In the 1880s and early 1890s, the Prague mathematician Eduard Weyr published his important results in matrix theory. His works represented the only significant contribution to matrix theory by Czech mathematicians in many decades that followed. Although Eduard Weyr was one of the few European mathematicians acquainted with matrix theory and working in it at that time, his results did not gain recognition for about a century. Eduard Weyr discovered the Weyr characteristic, which is a dual sequence to the better known Segre characteristic, and also the so-called typical form. This canonical form of a matrix is nowadays called the Weyr canonical form. It is permutationally similar to the commonly used Jordan canonical form of the same matrix and it outperforms the Jordan canonical form in some mathematical situations. The Weyr canonical form has become much better known in the last few years and even a monograph dedicated to this topic was published in 2011.

Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...

The thesis compiles my contributions to the tilting theory, mainly in the set- ting of a module category over a commutative ring. We give a classification of tilting classes over an arbitrary commutative ring in terms of data of geometrical flavor - certain filtrations of the Zariski spectrum. This extends and connects the results known previously for the noetherian case, and for Prüfer domains. Also, we show how the classes can be expressed using the local and Čech homology the- ory. For 1-tilting classes, we explicitly construct the associated tilting modules, generalizing constructions of Fuchs and Salce. Furthermore, over any commuta- tive ring we classify the silting classes and modules. Amongst other results, we exhibit new examples of cotilting classes, which are not dual to any tilting classes - a phenomenon specific to non-noetherian rings. 1

The goal of this thesis is to present the pretentious approach to analytic number theory recently developed by Granville, Soundararajan, and others. In the first four chapters, we show the classical proof of the prime number theo- rem. We then develop the pretentious approach, explain its differences, advan- tages, and disadvantages and present another proof of the prime number theorem based on Hal'asz's theorem. This theorem is then proven using new techniques of Granville, Harper, and Soundararajan, which are substantially easier than the previous proofs. In the last chapter, we show how pretentious techniques can be used to obtain more intuitive proofs of other classical theorems or obtain new results. 1

Postgraduate thesis focuses on docudrama format, definition and development of docudrama in Great Britain and USA.

This diploma thesis focuses on market anomalies, which are generally known as speculative bubbles. The work is performed in both theoretical and practical form. Theoretical part deals with the functioning of the capital markets, regulation and supervision, causes and consequences of speculative bubbles, basic approaches of efficient market theory and psychological analysis. The main part of this work and its goal is based on partial causal analysis of selected speculative bubbles, to give specific recommendations to regulators, financial intermediaries and individual investors to prevent and mitigate the consequences of the bubble bursting.

The thesis deals with the optimization of the stock portfolio using modern portfo-lio theory and mathematical programming. Optimization is achieved by Markowitz Model, the Capital Asset Pricing Model and Black-Litterman model. Stocks traded on the Prague Stock Exchange, Inc., are selected as exploration assets. The simula-tion technique Monte Carlo is used for the model evaluation.

My diploma work is an analyzation of a cooperation between the DOP and a director.

This diploma thesis analyses two films by Clint Eastwood Million Dollar Baby and American Sniper. Its focus is aimed at the formal storytelling aspects, structure of the storyline and plot devices in the screenplays. The first film is an example of misusing these plot devices; the theme being euthanasia remains irrelevant from the viewers perspective although it was meant to resonate strongly at first. Analysis of the second film shows us the discrepancy of what the film "wanted" to be and the actual message it implicitly presents to the audience. Instead of being an objective reflection of the real events (in this case the war in Iraq) it is on purpose misleading in presenting of commonly known facts and hence it becomes propaganda. The analysis of the storytelling devices in this thesis can be also applied on different films and cinema in general.

K tomu, abych ilustrovala jak se stejný příběh výrazně mění v závislosti na zemi původu, použiji příkladu Abre Los Ojos (Otevři oči, Španělsko, 1997) a jeho remake-u Vanilla Sky (Vanilkové nebe, USA, 2001). Cílem mé práce není dokazování které zpracování je lepší, ale spíše poukazování na skutečnost, že rozdíly jsou důsledkem rozdílné ideologické a kinematografické tradice. Nejprve budu psát o typech nových filmových zpracování, a o tom proč Hollywood předělává evropské filmy. Pak začnu porovnávat hlavní postavy obou filmů a ukáži jak odrážejí sociálně-behaviorální normy dle země původu. Poté budu pokračovat s dalšími kulturními rozdíly, které jsou patrné v jazyce, kinematografii, střihu, hudbě, herectví a režii. Hlavní sociologický, tím pádem i kinematografický rozdíl, který je přítomný ve všech aspektech a sekcích těchto filmů je ten, že zatímco Abre los Ojos se zabývá vnitřním zápasem protagonistů, Vanilla Sky je milostný film. Tento rozdíl v tématu odhaluje mnoho o preferencích v Evropě a v Americe.