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Ball-Evans approximation problem in one dimension
Petr, Jakub ; Hencl, Stanislav (advisor) ; Campbell, Daniel Cameron (referee)
Ball-Evans aproximation problem is a highly studied one in Geometric function theory. Approximation of homeomorphisms by diffeomorphisms would have many implications e.g. in the theory of regularity of minimizers or in Finite element method. Recently, this problem was solved in two dimensions. However, in 3D, which is the physically most interesting case, it remains open. In this thesis, we study the following two problems. Firstly, for some 1 ≤ p < ∞ and a given homeomorphism f ∈ Wk,p ((a, b)), can we approximate it by diffeomorphisms in ||·||Wk,p((a,b)) with an arbitrarily small error? Secondly, for some 1 ≤ p, q < ∞ and a given homeomorphism f ∈ W1,p ((a, b)) such that also f−1 ∈ W1,q ((c, d)), can we find a sequence of diffeomorphisms {fn}∞ n=1 such that ||fn − f||W1,p((a,b)) −−−→ n→∞ 0 and ⃓ ⃓ ⃓ ⃓ ⃓ ⃓f−1 n − f−1 ⃓ ⃓ ⃓ ⃓ ⃓ ⃓ W1,q((c,d)) −−−→ n→∞ 0? We show positive results for both problems. The latter one is not known in higher dimensions.
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Study of the production of lignolytic enzymes by white rot fungi
Vejdová, Markéta ; Bendová, Agáta (referee) ; Hudečková, Helena (advisor)
The topic of this bachelor thesis is the study of ligninolytic enzyme production by white rot fungi. The theoretical part of the thesis is focused on the characterization of wood-decay fungi, especially white rot fungi, and the ligninolytic enzymes produced on the synthetic and waste substrates for cultivation of the fungi and the impact of pH on the biomass growth. The experimental part focuses on the submerged cultivation of selected fungal strains Trametes versicolor CCBAS 1383 and Irpex lacteus CCBAS 196 at different pH levels. Samples were taken over a period of 36 days to observe the activities of individual ligninolytic enzymes, the content of total extracellular proteins, and biomass growth. The same parameters were also observed during the submerged cultivation of Trametes versicolor CCBAS 1383 on waste substrate. Based on the comparison of the results of selected fungal strains, it can be stated that the optimization of the cultivation medium, particularly the pH level, has a significant impact on the activity of produced enzymes. The highest enzyme activities were achieved by the submerged cultivation of Trametes versicolor at pH 5. An exception is lignin peroxidase, which reached a maximum activity of only (4 ± 1) · 10 U at this pH, while the highest activity of lignin peroxidase (1,2 ± 0,4) · 10 U was measured at pH 7. Overall, Trametes versicolor is a more suitable producer of ligninolytic enzymes compared to Irpex lacteus.
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Jelly candies with the addition of bilberry (Vaccinium myrtillus) extract
Knapovská, Pavlína ; Pořízka, Jaromír (referee) ; Vítová, Eva (advisor)
This thesis deals with the application of bilberry fruits (Vaccinium myrtillus) and their extract to jelly candies and the subsequent characterization of these candies in terms of volatile compounds, total phenolic compounds and anthocyanins, antioxidant activity and sensory quality. The volatiles were determined by headspace solid-phase microextraction coupled to gas chromatography with mass spectrometry and standard spectrophotometric methods were used for the determination of bioactive compounds. Total phenolic content was determined by the Folin-Ciocalteu method, antioxidant activity by the TEAC method and total anthocyanin content by pH differential analysis. The sensory quality of the samples was evaluated using unstructured graphical scales. The preparation of the bilberry extract was optimized on the basis of total phenolic content and the following conditions were selected as the optimal: a weight of 1000 grams of bilberries per litre of water, a temperature of 50 °C, and an extraction time of 2 hours. The optimum additions to candies were selected, by sensory analysis, as 25 wt. % of extract and 15 wt. % of bilberries. A total of 45 volatile compounds were identified in the candy with bilberry extract, the most abundant being (E)-9-hexadecen-1-ol (22,7 %), furfural (10,9 %) and 2-ethylhexan-1-ol (10,0 %). The total phenolic content was 1141 ± 11 gGAE · g-1, the antioxidant activity was 660 ± 66 gTE · g-1 and the total anthocyanin content was 418 ± 23 gC3G · g-1. A total of 40 volatile compounds were identified in the candy with bilberry and the most abundant were linalool (22,7 %), (E)-9-hexadecene-1-ol (16,1 %) and 2-ethylhexan-1-ol (8,4 %). The total phenolic content was 1735 ± 56 gGAE · g-1, the antioxidant activity was 1109 ± 32 gTE · g-1 and the total anthocyanin content was 745 ± 23 gC3G · g-1. With the addition of both the extract and the bilberries, the candies showed a significant increase in bioactive and volatile compounds content, and the colour and flavour of the enriched samples were positively evaluated, thus improving their overall acceptability.
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Welding of deep-drawing steels with protective layer by laser-TIG hybrid technology
Brehovský, Patrik ; Sigmund, Marian (referee) ; Mrňa, Libor (advisor)
The diploma thesis focuses on laser welding of extra deep-drawn steel sheet according to the standard WSS-M1A365-A14 with a protective zinc surface layer. A 0,9 mm thick steel sheet with a zinc layer with coating weight 50 g · m^-2 is welded by a hybrid welding method Laser-TIG. The laser, as the primary energy source, is used for welding the material. The arc, provided by a non-melting tungsten electrode, is used for preheating the material for melting and evaporation of the zinc layer. Based on the initial experiments, the magnitude of the laser power with the welding speed was chosen as a constant parameter. The magnitude of the electric current, as the variable parameter, was set up to 0, 20, 30 and 40 ampers for welding the lap and the butt welds. Only one piece of the each weld type combination was made. The welds were afterwards tested to verify their quality and material properties. The first differences between laser welding with or without TIG preheating were visible during the experiment. The positive effects of the laser welding with preheating by TIG were confirmed. The material properties of the joints achieved better values and a influence of the welding defects on the quality of the joints was reduced. The Laser-TIG is a good choice for welding galvanized steel sheets in the mass production of automotive industry and it could be improved by more researches.
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Comparison of the fruits of some honeysuckle varieties in terms of content selected biologically active compounds
Veselý, Ondřej ; Diviš, Pavel (referee) ; Vespalcová, Milena (advisor)
This thesis is focused to the analysis of selected varieties of honeysuckle kamtschatica (Lonicera caerula var kamtschatica) and their comparison in terms of the content of biologically active substances. There were analysed only varieties grown in 2014. Theoretical part elaborates and characterized various parameters of biologically active compounds such as phenolic, anthocyanins and ascorbic acid and possibilities of their determination. Further it briefly surveys Kamchatka honeysuckle, its taxonomic and morphological properties and its nutritional properties. The experimental part of the work was focused on the description of the methods used for the analysis of biologically active substances and their analysis. Polyphenolic compounds and anthocyanin’s were determined spectrophotometrically and vitamin C was determined by high-performance liquid chromatography. The results and varieties were compared with each other. Overall, we can say that the variety with the highest content of all three analysed biologically active substances is a variety Valchová, which had the second highest content of polyphenolic compounds (546.3 mg · 100 g-1 fruits), the third highest contend of ascorbic acid (35.1 mg · 100 g-1 fruits) and the sixth highest content of anthocyanin (170.8 mg · 100 g-1 fruits)
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Minion Cores of Clones
Kapytka, Maryia ; Barto, Libor (advisor) ; Zhuk, Dmitrii (referee)
This thesis provides a classification of the minion homomorphism preordering and minion cores within a class of multi-sorted Boolean clones. These clones can be described as those clones defined on the set {0, 1}k = {0, 1} × {0, 1} × · · · × {0, 1}, where the clone operations act component-wise on the k-tuples, which are determined by multi-sorted unary or binary relations. The second chapter of this thesis focuses on presenting the key findings. We introduce specific minion cores and establish the preordering among them. Furthermore, we prove that each clone falling under the aforementioned type is equivalent to one of these minion cores.
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Random Dynamical Systems and Their Applications
Iuzbashev, Artem ; Maslowski, Bohdan (advisor) ; Čoupek, Petr (referee)
This thesis extends the existing results in the theory of random dynamical systems driven by fractional noise in Hilbert space. In particular, it broadens the scope of ap- plicability of the results presented by Maria J. Garrido-Atienza, Bohdan Maslowski and Jana Snuparkova in Garrido-Atienza et al. [2016] for fractional noise whose sample paths have a Hölder exponent greater than 1/2. The main object of the research is the following stochastic equation: d u(t) = (A(t)u(t) + F(u(t)))d t + Bu(t)d ω(t), u(0) = u0 ∈ V, where (V, ∥ · ∥V ) is a separable Hilbert space, ω is a stochastic process and the stochastic integral is understood in the Zähle sense. This thesis contains the proof of a Fubini-type theorem for integration in the sense of Zähle. It is shown that the assumption about ergodicity for the underlying fractional noise in Garrido-Atienza et al. [2016] is redundant and the statements about random dynamical systems which are generated by the solution of the equation and its random attractor remain valid. The thesis also contains the proof of the existence and uniqueness of the solution to the equation above. 1
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Banach-Mazur distance between Banach spaces of continuous functions
Havelka, Jonáš ; Cúth, Marek (advisor) ; Rondoš, Jakub (referee)
In this bachelor thesis, we examine estimates of a Banach-Mazur distance between spaces C(ω) and C(ω · k) for various k ∈ N. With a properly chosen form of mapping, we constructively show the best currently known upper bounds of this distance for all k. Besides the known bounds d(C(ω), C(ω · k)) ≤ 2 + √ 5 for any k > 3, and d(C(ω), C(ω · 2)) ≤ 3, we are going to find, for k = 3, the better bound, namely d(C(ω), C(ω · 3)) ≤ 4 instead of already known 2 + √ 5. 1
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Low-temperature plastic deformation of BCC metals with internal magnetic order
Holzer, Jakub ; Máthis,, Kristián (referee) ; Mrověc, Matouš (referee) ; Gröger, Roman (advisor)
Přestože plastická deformace kovů s prostorově střeďenou kubickou mřížkou za nízkých teplot je dnes dobře vysvětlena, vliv vnitřního magnetického uspořádání na mechanické vlastnosti a vliv plastické deformace na vnitřní magnetické uspořádání zůstávají z větší časti nevysvětleny. Cílem této práce je popsat nízkoteplotní plastickou deformaci -železa a chromu pomocí analýzy skluzových čar, elektronovou zpětně odraženou difrakcí a transmisní elektronovou mikroskopií (TEM). Vnitřní magnetické uspořádání chromu je zkoumáno pomocí magnetické neutronové difrakce v neutronovém centru na Institutu Paula Scherrera ve Švýcarsku. Vibrační magnetometrie je využita pro hledání změn v hmotnostní susceptibilitě, aby byly rozeznány různé magnetické stavy. Anomální skluz byl poprvé pozorován v deformovaném vzorku chromu. Dislokační síť zodpovědná za anomální skluz je charakterizována pomocí g·b analýzy v TEM. Síť protínajících se 1/2111 šroubových dislokací a jejich 100 spoje se tvoří na nízkozatížených {110} rovinách. Dvojčata vytvořená antidvojčatovým smykem byla pozorována v chromu, ale nikoliv v -železe. Tento jev je vysvětlen pomocí atomárních simulací využívajících semiempirické interakční potenciály. Magnetické domény v -železe byly studovány pomocí Kerrovy mikroskopie. Výsledky ukazují, že dvojčata mohou efektivně blokovat pohyb doménových stěn a nukleovat nové.
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Uptake and translocation of buspirone in higher plant cultures
Schmidová, Anna ; Smrček, Stanislav (advisor) ; Petrová, Šárka (referee)
This bachelor thesis is devoted to the phytoextraction of the anxiolytic buspirone from a cultivation medium and to the study of the effect of plant stress on the plant metabolism. Two experiments were carried out with maize (Zea mays) grown hydroponically in a sterile medium for 10 and 14 days. After the addition of a solution of medium containing buspirone at concentrations of 10 and 5 mg · L-1 , samples of medium were collected at 1-day intervals from all experimental plants. The decreasing concentration of buspirone in the medium was monitored by reversed phase HPLC/UV at a wavelength of 240 nm. In the first experiment with 10 mg · L-1 as the initial concentration of buspirone in the medium, a 65 % decrease was observed over the 96 hours during which the phytoextraction was carried out. The overall decrease in buspirone concentration was 53 % in 144 hours of phytoextraction in the second experiment with an initial concentration of 5 mg · L-1 in the medium. After the completion of the phytoextraction experiments, the activities of total peroxidases, membrane-bound peroxidases, guaiacol peroxidase and ABTS-peroxidase were determined in the leaves and roots of the plants. Furthermore, the content of phenolic substances, which belong to the group of so-called secondary metabolites and their effects...
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