This thesis covers the topic of the computation of Galois groups over the rationals. Beginning with the classic algorithm by R. Stauduhar, we then review the theory necessary to explain the modular algorithm by K. Yokoyama. More precisely, we discuss the notion of the universal splitting ring of a polynomial. For a separable polynomial, we then study idempotents in the universal splitting ring. The modular algorithm involves computations in the ring of p-adic integers. Examples are given for polynomials of degree 3 and 4.

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The aim of the diploma thesis "Optimization of collection routes in a selected region" was to develop a method of evaluation of efficiency of current routes used for garbage collection in urban region and, if these are found inefficient, design more efficient ones. The analysis was performed on a data set pertaining to separated refuse in the city of České Budějovice.

Title: Generating polynomials for number field sieve Author: Anežka Pejlová Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc., Department of Algebra Abstract: The topic of this thesis is mainly focused on Kleinjung algorithm for generating polynomials within the General Number Field Sieve, which is the most efficient factorization algorithm nowadays. Commonly used consecu- tions are explained with respect to the fact whether they can be rigorously proven or they are based only on heuristic assumptions. Another contribution of this thesis is the attached implementation of Kleinjung algorithm develo- ped as a part of the Number Field Sieve project led by the Department of Algebra. The appropriateness of some heuristics used in the theory beyond the Kleinjung algorithm is supported by empirical data obtained from this implementation. Keywords: Number field sieve, Kleinjung algorithm

This thesis deals with the problem of TV commercials planning. This problem is getting more difficult as the number of different TV stations grows and naive algorithms become unable to scale with this number. In this work, we deal with the possibility to use evolutionary algorithms to solve this problem. The work also contains an implementation of a software, which is capable of testing the various versions of the algorithm and comparing them to a naive one. The results indicate that evolutionary algorithms are a suitable technique to solve the problem at hand. Powered by TCPDF (www.tcpdf.org)

The main focus of this thesis are hypercubes. In the first part, we introduce hypercubes, which form an interesting class of graphs that has practical uses in networks and distributed computing. Because of their varied applications, the thesis describes the graph-theory problems related to hypercubes such as searching for detour spanners, minimizing their maximal degree and finding multiple edge- disjoint spanners. It also overviews current results on selected hypercube problems and proposes a solution using a genetic algorithm. The genetic algorithm is designed, implemented and its performance is evaluated. The conclusion is that applying a genetic algorithm to some hypercube problems is a viable, but not the most effective method.

This thesis deals with creating a software guitar looper in a visual programming language called Pure Data and also building a specific remote controller for it. The remote cont- roller will be based on a MIDI protocol. As a part of the software, there will be a special aligning algorithm, that will take care of precise alignment of the created loop on beat in the way that no other intrusive rhythmical or tempo related elements are present.

This master’s thesis deals with phase-shifting transformers (PST) and coordination of electrically close devices in an interconnected region. Theoretical research is performed in the work, describing methods of power control, function and design of PST, as well as actual methods of PST coordination in the rest of the world. Based on the research there is an optimalisation algorithm designed in MATLAB, which computes recommended tap petting of PST based on the network configuration. In the second part of this thesis there are described components of this algorithm and also presented the results of three demonstrative scenarios. Algorithm is able to solve minor problems in the network; more complex problems are beyond its solving ability. For an improved functionality there is a necessity to further expand this algorithm by a network redispatch solving algorithm.

The aim of this master thesis is optimization of the rotor in the terms of efficiency. An analysis of the effects of rotor parameters is performed by RMXPRT. A genetic algorithm is created to find the optimal solution. Solutions are evaluated and adjusted according to the results. Measurements on the actual machine are performed and evaluated to verify the functionality of the simulation models.

This thesis deals with the distributed and stochastic algorithms, including testing their convergence in networks. The theoretical part briefly describes above mentioned algorithms, including their division, problems, advantages and disadvantages. Futhermore, two distributed algorithms and two stochastic algorithms are chosen. The practical part is done by comparing the speed of convergence on various network topologies in MATLAB.