model of the motion control of an autonomous solid body in stratified incompressible fluid which was presented by the authors at XII MTM Congress held in September 2015 and XIV MTM Congress held in September 2017. This paper presents an analytical mathematical model of a solid body, which surfaces in stratified viscous incompressible fluid, a difference scheme and its solution. The body is equipped with controlled rudders, wings of finite span, and does not have its own propulsion system. It is moved by the influence of the buoyancy force and wings lift effect. This body motion is considered to be planeparallel motion. The mathematical model synthesis is based on the hydrodynamic equations.

## MATHEMATICAL MODELING AND SIMULATION OF POWER UNIT WORKING ON MOTOR FUELS DERIVED FROM NATURAL GAS IN TOTAL LIFE CYCLE

Industry 4.0, Vol. 3 (2018), Issue 2, pg(s) 69-72

The article is devoted to the problem of comprehensive evaluation of the efficiency of the use of various alternative fuels obtained from natural gas (NG) in a total life cycle (TLC). Despite the fact that all types of motor fuel under consideration are produced from NG, the energy and environmental consequences of their use may vary significantly. Goals of this research are: developing TLC mathematical models of a power unit operating on motor fuels obtained from NG (compressed NG, liquefied NG, methanol, dimethyl ether, synthetic diesel fuel and hydrogen) and conducting a simulation in order to determine energy and environmental indicators for the use of the considered fuel types. The results of simulation allow to choose the most promising types of alternative fuels according to the criteria of energy efficiency and a level of environmental pollution by harmful substances and greenhouse gases.

## ILLUSTRATION OF MODEL CREATION ON EXAMPLE OF APPROXIMATIONS TO THE STEADY STATE CURRENT OF CHEMICAL CYCLIC PROCESSES

Mathematical Modeling, Vol. 1 (2017), Issue 3, pg(s) 159-162

An approach for creation of biophysically based models for the steady state current of cyclic processes is investigated. When the process (like chemical reactions) can be described by a system of linear ordinary differential equations, an analytic expression for its steady state exists. The analytic expression is especially simple for the current of single cycle processes. In biologic context, concentrations of many substances change in a very restricted (patho)physiological range. This allows neglecting some terms of the analytic expression and thus obtaining biophysically based models that are both simple and adequate for description of currents produced by enzymes, pumps or transporters. The approximations obtained could be reduced to the existing empirical models. A clear way of expanding a specific empirical model for obtaining the desired quality and range of validity is also represented. The described approach is general and can be useful for creating biophysically based models of other types of processes.