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Stability of the Zero Solution of Stochastic Differential System
Klimešová, Marie
Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems.
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Delay Difference Equations and Their Applications
Jánský, Jiří ; Hilscher, Roman Šimon (referee) ; Čermák, Libor (referee) ; Čermák, Jan (advisor)
Disertační práce se zabývá vyšetřováním kvalitativních vlastností diferenčních rovnic se zpožděním, které vznikly diskretizací příslušných diferenciálních rovnic se zpožděním pomocí tzv. $\Theta$-metody. Cílem je analyzovat asymptotické vlastnosti numerického řešení těchto rovnic a formulovat jeho horní odhady. Studována je rovněž stabilita vybraných numerických diskretizací. Práce obsahuje také srovnání s dosud známými výsledky a několik příkladů ilustrujících hlavní dosažené výsledky.
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Wideband transimpedance photodiode amplifier
Šťastný, Martin ; Roubal, Zdeněk (referee) ; Drexler, Petr (advisor)
This thesis deals with the design of transimpedance amplifier with high gain. There are described different principles of semiconductor sensors of optical signal. There is also a comparison of different methods of converting the photocurrent to voltage. It also discusses the design of an appropriate feedback capacitor in terms of stability in participation as a transimpedance amplifier. It examines the impact of non-zero currents flowing to the input operational amplifier circuit functionality and output offset compensation. Part of the thesis is a simulation that confirms the calculated values. The thesis also deals with the implementation of the receiver and the method of correct measurement of the cut-off frequency.
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Stability of Time Delay Feedback Controls of Dynamical Systems
Lovas, David ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
Tato diplomová práce pojednává o stabilitě zpětně-vazebných řízení dynamických systémů s časovým zpozděním, speciálně řízení mechanických oscilátorů. Dva základní druhy řízení jsou užity v lineárních systémech. Dále je zde ukázána synchronizace dvouprvkových systémů užitím zpětně-vazebných řízení. Práce se také zabývá funkcí v MATLABu pro řešení zpožděných diferenciálních rovnic.
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The Study of Biopolymers Stability Using Light Scattering Techniques
Kratochvíl, Zdeněk ; Sedláček, Petr (referee) ; Kalina, Michal (advisor)
The stability of chosen biopolymers (or simple carbohydrates and amino acids) was in-vestigated using light scattering methods. Samples were prepared by dissolving the sub-stance in deionised water or in diluted acetic acid. Firstly, the effect of increasing concen-tration on zeta potential was observed and the optimal concentration for the next measure-ments was determined. Afterwards, the stability and the molecular weight of used sub-stances were studied during long-time storage in different time intervals. It was found out that chitosan, CMC, hyaluronate and sodium alginate were subjected to degradation whereas increase of the molecular weight and the zeta potential was observed in case of BSA. In the end, the samples were exposed to several different external effects, namely the influence of different temperatures, UV radiation and increasing ionic strength. The results showed that rather higher temperature has a significant impact on biopolymers stability. However, used biopolymers were hardly affected by UV radiation except BSA whose molecular weight increased considerably. Decrease of the zeta potential absolute values and the molecular size usually occurred with increasing ionic strength. The change of molecular weight was not detected.
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Mathematical modelling of walking robots
Kiša, Daniel ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
Tato diplomová práce se zabývá matematickými modely kráčejících robotů. Dva z těchto modelů jsou vybrány a analyzovány. Pasivní model "rimless wheel" , který slouží jako základ pro další, složitější modely, je podrobně analyzován. "Compass gait" model dvounohého robota je v práci analyzován a numericky simulován v programovacím jazyce Python. Metoda pro nalezení podmínek pro pasivní chůzi robota je rovněž implementována.
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Construction of equipment for thin walled L-profiles instability testing
Polčák, Marek ; Vaněk, František (referee) ; Horák, Marek (advisor)
Bachelor’s thesis deals with the loss of stability of axially loaded thin-walled aluminium profi-les, which make up an important part in the aircraft structures. The loss of their stability is tes-ted by the compression test, which is used to determine the buckling load. Compression test may be influenced by many factors, which are related to the fixing to the testing machine. The aim of the thesis is to design a fixture, which would fix a specimen to the testing machine and improve the results of the test.
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Using mobile phone in feedback rehabilitation
Mynařík, Ondřej ; Žalud, Luděk (referee) ; Chromý, Adam (advisor)
The aim of this thesis is to evaluate sensors used in Android mobile phones for measuring inclination and their comparation with precise reference sensor Xsens. Another goal is to create Android application for measuring inclination of balance desk. This application communicates with a computer by Bluetooth. Results indicates that sensors in mobile phones are sufficient enough to replace the precise sensor Xsens for measuring inclination of balance desk. Based on the results mobile application was created. Using a mobile phone with this application can replace Xsens, which results in rapid decrease of the price and the possible use in rehabilitation centers or by patients.
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