In this paper we explore Fibonacci heaps and their variants. The alternative versions of the Fibonacci heap, the thin and thick heaps, were introduced by H. Kaplan and R. E. Tarjan in 2008. We compare these heaps from both experimental and theoretical point of view and we also include some classic types of heaps, namely regular and pairing heap. In our experiments we will be most interested in the total time required to run an algorithm that works with heap. The results show that thin and thick heaps are usually faster than the Fibonacci heap and slower than the regular heap. In conclusion, we summarize the knowledge gained from experiments.

Diploma thesis is intended as material for general public. The thesis includes construction methods of the Golden Section and calculation of the Golden Number and its properties. It makes aquainted with the history of the Golden Section and its shows occurrence in a plane geometry. The thesis describes the connection between the Golden Number and the Fibonacci Sequence, occurrence of the Golden Section, Fibonacci Sequnce and the logarithmic spirals in nature in both proportions of living organisms and in plants and on the human body. The text is completed with illustractive figures drawn mostly in GeoGebra. The Golden Number properties and the plane constructions are given. The Golden Section is completed with photos.

The thesis deals with the possibility of prediction of the exchange rate on forex. The combination of Elliott wave principle and Fibonacci numbers examines to what extent and in what time periods it is possible to predict exchange rate. The thesis use fundamental analysis and MACD oscillator to confirm the accuracy of this prediction.

This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what is the success rate for the signals they provide.

This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1

This dissertation consists of five articles about economics of sports. The first three articles investigate various types of outcome uncertainty and how they relate to match attendance demand, while the remaining two articles test the efficiency of sports betting markets. The first article presents a new method of calculating match importance. Unlike the previous approaches in the literature, it does not require ex-post information and can be used for any type of season outcome. The second article shows that the additional playoff stage in the Czech ice hockey "Extraliga" lowers the probability of the strongest team becoming a champion and thus increases seasonal uncertainty. The third article demonstrates that the inconsistent findings in the literature about the link between match uncertainty and attendance could be explained by wrongly specified regressions, proposes a new approach to analyzing the effect of match uncertainty and shows that attendance demand is maximized if teams of the same quality play against each other. The fourth article examines the favorite-longshot bias in the context of betting on tennis matches. It shows that the favorite-longshot bias pattern is consistent with bookmakers protecting themselves against both better informed insiders and the general public exploiting new information. The fifth article investigates the supposedly profitable strategy of betting on soccer draws using the Fibonacci sequence. The strategy is tested both in a simulated market and on a real data set and found to lose money.

This thesis deals with problems of biological and cultural determinants influencing perception of beauty. It attempts to find out if there is a common biological basis of perception of beauty or if beauty represents merely a sociocultural construct - product of a specific culture. With respect to biological determinants it concerns biological processes significantly influencing perception of beauty. In this context, these processes include probably innate evolutionary adaptations, effects of brain cognitive systems and neural correlates processing perceptions of beautiful objects. In connection with cultural determinants it presents studies emphasizing cross-cultural differences in perception of beauty. Further subject of the thesis is an aesthetic conception of subjective and objective beauty and related concept of beauty based on mathematical relations. In this connection, the creation of universally beautiful objects based on fixed mathematical rules as well as the possibility of exact measurement of beauty are discussed.