Liver perfusion can be modelled by Darcy's flow in multiple connected com- partments. The first part of the present thesis shows in detail the existence of a solution to the multi-compartmental model. The flow in each compartment in this model is characterized by a permeability tensor, which is obtained from the geometry of liver vasculature. It turns out that this tensor might be singular, which potentially causes solvability problems. The second part deals with this abnormality in one compartment. By using the theory of degenerate Sobolev spaces, an appropriate weak formulation is defined. Analogues of Poincar'e and traces inequalities in this degenerate setting are proved, which also imply the existence of the weak solutions. In addition, this part justifies another possibil- ity how to deal with degenerate permeability, which is regularizing the tensor by adding a small isotropic permeability to it. In the third part, the aim is to find subdomains of autonomous perfusion with respect to the source positions. This is formulated as a minimization problem and several numerical results are presented. 1

In this diploma thesis, there are described different types of soil tillage and options of their use. The thesis focuses on comparision selected plow in comparable conditions. Plows were compared by efficiency, possibilities of the type of rotation on headlands, fuel consumption and durability of wearing parts. For measuring were chosen lands with a slope as small as possible and with furrow that should be as long as possible to minimize distortion of the results.

Slepá dekonvoluce je metoda, při které je rozptylová funkce a skutečný obraz rekonstruován zároveň. Cílem této práce je představit různé metody slepé dekonvoluce a najít optimální metodu rekonstrukce původního obrazu a rozptylové funkce. Jako nejvhodnější metoda slepé dekonvoluce byl zvolen algoritmus střídavé minimalizace, který byl upraven a testován. Vlastnosti navrženého algoritmu byly testovány na uměle degradovaných datech a na reálných datech pořízených skenovacím transmisním elektronovým mikroskopem. Účinnost algoritmu byla hodnocena hned několika hodnotícími kritérii. Byla zjištěna omezení algoritmu a tím specifikováno jeho využití.

This diploma thesis is focused on influence of reduced tillage technology of soil processing on it´s near-surface soil layer (0 to 10 cm). The research was carried out on agricultural land near Šardičky village, where company ZEMO spol. s r.o. provides long-term use of reduced tillage technology. In 2016 the soil quality in this site was evaluated by using physical and hydrophysical parameters, results are presented in the previous bachelor thesis "Selected hydrophysical parameters as indicators of soil quality.". In diploma thesis in addition chemical and other hydrophysical properties have been evaluated to provide a comprehensive assessment of soil quality. In 2016, poppy seed was grown on this site and spring barley was grown in 2017 and 2018. Grab samples and intact soil cores were taken during the vegetation period of the crop. After three years of experimental research, in which I participated, it is possible to assess the development of individual parameters and the influence of reduced tillage technology on near-surface soil layer. The theoretical part of the diploma thesis deals with the description of the reduced tillage technology and problematics of the determination of soil parameters, which are used for evaluation of the quality of the near-surface layer. The practical part deals with evaluation of these parameters according to various authors and describes the development of soil quality during years 2016, 2017 and 2018.

Farmland is being handled by various the tillage of soil especially for the correct course of soil processes, plant growth and development and of course profit. There are two types of the tillage of soil are their conventional (classical) which involves plowing and minimization tillage, where is excluded plowing. The last few decades, the development the tillage of soil focuses on minimization tillage. This includes loosing up small depth, soil conservation tillage and direct seeding. This thesis is aimed at impact of minimization tillage on selected physical and hydraulic properties of the soil. Sampling undisturbed soil samples was performed on the experimental plot Kozlany by Kopecky rollers (V = 100 cm3) from depth of 0 - 10 cm, during the year 2016. On this plot was used minimization tillage in the form loosing up small depth and direct seeding.

Diploma thesis evaluates quality and healthiness of the soil health located close to Bohate Malkovice focusing on changes in both physical and chemical characteristics of the soil in time. The theoretical part describes physical, chemical, and biological parameters of the soil. Selected physical parameters are structure, texture, determination of measured weight, bulk density of the soil, porosity, actual volumetric water content of the soil, aeration, saturated and unsaturated hydraulic conductivity, infiltration, and colour. Chosen chemical parameters are pH, carbonates, soil electrical conductivity, and humus content. Picked biological parameters are microbial biomass, respiration, nitrogen content, and weed infestation. The practical part analyses selected indicators of quality of the soil from the location of the experiment close to Bohate Malkovice. The area under evaluation has been treated using reduced tillage for long term. The practical part is based on the laboratory examination of disturbed and undisturbed soil samples taken between years 2016 and 2018. Based on outcome results we can evaluate the quality of the soil considering plants growth, development, and soil fertility.

This Master Thesis deals with image restoration using deconvolution. The terms introducing into deconvolution theory like two-dimensional signal, distortion model, noise and convolution are explained in the first part of thesis. The second part deals with deconvolution methods via utilization of the Bayes approach which is based on the probability principle. The third part is focused on the Alternating Minimization Algorithm for Multichannel Blind Deconvolution. At the end this algorithm is written in Matlab with utilization of the NAG C Library. Then comparison of different optimization methods follows (simplex, steepest descent, quasi-Newton), regularization forms (Tichonov, Total Variation) and other parameters used by this deconvolution algorithm.