The master's thesis deals mainly with continuous nonlinear dynamical systems that exhibit chaotic behavior. The main goal is to create algorithms for chaos detection and their subsequent testing on known models. Most of the thesis is devoted to the estimation of the Lyapunov exponents, further it deals with the estimation of the fractal dimension of an attractor and summarizes the 0--1 test. The thesis includes three algorithms created in MATLAB -- an algorithm for estimating the largest Lyapunov exponent and two algorithms for estimating the entire Lyapunov spectra. These algorithms are then tested on five continuous dynamical systems. Especially the error of estimation, speed of these algorithms and properties of Lyapunov exponents in different areas of system behavior are investigated.

The diploma thesis should identify inconsistencies of the small hydraulic power plant Katovice. The fountain water turbine is now running in slower delivery because the original Francis high speed turbine achieved much smaller flow than a Kaplan type turbine. The aim of the thesis is a project of a spiral case and a distributor for the Kaplan turbine, which should work in higher flow and should be run in its optimum. This project will serve as a base for construction of distributor and spiral case for the small hydraulic power plant Katovice.

In der Natur und in technischen Anwendungen findet man viele dynamische System mit zeitlicher Verzögerung (delay),zum Beispiel die Mackey-Glass Gleichung, die als Beschreibung vom Aufbau der Blutzelle angewendet wird, und die Ikeda Gleichung, die ein Modell von einem optischen Resonator ist. Hier ist zeitliche Verzögerung τ eine Konstante, aber sie ist nicht immer konstant in der Natur und in der Praxis. Wie sieht das System aus und welche Stabilitätseigenschaften hat es, wenn die Verzögerung schwankt? In dieser Arbeit benutze ich einige einfache diskrete Abbildungen, um die resultierenden Effekte zu untersuchen.

The thesis examines the regulation of pastoral care in the sector of civil aviation by the laws of the Roman Catholic Church (Latin Church). The general part first describes the theological reasons for special pastoral care, as well as the inception and development of its institutional organisation. The core of the general part of the thesis consists of identifying and interpreting the relevant legal standards of the Roman Catholic Church's (Latin Church's) general canon law. Attention is devoted in particular to the possibilities of organisational arrangement, the issue of airport chapels, their canonical status and use, individuals providing pastoral care, the specific issues of communicatio in sacris and the possibility of regulation by particular law. The special part of the thesis describes how pastoral care in civil aviation is organised in selected European Union member states and how it may be modified by particular law. Keywords Canon law, particular law, pastoral care, civil aviation, airport, chaplain, airport chaplaincy.

The content of this diploma thesis is a feasibility study of a small hydropower station within the navigation lock Přelouč II. This work builds on the framework proposal of one variation of layout arragement of the navigation lock. In this variant is considered to build a lock, which also includes a small hydropower station. At the beginning, the location of individual building objects is resolved with respect to the conditions in the locality. This is followed by a more detailed development of the building and technological part of a small hydropower plant. Part of the thesis is accompanying and technical report, drawing documentation, hydrotechnical and hydroenergetic calculations and photographic documentation.

I denna rapport utreds olika metoder för att kunna reglera vattennivån i vattenkraftverket Avesta Lillfors i Dalarna. Två kraftverk ligger endast 900 m uppströms och detta gör att svarstiderna blir korta och regleringen blir lätt nervös. Att använda sig av vattennivåreglering i ett kraftverk för-enklar dess styrning då anpassning till inflödet sker automatiskt. En flödestabell har tagits fram genom mätningar i turbinen, med hjälp av Winter-Kennedy-metoden. Denna tabell används för att kunna fram-koppla regulatorn och därmed dämpa stora variationer i inflödet. Dessu-tom har en modell av älven skapats och testats med en återkopplad PID-regulator. Utefter dessa tester har lämpliga parametrar tagits fram, som ger önskad stabilitet, noggrannhet och snabbhet. Simuleringar har även gjorts med reglermetoden Fuzzy logic. / This report evaluates different methods to create a stable regulation of the water level in the hydro power plant Avesta Lillfors, in county Dalar-na. Another pair of plants are located just 900 m up the stream, which is why the regulation has to act fast. If the water level can be regulated and automatically adjust to the incoming flow, it facilitates the control of the plant. A flow chart is created from measurements in the turbine, using the Win-ter-Kennedy method. The results are used for feedforward control. A PID-regulator with feedback is also simulated in a model of the river. This helps finding the parameters that provide a stable, accurate and fast regu-lation. Fuzzy logic control has also been simulated.

The Birnbaum-Saunders (BS) distribution is a positively skewed distribution and is a popular model for analyzing lifetime data. In this thesis, we first develop an improved method of estimation for the BS distribution and the corresponding inference. Compared to the maximum likelihood estimators (MLEs) and the modified moment estimators (MMEs), the proposed method results in estimators with smaller bias, but having the same mean squared errors (MSEs) as these two estimators. Next, the existence and uniqueness of the MLEs of the parameters of BS distribution are discussed based on Type-I, Type-II and hybrid censored samples. In the case of five-parameter bivariate Birnbaum-Saunders (BVBS) distribution, we use the distributional relationship between the bivariate normal and BVBS distributions to propose a simple and efficient method of estimation based on Type-II censored samples. Regression analysis is commonly used in the analysis of life-test data when some covariates are involved. For this reason, we consider the regression problem based on BS and BVBS distributions and develop the associated inferential methods. One may generalize the BS distribution by using Laplace kernel in place of the normal kernel, referred to as the Laplace BS (LBS) distribution, and it is one of the generalized Birnbaum-Saunders (GBS) distributions. Since the LBS distribution has a close relationship with the Laplace distribution, it becomes necessary to first carry out a detailed study of inference for the Laplace distribution before studying the LBS distribution. Several inferential results have been developed in the literature for the Laplace distribution based on complete samples. However, research on Type-II censored samples is somewhat scarce and in fact there is no work on Type-I censoring. For this reason, we first start with MLEs of the location and scale parameters of Laplace distribution based on Type-II and Type-I censored samples. In the case of Type-II censoring, we derive the exact joint and marginal moment generating functions (MGF) of the MLEs. Then, using these expressions, we derive the exact conditional marginal and joint density functions of the MLEs and utilize them to develop exact confidence intervals (CIs) for some life parameters of interest. In the case of Type-I censoring, we first derive explicit expressions for the MLEs of the parameters, and then derive the exact conditional joint and marginal MGFs and use them to derive the exact conditional marginal and joint density functions of the MLEs. These densities are used in turn to develop marginal and joint CIs for some quantities of interest. Finally, we consider the LBS distribution and formally show the different kinds of shapes of the probability density function (PDF) and the hazard function. We then derive the MLEs of the parameters and prove that they always exist and are unique. Next, we propose the MMEs, which can be used as initial values in the numerical computation of the MLEs. We also discuss the interval estimation of parameters. / Thesis / Doctor of Science (PhD)

Indiana University-Purdue University Indianapolis (IUPUI) / Introduction: The prevalence of diabetes mellitus (DM) is rapidly increasing among the aging United States population. This poses a challenge to dental providers since DM and multiple oral conditions have been identified as comorbidities. Hypertension (HTN) is associated with more poorly controlled DM and has been identified as contributing to RCT tooth loss in prior studies. Links have also been established between DM and the survival rate of root canal treated teeth, however, previous research has focused on institutional settings despite the majority of RCT being performed in private dental practices. This study will use data from private dental practices to evaluate the survival rate of RCT teeth in patients with DM and HTN. Materials and Methods: This retrospective study evaluated the survival rate of endodontic treated teeth among patients with DM and HTN using National Dental PBRN Practice data. Electronic dental records from 42 private dental practices in the United States over a period of 15 years with a minimum 2-year follow-up comprising 11,532 root canal treated teeth were analyzed. Kaplan-Meier survival curves were used to demonstrate the effects of HTN and DM on RCT tooth survival and Cox proportional hazards survival analysis was used to evaluate the DM and HTN effects after accounting for age, gender, insurance, year of treatment, tooth type, and crown and filling placement as covariates. Results: Patients with HTN only had significantly lower risk of failure than patients with both HTN and DM (p=0.003). Patients with neither HTN nor DM had significantly lower risk of failure than patients with both HTN and DM (p=0.020). Patients with DM only did not have significantly different risk of failure than patients with both HTN and DM (p=0.223). Patients with DM only did not have significantly different risk of failure than patients with HTN only (p=0.361). Patients with neither HTN nor DM did not have significantly different risk of failure than patients with HTN only (p=0.121) or patients with DM only (p=0.800). Conclusions: Patients with both DM and HTN have an increased chance of root canal treated tooth failure while patients with only DM or only HTN do not. Evaluation of severity of DM may be more important in determining RCT failure and studies utilizing laboratory values should be considered for future research.

This master thesis examines technical requirements for small hydro power plants (HPP) to operate proximate parts of the power grid in island mode. The work examines how small hydropower can be modified and complemented with additional technologies to achieve sufficient frequency control capabilities. A case study was performed within the concession area of power grid operator Ålem Energy. One of the HPPs, located in Skälleryd, is owned by Ålem Energy and became the focal point of the study. Relevant parts of the concession area were surveyed for properties such as system inertia, electric load and available power. Furthermore, a model of Kaplan turbine 1 in Skälleryd HPP was created with the purpose of studying the benefits of bypassing regulation control from the wicket gates directly to the runner. The method was tested in an off-grid islanding test. Frequency control of the turbine was tested powering electric heaters and, using a new method, controlling a virtual power grid. Finally, a theory was developed to estimate the transient disturbance resilience (TDR) of a power grid. The theory was applied to the HPP in Skälleryd to suggest modifications for the plant to achieve sufficient islanding capabilities. The survey of the power system revealed a promising potential for the HPPs to operate in island mode, especially at later stages when the grid spans several HPPs for more system inertia. The available power from the HPPs was however strongly seasonal which imposes flexibility on a future plan of action for engaging the grid in island mode. The method of controlling the turbine power from the runner proved to have several difficulties. Firstly, the current hydraulics system was not able to freely control the runner as the hydrodynamic forces on the runner blades were too large. Secondly, the method was found to be unstable due to inherent amplification of speed deviations. Furthermore, the low inertia at Skälleryd is likely detrimental to the lone frequency control of the turbine. Therefore other methods for improving frequency control were suggested. The developed theory for TDR was used to create charts describing the TDR for various combinations of system inertia and regulation speed. By studying the proprieties of Skälleryd HPP in the charts the necessary modifications could be rationally chosen. A frequency regulating dummy load was found to be the simplest option. A control scheme was suggested with the dummy load performing primary frequency control and the turbines at Skälleryd performing secondary control, restoring the dummy load to its nominal state.

Health technology assessment: case study on breast carcinoma treatment in the Czech Republic Bc. Lenka Šlegerová January 4, 2019 Abstract This thesis proposes an original method for assessing total costs of med- ical treatment. It defines the semi-Markov model with four states that are associated with specific costs of the treatment, and not with patients' health statuses. This method is applied to individuals' treatment data drawn from the Czech clinical practice in the treatment of the metastatic HER2+ breast cancer. The aim is to assess the cost-effectiveness of adding medication per- tuzumab to the combination of trastuzumab+docetaxel within first-line therapy and to examine whether using individual data on Czech patients and the economic conditions leads to different results from foreign stud- ies. Furthermore, employing censored data from the clinical practice in the thesis complicates the estimation of patients' overall survival in compari- son to clinical-trials data that form random samples. Therefore, survival functions were not only estimated by the Kaplan-Meier estimator but also using the Cox proportional hazard model and the Accelerated failure time model that both control for the effects of included covariates. The addition of pertuzumab does not result in significantly longer pa- tients'...