Mathematical Package Mathcad Research Articles

Features of the Electrical Properties of Limited Diffusion Semiconductors in Contact Measurements

The purpose of this work is to study the features of the electrical properties of bounded semiconductors, as well as the effect of the inhomogeneous distribution of impurities in anisotropic semiconductors on the structure of electric fields with standard methods of contact measurements.Diffusion and ion-doped semiconductor structures, as well as composite structures with misalignment of film and substrate lattices, are currently a promising class of materials in micro- and nanoelectronics. The introduction of an impurity into a semiconductor crystal sample changes its electrical properties, which makes it possible to reduce the size of individual components of the chip, while maintaining or increasing their power.Methods. The results of the work are based on the known dependences of the distributions of impurities during diffusion alloying. To calculate the potential distribution, the Fourier method was used, which made it possible to solve the Poisson Equation with Neumann boundary conditions without approximations. The mathematical package MathCad was used to analyze the obtained expressions characterizing electric fields in inhomogeneous semiconductors.Results. A technique for solving the boundary value problem for the potential in bounded diffusion semiconductors is presented. Expressions in the form of series of analytical functions for the distribution of electric potential in conducting anisotropic structures are presented. The constructed models make it possible to determine and qualitatively describe the distributions of electric fields during probe measurements and to investigate their structure in diffusion semiconductors. Conclusion. On the basis of computer modeling, the importance of taking into account the parameters of inhomogeneity of conductivity is shown. The effect of concentration of current density lines in diffusion semiconductors is shown and quantified.

Using applied program packages in determining optimum cutting modes

Purpose. Comparison of the functionality of application program packages when determining optimal cutting modes during mechanical processing. Creation of a mathematical model with technological limitations when boring a shaft in one pass and carrying out calculations. The methods. Research methods were based on the principles of optimization of cutting processes, the theory of cutting and cutting tools, standard methods of determining correction factors were used when creating technological limitations. The smallest machine processing time is chosen as the objective function. Using the functionality of the mathematical package Mathcad and the "Turning optimization" program. Findings. The created mathematical model of turning optimization sufficiently fully describes the machining process. The difference between calculations by two methods is no more than 10%. The functionality of the application programs is enough to determine the optimal parameters of the cutting modes - the number of revolutions of the machine spindle and feed. In addition, when using the Mathcad package, it is possible to add or remove technological constraints. Without a suitable database of correction factors, the search and calculation process is complicated. On the other hand, the "Turning optimization" program works in automatic mode, you only need to enter the initial data. But it is impossible to change the technological limitations, the insufficient number of standard materials of cutting tools and parts. The originality. A mathematical model of optimization of cutting modes when boring a shaft to a pass with corresponding technological limitations was created and investigated. A comparison of application program packages was carried out when determining the optimal cutting modes. Advantages and disadvantages of application programs are defined. Practical implementation. The proposed mathematical model of optimization of cutting modes during turning allows to determine the optimal parameters of the number of revolutions and feed of the machine. Its use will greatly facilitate calculations carried out by designer-technologists when designing technological routes for processing parts and calculating cutting modes. This will significantly reduce production preparation time, especially when using CNC machines.

USE OF NEURAL NETWORKS FOR PLANNING THE CORRECT SELECTION OF PLANT AND SOIL SAMPLES IN PRECISION AGRICULTURE TECHNOLOGIES

The article is devoted to the study of the use of neural networks to optimize the selection of plant stands in precision agriculture technologies. The study takes into account the complex aspects of sample selection, such as the speed of image acquisition, the effectiveness of assessing the state of mineral nutrition and soil moisture, etc. This data is a necessary component for precision farming technologies and, in particular, crop management. Research was conducted on production fields in 2019-2020 in Boryspil district of Kyiv region. Spectral studies were performed using the Slantrange 3p complex installed on the UAV. Data processing was performed both with the specialized software for spectral data Slantview and with the mathematical package MathCad. The assessment of the nature of the distribution of both individual spectral channels and their combination in the form of vegetation indices turned out to be unprepared for the identification of uneven water supply of areas. The red channel and its derivatives turned out to be the most promising in the direction of identifying the water supply of wheat. The use of neural networks made it possible to identify probable areas with increased water supply on the maps of the distribution of vegetation indices in the field. The duration of identification using neural networks will not interfere with the sampling procedure, so that such a procedure can be effectively implemented in agronomic practices. Therefore, the use of neural networks allows you to automate and increase the accuracy of selection, improving the quality of the analysis of plant stands, subject to compliance with soil sample evaluation technologies. The obtained results indicate the prospects of implementing this approach in modern agriculture.

Mathematical programming in Mathcad and Mathematica

An article generalizes the long-term work of authors with packages of applied mathematical programs. It discusses and demonstrates the features and methods of solution of mathematical tasks in mathematical package Mathcad and Mathematica: from the simplest ones, included in the set of typical problems of mathematical disciplines for training specialists for shipbuilding, to complex computational tasks and applied problems of professional orientation, which require the construction of a mathematical model and analysis of the results obtained. The examples show the solution of mathematical problems in symbolic form, mathematical studies in the Mathcad and Mathematica environment, and mathematical programming with these packages.

Changes in the immunological reactivity in patients with coxarthrosis and the factors that determine them

Background. The participation of immune responses in the pathogenesis of degenerative-dystrophic diseases of the synovial joints determines the feasibility of using more rational approaches to assessing the immune status of patients with this pathology. Despite the ongoing immunological studies in patients with degenerative-dystrophic diseases of the hip joint, there are questions related to the functioning of the immune system as a whole, which require additional research.The aim of the study was to establish the features of the relationship between the indicators of the immune status and to identify the factors that determine the nature and severity of immunological disorders in patients with coxarthrosis.Material and methods. The study is based on the results of immunological parameters in 73 patients (mean age – 45.3 ± 2.56 years) with stage III dysplastic coxarthrosis. The data obtained using cluster analysis made it possible to distribute patients into two groups. The first clinical group included 46 patients, the second one – 27 patients. The control group consisted of 28 clinically healthy individuals. Mathematical processing of the results was carried out using the Statistica 6.0 software package (StatSoft Inc., USA) and the mathematical package Mathcad 2001 Pro (MathSoft Inc., USA).Results. The levels of CD4+ and CD8+ cells and IgA were determined as the classification features that make the greatest contribution to the division of the studied groups. Model experiments have shown that a specific combination of the magnitude of each of the noted factors with a certain degree of probability makes it possible to assess the state of the initial immunological reactivity and verify the nature and severity of immunological disorders.Conclusion. The information obtained is of great importance, since it allows predicting the course of the recovery period after surgery and assessing the risk of developing possible postoperative complications in patients with severe articular pathology.

Innovative methods and technologies while examining equations of mathematical physics

Teaching disciplines of physics and mathematics in the age of information technology requires innovative teaching methods application. These methods complement traditional forms; they are aimed at developing the systematic and creative thinking of students. The disciplines of the physical and mathematical profile include such discipline as “Equations of Mathematical Physics”. They help students develop skills in creating mathematical models of physical processes and phenomena. It is advisable to apply software packages to create computer models of situational problems when studying the discipline “Equations of Mathematical Physics”. The mathematical packages application makes it possible to take various situations by changing the input parameters of the model on the basis of computer models of physical processes. The problems of mathematical physics are based on the study of the second-order partial differential equations of three main types: hyperbolic, elliptic, and parabolic. The paper discusses the mathematical package MathCad application in the study of free and forced vibrations of a string. Mathematical models of free and forced oscillations are presented. The d’Alembert formula for solving equations of hyperbolic type is presented. The authors describe stages of the study of free vibrations of the membrane in MathCad. Bessel functions are constructed. Membrane surface animation has been created. Observations of membrane vibrations were carried out.

Visualization in Mathematical Packages When Teaching with Information Technologies

A method has been obtained for the use of visualization in computer mathematical packages, which is an effective means of overcoming difficult situations that arise for students when mastering such packages and solving computational problems. Depending on the complexity of the problem being solved, either the teacher or the students themselves can create special visual graphic (animation) objects. Such objects allow, initially without going into the intricacies of the functioning of the package and the mathematical apparatus used, to competently describe a complete picture of a difficult situation for students and indicate ways to resolve it. The method is considered through the example of the process of solving systems of equations using the mathematical package Mathcad and the WolframAlpha online resource. Graphical and animated objects are presented that clearly demonstrate the areas of the location of initial approximations, allowing you to numerically obtain all the real roots of systems of trigonometric and nonlinear equations. Similar objects are built to find the critical points of the Himmelblau’s special test function. Visualization materials are confirmed by the presented computational calculations. The proposed method is implemented in the form of plans for lectures and practical classes on mathematical modeling using computer technologies. The method was tested with university students at the National Research University Moscow Power Engineering Institute.

Simulation of the process of milling and grinding cylindrical surfaces by an oriented tool in one setup

Purpose. Improvement of schemes for processing the cylindrical surfaces of the shafts of gearboxes and transmissions of large-sized equipment. Development of modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles. Development of a model for dressing a grinding wheel with a diamond tool. Methodology. Creation of general and particular modular mathematical models of the processes of removal of allowance and shaping during rough and finish milling and finishing grinding of non-rigid cylindrical surfaces was carried out using a matrix apparatus for transforming coordinate systems. This made it possible to describe the treatment process using standard matrices. The calculations were carried out in the mathematical package Mathcad. To obtain a graphic display of the mathematical model of the instrumental and machined surfaces, the standard functions of the software package and the developed logical blocks were used. Findings. A technique for processing cylindrical surfaces of revolution with an oriented tool is proposed. Roughing, finishing and polishing are carried out in one setup. Roughing and finishing are carried out with an oriented cutter with replaceable multifaceted carbide inserts. The angle of orientation of the cutter is selected from the condition of maximum loading of the end section. Thus, the roughing stock is removed by the end face and by the finishing periphery, while the maximum component of the cutting force is directed along the axis of the part and does not cause deformations in the radial direction. Final finishing is carried out with a wide grinding wheel. The angle of orientation of the grinding wheel is selected from the condition of uniform distribution of the allowance along the periphery. A scheme for dressing the working surface of a grinding wheel with a diamond pencil with a constant feed is proposed. Originality. Modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles were developed. A model for dressing a grinding wheel is proposed. The use of the proposed models makes it possible to conduct a more detailed analysis of the processes of stock removal and shaping. Practical value. Dependencies are proposed for choosing the optimal angles of orientation of the cutter for roughing and finishing milling and the grinding wheel for finishing. The accuracy of parts is increased due to the elimination of the resetting error. The cost of manufacturing is reduced due to the maximum full use of cutting carbide inserts, by turning them and operating the worn finishing edge in the rough milling mode, as well as by increasing the resource of the grinding wheel.

Evaluation of the self-induced vibrations modes of bridge superstructure during monitoring

In the last 20–30 years, bridge condition monitoring during the operational cycle has become increasingly common on the Russian highway network. The monitoring ensures control of the bridge on an ongoing basis in a continuous mode. The task facing the monitoring systems developers is to expand the range of the parameters that can be used in real-time to monitor the bridge’s condition and the safe conditions for its operation. One way is to use indirect parameters obtained as a direct data processing result. Appropriate algorithms for converting information recorded by the system sensors and obtaining new parameters are needed. The most important design characteristics are dynamic characteristics, which include the frequencies and amplitudes of the self-induced vibration modes, and vibration decrements. This article discusses a technique for estimating the dynamic bridge characteristics, namely, the self-induced vibration modes frequencies and amplitudes using experimental data. A dynamic system mathematical model that performs self-induced vibration is considered in the system form with one input signal and n output signals. Formulas for the model frequency response and its components are given: the amplitude and phase response of the system. To calculate the frequency response, power spectra and cross-power spectra are needed, which are obtained using the Fourier transforms of the signal. The article shows how, to reduce the random error, to estimate the mutual spectrum by dividing the realizations into several adjacent intervals (segments) of length T each. The final spectrum (periodogram) is obtained as the arithmetic mean of the segment spectra. Monitoring systems using accelerometers that measure the structure linear accelerations of the record the output signals. One of the accelerometers is considered an input signal source. According to the proposed mathematical model, the self-induced vibration frequency response of the system characterizes the amplitudes and signs of the structure displacements at the accelerometers’ location at different frequencies. The mathematical apparatus considered by the authors is applied to the data obtained on a real object: a bridge crossing over the Volga river on the highway Nizhny Novgorod-Shakhunya-Kirov in the Nizhny Novgorod region — Borsky Bridge. The monitoring of the bridge state stream crossing the Volga by its purpose is control and research, in terms of the form of information presentation over time — continuous, in terms of the speed and synchronism of polling sensors — dynamic. The monitoring purpose is to monitor the bridge structure operation and its operating conditions, including the technical control of the stress-strain state (SSS) parameters. The bridge characteristics and the current monitoring system are given. The results of numerical calculations of the arch span for vibrations are presented. The authors performed periodogram calculations using the mathematical package MathCad using the signals of two accelerometers. To estimate the frequencies and amplitudes of the span structure vibration modes using monitoring data, periodogram calculations were performed using the SpektrKatKross program that implements the proposed algorithm. The correspondence results of the program to the results of the calculations by the program MathCad are shown. The calculated and experimental vibration modes of the span are close. As a result of using the proposed mathematical model, the reliability of this comparison is ensured both in terms of frequencies and in terms of amplitudes.

Simulation of operating modes of the refrigerating machine and the heat pump when drying fish

Saving energy resources in the fishing industry is an important task. The purpose of the study is to determine rational schemes and operating modes of air conditioning systems for drying fish. The methodology for calculating the air conditioning system for drying fish and on its basis a computer program in the mathematical package MathCAD is developed. Two air conditioning schemes are considered: a scheme using an air heater and a chiller and a scheme using a chiller and a heat pump. The schemes were analyzed from the standpoint of energy indicators. The parameters of the air supplied to the drying chamber were taken for calculations on the basis of the need to maintain the parameters set by the fish processing technology. In this paper, air conditioning schemes for drying fish are considered, an analysis of the main energy costs during the operation of equipment is carried out. On the basis of calculations, the advantages and disadvantages of the systems, their energy costs for maintaining the specified technological modes are shown. The influence of temperature and flow rate of cold outdoor air and the use of heat recovery units for the exhaust air are shown. It was established that when using outside air with heat exchangers, it is possible to significantly reduce the consumption of heat energy for the technological mode in the cold season. In the absence of heat sources, the scheme with a refrigeration machine and a heat pump has an advantage. The research results were introduced at the fish enterprise of the Astrakhan region by the LLC “Technology of comfort”.

RESEARCH OF TRANSIENT PROCESSES OF PRESSURE CHANGE WHEN OPERATING A HYDRAULIC SYSTEM WITH FOUR CONNECTED HYDRAULIC MOTORS

The publication is devoted to the study of the quality of the hydraulic system with four series-connected hydraulic motors. These hydraulic systems can be used to drive the working bodies of agricultural machines, have significant advantages in their layout, but at the same time and disadvantages, the elimination of which requires a detailed study of the processes occurring during the operation of this type of system. The analysis of the previous works of scientists in this area allows us to conclude that it is possible to conduct theoretical research in this direction. A mathematical model of the proposed hydraulic system has been developed, which takes into account the effect of external load on the shafts of hydraulic motors, the inertia of the system, the effect of leaks from the connections of the elements of the hydraulic system and possible overflows of the working fluid from the high-pressure zone to the low-pressure zone. At this stage, wave processes occurring in the cavities of the hydraulic system were not taken into account. The solution of the resulting system of differential equations was carried out using the Runge-Kutta-Feldberg method with automatic change of the integration step in the mathematical package MathCad. The resulting transient processes were analyzed for the amplitude of pressure surges and the frequency of its change. Carrying out this analysis allows you to obtain comprehensive information about the nature of transient processes in the hydraulic system in order to find such a ratio of design and technological parameters, in which the system under study met the requirements regarding the quality of work as part of a technological machine. During the research, special attention was paid to the processes occurring at the moment of starting the hydraulic system, and the moment of application of the technological load.

Information technologies of remote assessment of herbicide consequences on winter rape crops

A separate group of substances with potential phytotoxicity are herbicides. These chemicals contain potent biologically active substances designed to destroy certain types of vegetation. Residues of some of these substances can be stored in the soil for several years, showing interaction with other substances and, undesirably, a negative effect on cultivated plants. With increasing use and range of herbicides, the risk of aftereffects increases significantly. A clear description of the drugs, the mechanism of their action is indicated in the regulations of their use. However, in production, as a rule, there are subjective and objective factors, as well as a number of random factors that can lead to the manifestation of adverse effects or after-effects of drugs. In order to determine the possibility of using spectral monitoring from the platform of an unmanned aerial vehicle (UAV), research was carried out at the industrial fields and experimental experimental field of NUBiP of Ukraine, in the optical range, using the RGB camera and the Slantrange complex. The image processing was carried out using firmware (software), as well as the standard and stress indexes provided by the developer. Data obtained from the FC200 optical camera in RGB format was computed in the mathematical package MathCAD. It was found out that in winter crop rape, in the vegetative phase of 5-7 leaves, as a result of the action of the herbicide occurs anomalous coloring of the two lower leaves of the plant. To identify this feature in the optical range, the most informative are red and green channels. With the use of Slantrange 3 complex among the embedded stress indexes, SlantView software is the most informative of Veg. Fraction and Yield potential. It is shown that in order to increase the reliability of the data obtained, it is advisable to carry out additional research on the parameters of debugging the given system.

Implementation of an optimization algorithm using modified Lagrange functions on the example of a steel hinge-rod system

An example of the optimal design of a steel truss with the use of modified Lagrange functions is considered. To solve the problem, it is necessary to select the cross-sectional areas of the truss at a given interval by minimizing its volume, provided that the regulatory requirements for strength and rigidity are met. The external diameters of the sections of the truss elements vary. A detailed algorithm for solving the problem is presented. The algorithm is implemented in the mathematical package MathCAD, which allows you to visually trace the sequence of commands, as well as receive graphs reflecting the state of the problem at each iteration.

Computer modelling of physical processes described by parabolic type equations

The article considers the application of modern methods of mathematical modelling in the process of solving problems of mathematical physics in the aerospace industry. To describe the temperature distribution in a given area of space and its change in time, the heat conduction equation is used. This equation is a special case of the diffusion equation and is a second order partial differential equation. The tools of the mathematical package MathCad are considered, which can be used to study physical processes described by the heat conduction equation under various initial and boundary conditions.

Determination of the cutting force components while milling cylindrical surfaces with an oriented tool

Purpose. Construction of a general modular mathematical spatial model of the removal allowance process and shaping when milling round surfaces of rotation, such as camshaft necks, cylindrical surfaces of gearbox shafts and others. Determination of the components of the cutting forces when machining with crossed axes of the milling cutter and part in order to use the results when assigning machining modes. Methodology. Theoretical development of a modular mathematical model of the removal allowance process and shaping during milling of cylindrical surfaces was carried out using a matrix apparatus for converting coordinate systems. Unified modules were developed: instrumental, orientation and shaping, which allowed us to describe the processing of the part more clearly. All calculations were performed in the mathematical package Mathcad. Using the functions available in the package, a graphical representation of the mathematical model of the tool and machined surfaces was obtained. Using the logical blocks developed in the program, the characteristics of the treated surface were investigated, such as roughness in the axial and radial planes. The influence of the tool orientation angle and the number of cutter teeth on the roughness of the machined surface was investigated. The known formulas for calculating the cutting forces during milling are specified. Findings. A general modular mathematical spatial model is constructed of the removal process of an allowance and formation at milling by the oriented tool of round surfaces of rotation, such as necks of camshafts, cylindrical surfaces of shafts of transmissions and others. The roughness parameters of the treated surface are determined. The outflow of the tool characteristics and the angle of its orientation on the geometric roughness in the axial and radial sections is investigated. The area of the layer cut off by one tooth of a mill is defined. The calculation formulas are specified for finding the components of cutting forces during milling. Originality. A modular spatial model of the process of milling cylindrical surfaces with an oriented tool is proposed, on the basis of which the components of cutting forces are calculated, which can be used in designing new tools and improving machining conditions by the existing ones. Practical value. Based on the use of modern computer facilities and software, the developed calculation program allows controlling the process of forming cylindrical surfaces during their milling with an oriented tool. It also allows predicting the initial machining accuracy by determining the parameters of geometric roughness in axial and radial sections. This makes it possible to choose the optimal tool orientation angle, milling cutter parameters and cutting modes to achieve high productivity and processing quality.

PARAMETRIC OPTIMIZATION OF THE BEARING CAPACITY OF THE CLOSED PLANETARY MECHANISM FORMED BY TWO MECHANISMS OF TYPE ĀĪ

The dependences of the bearing capacity of a closed planetary mechanism formed from two simple planetary mechanisms of the type ĀĪ as a function of two kinematic parameters that determine the transmission ratios of simple planetary mechanisms are investigational. Dependences are obtained from the conditions of providing contact and bending strength of external gearing of simple planetary mechanisms. The influence of the number of its satellites on the choice of the kinematic parameter of a simple planetary mechanism is taken into account. A condition is given that provides the same bearing capacity of a closed planetary mechanism, taking into account both contact and bending strength, respectively. Various formulations of the optimization problem of determining the values of the kinematic parameters of simple planetary mechanisms and methods for solving it are considered. An example of decision of optimization task is made in the mathematical package Mathcad.

Исследование движения несжимаемого газа в вихревом теплогенераторе

The article presents the results of the performed analytical and experimental studies of the hydrodynamics of the translationalrotational motion of a viscous incompressible gas flow in the working space of a vortex heat generator of variable geometry, analytically determined the dependences of the effect of device performance, confuser opening angles, confuser channel width on the hydrodynamic parameters of the device and, as a consequence, its energy efficiency. The degree of energy efficiency of the swirler screw for the operation of a vortex heat generator at various loads on the working path has been experimentally estimated, according to the Euler number EUc. It has been proven that the energy efficiency of its operation is on average 35% higher when the swirler screw is installed. The influence of the geometry of the nozzle on the axial symmetry and smoothness of the flow of incompressible gas in the vortex chamber is investigated. It was found that the specified indicator is most satisfactory for a nozzle with a rectangular cross-section. The distribution of the temperature field of a moving incompressible gas along the height of the vortex chamber is investigated depending on the taper angle. The distribution of angular velocities along the axis of the flow swirler is investigated at various values of productivity. It was found that the angular velocity decreases according to the law of potential fluid flow. A mathematical model has been developed to optimize the operating modes and parameters of the vortex heat generator. A software block was built based on the mathematical package MathCAD version 11 for the implementation of the developed mathematical model. An optimal design of a vortex heat generator with a variable geometry of the working space has been developed, which has been tested in laboratory conditions. Laboratory studies have proven its high energy efficiency at the level of modern standards and the feasibility of using the device for heating buildings and structures in industry and the domestic sector. Keywords: incompressible gas, hydrodynamics of an incompressible gas flow, vortex motion, mathematical model, equation of motion, continuity equation, vortex heat generator, thermal energy, cavitation, turbulence, vortex zone, MathCAD package.

Using Screencasts in Computer Science Classes at a Technical University

The information technologies applications in various fields of human activity are developing exponentially now. The article considers possibility of using screencasting in a computer science course at a technical university. Screencast is a video that contains a record of actions performed on a computer with the author’s comments. The advantages and disadvantages of this technology in the learning process are considered. It is noted that the technology of on-screen video is distinguished by information richness and strong emotional effect on the student. The application of screencasting in computer science classes at the Tomsk Polytechnic University using the mathematical package MathCad, which has the means to solve all kinds of problems associated with symbolic operations, is presented. The motivation for this study is to increase the student learning process effectiveness. Therefore, the objectives of the study are: to study the possibility of screencasting in the student learning process organization, to study the possibility of using this technology during studying a computer science course, to find out how effectively this method allows to master knowledge in the relevant discipline. The results of study using this technology and the traditional method are analyzed. It is shown that the use of screencasting allows to improve the test results in comparison with the group trained by the traditional method.

Simulation of digital corrector of intersymbol signal distortions in the information transmission channel

A method of modeling a digital corrector of intersymbol distortions of signals in the information transmission channel, determining the optimal values of the weighting correctors when passing a sequence of random binary signals, checking the efficiency by determining the number of demodulation errors in signal distortion by noise. The demodulator adaptation model is shown, which is reduced to the calculation of the weighted sum of 4 samples of the input signal and the comparison of the obtained sum with the threshold. The basic operations on adaptation of weight coefficients of the corrector of the signals distorted by intersymbol interference at various types of transfer function of the channel of transfer of discrete signals are defined. The algorithm of the program for calculation of number of errors of demodulation at signal distortion by noises of intersymbol interference is offered. The calculation of the corrector optimization criterion is performed by the method of coordinate descent with the possibility of visualizing the iterative procedure of calculating the corrector optimization criterion at the selected values of the correction coefficients and calculation accuracy. The formation of the input and output signal is carried out using the built-in inverse fast Fourier transform function of the mathematical package MathCAD. The mathematical model of the digital corrector, which is a kind of FIR filter, allows us to investigate the effectiveness of compensation between character distortion and stationary linear distortion of information signals provided in discrete channels of information message transmission. The initial data for the calculation of the digital corrector are the readings of the pulse response, taken at time intervals in accordance with the conditions of Kotelnikov's theorem. To solve the system of linear algebraic equations when finding the coefficients of the digital corrector, the vector - matrix method of calculation and programming operators of the MathCAD system are used.

SIMULATION OF THE CURRENT-VOLTAGE CHARACTERISTICS OF SOLAR BATTERIES WITH CONSIDERING DECREASE OF LIGHTING DUE TO THE INFLUENCE OF JETS OF THE ELECTRIC PROPULSION

A model for calculating the voltage-current characteristic of a solar array in the presence of a temperature gradient by its photovoltaic converters and their variable illumination due to possible pollution under the action of space factors, including operation of electric rocket engines, is described. The model is based on the main equation of a solar cell. In this case both a one-dimensional and a two-dimensional temperature gradients are taken into account. The principles of constructing a model are given, and the initial data selection is made. To simulate the lighting conditions of the solar array such a concept as effective illumination is used, i.e. the density of the radiation flux which falls on photovoltaic converters passing through the protective coatings. The features of simulation of the temperature distribution in the solar array and the effective illumination of its surface in cases of parallel, serial and mixed switching of solar cells are described. The calculation procedures and examples of solar cells are given. The construction of the model in universal mathematical package Mathcad is described. Some simulation results are discussed. Key words: solar array, mathematical simulation, illumination, temperature gradient, electric rocket engine, spacecraft, Mathcad.