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International Conference on Mathematical Methods in Electromagnetic Theory (MMET)

作者： Viktor Hoblyk Nadiia Hoblyk Department of Electronics and Information Technology Lviv Polytechnic National University Lviv Ukraine Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine

This work presents results of computer simulation of a flat reflective array of rectangular waveguides and results of the investigation of the influence of phase errors on the formation of the radiation field.

关键词： Electromagnetic waveguides Reflector antennas Antenna arrays Antenna radiation patterns Mathematical model Apertures

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Investigation of Processes of Heating a Non-Ferromagnetic Rod under the Action of an Unsteady Electromagnetic Field

Investigation of Processes of Heating a Non-Ferromagnetic Ro...

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International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH)

作者： Roman Musii Khrystyna Drohomyretska Halyna Bilushchak Nataliia Melnyk Ihor Demkiv Andrii Kunynets Department of Mathematics Lviv Polytechnic National University Lviv Ukraine Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Software Lviv Polytechnic National University Lviv Ukraine

ISBN: (数字)9798350378627

ISBN: (纸本)9798350378634

A physical and mathematical model is formulated for determining the axial component of the magnetic field intensity vector and specific Joule heat density in a non-ferromagnetic conductive rod under the conditions of its induction heating through an unsteady electromagnetic field. The initial relations for the initial-boundary value problem of electrodynamics were written for the considered rod. We chose the axial component of the magnetic field intensity vector as a determining function. To obtain the solution, the cubic approximation along the radial coordinate of distribution of the determining function along the radius of the rod was used. In consequence of this, the original initial-boundary value problem is reduced to Cauchy problem in time for the integral characteristics of the determining function in the radial variable. Applying the integral Laplace transform, the expression for the integral characteristics and the axial component of the magnetic field intensity vector is written down. Expressions of Joule heat and the determining function in the considered rod under the action of an unsteady electromagnetic field were obtained. A numerical analysis of change in time and distribution along radius of the rod of the axial component of the magnetic field intensity vector and Joule heat was performed depending on frequency of the carrier electromagnetic oscillations and duration of the unstable electromagnetic field.

关键词： Electromagnetic heating Time-frequency analysis Numerical analysis Vectors Mathematical models Magnetic fields Electromagnetic fields

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The Mathematical Models of Mechanical and Electromechanical Systems Study via the Qualitative and Analytical Approach

The Mathematical Models of Mechanical and Electromechanical ...

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International Conference on CAD Systems in Microelectronics (CADSM)

作者： Petro Pukach Zinovii Nytrebych Volodymyr Ilkiv Myroslava Vovk Oksana Malanchuk Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mathematics Lviv Polytechnic National University Lviv Ukraine Department of Biophysics Lviv Danylo Halytskyi National Medical University Lviv Ukraine

The mathematical models of the transverse oscillations of the elastic two-dimensional body taking into account the nonlinear behavior of the external dissipative forces are obtained. There is developed the procedure to study these models in the case of the specified systems. This type models and the similar ones are used in the MEMS, in particular, to project and synthesize the technical oscillations systems parameters. There is proposed the analytical method to solve the two-point boundary problem modeling the wave process in the unperturbed case. The obtained solution is analyzed on the plate oscillations example. The numerical computation proved the method effectiveness.

关键词： Mathematical model Oscillators Biomembranes Micromechanical devices Force Numerical models Analytical models

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Analytical Method of Investigation of Wave Processes in Mathematical Models of Some Dynamic Systems

Analytical Method of Investigation of Wave Processes in Math...

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International Conference on CAD Systems in Microelectronics (CADSM)

作者： Zinovii Nytrebych Petro Pukach Volodymyr Ilkiv Oksana Malanchuk Department of Mathematics Lviv Polytechnic National University Lviv Ukraine Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Biophysics Danylo Halytskyi Lviv National Medical University Lviv Ukraine

The mathematical model of two-dimensional body oscillations with given profiles and stresses at two moments of time is proposed. The method of research of this model, in particular, in the case of longmeasuring systems is developed. The oscillatory processes are simulated by a two-point in time problem for a wave equation in an unbounded domain. A class of existence of a unique solution of a problem is established and an exact method of constructing a solution is proposed. Also, there is carried out the investigation of specific models of wave processes, which show the effectiveness of the developed method.

关键词： Mathematical model Oscillators Propagation Stress Seismic waves Blood

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A Modified Approach to the Mathematical Model of Crack with Pre-destruction Zones

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International Journal for Engineering Modelling 2023年第1期36卷 1-10页

作者： Stashchuk, Mykola Pukach, Petro Vovk, Myroslava Karpenko Physico-Mechanical Institute of the NAS of Ukraine Department of Mathematics Lviv Polytechnic National University Karpenko Physico-Mechanical Institute of the NAS of Ukraine Lviv Ukraine Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mathematics Lviv Polytechnic National University Lviv Ukraine

Generalized Griffith’s criterion and models with pre-destruction zones are considered in this paper. Unlike those models that used linear dependences, the authors proposed the destruction process to be represented by differential equations. The positive effect of such representation is the possibility to formulate boundary conditions using the corresponding constant in the differential equation solution. The result is that the critical load values responsible for the occurrence and propagation of quasi-brittle cracks in materials are obtained. It is stated that the maximum load of crack propagation completely or essentially depends on its initial length. These generalizations estimate the influence of stress caused by hydrogen close to crack-like defects. In the case of defect-free material, the established formula is used to determine the critical forces necessary for the occurrence of cracks with a definite length. Numerical examples for some types of materials are given to illustrate the theoretical estimates. © 2023, University of Split. All rights reserved.

关键词： Potential energy

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Simulation of Parameters and Modes of Wave Propagation in Electromechanical Systems Using Methods of Inverse ProblemsTheory

Simulation of Parameters and Modes of Wave Propagation in El...

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International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH)

作者： Petro Pukach Nataliya Protsakh Yurii Protsyk Ihor Demkiv Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mathematics and Physics Ukrainian National Forestry University Lviv Ukraine Department of Computer Sciences Ukrainian National Forestry University Lviv Ukraine

ISBN: (数字)9798350378627

ISBN: (纸本)9798350378634

This work is devoted to the determination of influence of the internal forces on the propagation of the waves in electromechanical systems. The task is simplified to an inverse problem for the third order hyperbolic equation with the integral overdetermination condition and with the unknown function in the right-hand side of the equation. Some numerical results are presented for viscoelastic medium and for liquid like water with solid parameters. The presented method gives us opportunity to find the precise analytical solutions to the mathematical problems that simulate the wave propagation.

关键词： Inverse problems Propagation Partial differential equations Solids Mathematical models Electromechanical systems Task analysis

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Generalization of proximate order and applications

arXiv

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arXiv 2020年

作者： Chyzhykov, Igor Filevych, Petro Rättyä, Jouni School of Mathematics Science Guizhou Normal University GuiyangGuizhou550001 China Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Physics and Mathematics University of Eastern Finland P.O. Box 111 JoensuuFI-80101 Finland

We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a quasi proximate order, i.e. a counterpart of Valiron’s theorem for a proximate order. As applications, we generalize and complement some results of M. Cartwright and C. N. Linden on asymptotic behavior of analytic functions in the unit *** Codes 30D15, 30J99. Copyright © 2020, The Authors. All rights reserved.

关键词： Functional analysis

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Problems of Designing the Information Systems for the Quality Monitoring of Protective Consortive Ecotones

Problems of Designing the Information Systems for the Qualit...

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International Conference on CAD Systems in Microelectronics (CADSM)

作者： Anatoliy Obshta Mykola Prodaniuk Ihor Kohut Maria Ruda Iryna Soroka Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Information Systems and Networks Lviv Polytechnic National University Lviv Ukraine Department of Environmental Safety and Nature Protection Activity Lviv Polytechnic National University Lviv Ukraine Department of Project Management Lviv Polytechnic National University Lviv Ukraine

We analyzed the methods and means of quality monitoring of the functioning of natural protective forest stands along the railroad tracks. On the basis of experimental studies, we identified the factors of horizontal and vertical structure of protective consortive ecotones (PCE), influencing the effectiveness of protection of the railroad tracks and the natural environment as a whole. We propose structures of basic modules for the quality monitoring system over the functioning of the PCE along the railroad tracks on the basis of the generalized structure of information systems (IS), smart measuring instruments of which can be automatically synthesized by MEMS technology. There was developed a mathematical model of tree diameter growth taking into account the effect of photosynthesis, which will allow predicting the index of PCE condition.

关键词： Monitoring Ecosystems Forestry Rail transportation Information systems Task analysis Organizations

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Sentiment Analysis Technology of English Newspapers Quotes Based on Neural Network as Public Opinion Influences Identification Tool

Sentiment Analysis Technology of English Newspapers Quotes B...

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International Computer Sciences and Information Technologies (CSIT)

作者： Serhii Voloshyn Victoria Vysotska Oksana Markiv Ivan Dyyak Ihor Budz Vadim Schuchmann Information Systems and Networks Department Lviv Polytechnic National University Lviv Ukraine Lviv Polytechnic National University Lviv Ukraine Osnabrück University Osnabrück Germany Applied Mathematics Department Ivan Franko National University of Lviv Lviv Ukraine Computational Mathematics and Programming Department Lviv Polytechnic National University Lviv Ukraine Software Engineering Department West Ukrainian National University Ternopil Ukraine

ISBN: (纸本)9798350334326

This article dwells upon research concerning human language processing techniques, namely emotion analysis, conducted to identify emotions of author quotations in English newspaper articles. The publication describes general information about human language processing, brief description of analogues based on machine learning and neural network to analyse emotions in text. The main goal is to develop intelligent system for sentiment analysis of English language quotations and keywords identification that influences public opinion. The article describes sequence of program actions and tools that have been used. Then, statistics of tasks performed by neural networks with various functions of activators have been described. In the publication, product demo version has been described, and primary usage scenario has been depicted. In the end, research results have been summarised.

关键词： Training Sentiment analysis Vocabulary Dictionaries Mood Neural networks Text categorization

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The Studying of Hydrogen Diffusion Non-Stationary Processes Near a Crack in the Field of Heterogeneous Mechanical Tensions for the Encapsulated MEMS Devices

The Studying of Hydrogen Diffusion Non-Stationary Processes ...

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International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH)

作者： Winfried Auzinger Roksolyana Stolyarchuk Yaroslav Pelekh Oksana Kozar Serhii Mentynskyi Mykola Ihnatyshyn Institute for Analysis and Scientific Computing Vienna University of Technology (TU Wien) Wien Austria Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mechanical Engineering Natural Sciences and Information Technologies Mukachevo State University Mukachevo Ukraine Department of Light Industry and Professional Education Mukachevo State University Mukachevo Ukraine

ISBN: (数字)9781728171807

ISBN: (纸本)9781728171814

In this paper we study an elastic-plastic isotropic body weakened by a rectilinear crack, directed along the abscissa axis, under the action of stresses symmetrical about its plane. An approximate (analytical and numerical) solution of this problem is constructed under the condition that the hydrostatic deformation of the split expansion is approximated by a parabola. The concentration of hydrogen near the top of the crack is calculated. Note that when using the above calculation formulas, at each node we get several approximations to the exact solution. In the proposed methods, only three appeals to the right-hand side of the differential equation are necessary to obtain both the third order accuracy method and the two approximations (upper and lower) of the second order of accuracy.

关键词： mathematical model elastic-plastic isotropic body hydrogen diffusion internal crack continued fractions two-sided approximations nonlinear methods diffusion of hydrogen internal cracks MEMS devices cracks Cocaine Fissure Mathematical Model Continued fraction Fields

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