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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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On the Discursive Constitution of Language Norm Authorithies in German Schools and Their Influence on the Creation of the Standard Variety
Horbank, Olivia Josephine ; Dovalil, Vít (advisor) ; Sherman, Tamah (referee)
This master thesis analyzes the question, how norm authority constitutes itself in the context of school education. It is based on firsthand data from several adio- and audiovisual recordings of classes in two German schools (trade school and high school). The project provides a description of the mechanism by which the teacher establishes himself as the norm-authority and how he is able to assert this authority towards the student, the norm subject. At the same time, the reaction of the norm subjects towards the intervention of the norm authority into their language production is analyzed. Theoretically, the essay is embedded in the social force field of a standard-variety ("soziales Kräftefeld einer Standardvarietät") by Ulrich Ammon and the language management theory. By following the steps of the language management process, the handling of the language norm is described and an analysis is made of how language norms are actively adopted into the learning process. The analysis and evaluation of the class recordings underline the dynamic character of language norms and show the procedural nature of norm formation and their adoption. Key Words: norm, variety, social force field, language management, macro and micro level, norm authority, norm subject
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Singular points of algebraic varieties
Vančura, Jiří ; Příhoda, Pavel (advisor) ; Šťovíček, Jan (referee)
This thesis is an introduction to exploring singularities of algebraic varieties. In the first chapter, we state basic definitions and theorems necessary for exploring singularities. Firstly, we define algebraic varieties and their corresponding ideals and explain the term of Krull dimension. We also focus on the local properties of varieties. In the second chapter, we begin by examining the term of singularity in detail and introducing methods for searching for singularities. We prove two theorems about the shape and the dimension of singularities. In the second part, we prove theorems about the zero divisors, which enable us to define Cohen-Macaulay and Gorenstein rings. We use them to roughly classify singularities of algebraic varieties.
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