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Slowly rotating sources around static black holes
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we study the possibility of perturbative solution of the Einstein equations in the case of stationary and axially symmetric metric. The method is motivated by the pursuit of describing the astrophysically important system of a black hole surrounded by a thin disc or a ring. A Schwarzschild black hole is thus considered as a central source, with a light and/or slowly rotating disc around. We show that the metric can be found in terms of perturbative expansions in relative disc mass or in inverted distance from the hole, and point out where problems occur. The approach can be applied to a disc "given in advance" as well as in the "self-consistent" case when the disc elements orbit on circular geodesics in the desired total eld. It can also be generalised to the discs composed of more dust components.
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Go on Small Boards
Čížek, Pavel ; Majerech, Vladan (referee) ; Hric, Jan (advisor)
In presented work we study applicability of the heuristics used in computer analysis of the chess (to be specific we will consider transposition tables, killer moves, history heuristics and counter-moves) for the valuation of the position in the go. In the first part will try to deal with problems which arises, because rules and behaviour of the chess and go are really different in some ways. Obtained heuristics had been implemented and at the end we will try to evaluate their efficiency and mutual (in)dependence experimentally using this program to solve some simple positions.
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Mathematical analysis and numerical simulation of bone remodeling
Čížek, Pavel ; Hron, Jaroslav (referee) ; Maršík, František (advisor)
In the presented work, we study a model of bone deformation caused by action of external forces. After the biological introduction, in which we describe a bone remodelling process and its connection with bone deformation, we deal with conservation laws and material characteristics of a bone. We define weak formulation. Further, we linearize the equations and prove existence and uniqueness of the solution. Consecutively, we describe the finite element method and the programming of this method for the computing of the approximate solution of the problem using the logic of object-oriented programming. We also adduce a description of the used data structures. In the conclusion, we present numerical results reached by the described program that represent deformation of femur and deformation of vertebras and intervertebral foramina.
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Control Problems in Epidemiology
Čížek, Pavel ; Pražák, Dalibor (referee) ; Milota, Jaroslav (advisor)
Na/.ev prace; Ki/cnf \) eh modeled] Aulor: Pavel Ci/ek Kaledra; Kaledra matemaliekc analy/.y Vcdouef bakala'rskc prace: Doc. KNDr. Jarosla\. CSc. c-inait vedouci'ho: niilota(« karlin.mff.cuni.c/ Ahsirakl: V predlo/cne praci studujeme model maso\. inlekcm mikropara/iiicke epidcinie. Co oduv.eni" modeiu, klcre \ycha/( / hiologickyeh po/nulku o sludovaiicni lypu epideiuii. u\a\liine |eho /a'kladm nialeniaiicke \htslmMi. /.axx'dcni'in ock(i\';ii:i' niotlei iransloriiiujcrnc. I);ile ^o /ah\\anie \laslnosUni feseni piivodm'ho i iransiorinox anelio niodelu a siahililou siaciona'nueli Inidii. PoroMuixanfni vysiedkii pro model puvodm a model iran>Jormovan\, /da je ocko\ain' /.a\edeno spra\-nc. lA.idinie i jiiie mo/noMi jcho /a\'edem. N;is!cdnc se /.ahvvanie cenou Icehy a ockovant'. Illedamc linancne n e j \ i re^cnf ma/k\k \'clikou cast populace oekovat. Tiile; Isi/em \h modeled! Auihor: Pa\el C ' f / e k Departnicnl: Kaledra iimlematickr aiialv/y Sii|)er\: Doe. RNDr. Jaio^lax Miloia. C'Se. Super\s e-mail adress: nii]o{a('1''karliu.n)tT.cuni.c/ Ahsii'acl: In the present work \\ studx a model of a ma^-action mieniparasiue epidoniic. After the deduction of llie motlel. \\lilcli issues from biologic in for uiafioii ahiui! ihe studied l\pe of epidemic. \\ mention basic maihematic.il chaiactcrislies. \\"e transform die...
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Analysis of household consumption expenditure with respect to VAT
Čížek, Pavel ; Janíčko, Martin (advisor) ; Chytilová, Helena (referee)
The constant increase in public sector spending in the advanced economies, increases pressure on the revenue side of public budgets. The primary sources of public budgets are taxes. This raises a question of what type of tax instrument to choose in respect to meet the high efficiency in sourcing public budgets restriction and at the same time, to minimize the negative impact on the private sector and households. As generally effective tax is considered a consumption tax. But what is the real effect of this tax in the short run and long run? The aim of this thesis is to analyze the influence of value -- added tax (VAT) on household expendictures in the short and long run. At first I provide empirical test of the short-term effect of VAT on household spending using quarter panel data for Visegrad fore countries, as I am focused mostly on the Czech Republic and Slovakia. Then construct a broader set of data for 14 EU countries, in purpose to test the long-term effect. For testing, I use several estimation techniques for panel data, taking into account the dynamic nature of these data sets.
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The effect of monetary policy on the Japanese economy during the 90 years
Čížek, Pavel ; Dočkal, Dalibor (advisor) ; Štěpánek, Pavel (referee)
The aim of this paper is to analyze the effects of monetary policy to the Japanese real economy during the eighties and nineties, whichare often referred to as the the Lost Decade. The theoretical part is devoted to the basic description and comparison of selected theories of monetary policy. It focuses primarily on the Liquidity trap, Friedman's monetarism and also deals with the benefits of mainstream economics and Austrian School. The maen finding is analysis of selected data in the Japanese economy sensitive to monetary policy. On the basis of evaluated data shows to what extent the real product influenced monetary policy. As exploration of the data is chosen short-term interest rate at which banks offer loans to investors, share prices, changes in money supply and demand and the development of gross domestic product. The result of the examination is to determine the proportion of the impact of monetary policy to fluctuations in the so-called Lost decade.
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