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Lie groups and their physical applications
Kunz, Daniel ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
In this thesis I describe construction of Lie group and Lie algebra and its following usage for physical problems. To be able to construct Lie groups and Lie algebras we need define basic terms such as topological manifold, tensor algebra and differential geometry. First part of my thesis is aimed on this topic. In second part I am dealing with construction of Lie groups and algebras. Furthermore, I am showing different properties of given structures. Next I am trying to show, that there exists some connection among Lie groups and Lie algebras. In last part of this thesis is used just for showing how this apparat can be used on physical problems. Best known usage is to find physical symmetries to establish conservation laws, all thanks to famous Noether theorem.
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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Density of Minkowski functionals of stationary random sets
Dohnálek, Filip ; Rataj, Jan (advisor) ; Beneš, Viktor (referee)
Title: Density of Minkowski functionals of stationary random sets Author: Bc. Filip Dohnálek Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jan Rataj, CSc., Mathematical Institute of Charles University Abstract: In the presented work we can find the created theory of random closed excursion set generated by means of Gaussian real random field. We specialize in a real random field, which is defined on the regular stratified manifold. The text includes a determination of conditions for a random field and stratified manifold in which densities of the intrinsic volumes for excursion sets exist. Then subsequently attributes and relations of the excursion set are derived for the existence of densities of the intrinsic volumes. Finally, a simulated study is made where we compare theoretical and estimated values of densities. This is followed by a discussion on the results, which we compare to the Boolean model. Keywords: Densities of the intrinsic volume, Excursion set, Manifold, Real random field
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Instalation of AR64304 Engine
Kubiš, Vojtěch ; Beran, Martin (referee) ; Svída, David (advisor)
This diploma thesis is concerned about installation of AR64304 engine into Alfa Romeo 75. The main goal of this thesis is a design of exhaust system for AR64304 engine installed in the engine bay of the vehicle. The design of the exhaust system was done with a respect to the noise and emission requirements, as well as with a respect to the performance of the engine. Lotus Engine Simulation software was used for the simulation of the engine with proposed exhaust system. Input data for the simulation were obtained from measurements of the cylinder head on a flow bench and precise measurement of camshaft profile. The essential contribution of this work is a set of construction parameters of the exhaust system. This thesis also contains technical specifications of AR64304 engine and the installation process.
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Heating of panel house with alternative preparation of TV
Bílek, Martin ; Adam, Pavel (referee) ; Horák, Petr (advisor)
The subject of this thesis is the heating and hot water preparation in the residential house in Brno. object has eight floors and basement. In each floor there are five residential units. In the basement there is a utility room with heating, gas boiler cascade. Used to heat-pipe heating system. Heating surfaces are plate and tubular body. The primary source of hot water is gas boiler. As a secondary source of alternative preparation with solar home stations. Each apartment has its own solar station.
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