MATHEMATICAL MODELING IN PHYSICS AND ENGINEERING Wydawnictwo Wydziału Zarządzania Politechniki Częstochowskiej Cz ęstochowa 2018 Scientific editors: Technical editors: Andrzej Grzybowski Katarzyna Freus Jolanta Pozorska Katarzyna Szota Cover design: Tomasz Błaszczyk Jock Cooper, www.fractal-recurrious.com Scientific committee: Andrzej Grzybowski CUT - Chair Bohdan Mochnacki UOSM Tomasz Błaszczyk CUT Valerie Novitzká, TUK Jan Čapek UP Antoni Pierzchalski UL Mariusz Ciesielski CUT Jolanta Pozorska CUT Zbigniew Doma ński CUT Zbigniew Pozorski PUT Andrzej Drzewi ński UZG Piotr Puchała CUT Małgorzata Klimek CUT Gra żyna Rygał JDU Bohdan Kopytko CUT Norbert Sczygiol CUT Mariusz Kubanek CUT Urszula Siedlecka CUT Stanisław Kukla CUT Krzysztof Sokół CUT Adam Kulawik CUT William Steingartner TUK Jacek Leszczy ński AGH UST Oleg Tikhonenko CWU Zhbing Li SYSU Jerzy Winczek CUT Ewa Majchrzak SUT Izabela Zamorska CUT Organizing committee: Jolanta Pozorska -Conference General Mariusz Ciesielski Manager Zbigniew Doma ński Urszula Siedlecka- Secretary Katarzyna Freus Izabela Zamorska - Secretary Andrzej Grzybowski Jolanta Borowska Katarzyna Szota The materials submitted by the authors were reviewed and accepted by the Scientific Committee ISBN © Copyright by Wydawnictwo Wydziału Zarz ądzania Politechniki Cz ęstochowskiej Cz ęstochowa 2018 Wydawnictwo Wydziału Zarz ądzania Politechniki Cz ęstochowskiej 42-200 Cz ęstochowa, al. Armii Krajowej 36 B tel. 34 325 04 80, dystrybucja 34 325 08 67 e-mail: [email protected] Mathematical Modeling in Physics and Engineering The conference Mathematical Modeling in Physics and Engineering – MMPE’18 is organized by Czestochowa Branch of Polish Mathematical Society jointly with the Institute of Mathematics of Czestochowa University of Technology. Mathematical modeling is at the core of contemporary research within a wide range of fields of science and its applications. The MMPE’18 focuses on various aspects of mathematical modeling and usage of computer methods in modern problems of physics and engineering. The goal of this conference is to bring together mathematicians and researchers from physics and diverse disciplines of technical sciences. Apart from providing a forum for the presentation of new results, it creates a platform for exchange of ideas as well as for less formal discussions during the evening social events which are planned to make the conference experience more enjoyable. This year’s conference is organized for the 10th time. Every year the conference participants represent a prominent group of recognized scientists as well as young researchers and PhD students from domestic and foreign universities. This time we have invited speakers from Silesian University of Technology and University of Occupational Safety Management in Katowice as well as from other higher education institutions: Technical University of Košice, Vasyl Stefanyk Precarpathian National University, Jan Długosz University, Poznan University of Technology, University of Lodz and Technical University of Czestochowa. Organizers 3 Mathematical Modeling in Physics and Engineering 4 Mathematical Modeling in Physics and Engineering CONTENTS 1. NUMERICAL ALGORITHMS FOR FRACTIONAL OPERATORS Krzysztof Bekus............................................................................................ 9 2. POLYNOMIAL MAPPINGS WHICH HAVE TWO ZEROS AT INFINITY Grzegorz Biernat .......................................................................................... 11 3. FRACTIONAL STURM-LIOUVILLE PROBLEM WITH DIFFERENT TYPES OF BOUNDARY CONDITIONS – NUMERICAL APPROACH Tomasz Błaszczyk, Mariusz Ciesielski, Małgorzata Klimek ...................... 13 4. CLASSIFICATION OF THE BRAVAIS LATTICE AND CRYSTALLINE STRUCTURES Lena Caban, Joanna Kurek .......................................................................... 15 5. APPLICATION OF THE KRONECKER TENSOR PRODUCT FOR MODELLING THE DEPHT OF NITROGEN DIFFUSION PROCESS Anita Ciekot ................................................................................................. 17 6. FIBER BUNDLE MODEL WITH FRÉCHET DISTRIBUTED BREAKING THRESHOLDS Tomasz Derda .............................................................................................. 19 7. MIXED MATRIX PROBLEMS AND THEIR APPLICATIONS Nadiya Gubareni .......................................................................................... 21 8. ON ONE CLASS OF NONLOCAL PARABOLIC CONJUGATION PROBLEMS IN THE THEORY OF DIFFUSION PROCESSES WITH MEMBRANES Bohdan Kopytko, Roman Shevchuk ........................................................... 22 9. A NEW APPROACH TO SPEECH RECOGNITION USING CONVOLUTIONAL NEURAL NETWORKS Mariusz Kubanek ......................................................................................... 24 10. FRACTIONAL HEAT CONDUCTION IN A COMPOSITE CYLINDER Stanisław Kukla, Urszula Siedlecka ............................................................ 31 5 Mathematical Modeling in Physics and Engineering 11. ABOUT SOME UNIFORMLY BOUNDED SUPERPOSITION OPERATORS Maria Lupa, Małgorzata Wróbel ..................................................................33 12. A FEW WORDS ABOUT SUPPLY AND DEMAND Ewa Ładyga, Marek Ładyga .........................................................................35 13. METHODS OF MULTIDIMENSIONAL COMPARISON ANALYSIS IN ENTERPRISE MANAGEMENT Marek Ładyga, Ewa Ładyga .........................................................................38 14. APPLICATION OF NUMERICAL METHODS FOR SOLVING THE NON- FOURIER EQUATIONS. REVIEW OF OWN AND COLLABORATORS WORKS Ewa Majchrzak, Bohdan Mochnacki ............................................................42 15. THE ADVANTAGES OF LINEAR LOGIC IN COMPUTER SCIENCE Valerie Novitzká, William Steingartner, Mohamed Ali M. Eldojali ............44 16. FRACTIONAL HEAT CONDUCTION AND DIFFUSION EQUATIONS AND ASSOCIATED THEORIES OF THERMAL AND DIFFUSIVE STRESSES Yuriy Povstenko ...........................................................................................51 17. THE INFLUENCE OF THE BOUNDARY CONDITIONS ON THE SHEAR STRESSES IN SANDWICH PANELS SUBJECTED TO TORSION Zbigniew Pozorski, Szymon Wojciechowski ...............................................52 18. CONVERGENCE OF THE SEQUENCES OF HOMOGENEOUS YOUNG MEASURES Piotr Puchała .................................................................................................54 19. MATHEMATICAL THINKING AS AN INDISPENSABLE SKILL TO SOLVE BOTH EVERYDAY PROBLEMS AND PURELY MATHEMATICAL ISSUES Gra żyna Rygał ..............................................................................................56 20. THE CONTROL OF LOCAL AND GLOBAL INSTABILITY REGIONS OF THE SLENDER STRUCTURES Krzysztof Sokół ............................................................................................57 6 Mathematical Modeling in Physics and Engineering 21. REMARKS ABOUT GEOMETRIC SCALE IN ANALYTIC HIERARCHY PROCESS Tomasz Starczewski .................................................................................... 59 22. NEW LEARNING TOOLS FOR TEACHING THE SEMANTICS OF PROGRAMMING LANGUAGES William Steingartner, Valerie Novitzká ...................................................... 63 23. THE INFLUENCE OF MOUNTING RIGIDITY ON STABILITY AND STRENGTH OF CYLINDER BARRELS OF A TELESCOPIC HYDRAULIC CYLINDER Sebastian Uzny, Łukasz Kutrowski ............................................................. 69 24. NONLINEAR COMPONENT OF FREE VIBRATION FREQUENCY OF PARTIALLY TENSIONED SYSTEM WITH CONSIDERATION OF ROTATIONAL STIFFNESS OF SUPPORT Sebastian Uzny, Michał Osadnik ................................................................. 73 25. THE DETERMINATION OF STRESS-STRAIN RELATIONS FOR STEELS CONSIDERING THE INFLUENCE OF TEMPERATURE Jerzy Winczek .............................................................................................. 77 26. COMPARISON OF THE ANALYTICAL AND NUMERICAL SOLUTIONS OF THE LAPLACE EQUATION Ewa W ęgrzyn-Skrzypczak, Tomasz Skrzypczak ........................................ 83 27. INVERTIBLE POLYNOMIAL MAPPINGS WHICH HAVE ONE ZERO AT INFINITY STABILITY Magdalena Wo źniakowska .......................................................................... 85 28. DIFFERENTIAL TRANSFORMATION METHOD FOR A CANTILEVER BEAM WITH DAMAGE Izabela Zamorska ......................................................................................... 87 THE DIDACTIC PANEL ………………………………………………………………………………89 29. PROFESSIONAL PRACTICES IN THE STUDY PROGRAM ACCORDING TO LAW 2.0. REGIONAL POSSIBILITIES OF PROFESSIONAL PRACTICES Jolanta Borowska ......................................................................................... 91 7 Mathematical Modeling in Physics and Engineering 30. INTERDISCYPLINARY STUDIES ACCORDING TO LAW 2.0 Joanna Klekot ...............................................................................................92 31. THE REQUIREMENTS FOR GRANTING THE RIGHT TO CONDUCT STUDIES WITH A PRACTICAL PROFILE IN THE CONTEXT OF THE HIGHER EDUCATION AND SCIENCE LAW (ACT 2.0) Sylwia Lara-Dziembek .................................................................................93 32. THE REQUIREMENTS FOR GRANTING THE RIGHT TO CONDUCT STUDIES WITH A GENERAL ACADEMIC PROFILE IN THE CONTEXT OF THE HIGHER EDUCATION AND SCIENCE LAW (ACT 2.0) Edyta Pawlak ................................................................................................94 33. PRINCIPLES OF CLASSIFICATION OF SCIENTIFIC DISCIPLINES ACCORDING TO LAW 2.0 (LAW ON HIGHER EDUCATION AND SCIENCE), STATE ON