ISSN 2224087X (Print) ISSN 22240888 (Online)
Collected scientific papers "Electronics and information technologies"
(In 19662010 published under the title "Electrical engineering")
(Certificate of State Registration ÊÂ ¹176186468ÏÐ from February 11, 2011)
Issue 11, Pages: 320 
DOI: https://doi.org/10.30970/eli.11.1 
CALCULATION METHODS AT THE PLASMONIC. 3. FINITE DIFFERENCE TIME DOMAIN 
I. Bolesta, A. Demchuk, O. Kushnir 
The article presents the third part of the review of computational methods that are actively used in the problems of plasmonics, namely, the method of integrating Maxwell’s equations in the time domain (FDTD). The FDTD method is a direct implementation of timedependent Maxwell equations for solving a temporary change in electromagnetic waves within a finite space containing an object of arbitrary geometry and composition. In practice, the space is discretized by a grid of the grid, and the existence of the scattering particle is determined by the proper assignment of the electromagnetic constants, including dielectric permittivity, permeability and conductivity over the grid points. Maxwell’s Rolling Equations are subsequently discretized using convergence of approximation with a difference both in time and in space. The main advantages of this method lie in several aspects. First, the whole rangefrequency band can only be obtained by one calculation in the time domain. Secondly, the simplicity of an explicit numerical FDTD scheme. The FDTD method can easily simulate complex objects. However, the universality of the method imposes high requirements for computing, so for real simulation it is necessary to optimize to improve the efficiency of the calculation. One of these optimization options is the parallelization of computations. It is shown that it is an efficient calculation within this model. To show the effectiveness of the application of FDTD in plasmonic problems, the original results of the authors of the simulation of the optical spectra of a metal ball and the pair of interacting metal balls of different sizes are presented. Also, the results of simulation of the local amplification of the electromagnetic field of light waves, obtained by the authors, are presented in the article. Both numerical experiments give results similar to those obtained on an experiment. The simulation of the interaction between particles can be used to solve the inverse problem, to determine the distance between metal particles from absorption spectra of plasmon material. The simulation shows the local amplification of the wave field of light, which was fixed by the authors and for real samples of metal films. 

Issue 11, Pages: 2129 
DOI: https://doi.org/10.30970/eli.11.2 
SIMULATION OF THE RESONANT EDDYCURRENT CONVERTER OF THE TRANSFORMER TYPE FOR THE GAP CONTROL BETWEEN MAGNETIC CORE AND FERROMAGNETIC SAMPLES 
D. Trushakov, O. Kozlovskyi, S. Rendzinyak 
The results of theoretical researches of the interaction between resonant eddycurrent converter of the transformer type with a coupled measuring oscillatory circuit and ferromagnetic samples for improve the accuracy of the eddycurrent control are presented. The main operation procedure of the eddycurrent converter is the resonant method of adjustment from the effect of the gap. The interaction of the electromagnetic field of the winding of the eddycurrent converter and the ferromagnetic sample is investigated. On the basis of the presented mathematical model, the eddycurrent defectoscope was improved. Its measuring subsystem contains two identical oscillatory circuits with a transformer coupling, namely the coupled measuring and standard circuits. The measuring oscillatory circuit consists of an overhead eddycurrent current converter, which is installed on a controlled surface of a ferromagnetic product with some appear gap due to surface dirtying. The output of the sinusoidal selfoscillator is connected in parallel to the inputs of the connected measuring and associated reference oscillatory circuits. The output of the connected measuring oscillatory circuit is connected through the high pass filter to the indicator. The outputs of the connected measuring and associated reference oscillatory circuits are connected to the inputs of the adder, the output signal of which is stimulated to the control input of the sinusoidal selfoscillator through a low pass filter. The appearance of the crack results in a sharp change in the output signal from the coupled measuring oscillatory circuit with a transformer coupling. Such fast impulse changes are smoothed by the low pass filter and do not affect the selfoscillator, but the signal from them is received to the indicator. The signal due to the gap change is slow and take places in the bandwidth of the low pass filter and is received to the controller input of the selfoscillator. It thus maintains a constant value of the frequency in a coupled measuring oscillatory circuit of the transformer type. Such an appliance is used in the eddycurrent (electromagnetic) defectoscopy for automatic and manual control of metal products in cases where it is important to fix the gap between the overhead eddycurrent converter (inductor) with the measuring oscillatory circuit and the controlled surface of the ferromagnetic product. The problem of increase the accuracy of the eddycurrent control by the specified calculation of the characteristics of the measuring system of the resonance eddycurrent defectoscope is solved. 

Issue 11, Pages: 3038 
DOI: https://doi.org/10.30970/eli.11.3 
THE INFLUENCE OF ANISOTROPIC INTERACTION OF THE INCOMENSURATE SUPERSTRUCTURE ON THE BEHAVIOR OF THE LYAPUNOV’S EXPONENTS 
S. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, Ya. Shmygelsky 
Lyapunov’s exponents for a wide range of parameters were first calculated for the $mathrm{A_{2}BX_{4}}$ family of crystals, which have an incommensurate superstructure. Lyapunov’s exponents determine the dynamics of the incommensurate superstructure. They were calculated by the implicit AdamsMulton and RungeKut method in the Python software environment using the jitcode library. The AdamsMulton (BDF) method, in comparison with the RungeKut method (RK45), allows us to obtain a thin structure of Lyapunov’s exponents. The positive value of one Lyapunov’s exponent, and the negative value of the other three exponents, is characteristic of the incommensurate superstructure, which was established. Since the third exponent acquires a value that far exceeds the sum of all others, the incommensurate superstructure is characterized as a system having an attractor. For an incommensurate superstructure which is described by a twocomponent order parameter, the characteristic range of Lyapunov’s exponents is characterized, which is characterized by constant positive values of the first Lyapunov’s exponent. The strongly degenerate abnormal behavior of Lyapunov’s third and fourth exponents shows that the incommensurable superstructure is inherent in both hyperchaos and the establishment of a quasistable state with the appearance of longperiodic commensurate phases. A incommensurate phase in sinusoidal mode can be considered as a phase characterized by a strange attractor with one positive Lyapunov’s exponent (+, , , ). The soliton mode of the incommensurate superstructure is characterized by the appearance of longperiodic commensurate phases, and the chaotic phase in the transition between two commensurate longperiodic phases. So there is a situation called hyperñhàos: (+, +, , ), when there are two positive exponents. The Fourier obtained spectra of the incommensurate superstructure indicate that the ground state of the system is characterized by a boundary cycle. The Fourier spectrum of the boundary cycle is discrete with distinct peaks at frequencies corresponding to the fundamental harmonics of the cycle. The distribution of the spectral density of the chaotic attractor, which arises at T = 1.0 and K = 2.0 in comparison with the limit cycle, is continuous, but all peaks are preserved in it, which, conventionally speaking, is a "memory" of the harmonics of the missing boundary cycle. They are clearly distinguished in a continuous Fourier spectrum. The abnormal spatial behavior of the amplitude and phase of the order parameter is characterized by a chaotic attractor. 

Issue 11, Pages: 3951 
DOI: https://doi.org/10.30970/eli.11.4 
IMPLEMENTATION OF SIGMOID ACTIVATION FUNCTIONS ON FPGA FOR NEURAL NETWORKS 
I. Tsmots, V. Rabyk, I. Ignatyev 
The paper presents a literature review of the main methods of neural networks activation function approximation (sigmoidal function, hyperbolic tangent). The attention is focused on the accuracy and speed of the methods of approximation of the activation function and the advantages and disadvantages of these methods in their hardware implementation on the FPGA. The mathematical descriptions of the sigmoidal function, the hyperbolic tangent and their derivatives are considered. The ratios for calculating sigmoidal functions with negative arguments are given. In order to evaluate the accuracy of the approximation of the activation functions and their derivatives, the mean absolute and mean maximum errors were used. The conversion of valid input data into an integer format is achieved by its multiplication by 210 and cutting off the fractional part. In the implementation, the following format of representation of real numbers is used: 16 bits, 1 sign bit and 15 bits for storing the resulting integer number. Negative numbers are presented in two’s complement. Three methods of approximation of sigmoidal function are considered. The first one is a piecewise linear approximation. A nonlinear function with positive arguments is replaced by four straight lines. The second method is the approximation by the secondorder polynomial. A system of equations for calculating a, b and c coefficients for polynomials is obtained and values of these coefficients are calculated. The third method is the approximation by the secondorder polynomial with a simplified expression. A comparison is made for the accuracy of approximations by three methods of sigmoidal function and its derivatives. It is noted that the errors of the approximation of the sigmoidal function are smaller than the errors of approximation of its derivatives. For the considered approximation methods, integer expressions were obtained, according to which the structural schemes of the implementation of the sigmoidal function on the FPGA were developed. The main elements of these schemes are registers, comparators, multipliers, adders, subtraction devices and threestate buffers. Digital hardware implementation of sigmoid activation functions was performed in VHDL language in the Quartus II development environment using elements from standard library. Devices with the functiionality of sigmoidal function element are realized on FPGA EP3C16F484C6 of Cyclone III family. The simulation of the device calculating the sigmoidal function FA_Sigm_N3 in the time domain for positive and negative input data was carried out. The diagram of the device and its description and hardware resources necessary for the realization and calculation time are presented. The hardware realization of the sigmoid activation function on the DE0 stand was performed and the testing of its work was carried out. 

Issue 11, Pages: 5260 
DOI: https://doi.org/10.30970/eli.11.5 
CAN TWITTER PREDICT ROYAL BABY’S NAME? 
B. Ì. Pavlyshenko 
In this paper, we analyze the possible correlation between public opinion of twitter users and the decisionmaking of persons who are influential in the society. We carry out this analysis on the example of the discussion of probable name of the British crown baby, born in July, 2013. In our study, we use the methods of quantitative processing of natural language, the theory of frequent sets, the algorithms of visual displaying of users’ communities. We also analyzed the time dynamics of keyword frequencies. The analysis showed that the main predictable name was dominating in the spectrum of names before the official announcement. Using the theories of frequent sets, we showed that the full name consisting of three component names was the part of top 5 by the value of support. It was revealed that the structure of dynamically formed users’ communities participating in the discussion is determined by only a few leaders who influence significantly the viewpoints of other users. 

Issue 11, Pages: 6172 
DOI: https://doi.org/10.30970/eli.11.6 
DESIGN OF INTELLECTUAL INFORMATION SYSTEMS ON THE BASIS OF MK RASPBERRI PI 
O. Babich, Ya. Boyko, V. Galin, O. Chuprinsky 
The paper considers the features of the structure and work of the MÑ Raspberry Pi. Based on the comparative analysis of three popular platforms substantiated the choice of this microcomputer. Selected equipment for development. The designing of intelligent information systems for the car and video surveillance on the basis of the MC Raspberry Pi is considered. developed of a system that helps a driver to interact with the environment, other drivers, obstacles and automates basics ³n work the car. Moreover, the driver has the opportunity to remotely monitor the status of the vehicle, its location and is able to get information about accessing the car. The work was implemented on the Raspberry Pi 3 Model B microcomputer. Different tools like modern libraries, a temperature sensor, a card reader, a GPSnavigator were used . This software helps the driver to reduce the human factor and possible mistakes using the Lidar  rangefinder of the optical range. In the course of the study, a comparative analysis of microcomputers was conducted; the choice of the platform for the creation of a video surveillance system was substantiated. The work shows the solution of the problem with the help of local observation through a static address, using motion sensor. An application is implemented that allows you to perform the following on the vehicle: display distances to obstacles using Ultrasonic, remote control of the level of lighting, open with a card and remotely using a web server; measure the temperature under the hood, using appropriate sensors, track the geolocation of the car. The use of the Raspberry Pi microcomputer allows you to automate routine driving and reduce the number of road accidents. In the process of creating a video surveillance system, it became clear that the Raspberry Pi has a very wide functionality  in fact, it can be successfully applied wherever compact, low cost and energy efficient. The system of video surveillance, which uses the motion sensor SR501P1 and a simple webcam, allows you to capture motion in the room, make a photo and send it to Telegram, was developed. 

Issue 11, Pages: 7380 
DOI: https://doi.org/10.30970/eli.11.7 
GENERAL SCHEME FOR CONSTRUCTING THE MOST COMPLEX LOGICAL TREE OF CLASSIFICATION IN PATTERN RECOGNITION DISCRETE OBJECTS 
I. Povhan 
The work raises an important question in the theory of recognition of discrete objects associated with the General scheme of construction of the most complex resulting logical classification tree. The General stepbystep scheme of construction of such tree is offered, and the estimation of complexity of the received graphcircuit models is given. Numerical estimates in the long term allow us to develop effective models of minimization schemes of logical classification trees. The result obtained is of fundamental importance in the problem of estimating the stability of the maximum logical classification tree with respect to the permutation of tiers and the effect of such a permutation on the overall complexity of the tree. The work is relevant for all methods of pattern recognition in which the resulting classification function can be represented as a logical tree. 

Issue 11, Pages: 8198 
DOI: https://doi.org/10.30970/eli.11.8 
LONG ARITHMETIC IN EXCEL. I. VBAIMPLEMENTATION 
V. Fourman, M. Khomyak, Ya. Marko 
Approaches that increase the accuracy of computations occupy a special place in computational methods. The use of integer arithmetic of arbitrary precision requires à software implementation of operations based on 32 or 64bit types supported by modern processors. The software and Internet resources for full precision computations representing the commercial sector and freecode programs are analyzed. We propose to use widepopular Excel spreadsheets as a convenient and sufficiently powerful symbolic calculator as an alternative to wellknown powerful but highpriced packages. The basic operations are implemented in VBA: comparison, arithmetic actions and finding of the greatest common divisor for two integers with arbitrary digits saved in cells as text. At internal level an integer is represented by a BCDarray of digits with variable dimension, and its sign is stored separately. So we have two levels of implementation: through text strings and their internal representation. Operations "add", "subtract", "multiply" correspond to schoolbook algorithms but "divide" is more complex. The algorithm of short dividing for decimal numbers is justified which do not require the subtraction loop to correction the result digit. Numerical experiments have confirmed the effectiveness of the algorithm named as "3:2"class: in this case, we take into account 3 digits of the dividend and 2 digits of the divisor to obtain one digit of the result. These algorithms are necessary to work with rational numbers and for more complex calculations on their basis (for example, to solve systems of linear algebraic equations). In future, this version may be a prototype for more efficient redesign, especially with use of binary algorithms implemented in modern processors. 

Issue 11, Pages: 99108 
DOI: https://doi.org/10.30970/eli.11.9 
LONG ARITHMETIC IN EXCEL. II. RATIONAL NUMBERS 
V. Fourman, M. Khomyak, Ya. Marko 
Within VBA and Excel framework the arithmetic operations for rational numbers with arbitrary digits in the fraction "numerator per denominator" are implemented. Symbolic calculations work with their representation in electronic spreadsheet cells as text and full precision integer algorithms. Using the objectoriented approach, a typical interface of the class SRational is constructed and its functionality is described. Class methods can be grouped as constructors, arithmetic operators and functions to print a rational number back into a symbolic string. Constructors convert symbols into internal representations as arrays of digits. The result of some operation can be returned to the user as one of the intuitive formats, in particular, as a fraction with a separated integer part, or as a triple of numbers, or as an arithmetic expression. Also a routine to simplify the fraction "on demand" is implemented, which is not always necessary in the intermediate calculations.There is provided a multivariate symbolic representation of rational numbers structurally having up to three fields: an integer, a numerator, and a denominator. Between them can be intuitive separators, in particular, symbols of arithmetic operations and brackets. To calculate arithmetic expressions, we use their representations as binary trees. The complex of the functionality to parse rational numbers in the symbolic input information is analyzed. Instead of manual input of large rational numbers, you can use already formed arrays. Therefore, data import from text files of various formats is important. It provides interaction with other programs. 

Issue 11, Pages: 109119 
DOI: https://doi.org/10.30970/eli.11.10 
THE EXPERT SYSTEM FOR DETERMINATION OF HOTEL ROOM COST 
S. Sveleba, N. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, Ya. Shmygelsky 
Methodological aspects of the calculation of the cost of hotel services, taking into account the characteristics of operational activities, were investigated. Methods of calculating the cost of services were considered. The method of calculating the cost of operating a hotel room for the determination of tariffs has been proposed. Proposals for the formation of the cost of hotel services on the example of the hotel business were developed. The demonstration knowledge base in Python has been created. It contains the value of the number, the factors that affect this value, and the causal relationship between these concepts. The framing model of presentation of knowledge for building a knowledge base has been applied. The module containing the knowledge base and requests for it has a block structure. Classes are first created, then instance of the class, then the properties of instance are specified, and in the end, requests are executed. Ontology classes correspond to Python language classes, and subclasses are created using the Python. The created expert system is based on the method of calculating the cost of operating a hotel room by a complex method. It makes it possible to determine tariffs at different levels of planned profitability and loading of the number fund. However, to reduce the complexity and improve the results of the calculation calculations, somewhat changed the grouping of costs in their consolidated accounting. In order to increase the capacity of the numbering foundation and increase the profitability of the hotel sector, it is necessary to develop a system of tariff supplements for periods with high demand for hotel services and discounts to them in the days of a steady decline in demand, as well as to offer a reasonable system of discounts for certain categories of customers. 

Issue 11, Pages: 120127 
DOI: https://doi.org/10.30970/eli.11.11 
TRANSPORT MANAGEMENT WITHIN THE LIGHTLESS MOTION CONCEPT 
D. Nalivko, V. Shuts 
The paper considers the concept of lightless traffic, which allows increasing the throughput capacity of the city’s transport network by replacing the stochastic traffic flow model with a deterministic one. Efficiency improvement is achieved due to high determinism, the ability to identify and solve problem situations before they appear. The purpose of the study is to develop a management apparatus using graph theory and a multiagent approach for planning the movement of exchanges in the early stages. In such a system, there is no need for traffic control. It is assumed that this approach will prevent the occurrence of congestion due to their prediction and prechange the behavior of the AV before the possible occurrence of traffic jams. 

Issue 11, Pages: 128137 
DOI: https://doi.org/10.30970/eli.11.12 
COMBINED OPTICAL METHOD FOR MONITORING OF THE PHYSICAL PARAMETERS OF THIN DIELECTRIC FILMS ON THE SURFACE OF SINGLECRYSTAL SILICON 
V. Belyukh, B. Pavlyk 
A combined optical method for monitoring the physical parameters of thin dielectric films on the surface of singlecrystal silicon is proposed. The method consists of two stages. At the first stage, the answer is given to the question of the applicability of the model "transparent optically isotropic film  absorbing optically isotropic substrate" to the "film  substrate" systems obtained in the technological process, and determine the film thickness. To do this, it is necessary to perform ellipsometric measurements at different points on the surface of the "filmsubstrate" system and at different angles of incidence of the laser beam of the ellipsometer. As a result of such measurements, the values of the refractive index $(n_1pm Delta n_1)$ and film thickness $(dpm Delta d)$ and the corresponding spreads of these quantities $(Delta n_1,Delta d)$ are obtained. From the magnitude of these variations $(Delta n_1,Delta d)$, we can draw the first conclusion about the applicability of this model to the object of study. The main goal of the first stage of the combined optical method is to determine the thickness of the dielectric film as precisely as possible. At the second stage, measurements of the reflection spectra of films on the surface of silicon wafers are performed in order to obtain a clear interference pattern. From the obtained spectra determine the exact spectral position of the interference minima $(lambda_{min})$ and maxima $(lambda_{max})$. On the basis of these values and the film thickness d determined at the first stage, the dispersion of the refractive index of the dielectric film $[n_1 = f(lambda )]$ is calculated. According to the results of research at two stages, a final conclusion is made about the suitability of the object under study for further operations of the manufacturing process of manufacturing integrated circuits. The applicability of the proposed method has been tested on $mathrm{Si_3N_4  Si}$ systems. The results of testing the combined optical method on $mathrm{Si_3N_4  Si}$ systems convincingly prove its effectiveness for monitoring the physical parameters of thin dielectric films on the surface of singlecrystal silicon. In our article, the main emphasis is placed on the applied value of this method for integrated circuit technology. That is why silicon, the main material of modern microelectronics, appears in the title of the article and in the examples given. However, from the description of this optical method it is quite obvious that it is quite applicable to the study of any systems "dielectric film  semiconductor substrate". A prerequisite is the fulfillment of two basic requirements. First, the quality of the surface treatment of the semiconductor substrate on which the film is deposited must be high. Secondly, the film thickness should be sufficient to obtain a clear interference pattern at least in the visible and near ultraviolet spectral regions. 

© Ivan Franko National University of Lviv, 2011
Developed and supported  Laboratory of high performance computing systems
