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Legal regulation of employment termination
Kučera, Václav ; Vysokajová, Margerita (advisor) ; Štefko, Martin (referee)
Presented rigorous thesis deals with legislation of employment termination and also institutions included in the employment termination. The termination notice is very frequented way of ending the employment although this unilateral juridical proceedings may be find as complications free, questions are arising during its application in place, and this thesis is trying to find satisfactory answers. It can be considered, that application of the institute has been carrying on contra legem, especially in terms of application by the employer, as we can find in rich court juridical. Employers do not hesitate to terminate employment by using termination notice even though, they did not meet legal conditions or they just simply feign meeting legal conditions. It depends on the employee and his willingness with strength to undergo law enforcement of his claims at independent courts. This thesis examines in detail the institute of dismissal, pointing out the historical adjustments and adjustments in international documents, closely devoting the employment itself, object, subject, content, commencement and duration of the employment and also employer duties connected to the employment. Thereafter the thesis deals with legal actions and their validity or otherwise. Delivering, typical for directed legal...
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Reorthogonalization strategies in Golub-Kahan iterative bidiagonalization
Šmelík, Martin ; Hnětynková, Iveta (advisor) ; Kučera, Václav (referee)
The main goal of this thesis is to describe Golub-Kahan iterative bidiagonalization and its connection with Lanczos tridiagonalization and Krylov space theory. The Golub-Kahan iterative bidiagonalization is based on short recurrencies and when computing in finite precision arithmetics, the loss of orthogonality often occurs. Consequently, with the aim to reduce the loss of orthogonality, we focus on various reorthogonalization strategies. We compare them in numerical experiments on testing matrices available in the MATLAB environment. We study the dependency of the loss of orthogonalization and computational time on the choice of the method or the attributes of the matrix.
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Segmentace mikroskopických snímků pomocí level-set metod
Bílková, Zuzana ; Kučera, Václav (advisor)
Název práce: Segmentace mikroskopických snímků pomocí level-set metod Autor: Zuzana Bílková Katedra: Katedra numerické matematiky Vedoucí diplomové práce: RNDr. Václav Kučera, Ph.D., KNM, MFF UK Konzultant: RNDr. Jindřich Soukup, ÚTIA, AV ČR Abstrakt: Tato diplomová práce představuje novou metodu pro segmentaci snímků pořízených mikroskopem s fázovým konrastem. Cílem je oddělit buňky od pozadí. Algoritmus je založen na variační formulaci level set metod, tedy na minimalizaci funkcionálu popisujícího level set funkci. Funkcionál je minimalizován gradientním tokem popsaným evoluční parciální diferenciální rovnicí. Nejdůležitější nové myšlenky jsou inicializace pomocí prahování a nové členy ve funkcionálu, které zrychlují konvergenci a zpřesňují výsledky. Také jsme použili nové funkce napsané v jazyce C k počítání gradientu a Laplaceova operátoru. Tato implementace je třikrát rychlejší než standardní funkce v MATLABu. Dosáhli jsme lepších výsledků než algoritmy, se kterými jsme metodu porovnávali. Klíčová slova: Segmentace, level set metody, aktivní kontury Title: Segmentation of microscopic images using level set methods Author: Zuzana Bílková Department: Department of Numerical Mathematics Supervisor: RNDr....
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Diet supplemantation among para troops in the Army of the Czech Republic
Kučera, Václav ; Michalička, Vladimír (advisor) ; Šťastný, Petr (referee)
Title Use of Dietary Supplements at the Czech Airborne Force. Objective The objective of my work was to examine the use of supplements in the Czech Airborne Battalions through the use of questionnaire method and analysis of professional literature. Professional soldiers, especially in airborne battalions, are expected to have a high level of psychological as well as physical readiness. Building on professional literature, articles, internet resources, and information from leading nutrition and supplementation experts I sought to compile a work that would provide basic information on the use of supplementation. Plan of processing At the very beginning, it was necessary to have a comprehensive idea of the implementation of the questionnaire method in the Czech Airborne Forces. A review of available materials was followed by a summary of the basic nutrients and supplements that are, in our opinion, the most used in paratroopers. As a next step a questionnaire was created. Then, we handed out and collected questionnaires at individual crews. This was followed by the questionnaire evaluation, charting, and finishing the bachelor's thesis. Results Supplementation is very popular with the Czech Army paratroopers. A total of 86.7 % of respondents use dietary supplements. The results show, that the main...
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The choice of the step in trust region methods
Rapavý, Martin ; Tichý, Petr (advisor) ; Kučera, Václav (referee)
The main goal of this thesis is the choice of steps in trust region methods for finding a minimum of a given function. The step corresponds to the problem of finding a minimum of a model function on a trust region. We characterize a solu- tion of this problem (Moré-Sorensen theorem) and consider various techniques for approximating a solution of this problem (the Cauchy point method, the dogleg method, the conjugate gradients method). In the case of the first two techniques we prove convergence of the optimization method. Finally, the above techniques are tested numerically in MATLAB on properly chosen functions and initial data. We comment on advantages and disadvantages of considered algorithms. 1
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Methods for the solution of nonlinear equations
Havelková, Eva ; Kučera, Václav (advisor) ; Tichý, Petr (referee)
The aim of this bachelor thesis is to present an overview of elementary numerical methods for solving nonlinear algebraic equations in one variable. Firstly, related concepts from numerical mathematics and mathematical analysis are explained. The main part of the thesis provides a detailed description of chosen iterative methods as well as the proofs of their orders of convergence. The methods covered are namely the bisection method, fixed-point iteration, regula falsi method, Newton's method, secant method and methods that are based on quadratic interpolation. The practical part of the thesis presents results of numerical experiments that were carried out with Matlab software on various types of nonlinear equations. These results are compared with the theory introduced in the preceding parts. The contribution of this thesis is to provide a comprehensive overview and comparison of the characteristics of basic methods for solving nonlinear equations based on a variety of literature. Powered by TCPDF (www.tcpdf.org)
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Segmentace mikroskopických snímků pomocí level-set metod
Bílková, Zuzana ; Kučera, Václav (advisor) ; Zitová, Barbara (referee)
Název práce: Segmentace mikroskopických snímků pomocí level-set metod Autor: Zuzana Bílková Katedra: Katedra numerické matematiky Vedoucí diplomové práce: RNDr. Václav Kučera, Ph.D., KNM, MFF UK Konzultant: RNDr. Jindřich Soukup, ÚTIA, AV ČR Abstrakt: Tato diplomová práce představuje novou metodu pro segmentaci snímků pořízených mikroskopem s fázovým konrastem. Cílem je oddělit buňky od pozadí. Algoritmus je založen na variační formulaci level set metod, tedy na minimalizaci funkcionálu popisujícího level set funkci. Funkcionál je minimalizován gradientním tokem popsaným evoluční parciální diferenciální rovnicí. Nejdůležitější nové myšlenky jsou inicializace pomocí prahování a nové členy ve funkcionálu, které zrychlují konvergenci a zpřesňují výsledky. Také jsme použili nové funkce napsané v jazyce C k počítání gradientu a Laplaceova operátoru. Tato implementace je třikrát rychlejší než standardní funkce v MATLABu. Dosáhli jsme lepších výsledků než algoritmy, se kterými jsme metodu porovnávali. Klíčová slova: Segmentace, level set metody, aktivní kontury Title: Segmentation of microscopic images using level set methods Author: Zuzana Bílková Department: Department of Numerical Mathematics Supervisor: RNDr....
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Removal of JPEG compression artefacts in image data
Lopata, Jan ; Kučera, Václav (advisor) ; Šroubek, Filip (referee)
This thesis is concerned with the removal of artefacts typical for JPEG im- age compression. First, we describe the mathematical formulation of the JPEG format and the problem of artefact removal. We then formulate the problem as an optimization problem, where the minimized functional is obtained via Bayes' theorem and complex wavelets. We describe proximal operators and algorithms and apply them to the minimization of the given functional. The final algorithm is implemented in MATLAB and tested on several test problems. 1
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Metody vyššího řádu založené na rekonstrukci
Dominik, Oldřich ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
This work is concerned with the introduction of a new higher order numerical scheme based on the discontinuous Galerkin method (DGM). We follow the methodology of higher order finite volume (HOFV) and spectral volume (SV) schemes and introduce a reconstruction operator into the DGM. This operator constructs higher order piecewise polynomial reconstructions from the lower order DGM scheme. We present two variants: the generalization of standard HOFV schemes, already proposed by Dumbser et al. (2008) and the generalization of the SV method introduced by Wang (2002). Theoretical aspects are discussed and numerical experiments with the focus on a 2D advection problem are carried out. Powered by TCPDF (www.tcpdf.org)
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Fractional derivatives, theory and applications
Pelech, Petr ; Kučera, Václav (advisor) ; Dolejší, Vít (referee)
This work represents an overview of the given topic. After a short historical intro- duction, we present all necessary results from the classical theory of differentiation and integration. The core of the thesis is concerned with the Riemann-Liouville (R-L) integral and derivative of real functions defined on compact intervals. We prove basic properties for integrable as well as continuous functions. Along with the R-L definition, we also give the Caputo and Grünwald-Letnikov definitions and their mutual relations. Furthermore, we calculate the R-L derivatives of some elementary functions as well as basis functions from the finite element method. The last part is concerned with the numerical approximation of R-L derivatives. We describe and implement two algorithms, which we test on several functions. 1
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