In this work we have examined different methods of averaging in general relativity and cosmology. We developed the method based on Cartan scalars. We computed the backreaction term for a flat LTB model with a special ansatz for the radial function. We found out that it behaves as a positive cosmological constant. In the next part of this thesis we were interested in averaging inside LRS class II dust model. For this family we averaged all the Einstein equations and the resulting system generalizes the Buchert equations. We numerically worked out two concrete examples where deceleration parameter changes its sign from positive to negative. Powered by TCPDF (www.tcpdf.org)

This thesis covers non-homogeneous Poisson processes along with estimation of the intensity (rate) function and some selected simulation methods. In Chapter 1 the main properties of a non-homogeneous Poisson process are summarized. The main focus of Chapter 2 is the general maximum likelihood estimation procedure adjusted to a non-homogeneous Poisson process, together with some recommen- dations about calculation of the initial estimates of the intensity function param- eters. In Chapter 3 some general simulation methods as well as the methods designed specially for log linear and log quadratic rate functions are discussed. Chapter 4 contains the application of the described estimation and simulation methods on real data from non-life insurance. Furthermore, the considered sim- ulation methods are compared with respect to their time efficiency and accuracy of the simulations. 1

The diploma thesis deals with the topic of discounts and premiums in the valuation theory. More specifically, it covers the area of entity-level discounts. First part of the thesis is devoted to general theoretical analysis of the topic. Next chapter is dedicated to key person discount and portfolio discount, including empirical evidence, relevant factors of influence, their quantification and several case studies. Final part of the thesis describes possibilities of utilization of these two types of discounts in Czech practice.

In this work we study inhomogeneous cosmological models. After a brief review of applications of inhomogeneous solutions to Einstein equations in cosmology, we give a short description of the most widely used inhomogeneous cosmological models. In the second chapter we study in detail geometrical prop- erties of the Szekeres spacetime and we are concerned with the interpretation of the metric functions in different types of geometries. In the last chapter we model inhomogeneity in Szekeres spacetime. We derive formula for the density contrast and investigate its behaviour. We also derive conditions for the density extremes that are necessary for avoiding the shell crossing singularity in Szekeres spacetime. 1

The problem of creating dynamic fare model consists of two tasks - estimating demand for train tickets and multistage optimization of price of fare. We introduce a model of inhomogeneous Markov process for the process of selling the tickets in this thesis. Because of the complexity of the state space the optimization problem needs to be solved using simulation methods. The solution was implemented in R language for single-stage and two-stage problems. Before this application we summarize the theory of inhomogeneous Markov process with special attention to process with separable inhomogeneity. Then we propose methods for estimating the intensity using maximum likelihood theory. We also describe and compare two algorithms for simulated optimization. Powered by TCPDF (www.tcpdf.org)

This work deals with image enhacements technology for 2D faces.. Describes methods of image processing, which are used in the proposed methods. These methods eliminate inhomogeneous lighting and shadows in the face. It also suggests the detector face, which is used as input for the method to eliminate shadows.

This thesis deals with a study of methods sufficient to describe the behavior of bulk materials (homogeneous and non-homogeneous) during their transport by bucket elevators in the application focused on the optimization of the bucket shape and also on the optimization of operating parameters of whole elevator. More specifically, this thesis is based on the studying and creating analytical and numerical computational models which are used for description of flows and deformations especially of particulate materials. Firstly, the thesis is focused on the process of discharging the bucket – the relationship among the shape of the surface of a particulate material and geometry, position and movement of the bucket. The beginning and way of discharge of the bucket will be determined. Secondly, the thesis includes the overall computational model of a bucket elevator which is based on discrete element method and presented in the case study. The goal is to determine the limits of some classical physical and mathematical descriptions.

This diploma project works out and is focused on the continual mixing process of the particular matters. The project is divided into following chapters. Chapter 1 includes mixing theory and information of the experimental work of the particular matters for blade using. In chapter 2 there is Evaluation and calculation of the technical parameters for the mixer. Chapter 3 deals with the engine proposal and chapter 4 includes calculation and design work of the gear transmission. Chapter 5 includes the stress analysis of the shaft and blade with the I-deas software. In attachment there are also the mixer arrangement drawing and detailed drawings of the key parts and groups for the mixer.

This master’s thesis is about earth fault locator testing on the model of unsymmetrical lines. The introductory part of thesis describes the function of the selected locator, mainly for the used calculation algorithm of fault location, options setting of fault locator and connection of the locator to the network. Master’s thesis in its practical part deals, with the setting fault locator for a particular test system on the model of the MV line and implementation of selected testing on the model unsymmetrical lines. The first part of the testing is focusing on verify the accuracy locator on an unsymmetrical line. The second test is then designed for obtaining the most accurate information on the distance of the fault, which fault locator can give. The final part is focused on verification algorithm for more accurate calculation of the fault location.

The work considers pulse wire-guided electromagnetic (EM) waves. The main contribution of the work is the original design of the isolation bushing for maximizing of the received wave (echo) thanks to the results of the numerical simulations, the acquirement of the new acknowledges of the reflections of the guided EM wave from the various boundaries, the construction of PML layers for FDTD simulations in rotational coordinates, the advances made in temporary excitation sources for FDTD and the formulation of the program code for FDTD in rotational coordinates in Matlab environment. The rightness of the numerical simulations was verified in practical experiments. The practical exploitation of the results is supposed in instrumentation and control technology - the level measurement in reservoirs.