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Solving systems of equations over commutative rings
Seidl, Jan ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b over principal ideal rings. We prove that for every nonzero matrix over principal ideal rings there exists its Smith form. Using Smith form we transform the system of equations to simple diagonal form and we show how we can obtain the solution of the original system from its diagonal form. Whole procedure we demonstrate by the examples over Z, Zm and Q[x]. Thereafter we show how is possible to implement the algorithm for these rings by using software Mathematica. The work should provide procedure according to which shold not be difficult to modify algorithm to gain solution over another rings. 1
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Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.
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Applications of wavelet transform in Mathematica and Sage
Novotný, Radek ; Trzos, Michal (referee) ; Rajmic, Pavel (advisor)
This thesis focuses on image processing using wavelet transform. The usage of wavelet transform is analysed especially for image compression and image noise reduction purposes. The analysis describes in detail aspects and application of the following wavelet transform methods: CWT, DWT, DTWT, 2D DWT. The thesis further explains the meaning of the mother wavelet and studies certain specific kinds of wavelets, kinds of thresholding and its purposes and also touches on the JPEG2000 standard. Mathematica and Sage software packages were used to design algorithms for image compression and image noise reduction, utilising relevant wavelet transform findings. The concluding part of the thesis compares the two software packages and results obtained using different algorithms.
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Optimalizace portfolia cenných papírů pomocí strukturovaných produktů
Ondřej, Petr ; Žamberský, Pavel (advisor)
Diplomová práce popisuje vlastnosti a rizika investování do strukturovaných produktů v Německu. Součástí práce je zároveň otestování efektivnosti využití Bonus, Diskont a Outperformance certifikátů při správě finančních prostředků. Analýza ukazuje, že je možné pomocí Diskont a Bonus certifikátů dosáhnout vyššího výnosu očištěného o riziko. Outperformance certifikáty umožňují dosáhnout vyššího výnosu pouze při výrazném růstu (zároveň s vyšším rizikem). Veškeré investice do strukturovaných produktů jsou porovnávány s výnosem u indexu DJ Euro Stoxx 50 (Total Return).
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Java Grid Computing or how to find large primes
PAPEŽ, Petr
This Bachelor work contains methods of searching for Mersenne primes using Grid Computing technology. The goal of this work is to implement a network-based computing framework and an implementation of an algorithm for searching for large Mersenne primes. Part of this work is a theory of searching for Mersenne primes and historical methods of searching for such numbers, GIMPS project description and its results, Grid Computing technology explanation, and Grid Computing capabilities of Mathematica 7 software for searching for Mersenne primes.
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