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Geometric transformations in secondary school mathematics
Smetana, Adam ; Surynková, Petra (advisor) ; Hromadová, Jana (referee)
The current availability of computers and mobile devices in school facilities and the affordability of mobile devices for everyone provide for an increasing use of interactive geometry in the curriculum. The aim of this thesis is to summarize the printed and electronic resources used for teaching geometry, to study them in detail and to use them to build an electronic textbook and a collection of exercises in interactive geometry environment. GeoGebra is used among the interactive geometry environments, mainly because it offers the greatest variability for the purposes of this publication. The electronic publication can be used by both students and their teachers. Electronic publications were an essential part of the Czech education system during the period of compulsory distance education in years 2020 and 2021. The thesis includes a short questionnaire survey that aims to find out what textbooks or exercise collections are being used by teachers, what transformations are taught in secondary schools and to what extent. The results show that among teachers specific printed textbooks and collections are still more popular than interactive resources. Keywords: geometric transformations, rotation, translation, homothety, GeoGebra
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Zaměření a dokumentace části rozvodné sítě elektrické energie
SMETANA, Adam
The topic of this diploma thesis is the focus and documentation of a part of the power grid. The main goal of the work is to perform the survey and preparation of documentation of rural lines very high voltage 110 kV according to the requirements of the distribution network operator. The diploma thesis describes the basic requirements of the distribution network administrator for the processing of documentation. Furthermore, the work describes geodetic reference systems in the Czech Republic, geodetic measurement methods and GNSS.
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Electroweak symmetry breaking by dynamically generated masses of quarks and leptons
Smetana, Adam ; Hošek, Jiří (advisor) ; Hořejší, Jiří (referee) ; Olejník, Štefan (referee)
Title: Electroweak symmetry breaking by dynamically generated masses of quarks and leptons Author: Adam Smetana Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic Abstract: The aim of the thesis is to study models of the electroweak symmetry breaking caused by dynamically generated masses of quarks and lep- tons. (1) We perform the basic analysis whether the main underlying idea, that the masses of only known fermions can provide the elec- troweak symmetry breaking, is actually feasible. For that we elaborate a two-composite-Higgs-doublet model of the top-quark and neutrino condensation. The model suggests rather large number, O(100), of right-handed neutrinos. (2) We analyze the model of strong Yukawa dynamics where the dynamical fermion mass generation is provided by exchanges of new elementary massive complex doublet scalar fields. We focus on solving the coupled Schwinger-Dyson equations for fermion and scalar self-energies by means of approximative methods. We doc- ument that strongly hierarchical mass spectra can be reproduced. (3) We elaborate the flavor gauge model where the dynamical fermion mass...
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Witten's loop in simple extensions of the Standard Model of particle interactions
Miřátský, Václav ; Malinský, Michal (advisor) ; Smetana, Adam (referee)
The goal of this Master thesis is to demonstrate Witteńs mechanism in selected extensions of the Standard model based on the Pati-Salam gauge group. The purpose of this mechanism is to obtain an extremely large Majorana mass term for right-handed neutrinos at the two-loop level and consequently light physical masses of neutrinos using the type I see-saw mechanism. The existence of corresponding Feynman diagrams without any interactions of vector bosons is presented. While it is impossible to construct this type of corrections in minimal SO(10) or SU(5)xU(1) model in Pati-Salam model they may be even dominant. Subsequently, implications of possible partial gauge coupling unification or even embedding of the Pati-Salam group into a gauge group of "Great Unified Theory" are considered. At the end the possibility of unacceptably fast proton decay is inspected. The discussed models are concluded to be potentially realistic but only at the cost of predictivity, since completely unknown Yukawa couplings appear in numerous key relations. 1
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Spatial Geometry in Secondary School Education
Smetana, Adam ; Surynková, Petra (advisor) ; Šarounová, Alena (referee)
1 Title: Curriculum of solid geometry at czech high schools Author: Adam Smetana Department: Department of Mathematics Education Supervisor: RNDr. Petra Surynková, Ph.D Abstract: The topic of the bachelor thesis is Curriculum of solid geometry at Czech high schools. All of the basic and advanced terms are explained and shown in simple illustrations. The thesis contains a number of solved examples and exercises that are being taught at Czech high schools. All the examples are supported by 2D and 3D applets in GeoGebra software. Keywords: curriculum, solid geometry, cross sections, GeoGebra
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Total stations test according to ISO 17123.
SMETANA, Adam
This bachelor thesis deals with testing the accuracy of total stations Leica TCRA 1203+ R400 and Thrimble M3 5'' according to the processes outlined in the norm ČSN ISO 17123 Optics and optical instruments - Field procedure for testing geodetic and surveying instruments - Part 3: Theodolites and ČSN ISO 17123 Optics and optical instruments - Field procedure for testing geodetic and surveying instrument - Part 4: Electro-optical distance meters (EDM). The aim is to determine the accuracy of measurement of horizontal directions, zenith angles and lenghts. To determine the accuracy, the test point field was built in the University of South Bohemia. The result was calculated standard deviation of measured directions, angles and lengths.
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Quantum aspects of grand unified theories
Gráf, Lukáš ; Malinský, Michal (advisor) ; Smetana, Adam (referee)
In this thesis we focus on Grand Unified Theories based on the SO(10) gauge group and, in particular, on the viability of the minimal nonsupersymmetric SO(10) models. Technically, this amounts to a detailed assessment of their vac- uum stability and related (non-)tachyonicity of their scalar spectrum. It turns out that the one-loop scalar mass corrections are important for elimination of the tachyonic behaviour of certain pseudo-Goldstone bosons. In this work these issues are briefly reviewed and two distinct methods for the calculation of the critical radiative corrections are discussed. More specifically, besides the revision of the effective potential approach to the 45 ⊕ 16 Higgs model also the standard perturbative theory method is employed for this purpose. The latter approach is particularly suitable for the more realistic 45 ⊕ 126 Higgs model since it appears to be practically impossible to construct the corresponding effective potential in that case. Consequently, diagrammatic methods are used to calculate the SO(10)- invariant leading scalar quantum correction to the problematic pseudo-Goldstone masses in the 45 ⊕ 126 model. 1
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Electroweak symmetry breaking by dynamically generated masses of quarks and leptons
Smetana, Adam ; Hošek, Jiří (advisor) ; Hořejší, Jiří (referee) ; Olejník, Štefan (referee)
Title: Electroweak symmetry breaking by dynamically generated masses of quarks and leptons Author: Adam Smetana Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic Abstract: The aim of the thesis is to study models of the electroweak symmetry breaking caused by dynamically generated masses of quarks and lep- tons. (1) We perform the basic analysis whether the main underlying idea, that the masses of only known fermions can provide the elec- troweak symmetry breaking, is actually feasible. For that we elaborate a two-composite-Higgs-doublet model of the top-quark and neutrino condensation. The model suggests rather large number, O(100), of right-handed neutrinos. (2) We analyze the model of strong Yukawa dynamics where the dynamical fermion mass generation is provided by exchanges of new elementary massive complex doublet scalar fields. We focus on solving the coupled Schwinger-Dyson equations for fermion and scalar self-energies by means of approximative methods. We doc- ument that strongly hierarchical mass spectra can be reproduced. (3) We elaborate the flavor gauge model where the dynamical fermion mass...
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