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Filtering for Stochastic Evolution Equations
Kubelka, Vít ; Maslowski, Bohdan (advisor)
Filtering for Stochastic Evolution Equations Vít Kubelka Doctoral thesis Abstract Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to linear SPDEs driven by Gauss-Volterra process observed at finitely many points of the domain and to delayed SPDEs driven by white noise. Subsequently, the continuous dependence of the filter and observation error on parameters which may be present both in the signal and the obser- vation process is proved. These results are applied to signals governed by stochastic heat equations driven by distributed or pointwise fractional noise. The observation process may be a noisy observation of the signal at given points in the domain, the position of which may depend on the parameter. 1
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Development of HPLC method for evaluation of tryptophan metabolites
Pšenčíková, Barbora ; Kastner, Petr (advisor) ; Kučera, Radim (referee)
Charles University Faculty of Pharmacy in Hradec Králové Department of Pharmaceutical Chemistry and Pharmaceutical Analysis Candidate: Barbora Pšenčíková Supervisor: PharmDr. Petr Kastner, Ph.D. Title of thesis: Development of HPLC method for evaluation of tryptophan metabolites The essential amino acid tryptophan is a precursor of several important bioactive compounds. In recent years it was found out that tryptophan metabolites are involved in the pathogenesis of many diseases, including neurodegenerative and psychiatric disorders, autoimmune diseases, or cancer. Therefore, the analytical methods for simultaneous determination of tryptophan and its metabolites are highly required. The purpose of this diploma thesis was to develop an optimal HPLC method for determination of tryptophan and its metabolites (kynurenine, kynurenic acid, serotonin and 5-hydroxyindole-3-acetic acid) and to consider all the possible options of determination of quinolinic acid and melatonin. The chromatographic separation was carried out by Supelco Ascentis Express F5 column, 2.7 μm particle size, 15 cm × 3 mm, using spectrophotometric and fluorescence detection. Parameters of detection were for kynurenine UV detection 369 nm, 254 nm, fluorescence detection Ex/Em: 369/475; for kynurenic acid UV detection 244 nm; for...
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Magdeburg law in Bohemia and Moravia in the period of 14th to 16th century
Dolečková, Martina ; Starý, Marek (referee)
Magdeburg law in Bohemia and Moravia in the period of 14th to 16th century Abstract This thesis aims to discuss the development and form of Magdeburg law in the period of 14th to 16th century including the analysis of existing research about Magdeburg law. The thesis is mainly focused on Litoměřice and Olomouc as the heads of Magdeburg municipal family in Bohemia and Moravia. The thesis is based on the comprehensive analysis of Magdeburg law beginning with its origins and development trends and ending with the description and characteristic of its legal sources as well as its most important legal institutes. The thesis uses not only legal-historical, but also historical and auxiliary historical methods, specifically the method of legal analysis of the text, diplomatic method, comparative method and analysis of the literature. The aim of the thesis is first, to present the state of historical research and literature on Magdeburg law. The goal here is to offer the reader a comprehensive overview of current trends in the research, pending discourse and the various approaches to Magdeburg law. The second aim is to analyse the development of Magdeburg law with the special focus on Litoměřice and Olomouc, which could be described as the most important appealing cities within the Magdeburg legal area in Bohemia...
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Criminal Proceedings against Legal Entilities
Kajnová, Adéla ; Mulák, Jiří (referee)
This diploma thesis is focused on a comprehensive analysis of criminal proceedings against legal entities using Act No. 141/1961 Coll., On Criminal Procedure (Criminal Procedure Code) in combination with Act No. 418/2011 Coll., On Criminal Liability of Legal Entities and Proceedings against them. The adoption of Act No. 418/2011 Coll., On Criminal Liability of Legal Entities and Proceedings against them, introduced criminal liability of legal entities into the legal order of the Czech Republic since 1st January 2012 but the institute of criminal liability of legal entities is constantly evolving to respond to the needs of society. The diploma thesis is conceived from a procedural point of view with the current use of the substantive bases of the issue of criminal liability of legal entities. The thesis further explains important terms and outlines the development of criminal liability of legal entities in the Czech Republic. The aim of the thesis is to provide a comprehensive view of phases of criminal proceedings against legal entities and to evaluate selected problematic aspects of the legal regulation which are accordance with the interpretation of the professional public and with the developing jurisprudence of the domestic courts. The thesis is divided into five chapters. The first three are...
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Additive combinatorics and number theory
Hančl, Jaroslav ; Klazar, Martin (advisor)
We present several results for growth functions of ideals of different com- binatorial structures. An ideal is a set downward closed under a containment relation, like the relation of subpartition for partitions, or the relation of induced subgraph for graphs etc. Its growth function (GF) counts elements of given size. For partition ideals we establish an asymptotics for GF of ideals that do not use parts from a finite set S and use this to construct ideal with highly oscillating GF. Then we present application characterising GF of particular partition ideals. We generalize ideals of ordered graphs to ordered uniform hypergraphs and show two dichotomies for their GF. The first result is a constant to linear jump for k-uniform hypergraphs. The second result establishes the polynomial to exponential jump for 3-uniform hypergraphs. That is, there are no ordered hypergraph ideals with GF strictly inside the constant-linear and polynomial- exponential range. We obtain in both dichotomies tight upper bounds. Finally, in a quite general setting we present several methods how to generate for various combinatorial structures pairs of sets defining two ideals with iden- tical GF. We call these pairs Wilf equivalent pairs and use the automorphism method and the replacement method to obtain such pairs. 1
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Acquisition of the property right from an unauthorized person
Cmíralová, Natálie ; Lederer, Vít (referee)
The diploma thesis deals with the topic of acquisition of the property right from an unauthorized person, representing an exception to the Roman law principle nemo plus iuris ad alium transferre potest quam ipse habet, which means that no one can transfer more rights to another than he or she has. Acquisition of the property right from an authorized person represents one of the original ways of acquiring the property right, which significantly infringes on constitutionally guaranteed property right. For this reason, it is necessary to subject the legal regulation of acquisition of the property right from an unauthorized person to closer and critical examination and to assessment whether it complies with European standards of legal regulation of acquisition of the property right from an unauthorized person and whether it satisfies the reproaches aimed at previous legal regulation of acquisition of the property right from an unauthorized person, all after nearly six years after the recodification of private law in the Czech Republic. The diploma thesis in its five chapters presents to the reader a presentation of the nature of rights in rem and property right, historical grounds of the acquisition of the property right from an unauthorized person, a thorough analysis of current Czech legal...
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Test anxiety in perspective of the graduation exam
Slavík, Radovan
The subject of this thesis is test anxiety in Czech secondary school students in perspective of the graduation exam and its influence over their overall academic performance in this exam. Results of a study conducted in the academic year 2017/2018 among 439 graduating secondary school students in six secondary schools in Prague is presented The aim of the study was to verify a test anxiety model based on Lazarus's transactional model of stress, Ellis's cognitive A-B-C model and other subsequent models of different authors (e.g. Hodapp and Rost). The model used in this study thus approaches test anxiety as a form of a stress reaction that consists of three successive steps: (A) activating event in the form of a test situation, (B) cognitive appraisal, and (C) emotional and behavioral consequences part of which is the academic performance. Both steps B and C further consist of a variety of unique components and outcomes. Quantitative data collected with the utilization of an extensive test battery of eight self- evaluating tests, an anamnestic questionnaire and exam results allowed for a further statistical elaboration. Multiple linear regression, Spearman correlation and factor analysis were utilized to reduce total number of variables of the original theoretical model so that it would better and...
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Hydrological function of peat bogs and peat water properties of the Vydra River headwaters
Doležal, Tomáš
The retention potential of landscapes, along with the water regime of spring areas, are important hydrological topics of research, particularly in the current context of increasing extreme drought frequencies. The present work is focused on monitoring the mountain peat bogs, which, due to their overall frequency of occurrence in the spring area of the Vydra river, represent a significant constituent of the rainfall-runoff process of the area of interest. The specific hydropedological features of the organogenous soils (Histosol type soil) provide the high retention potential of the area, however, the influence of these soils on the runoff process is determined by complex physicogeographical factors. The general opinion on the hydrological function of the peat bogs has changed in recent years and the most important factor in the runoff formation in the mountain area of the Šumava Mts. is now thought to be the actual saturation of the headwater, which is predominantly composed of hydromorphic and organogenous soils. The organogenous soils are significant water reservoirs and have an important impact on the landscape. However, they may also intensify the extreme values of the watercourses during extreme precipitation events. The fundamental part of this work focuses on detailed observations of the...
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Asymmetric allylic amination of MBH carbamates
Dočekal, Vojtěch
Enatiomerically enriched allylic amines are important synthons for the synthesis of biologically active compounds. This diploma thesis is focused on the preparation of these amines via organocatalytic allylic substitution reaction of Morita-Baylis-Hillman (MBH) alcohol derivates. We found an asymmetric decarboxylative reaction of MBH carbamates catalyzed by commercially available dimeric cinchona catalysts. This reaction provides corresponding products in yields up to 98% with enatiomeric excess up to 97%. Our attention was also given to the transformation of allylic amines to the corresponding β-lactams. We found an one-pot reaction consisting of hydrolysis and following lactamization leading to β-lactams. This reaction provides corresponding lactams in isolated yield up to 86% with retained enantioselectivity. Enantiomerically enriched intermediate that is pivotal for the synthesis of Ezetimibe was prepared via this organocatalytic reaction. Possible reaction mechanism of this transformation was proposed based on carried out cross experiment and calculations.
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Microevolutionary processes in selected genera of the Rosaceae family
Macková, Lenka
Polyploidization, hybridization and various reproductive strategies significantly contribute to plant evolution and diversity. Their direct influence on plant evolution is especially apparent in the Rosaceae family and is also mirrored in its still partly unclear and reticulate phylogeny. Two model genera were chosen to add a piece of knowledge to the puzzle of polyploidization, hybridization and apomixis in the Rosaceae. The results demonstrate both the creative and destructive force of hybridization and polyploidization, particularly in the genus Prunus. A significant proportion of wild Prunus fruticosa populations under examination underwent hybridization and genetic erosion. Crop-to-wild hybridization with both cultivated sour and sweet cherries has resulted in two morphologically indistinguishable hybrids markedly differing in ploidy level and reproductive potential. On the one hand, a triploid block was manifested in sterile triploid hybrids, but, on the other, partial fertility of tetraploid hybrids allowed repeated backcrossing (i.e. introgression). The crop-to-wild phenomenon has significant consequences for both conservation and agriculture. Polyploidization and hybridization are frequently accompanied by apomixis among the Rosaceae. Apomixis may play a substantial role in the...
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