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Mercator projection, loxodromes, and related topics
Rauš, Jaroslav ; Slavík, Antonín (advisor) ; Boček, Leo (referee)
anglicky- Mercator projection, loxodromes, and related topics This bachelor thesis deals with the Mercator projection from both today's and historical point of view. Special emphasis is placed on the formal derivation of the projection, and on the studying of its properties. The projection for the surface of revolution is also considered. Then the thesis deals with the loxodromes, their properties, and their relation to the Mercator projection. The loxodromes on the surface of revolution are also considered, again. And the thesis ends with some relations between the Mercator projection, the stereographic projection, and the complex exponential function. 1
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Multivariate risk measures in stochastic optimization
Rauš, Jaroslav ; Branda, Martin (advisor) ; Dupačová, Jitka (referee)
The thesis deals with possible generalization of widely used risk measures, Value-at-Risk and Conditio- nal Value-at-Risk, to the multivariate case. First, the theory of p-efficient points, possible generalization of a quantile, is presented. The Prékopa-Vizvári-Badics algorithm for finding p-efficient points in case of random vectors with finite support is presented and a generalization of the algorithm in special case is proposed. Multivariate Value-at-Risk and Multivariate Conditional Value-at-Risk are defined and some of the properties are discussed. A lot-sizing problem for different time horizons is solved. 1
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Mercator projection, loxodromes, and related topics
Rauš, Jaroslav ; Slavík, Antonín (advisor) ; Boček, Leo (referee)
anglicky- Mercator projection, loxodromes, and related topics This bachelor thesis deals with the Mercator projection from both today's and historical point of view. Special emphasis is placed on the formal derivation of the projection, and on the studying of its properties. The projection for the surface of revolution is also considered. Then the thesis deals with the loxodromes, their properties, and their relation to the Mercator projection. The loxodromes on the surface of revolution are also considered, again. And the thesis ends with some relations between the Mercator projection, the stereographic projection, and the complex exponential function. 1
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