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Ultrafast laser-induced control of magnetic materials
Opršal, Jakub ; Wojewoda, Ondřej (referee) ; Arregi Uribeetxebarria, Jon Ander (advisor)
Magnetické materiály jsou ve velkém používány pro ukládání dat, která jsou zapisována ve formě bitů pomocí externího magnetického pole. Dlouho se věřilo, že doba potřebná pro změnu magnetizace je v řádu desítek až stovek pikosekund. Revoluční experiment v roce 1996 položil základ pro nový obor ultrarychlého ovládání magnetických materiálů, řádově zkracující čas potřebný pro změnu magnetizace. Mimo jiné ukázal, že magnetizace materiálu může být ovlivněna i světelnými pulzy. V této práci jsme replikovali fundamentální, laserem indukované experimenty ve ferromagnetických a ferrimagnetických materiálech. Postavili jsme optickou sestavu schopnou provádět tyto experimenty pro různé polarizace světla. Tato variabilita umožňuje rozlišit různé mechanismy a jevy, které se vyskytují při ultrarychlém ovládání magnetizace magnetických materiálů.
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Cyclic soil behaviour - numerical modelling and laboratory testing
Opršal, Jakub ; Mašín, David (advisor) ; Janda, Tomáš (referee)
Cyclic soil behavior is nowadays a popular subject of studies. One of its applications is geotechnical design and numerical simulation of foundation of offshore wind turbines. This master thesis is a part of a wider scientific research on cyclic soil behavior done at Charles University. One of the goals of this thesis is to define reference sand material, which could be used for another scientific projects. Therefore it was necessary to perform sufficient number of laboratory tests to create a representative volume of experimental data. Results and problems are commented in this thesis. The obtained experimental data are then used for calibration of hypoplastic model for sands. Numerical back analysis of cyclic loading of pile is also part of this work, where experimental data of pile cyclic loading is taken from the literature.
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Ultrafast laser-induced control of magnetic materials
Opršal, Jakub ; Wojewoda, Ondřej (referee) ; Arregi Uribeetxebarria, Jon Ander (advisor)
Magnetické materiály jsou ve velkém používány pro ukládání dat, která jsou zapisována ve formě bitů pomocí externího magnetického pole. Dlouho se věřilo, že doba potřebná pro změnu magnetizace je v řádu desítek až stovek pikosekund. Revoluční experiment v roce 1996 položil základ pro nový obor ultrarychlého ovládání magnetických materiálů, řádově zkracující čas potřebný pro změnu magnetizace. Mimo jiné ukázal, že magnetizace materiálu může být ovlivněna i světelnými pulzy. V této práci jsme replikovali fundamentální, laserem indukované experimenty ve ferromagnetických a ferrimagnetických materiálech. Postavili jsme optickou sestavu schopnou provádět tyto experimenty pro různé polarizace světla. Tato variabilita umožňuje rozlišit různé mechanismy a jevy, které se vyskytují při ultrarychlém ovládání magnetizace magnetických materiálů.
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Kategoriální metody v teorii struktur
Opršal, Jakub ; Trnková, Věra (advisor) ; Kepka, Tomáš (referee)
Title: Categorial methods in structure theory Author: Jakub Opršal Department / Institute: Mathematical Institute, Charles University Supervisor of the master thesis: prof. RNDr. Věra Trnková, DrSc. Abstract: In the first part of the thesis we investigate functor algebras. Initial algebras have distin- guished role in the study of these structures, and it can be constructed by certain transfinite construction, which is called initial algebra construction. Sooner this year Adámek and Trnková have prooved, that the construction stops in either at most three, or in κ steps where κ is a regular cardinal. We continue with their work, and we study the relation between the size of the algebra and the length of the convergence. We prove that the length of the convergence never exceeds the cardinality of the initial algebra. Another transfinite construction has been studied in 1980 by Kelly. He has described the construction of free algebras for a pointed functor and defined a class of well-pointed functors for which the construction is especially simple (and is in fact special case of the construction of relatively terminal coalgebra which has been recently defined by Adámek and Trnková). In the last chapter we describe all well-pointed functors in categories of sets and the dual category, and we provide list of...
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Application of group theory in solving puzzles
Pavlík, Tomáš ; Opršal, Jakub (advisor) ; Tůma, Jiří (referee)
This thesis studies the theory of combinatorical puzzles and its connection to the group theory. The aim of this work is to introduce the concept of puzzle to mathematics and to use group theory to solve it, special attention will be focused on solvable groups. Everything is interspersed with a number of practical examples to better understand the topic.
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Relational Approach to Universal Algebra
Opršal, Jakub ; Barto, Libor (advisor) ; Růžička, Pavel (referee) ; Mayr, Peter (referee)
Title: Relational Approach to Universal Algebra Author: Jakub Opršal Department: Department of Algebra Supervisor: doc. Libor Barto, Ph.D., Department of Algebra Abstract: We give some descriptions of certain algebraic properties using rela- tions and relational structures. In the first part, we focus on Neumann's lattice of interpretability types of varieties. First, we prove a characterization of vari- eties defined by linear identities, and we prove that some conditions cannot be characterized by linear identities. Next, we provide a partial result on Taylor's modularity conjecture, and we discuss several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and the analogue for idempotent va- rieties with a cube term. In the second part, we give a relational description of higher commutator operators, which were introduced by Bulatov, in varieties with a Mal'cev term. Furthermore, we use this result to prove that for every algebra with a Mal'cev term there exists a largest clone containing the Mal'cev operation and having the same congruence lattice and the same higher commu- tator operators as the original algebra, and to describe explicit (though infinite) set of identities describing supernilpotence...
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Kategoriální metody v teorii struktur
Opršal, Jakub ; Trnková, Věra (advisor) ; Kepka, Tomáš (referee)
Title: Categorial methods in structure theory Author: Jakub Opršal Department / Institute: Mathematical Institute, Charles University Supervisor of the master thesis: prof. RNDr. Věra Trnková, DrSc. Abstract: In the first part of the thesis we investigate functor algebras. Initial algebras have distin- guished role in the study of these structures, and it can be constructed by certain transfinite construction, which is called initial algebra construction. Sooner this year Adámek and Trnková have prooved, that the construction stops in either at most three, or in κ steps where κ is a regular cardinal. We continue with their work, and we study the relation between the size of the algebra and the length of the convergence. We prove that the length of the convergence never exceeds the cardinality of the initial algebra. Another transfinite construction has been studied in 1980 by Kelly. He has described the construction of free algebras for a pointed functor and defined a class of well-pointed functors for which the construction is especially simple (and is in fact special case of the construction of relatively terminal coalgebra which has been recently defined by Adámek and Trnková). In the last chapter we describe all well-pointed functors in categories of sets and the dual category, and we provide list of...
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Application of group theory in solving puzzles
Pavlík, Tomáš ; Opršal, Jakub (advisor) ; Tůma, Jiří (referee)
This thesis studies the theory of combinatorical puzzles and its connection to the group theory. The aim of this work is to introduce the concept of puzzle to mathematics and to use group theory to solve it, special attention will be focused on solvable groups. Everything is interspersed with a number of practical examples to better understand the topic.
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Minimální KC prostory
Opršal, Jakub ; Hušek, Miroslav (referee) ; Simon, Petr (advisor)
Spaces, in which each compact subset is closed are called, KC spaces (we do not require any separation axioms). Obviously every Hausdorff space is KC and every KC space is T1. This thesis answers the question, whetever every KC space, which has no strictly weaker KC topology, is necessary compact. In the year 2002 T. Vidalis proved that every such space is countably compact, however his proof contains an error. The same problem was affirmatively solved in 2007 by A. Bella and C. Constantini.
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