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Radiation problems of relativistic systems with symmetries
Bohata, Martin ; Bičák, Jiří (advisor) ; Ledvinka, Tomáš (referee)
The thesis deals with system of interacting particles producing eld with helical symmetry within linear theories of scalar and electromagnetic elds in Minkowski spacetime. Advanced and retarded elds are found of a particle on a circular orbit in space - thus moving along a helical trajectory in spacetime. The results are used in a dynamic (self-consistent) two-body problem under the assumption that the interaction between the particles is mediated by both retarded and advanced elds. As a consequence no radiation reaction force arise and the helical symmetry is maintained. The two-body problem of scalar and electromagnetic elds is discussed in a noninertial system in which particles are at rest. In both cases equilibrium conditions are found and the existence and uniqueness of solution is proved. The equilibrium radius is found explicitly in case of two-body electromagnetic problem in an aproximation of small velocities. In the next part the problem is generalized to the case of N particles producing electromagnetic eld with helical symmetry. The existence of equilibrium conguration is proved in general, and the uniqueness is shown in the aproximation of small velocities.
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Technique of operator algebras in quantum structures
Bohata, Martin
Title: Technique of operator algebras in quantum structures Author: Mgr. Martin Bohata Institution: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague Supervisor: Prof. RNDr. Jan Hamhalter, CSc. Abstract: The thesis deals with Bell inequalities and a partial order called star order. These two structures are investigated by means of the theory of operator algebras. The study of Bell inequalities is focused on the CHSH version of Bell inequality and its quantum version called Cirel'son inequality. The Cirel'son inequality is generalized to real and complex linear spaces with a pseudo inner product. The results obtained on this abstract level are applied to the study of maximal violation of the (CHSH version of) Bell inequality formulated in the mathematical framework of *-algebras. It is shown that elements maximally violated the Bell inequality are closely related to Pauli spin matrices. These results are also generalized to the nonassociative case of Jordan algebras. The next field of our interest is the star order. This partial order is considered on certain *-algebras. As a consequence of our analysis of the star order on partial isometries, we obtain a new characterization of infinite C*-algebras. Then we investigate the infimum and supremum problem for the...
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Matrix Krein-Milman theorem
Surma, Martin ; Spurný, Jiří (advisor) ; Bohata, Martin (referee)
This thesis deals with the generalized version of the Krein-Milman theorem, as it was stated in the work of Webster-Winkler. We introduce basic definitions, extending convexity notions in the classical sense to the setting of matrix convex sets. Further on, we study important theorems which are needed to prove the main result, for example, a representation result, which states that any compact matrix convex set is matrix affinely homeomorphic to the matricial version of the state space on some operator system. In the final part, we provide a proof of the matrix Krein-Milman theorem. 1
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The impact of establishing euro in the Czech Republic on economic policy by 2020
Bohata, Martin ; Štěpánek, Pavel (advisor) ; Ševčíková, Michaela (referee)
The thesis addresses the points of interest related to establishing the euro currency in the Czech Republic by 2020. What are the connected costs and benefits? Is euro going to be a contribution to the Czech economy? The theoretical part describes the creation process of European monetary union. The paper then works with advantages and risks associated with euro. The main cost of membership in the eurozone being the loss of independent monetary policy and the loss of the exchange rate mechanism is estimated in range of 0.59 to 2.34 % of GDP. Comparing the direct costs and benefits then leads to a net loss for the Czech Republic. Mutual comparison is conducted between the Czech Republic and Slovakia. It is shown that the difference in economic progress between these two countries is statistically insignificant. Thus the thesis concludes that establishing the euro in the Czech Republic by 2020 would be of no benefit.
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Technique of operator algebras in quantum structures
Bohata, Martin
Title: Technique of operator algebras in quantum structures Author: Mgr. Martin Bohata Institution: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague Supervisor: Prof. RNDr. Jan Hamhalter, CSc. Abstract: The thesis deals with Bell inequalities and a partial order called star order. These two structures are investigated by means of the theory of operator algebras. The study of Bell inequalities is focused on the CHSH version of Bell inequality and its quantum version called Cirel'son inequality. The Cirel'son inequality is generalized to real and complex linear spaces with a pseudo inner product. The results obtained on this abstract level are applied to the study of maximal violation of the (CHSH version of) Bell inequality formulated in the mathematical framework of *-algebras. It is shown that elements maximally violated the Bell inequality are closely related to Pauli spin matrices. These results are also generalized to the nonassociative case of Jordan algebras. The next field of our interest is the star order. This partial order is considered on certain *-algebras. As a consequence of our analysis of the star order on partial isometries, we obtain a new characterization of infinite C*-algebras. Then we investigate the infimum and supremum problem for the...
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Radiation problems of relativistic systems with symmetries
Bohata, Martin ; Bičák, Jiří (advisor) ; Ledvinka, Tomáš (referee)
The thesis deals with system of interacting particles producing eld with helical symmetry within linear theories of scalar and electromagnetic elds in Minkowski spacetime. Advanced and retarded elds are found of a particle on a circular orbit in space - thus moving along a helical trajectory in spacetime. The results are used in a dynamic (self-consistent) two-body problem under the assumption that the interaction between the particles is mediated by both retarded and advanced elds. As a consequence no radiation reaction force arise and the helical symmetry is maintained. The two-body problem of scalar and electromagnetic elds is discussed in a noninertial system in which particles are at rest. In both cases equilibrium conditions are found and the existence and uniqueness of solution is proved. The equilibrium radius is found explicitly in case of two-body electromagnetic problem in an aproximation of small velocities. In the next part the problem is generalized to the case of N particles producing electromagnetic eld with helical symmetry. The existence of equilibrium conguration is proved in general, and the uniqueness is shown in the aproximation of small velocities.
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Do legal measures affect road accidents´ rate in the Czech Republic?
Bohata, Martin ; Melzochová, Jitka (advisor) ; Svoboda, Miroslav (referee)
There are more than 1.3 million people killed and tens of millions of people injured every year in road accidents. In the Czech Republic the financial losses due to road accidents are more than 50 billion Czech crowns a year, in the EU it is almost 200 billion euros a year. That is why the goal of every lawmaker should be to rationally affect the traffic flow and to try to lower the number of road accidents and their consequences. In 2005 Czech legislators ratified law no. 411/2005 introducing the "point" system and law no. 133/2011 in 2011 forcing the use of winter tyres. This paper studies the impact of these laws on road accidents a on the number of killed and injured people due to road accidents. It studies other possible elements which are likely to affect road accidents. The paper confirms positive influence of the law no. 411/2005 containing the "point" system. There has been a significant decrease in the number of killed and injured people. This fact is accepted at the .01 level. . The effect of the law no. 133/2011 has not been proved for now. That is because of short evaluation time, ergo lack of data.
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