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Invariants of jet groups and applications in continuum mechanics
Buriánek, Martin ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
This thesis is focused on jet groups and their matrix representations. The opening section deals with group representations, group actions on sets and invariants of actions. Another section explains terms such as smooth manifolds, Lie group and Lie algebra. The following part clarifies terms jet and jet group as a special example of Lie group. First of all, groups $G_1^r$ and $G_n^1$ are described, then description of group $G_n^2$ and its subgroups ensues. Representations of these jet groups are proposed. Finally, applications of jet groups in continuum mechanics are mentioned. The thesis is complemented with algorithm of chosen problems in program Wolfram Mathematica.
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Mass actions in Czech civil procedure
Novotný, Vojtěch ; Smolík, Petr (advisor) ; Winterová, Alena (referee)
Group actions in Czech procedural law Summary The thesis deals with an issue of group actions, which is a legal instrument of collective protection of private rights in civil proceedings. The aim of this thesis is to analyze this procedural institute, to point out shortcomings of current legislation and to propose it's acceptable solution. The thesis is divided into three relatively independent sections. The first section focuses on theoretical basis (including a brief outline of the historical development) and defines basic terminology used in the thesis. Then it describes the most general division of the collective enforcement mechanisms into a group action and a representative action. The second section concentrates on legislative schemes of group actions in certain foreign jurisdictions. Specifically, it deals with a legal conception of class action in the legal system of the USA, where it is applied as a kind of a opt-out group proceedings (group members, who does not agree with adjudication of their claims, may opt-out), then it deals with opt-in group proceedings in Sweden (group members can be required to enter the suit individually) and finally it describes a German model proceedings in capital market disputes, which represents a compromise between individual and collective proceedings. The third...
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Invariants of jet groups and applications in continuum mechanics
Buriánek, Martin ; Doupovec, Miroslav (referee) ; Kureš, Miroslav (advisor)
This thesis is focused on jet groups and their matrix representations. The opening section deals with group representations, group actions on sets and invariants of actions. Another section explains terms such as smooth manifolds, Lie group and Lie algebra. The following part clarifies terms jet and jet group as a special example of Lie group. First of all, groups $G_1^r$ and $G_n^1$ are described, then description of group $G_n^2$ and its subgroups ensues. Representations of these jet groups are proposed. Finally, applications of jet groups in continuum mechanics are mentioned. The thesis is complemented with algorithm of chosen problems in program Wolfram Mathematica.
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Visibly irreducible polynomials
Bžatková, Kateřina ; Kala, Vítězslav (advisor) ; Tinková, Magdaléna (referee)
Thesis is focused on the irreducibility of polynomials over finite fields. Paper Evan M. O'Dorney, Visibly irreducible polynomials over finite fields, when prooving irreducibility uses visibly irreducible decomposition VID, which is type of decomposition easily determinating irreducibility. In the thesis we analyse in detail results from this paper. Furthermore we generalize the definition of VID from mentioned paper by omitting a condition on any degree of polynomials.
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Invariant theory for finite groups
Žurav, Martin ; Šťovíček, Jan (advisor) ; Šaroch, Jan (referee)
The prime goal of this thesis is to give a decent introduction to the theory of invariants for finite groups. We begin our characterisation with symmetric polynomials and their fundamental properties. In particular, we study the ring of symmetric polynomials and we prove that it is finitely generated by elementary symmetric functions. Then we deal with some of the criteria for a polynomial to be symmetric. In the second part, we generalise these ideas for any finite subgroup of GL(n,k). We define an action of a finite linear group on k[x_1,...,x_n] and consider polynomials that are invariant under such action. We show that they form a ring which is always finitely generated, as follows from the Noether's bound theorem. At the end, we describe the ring of invariants and relations among its generators more profoundly.
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Mass actions in Czech civil procedure
Novotný, Vojtěch ; Smolík, Petr (advisor) ; Winterová, Alena (referee)
Group actions in Czech procedural law Summary The thesis deals with an issue of group actions, which is a legal instrument of collective protection of private rights in civil proceedings. The aim of this thesis is to analyze this procedural institute, to point out shortcomings of current legislation and to propose it's acceptable solution. The thesis is divided into three relatively independent sections. The first section focuses on theoretical basis (including a brief outline of the historical development) and defines basic terminology used in the thesis. Then it describes the most general division of the collective enforcement mechanisms into a group action and a representative action. The second section concentrates on legislative schemes of group actions in certain foreign jurisdictions. Specifically, it deals with a legal conception of class action in the legal system of the USA, where it is applied as a kind of a opt-out group proceedings (group members, who does not agree with adjudication of their claims, may opt-out), then it deals with opt-in group proceedings in Sweden (group members can be required to enter the suit individually) and finally it describes a German model proceedings in capital market disputes, which represents a compromise between individual and collective proceedings. The third...
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