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Fault relevance diagnostics of the PMSM under the inter-turn short circuit fault
Zezula, Lukáš ; Václavek, Pavel (referee) ; Blaha, Petr (advisor)
Tato práce popisuje matematické modelování mezizávitových zkratů fázového vinutí synchronního motoru s permanentními magnety, diskretizaci odvozeného modelu a diagnostiku závažnosti zkratu založenou na referenčním modelu. Popis zkratovaného stroje je vytvořen v proměnných statoru s uvažováním sérioparalelního zapojení vinutí a následně transformován do referenčního rámce rotoru pomocí rozšířené Clarkové a Parkovy transformační matice. Diskrétní ekvivalent navrženého modelu je vytvořen pomocí definované diskretizace lineárních časově variantních systémů, přičemž je uvažováno, že elektrická úhlová rychlost je časově variantní parametr s definovaným integrálem. Diskrétní model je transformován do referenčního rámce statoru, aby se maximalizovala perzistence vstupních signálů. Diagnostika závažnosti zkratu je poté realizována pomocí rekurzivního parametrického odhadu diskrétního modelu. Jedna z kapitol je věnována i popisu řídicího systému, neboť zkraty mohou ovlivnit stavové proměnné různým způsobem v závislosti na architektuře a volbě parametrů řídicího systému. Za každou kapitolou následuje experimentální ověření prezentovaných myšlenek.
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Mathematical Analysis of Captured Network Traffic
Soós, Tibor ; Koutný, Martin (referee) ; Hošek, Jiří (advisor)
This thesis is considering with network traffic analysis and prediction of real networks default services. The first part of this paper is containing the theoretical explanation of the mathematical model’s needs. These models are mainly used as a part of simulation algorithms which are describing the processes of network traffic simulations. The second part is describing the process how to apply the models to mathematically analyze the captured traffic. The capture is including all kind of packet types which can appear on the real network. At the last part of the thesis is described the detailed design of the prediction algorithm’s which are developed in programing language of Matlab® Mathworks®.
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Teaching basic calculus at the secondary school, case study
Hamšík, Karel ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
This thesis deals with teaching the basics of calculus in secondary school. These are specifcally those areas of mathematics (functions, derivatives, integrals) that are subsequently discussed in more depth at universities of science, technology, economics, and also other felds. Most university students will encounter these math problems at least to a small extent. Therefore, I am interested in the extent to which pupils are prepared to solve these problems after leaving high school. The second topic that I am interested in is how much the pupils encountered the topics and terms of calculus during their secondary school studies, how they understand them and whether or not they can use them. The aim of this thesis is to describe the methods used in education of elementary school calculus in a specifc seminar where this material is discussed and subsequently verify the ability of the pupils to independently solve problems from this feld of mathematics by a set of didactic tests and their subsequent analysis. The analysis showed that the subject of calculus is for the most part well understood by the pupils. The seminar therefore fulflls the prerequisites for a successful introduction to this subject, which can be successfully expanded on in further higher education. Key words: teaching calculus,...
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Fault relevance diagnostics of the PMSM under the inter-turn short circuit fault
Zezula, Lukáš ; Václavek, Pavel (referee) ; Blaha, Petr (advisor)
Tato práce popisuje matematické modelování mezizávitových zkratů fázového vinutí synchronního motoru s permanentními magnety, diskretizaci odvozeného modelu a diagnostiku závažnosti zkratu založenou na referenčním modelu. Popis zkratovaného stroje je vytvořen v proměnných statoru s uvažováním sérioparalelního zapojení vinutí a následně transformován do referenčního rámce rotoru pomocí rozšířené Clarkové a Parkovy transformační matice. Diskrétní ekvivalent navrženého modelu je vytvořen pomocí definované diskretizace lineárních časově variantních systémů, přičemž je uvažováno, že elektrická úhlová rychlost je časově variantní parametr s definovaným integrálem. Diskrétní model je transformován do referenčního rámce statoru, aby se maximalizovala perzistence vstupních signálů. Diagnostika závažnosti zkratu je poté realizována pomocí rekurzivního parametrického odhadu diskrétního modelu. Jedna z kapitol je věnována i popisu řídicího systému, neboť zkraty mohou ovlivnit stavové proměnné různým způsobem v závislosti na architektuře a volbě parametrů řídicího systému. Za každou kapitolou následuje experimentální ověření prezentovaných myšlenek.
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range
Kulvait, Vojtěch ; Málek, Josef (advisor)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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Reeducating university students' mechanical knowledge in mathematical analysis
Šmídová, Kristýna ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The topic of this thesis is the didactics of mathematical analysis. The thesis describes selected observations from the reeducation in an individual tutoring environment of for- mal knowledge of university students in the field of calculus. The aim of the thesis is to describe what formal knowledge appeared, to describe and evaluate selected reeducation interventions and on this basis formulate appropriate methodological recommendation. In the first chapter we deal with the contradiction between definition and concept concept of students, we outline how to convey to students the purpose of definitions and we suggest how to teach students to work with definitions properly, including understanding quan- tified propositions. In the second chapter we present the theory of process and concept together with the generic model theory. In the third chapter we explain the methods of work with students and the methods of the analysis of videos from tutoring. In the fourth chapter we analyze cognitive processes of the concept of sequence limits. KEYWORDS reeducation, individual tutoring, mechanical knowledge, calculus, definitions, quantified proposition, infinity, sequence, limit 1
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Euler's number in calculus
RÁLKOVÁ, Lucie
The main aim of my thesis on the topic of "Euler's number in mathematical analysis" is to create an overview of the Euler numbers in calculus. This essay in the first part deals with the rise of the number e, in other parts of the current use of calculus. Purpose of this work is the insight students of secondary schools and universities to problems Euler numbers and to better understand the importance of e not only in mathematics.
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range
Kulvait, Vojtěch ; Málek, Josef (advisor)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range.
Kulvait, Vojtěch ; Málek, Josef (advisor) ; Kovtunenko, Victor A. (referee) ; Kružík, Martin (referee)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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