### EXCEL VBA FUNCTIONS FOR NUMERICAL SOLUTION OF A CAUCHY PROBLEM OF THE FIRST-ORDER ODE SYSTEM

The current study presents program codes of custom VBA Excel functions that implement numerical methods for solving the Cauchy problem for a system of 1st order ordinary differential equations using the Euler and Runge-Kutta 4th order methods. The parameters of the functions are the initial and final values of the independent variable, an array of initial values of the dependent variables, and the number of steps. Program codes use dynamic arrays. Custom functions can be applied to the Cauchy problem and one of the 1st order differential equations. All of the custom functions have descriptions that explain their purpose. The article demonstrates the use of custom functions using specific examples of numerical solutions to the Cauchy problem of 1st order differential equations system and individual 1st-order differential equations.

Read More### GAS DISCHARGE WITH A LIQUID ELECTROLYTE CATHODE IN CREATING A FLOW OF STEAM WATER PLASMA

The current article presents the results of an experimental study of a gas discharge with a flowing liquid electrolyte cathode under combustion conditions inside a chamber with walls made of refractory material. The copper anode was located above the cathode. The interelectrode distance was 20 cm. Aqueous solutions of sodium chloride with a concentration of 0.2-0.3 mol / l were used as an electrolyte. The electric power source was a three-phase rectifier with an output voltage of 2100 V. The discharge burned steadily without a ballast resistor in the power range of 25-30 kW. As a result, the researchers obtained a flow of steam water plasma with a mass velocity of 1.0-1.7 g/s. The total heat loss through the electrodes did not exceed 30% of the overall power consumption.

Read More### A SIMULATION OF HEATING A DIELECTRIC MEDIUM

The study explores the mathematical models of the process of heating a dielectric medium under the influence of ultrahigh-frequency electromagnetic energy. On the basis of the examined mathematical models describing the physical process of heating a dielectric medium by irradiation with ultrahigh–frequency (microwave) energy, the study obtains various analytical solutions [1], [2]. The authors introduce an original Python 3.9 based software and present an authorship certificate. The developed software allows the authors to obtain the temperature distribution in the depth of the dielectric medium depending on the parameters of the acting wave in the form of visual graphs and to obtain results that allow comparing the obtained analytical solutions.

Read More### RESTORATION OF THE STIFFNESS PARAMETERS OF A TWO-SEGMENT BEAM, TAKING INTO ACCOUNT RIGID ATTACHMENT

The current study examines the inverse problem of diagnosing the stiffness parameters of flexural vibrations of a two-segment beam from known values of its vibration frequencies. The author of the study shows the uniqueness of the solution of the inverse problem as well as formulates and proves the corresponding theorem. The article introduces an algorithm for solving the problem that confirms the uniqueness of restoring the stiffness parameters of beam bearings, which is also applicable for the case of rigid attachment of the edges of a two-segment beam. The solution algorithm is confirmed by numerical examples.

Read More### LASER PROCESSING OF DISPERSED MINERAL FORMATIONS

The paper considers the possibility of using laser technologies for processing mineral raw materials. The article analyzes the effect of laser radiation on natural mineralogical samples of a placer deposit of an aluminosilicate matrix containing metal particles, including gold, in the form of impurities. As a result of laser irradiation on the material under study, the research establishes the formation of fused objects — conglomerates. Atomic and scanning electron microscopy reveals that after laser treatment, the samples were surface-microheterogeneous silicate specks, on the surface of which the formation of agglomerated crystal structures of gold, ranging in size from 300 nm to 30 microns, was revealed.

Read More### BIG DATA IN THE AVIATION INDUSTRY: CASES OF APPLICATION

Aviation industry currently faces significant safety and performance challenges. It is expected that these problems can be solved using big data technologies. This article focuses on the impact of big data technologies on aviation industry and describes the possibility of developing aviation big data information platform. Firstly, this article analyzes the relationship between big data technologies and the development of intellectual aviation industry. In addition, this article considers the main ideas and the area of development of aviation big data information platform and its systems. The study shows that big data technologies plays a very important role in the development of intellectual aviation industry, aviation safety can be improved, and aircraft performance can be significantly increased through the development of aviation big data information platform. This article presents approaches to the planning and implementation of the development of aviation big data information platform, the creation of global big data cooperation mechanism and the development of big data technologies in aviation industry.

Read More### A CLASSIFICATION OF GENERALIZED SECOND-ORDER BÖTTCHER’S EQUATIONS

The authors of the article summarize their research on the solution of generalized Böttcher’s equation of the second order from two arguments. The aim of the study is to describe a class of smooth solutions of these equations defined on a certain conic domain with a vertex at the origin. The method of direct description of the orbits of the action of a general linear group on the space of tensors of type (2,1), which are symmetric with respect to covariant indices, proved to be resolving. In the article, structural theorems on the structure of orbits were proved (Theorems 1-4). It was also proved that any generalized second-order Böttcher’s equation belongs to one of the thirteen types of equations corresponding to tensors, which were called canonical by the authors (Theorem 5). In this article, part of the generalized Böttcher’s equation is solved completely and the rest is reduced to four one-parameter and two two-parameter families of the functional Schröder’s equations from one variable. The study also presents partial solutions to these equations.

Read More### NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATION BY EULER-MARUYAMA METHOD

In the article described one of the most popular numerical methods for solving stochastic differential equations. It includes a review of fundamental concepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. The solutions will be continuous stochastic processes that can be used for prediction process of energy consumption.

Read More### THE SIMULATION OF FRACTIONAL BROWNIAN IMAGES

The modeling algorithm of fractal Brownian images has been proposed and studied. It is established that an integral characteristic of the spectrum of Brownian image with Hurst’s parameter is well approximated by a function power with an exponent 12-05-2021 11-57-44 in 12-05-2021 11-57-53 and the exponent which is equal to 3, for 12-05-2021 11-58-06.

Read More### MODELING THE STRUCTURE OF AMORPHOUS ALLOYS BY MEANS OF GRAPHICS PROCESSORS (GPGPU)

This work is devoted to modeling the atomic structures of amorphous alloys by means of GPU. The model of the amorphous alloy is represented as a set of atoms. There are two variants of modeling: it is a two-dimensional variant, where images are as electron microscopic and three-dimensional images as the 3d- model atoms of the alloy. In the first case, the high speed calculation frame is achieved through the use of parallel computing, using the API of CUDA. For visualization of three-dimensional models used Vertex Array Object (VAO) – extension of OpenGL.

Read More### PROCESSING OF ELECTRON MICROSCOPIC IMAGES WITH THE GPU

This work is devoted to the analysis of series images of amorphous alloys obtained by transmission electron microscopy. The method of separating of roughness on the alloy surface is offered on the basis of spectral estimation.

Read More### CUSTOM EXCEL VBA FUNCTIONS FOR NUMERICAL SOLUTION OF A FIRST-ORDER CAUCHY ODE

The current study provides basic formulas for approximate solutions of a Cauchy problem of the first order ordinary differential equations by the methods of Euler, Adams, in which finite differences of the first and second-order, and Runge-Kutta of the fourth order are applied. The program codes of the VBA Excel custom functions that implement these methods are also provided. These custom functions allow finding approximate solutions to the Cauchy problem for the first order ordinary differential equations online. All custom functions have descriptions explaining their purpose. The use of custom functions is shown in solving specific problems, including when the solution must be found on a finite sequence of equidistant values.

Read More### INVESTIGATION OF THE DEFECT DISTRIBUTION GRADIENT IN SINGLE-CRYSTAL SILICON AND GALLIUM ARSENIDE PLATES USING X-RAY TOPOGRAPHY

The current paper investigates the dependence of diffusion scattering on the density of structural imperfections in single-crystal silicon and gallium arsenide, which allows for the estimation of the concentration gradient of structural imperfections. This gradient appears due to the properties of the growth technology of such crystals (via the Czochralski method), namely, the inhomogeneity of the crystallization front, which leads to the formation of regions with a high dislocation density.

One of the most important technological requirements is the uniformity of such crystals in order to ensure their most effective further electronics use. The proposed research method allows for prompt identification of an increase in the gradient so that one can then adjust the technological parameters of growth in order to avoid deterioration of product quality.

Read More### OVERVIEW OF METHODS FOR STATIC AND DYNAMIC CLUSTERING OF SECURITY EVENT LOGS

Security event log files provide insight into the state of the information system and allow detecting anomalies in user behavior and information security incidents. However, automatic analysis of security event log data is difficult because it contains a huge amount of unstructured data collected from various sources. This article provides an overview of existing approaches that condense or summarize log data using clustering methods, namely static and dynamic clustering methods. The study examines the examples of using static and dynamic clustering of security event logs as well as limitations and problems in the use of these methods.

Read More### DETERMINING THE ORIENTATION OF A SINGLE CRYSTAL BY ANALYZING THE INDENTATION GEOMETRY

The current study discusses the development of a technique for determining the crystallographic orientation of a single crystal. Single crystals of gallium arsenide grown by the Czochralski method in the crystallographic direction of <100> were used as the subject of research.

The study describes classical approaches to the determination of plane indices using selective etching (based on the shapes of etch pits) and X-ray diffraction analysis.

It also presents the results of experimental studies of single crystals of orientation <100>, aimed at detecting the planes of the {110} family, which are the planes of the primary flat. The authors analyze the processes of formation of microcracks that occur during standard tests for the determination of microhardness and demonstrate the regular nature of their propagation over the surface.

Read More### DEVELOPMENT OF PROGRAM FOR DETERMINATION OF FRACTAL DIMENSIONS OF IMAGES

The purpose of the work is to create a program for determining the fractal (fractured) dimension of 2D images. This is necessary, for example, for fractal analysis of surface roughness, paintings of convection, turbulence, meteorological phenomena, and can help in creating the most adequate models of physical processes.

The calculation of fractal dimension is carried out by the so-called box counting method. Program code is written in Python, chosen for convenience reasons with matrices filled with image pixel values and calculated values.

As examples, the difference between fractal dimensions of urban and natural landscape is shown. Recommendations were made on the application and development of created program.

Read More### IMBALANCE OF ELECTRON-BEAM ENERGY IN INDUCTION CYCLIC ACCELERATOR

Under inductive cyclic acceleration of charged particles the beam current of which exceeds several hundred amperes, a large amount of energy is accumulated in its electromagnetic field. These results in energy imbalance, i.e. inconsistency between energy received by the electron beam from betatron’s eddy electric field and energy required for the electron beam to stably move along the equilibrium orbit. This is one of the reasons for beam instability and large loss of accelerated particle charge. Thus, the paper presents an estimation of the occurred imbalance degree and considers possibilities of eliminating its negative effect on the process of acceleration.

Read More### LOW-FREQUENCY MAGNETOELECTRIC EFFECT IN A TWO-LAYER MAGNETOSTRICTIVE-PIEZOELECTRIC STRUCTURE

The study presents a theory of the magnetoelectric effect in a two-layer magnetostrictive and piezoelectric structure of magnetic and piezoelectric materials in the low-frequency region of the spectrum. Based on the solution of the equations of the theory of elasticity and electrostatics, a simple expression for the magnetoelectric stress coefficient is obtained via the physical parameters of the material and the geometric characteristics of the structure. The study examines the contribution to the value of the effect caused by flexion strain and planar deformations. It is shown that the contribution from planar deformations to the value of the effect significantly exceeds the value of the contribution from flexion strains. The authors demonstrate the calculation results for the nickel – lead zirconate titanate and permendur – lead zirconate titanate structures.

Read More### ALTERNATIVES TO THE EGOROV’S AND KOBAYASHI’S THEOREMS ON COMPLETE AFFINE CONNECTIONS

The article concludes the research of completeness of the symmetry and geodesic flow of affine connections. The study aims to find and describe linear spaces over complete fields on the tangent bundle. The article verifies 3 new results. The developed theorems are alternatives to the Kobayashi’s theorem on complete affine connections. The study examines a metric situation (theorem 7) and an affine situation (theorem 8). The article verifies an alternative to the Egorov’s lacunarity in complete manifold dimensions. The paper verifies the evaluation of dimension borders of the first-order complete field which allows completeness of the connection itself (theorem 10). The article suggests a scheme of obtaining an alternative evaluation of higher order complete field dimension borders. The study sets up the ways of further research. The results could be used to classify the affine connections that accept extensive symmetry algebras of the geodesic flow.

Read More### TRACKING SYSTEM BASED ON IR SENSOR CONTROLLED BY ATMEGA16 MICROCONTROLLER

In this article will be described the tracking system implementation based on infrared distance sensor SHARP GP2Y0A02 controlled by microcontroller Atmega16. This system is a essential part of the various robotic systems (various platforms) used for targeting and for tracking other objects.

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