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Samodlážditelné simplexy
Safernová, Zuzana ; Matoušek, Jiří (advisor)
of the Master thesis Reptile simplices Zuzana Safernová In the present work we study tetrahedral k-reptiles. A d-dimensional simplex is called a k- reptile if it can be tiled in k simplices with disjoint interiors that are all congruent and similar to S. For d=2, triangular k-reptiles exist for many values of k and they have been completely characterized. On the other hand, the only simplicial k-reptiles that are known for d>=3 have k=md , where m>=2 (Hill simplices). We prove that for d=3, tetrahedral k-reptiles exist only for k=m3 . This partially confirms the Hertel's conjecture, asserting that the only tetrahedral k-reptiles are the Hill tetrahedra. We conjecture that k = m^d is necessary condition for existence of d-dimensional simplicial k-reptiles, d > 3.
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Approximation of a non-increasing rearrangement of a function
Franců, Martin ; Pick, Luboš (advisor) ; Felcman, Jiří (referee)
The non-increasing rearrangement of a measurable real function defined on an appropriate measure space is of the enormous significance in disciplines such as theory of function spaces or interpolation theory and their applications in PDEs. Unfortunately, while it has good and widely applicable mapping properties, it is virtually impossible to calculate the non-increasing rearrangement of a concrete given function precisely. Numerical algorithms for approximation are desirable for this reason. Such method of approximation, based on interpolation by a linear spline, is presented in this thesis. In the first half of this thesis, the developed method is described, while the error estimates of the method are subject to the second part.
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Topological and descriptive methods in the theory of function and Banach spaces
Kačena, Miroslav
The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.
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Topological and descriptive methods in the theory of function and Banach spaces
Kačena, Miroslav ; Spurný, Jiří (advisor) ; Netuka, Ivan (referee) ; Kalenda, Ondřej (referee)
The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.
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Laboratory tasks for Feedback 38-001
Gléba, Gergely ; Veselý, Libor (referee) ; Blaha, Petr (advisor)
The aim of this project was to get acquainted with the preparation Feedback 38-001, regenerate and establish several demonstration tasks. The first part deals with the description and the resurgence of the device. The second section describes the activities of modernization and innovation the teaching facilities. The main care was to focus on the implementation of connection with the computer supplementing measuring card and obtaining information of the regulation in real time. The third part includes the proposed laboratory tasks. The first task is based on the on-off control, which is mostly used in practice for its ease of use, with no major claims. The second task is defined for continuous control, which ensures better quality and comfort of controlling the level and the water flow. The third contains a task for identification of system parameters.
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Approximation of Terrain Data Utilizing Splines
Tomek, Peter ; Kunovský, Jiří (referee) ; Chudý, Peter (advisor)
Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané terenní data na určitých bodech spolu s gradientem pomocí vícerozměrných splajnů. Program by měl vyčíslit více bodů najednou a měl by pracovat v $n$-dimensionálním prostoru.
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Quality of fuel atomization from small pressure-swirl atomizers
Malý, Milan ; Broukal, Jakub (referee) ; Jedelský, Jan (advisor)
Tato bakalářská práce se zabývá měřením charakteristik spreje z tlakové vířívé trysky za použití fázového doplerovského analyzátoru. Cílem měření bylo stanovit a porovnat charakteristiky spreje za použití různých kapalin a různých režimů tlaků a rozhodnout, jestli je možné nahradit kerosin biopalivy z pohledu kvality atomizace. Teoretická část se zabývá základy rozpadu kapalin z tlakových vířivých trysek a principy laserové anemometrie. Experimentální část popisuje testovací trať, provozní podmínky a nastavení experimentu. Výsledy obsahují vizualizaci spreje, velikostní rozložení kapek uvnitř spreje, profily rychlosti a Sautrova středního průměru za použití různých provozních podmínek jako je různá vzdálenost od trysky, rozdílný vstupní tlak a různé kapaliny.
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