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Complex numbers, quaternions and their applications
BRDLÍK, Pavel
The bachelor thesis is dedicated to the topic of complex numbers and quaternions and their application. The main goal of this thesis is to familiarize with the subject of complex numbers and quaternions and their important properties and to present these terms with suitably selected examples. Complex numbers can be used among others to represent a planar rotational movement, quaternions can be used to represent rotations in three-dimensional space. The aim of this thesis is to provide a well arranged summary of the theory and a sample solution of practical examples that would illustratively demonstrate the application of complex numbers and quaternions by description of planar or spatial movements or their further applications.
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Design of total station
Rozehnalová, Magda ; Chorý, Tomáš (referee) ; Křenek, Ladislav (advisor)
This diploma thesis presents a design solution of a total station. The proposal is processed especially with regard to technical, ergonomic and aesthetic requirements. The main inovation of the proposal lies in a complex ergonomic and aesthetic solution that better reflects modern trends in the field of surveying technology. In comparison to current designs of the device, new proposal of the total station perfectly integrates certain parts of the device, such as a control panel. Since it is a relatively small device, it is important to design all details properly, especially the form and arrangement of controls. The thesis also suggests a number of alternative solutions to particular problems. The proposal of a total station is suitable for various types of work and methods of surveying.
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Speculative bubbles in financial markets
Roček, Jindřich ; Brada, Jaroslav (advisor) ; Kubát, Max (referee)
The bachelor thesis explores the phenomenon of speculative bubbles in financial markets. The aim is to define possible causes of speculative bubbles, and specify circumstances under which they can be prevented. The first chapter explains the essence of the examined phenomenon. In the following chapter, two theoretical approaches to the formation of asset prices in markets are explained, the efficient market theory and behavioral finance. The third chapter analyses causes, coarse and collapse of each individual bubble. The work uses twelve samples of asset price bubbles from history to meet the objectives. The final chapter examines the influence of government intervention and monetary policy on the formation of bubbles and proposes stemming recommendations for the responsible authority. The considerable complexity of the phenomenon and a large number of factors influencing price movements means that bubbles cannot be quantified ex ante. Given the current market conditions it is reasonable to expect further occurence of asset price bubbles in financial markets.
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Drugs and activities that could cause danger to life, health or damage to property
HANDSCHUHOVÁ, Silvie
The objective of this thesis is to summarize the effects of drugs, especially of the cannabinoids and amphetamine type stimulants, and to analyse which of these substances leads to high-risk activities, that could endanger life, health or result in damage to property. One of these activities, an important one, is driving under the influence of drugs. Driving itself is a complex demand, involving perception, decision making, psychomotor skills, knowledge, as well as attitudes and personality characteristics. Substance use and abuse has an impact on the functioning of the brain and mental processes and therefore on the performance of the driving task. Driving under the influence of drugs is a high risk activity which endangers not only the driver but also their surroundings. In the last few years, the Czech Republic registered a rapid increase in the number of impaired drivers, namely at police check points and in car accidents. The young drivers are mostly under influence of marijuana, respectively tetrahydrocannabinol (THC). Its negative effect on driving results from impaired co-ordination, slowed complex reaction time and in space and time distortion. The second group of drugs which can impair drivers is amphetamine type stimulants. Amphetamines are frequently sought by truck drivers, especially long-haul drivers, in Western Europe for its stimulative effects. In the Czech Republic the methamphetamine, Pervitin, is much more common. Intoxication is characterized by increased wakefulness, increased physical activity, increased respiration, rapid heart rate and an irregular heartbeat. The risk factors for driving are a lack of concentration and an overestimation of one{\crq}s own capabilities. After the acute phase of intoxication subsides, fatigue or states of narcolepsy may occur. Another amphetamine-based drug is methylenedioxymethamphetamine, MDMA or Ecstasy. This synthetic substance, chemically related to mescaline, is dangerous due to its ability to regulate body temperature. On rare but unpredictable occasions, this can lead to sharp hyperthermia, resulting in liver, kidney and cardiovascular system failure, and death. It can also cause hallucinations. All common drugs are easily detectable with ``drug test-cards{\crqq}, which are used during police checks around the the world. The Czech Republic is currently testing their utilization and is preparing legislation accordingly. Utilization of these tests during random checks could help to decrease the number of fatal road accidents and could help to decrease the number of impaired drivers on the roads.
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Numerické modelování složitých turbulentních proudění
Kozel, K. ; Louda, Petr ; Příhoda, Jaromír
The work deals with the numerical solution of turbulent impinging jet and round jet in a cross flow. The mathematical model is based on averaged Navier-Stokes equations closed by a turbulence model. Turbulence models used are a low-Reynolds-number eddy-viscosity model and/or an explicit algebraic Reynolds stress model. Numerical results are compared with experimental data. In case of impinging jet flow, the heat transfer is also solved.
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Use of Interest Rate Models for Interest Rate Risk Management in the Czech Financial Market Environment
Cíchová Králová, Dana ; Arlt, Josef (advisor) ; Cipra, Tomáš (referee) ; Witzany, Jiří (referee)
The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.
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Universality in Amorphous Computing
Petrů, Lukáš ; Wiedermann, Jiří (advisor) ; Janeček, Jan (referee) ; Neruda, Roman (referee)
Amorphous computer is a theoretical computing model consisting of randomly located tiny devices (called nodes) in some target area. The nodes of an amorphous computer can communicate using short-range radio. The communication radius is small compared to the size of the target area. The nodes are all identical, initially have no identi ers, work asynchronously and there is no standard communication protocol. An amorphous computer must work for any number of nodes under reasonable statistical assumptions concerning the spatial distribution of nodes. Moreover, the computation should use very limited amount of memory on each node. For the just described concept of amorphous computer we investigate the question whether a universal computation is possible at all in a corresponding theoretical model. To answer this question, several subsequent steps are performed. In the rst step, we design a formal minimalist model of a node and of the amorphous computer as a whole. In the second step, we develop communication protocol for the amorphous computer. In the last step, we show the universality by simulating a computation of a universal machine. The size of the amorphous computer will depend on the space complexity of the simulated machine. All the previously mentioned steps are described in detail in this work....
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Geometric structures based on quaternions.
Floderová, Hana ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
A pair (V, G) is called geometric structure, where V is a vector space and G is a subgroup GL(V), which is a set of transmission matrices. In this thesis we classify structures, which are based on properties of quaternions. Geometric structures based on quaternions are called triple structures. Triple structures are four structures with similar properties as quaternions. Quaternions are generated from real numbers and three complex units. We write quaternions in this shape a+bi+cj+dk.
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Mappings in geometry
Trkovská, Dana ; Boček, Leo (referee) ; Kubát, Václav (advisor)
This diploma dissertation is dedicated to applications of geometrical mappings. It is intended as a tuitional material specially for students of the third year of the mathematics teachers programm at Mathematical and Physical faculty of Charles University in Prague. The text can be used as a supplementary material for a seminar at secondary school as well. It is based on lectures of the course Geometry II. Students are familiar with the term mapping already during the lessons at elementary and secondary schools. Therefore in the diploma dissertation we at first give only a summary of basic knowledge about mappings in geometry, in the language of mathematics textbooks. Next part of this thesis includes theoretical knowledge about mappings in geometry in the form of definitions and propositions together with their proofs. A great part is dedicated to characterization of affine mappings, specially isometries and similarities. At the end circular inversion is explained as an example of a mapping that is not affine. For better imagination the whole text is complemented with a number of figures. Theoretical part is followed by a collection of exercises. Of course, solutions of all exercises are given.
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The Role of Gut Microbiota and Lipopolysachaide Content of the Diet in the Development, Maturation and Function of the Immune System
Hrnčíř, Tomáš ; Tlaskalová - Hogenová, Helena (advisor) ; Prokešová, Ludmila (referee) ; Macela, Aleš (referee)
Mammals are essentially born germ-free but the epithelial surfaces are promptly colonized by astounding numbers of bacteria soon after birth. The most extensive microbial community is harboured by the distal intestine. The gut microbiota outnumbers ~10 times the total number of our somatic and germ cells. The hostmicrobiota relationship has evolved to become mutually beneficial. Studies in germfree mice have shown that gut microbiota is essential for the proper development of the immune system. The pivotal role of the innate immune system in the complex and dynamic host-microbiota interactions has become increasingly evident. The principal aims of the present study were: firstly, to determine whether LPS-rich sterile diet can promote maturation of the immune system in germ-free mice, secondly, to elucidate whether gut microbiota and LPS-rich sterile diet influence the LPS susceptibility, and finally, to investigate a role of the adaptive immunity in endotoxin shock. Our data clearly show that both live gut microbiota and LPS-rich sterile diet increase susceptibility to endotoxin shock. Further, we demonstrate that immunodeficient SCID mice, which lack mature B and T cells, are more sensitive to endotoxin shock than immunocompetent Balb/c mice. In addition, we show that not only live gut microbiota but also...
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