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Gravitational perturbations in NP/GHP formalism
Pospíšil, Marek ; Kofroň, David (advisor) ; Ledvinka, Tomáš (referee)
This work gets the reader acquainted with tetrad approaches to general theory of re- lativity (GTR), namely with Newman - Penrose (NP) and Geroch - Held - Perose (GHP) formalisms. Obtained expressions are expressed in coordinates. Subsequently, this work concerns with the perturbation techniques in GTR, including both metric perturbation and the method of superpotential, the latter being more common in GHP formalism. Following is the recapitulation of important results based on this method. The core of the work is in generalization of known results for spacetimes with ac- celeration (so called C-metric) and checking previous results using computation in the Wolfram Mathematica program. In order not to work just with rather complicated GHP and NP formalisms, the main result is checked also by transcription into coordinate par- tial derivatives. 1
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Numerical solution of the Ernst equation
Pospíšil, Marek ; Ledvinka, Tomáš (advisor) ; Svítek, Otakar (referee)
This work is concerned with solving the Ernst equation using numerical techniques, namely pseudospectral methods. In theoretical chapters, we summarize the properties of some black-hole space-times. The work then cites the derivation of the Ernst equation and the Kerr solution. Afterwards we present pseudospectral techniques on the example of a numerical solution of the Laplace equation with a boundary condition at infinity. Finally we solve a non-linear differential equation, thus proving, that pseudospectral methods might be used even on the Ernst equation. 1
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Microscopic sets and drops in Banach spaces
Pospíšil, Marek ; Lukeš, Jaroslav (advisor) ; Fabian, Marián (referee)
First we define microscopic sets on the real axis and study their relation to the sets of Hausdorff and Lebesgue measure zero and the sets of first category. In the second part, we prove the Bishop-Phelps' theorem and its equivalence with the Ekeland's variational principle, the Daneš's drop theorem, the Brézis-Browder's theorem and the Caristi-Kirks's theorem. Doing so we define the notion of a drop as the convex hull of a set and a point. In the third part we prove that the drop property equals reflexivity in some sense. A space has the drop property if it is possible to find the drop from the Daneš's theorem even in a more general case than the theorem itself guarantees. Furthermore, we characterize this property using the approximative compactness. Last, we study the microscopic drop property that is more relaxed than the original drop property. We find out that those two notions are for noncompact sets in reflexive spaces equivalent. Powered by TCPDF (www.tcpdf.org)
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Microscopic sets and drops in Banach spaces
Pospíšil, Marek ; Lukeš, Jaroslav (advisor) ; Zelený, Miroslav (referee)
First we define microscopic sets on the real axis and study their relation to the sets of Hausdorff and Lebesgue measure zero and the sets of first category. In the second part, we prove the Ekeland's variational principle and its equivalence with the the Daneš's drop theorem, the Brézis-Browder's theorem, the Phelps' lemma and the Caristi-Kirks's theorem. Furthermore, we discuss its relation to the Bishop-Phelps' theorem. Doing so we define the notion of a drop as the convex hull of a set and a point. In the third part we prove that the drop property equals reflexivity in some sense. A space has the drop property if it is possible to find the drop from the Daneš's theorem even in a more general case than the theorem itself guarantees. Furthermore, we characterize this property using the approximative compactness. Last, we study the microscopic drop property that is more relaxed than the original drop property. We find out that those two notions are for certain sets in reflexive spaces equivalent.
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Data migration and quality assurance and testing projects methodology of Deloitte CZ
Pospíšil, Marek ; Bruckner, Tomáš (advisor) ; Šedivý, Josef (referee)
The main purpose of the thesis is to introduce a method for data migration quality assurance or completeness and accuracy testing of migrated data. Method will become part of the knowledge base of Deloitte Czech Republic for projects in the Enterprise Risk Services department. Data migration quality assurance projects carried by Deloitte in the Czech Republic have its own specifics. Although there exists methodology "Systems Development Playbook" which also includes a data migration methodology, the problem especially of the Prague branch is the fact that the procedures and methods for consulting projects in the area of data migration are not described in current methodological documentations including specifics of the Czech and Slovak projects. This represents a risk of inconsistencies in the implementation of this type of consulting projects in case of key employees leaving. Improving procedures and optimization of human resources engagement in data migration projects can't be measurably compared among projects, if there don't exists a basic methodology against which specific projects can be measured. The objectives of the work are achieved by consolidating experience from past projects involving data migration within Deloitte Czech Republic and designing improvement of existing processes by integrating information from external sources and internal sources of the global Deloitte Touche Tohmatsu.
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Credit risk insurance
Pospíšil, Marek ; Ducháčková, Eva (advisor) ; Daňhel, Jaroslav (referee)
The theme of the work is credit risk insurance. The main objective is to analyze this specific type of insurance, define its role in insurance system and for covering credit risk. Analyzed are both commercial insurance and insurance with state support. The important part of this work is also analysis of czech and world insurance markets and influence of global economic recession. At the end of the work there are presented alternative instruments for minimizing credit risk and their comparison with insurance products.
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Eclipse Process Framework Composer
Pospíšil, Marek ; Buchalcevová, Alena (advisor) ; Balada, Jakub (referee)
The goal of the bachelor thesis is to create a user manual in Czech language for new users of the Eclipse Process Framework Composer. In the first part of my thesis, Eclipse Process Framework Composer and basic issues of software development methods focused on OpenUp method are introduced to the reader. Second part of my thesis describes possibilities and usage of this tool from installation to publication of created processes. There are also examples provided to clarify the description.
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Analysis of credit risk insurance on Czech insurance market
Pospíšil, Marek ; Ducháčková, Eva (advisor)
The theme of the work is analysis of the credit risk insurance. The main objective is to analyze this specific type of insurance, description of insurance companies and charakteristic of their products. The work is divided into the three main parts. First chapter is about definition of credit risk, reasons for the existence and importance of this insurance. The second part is focused on the individual components of insurance. The third part is the analysis of insurance companies and charakteristic of their products.
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