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Inequalities for discrete and continuous supremum operators
Oľhava, Rastislav ; Pick, Luboš (advisor) ; Nekvinda, Aleš (referee)
Inequalities for discrete and continuous supremum operators Rastislav O , lhava In this thesis we study continuous and discrete supremum operators. In the first part we investigate general properties of Hardy-type operators involving suprema. The boundedness of supremum operators is used for characterization of interpo- lation spaces between two Marcinkiewicz spaces. In the second part we provide equivalent conditions for boundedness of supremum operators in the situation when the domain space in one of the classical Lorentz spaces Λp w1 or Γp w1 and the target space Λq w2 or Γq w2 . In the case p ≤ q we use inserting technique obtaining continuous conditions. In the setting of coefficients p > q we provide only partial results obtaining discrete conditions using discretization method. In the third part we deal with a three-weight inequality for an iterated discrete Hardy-type operator. We find its characterization which enables us to reduce the problematic case when the domain space is a weighted ℓp with p ∈ (0, 1) into the one with p = 1. This leads to a continuous analogue of investigated discrete inequality. The work consists of author's published and unpublished results along with material appearing in the literature.
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The effect of sampling period error on frequency analysis
Pietrowicz, Daniel ; Marada, Tomáš (referee) ; Zuth, Daniel (advisor)
This thesis will be focused on signal measurement in connection with digitization and analysis inaccuracy of sampling peroid effect. Brief narration of frequency analysis and description of Matlab and his capabilities with this issue. Then creation procedure for simulation model of analog signal and his fault digitization via sampling period. Systematic comparation of this effect on inaccuracy of sampling period on frequency analysis.
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Bingham-Korteweg fluids - modeling, analysis and computer simulations
Los, Tomáš ; Málek, Josef (advisor) ; Bulíček, Miroslav (referee)
Flow of granular materials is usually initiated when the shear stress is large enough and exceeds certain critical value. This can result in the presence of the dead-zones in which the flow itself does not take place. Motions of such materials are frequently described by Bingham model. Flows of granular fluids are frequently connected with the presence of free surface. In the thesis Bingham model is incorporated into a more general framework of Bingham-Korteweg fluids, which is a suitable way how to transfer free- boundary problems into the problems on fixed domains. A part of the thesis concerns mathematical analysis of interesting relevant problems for incompressible fluids. 1
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Probabilistic Spacetimes
Káninský, Jakub ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
Probabilistic Spacetime is a simple generalization of the classical model of spa- cetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a generalization is a possible application in the context of some quantum gravity approaches, na- mely those using the path integral. It is argued that this model might be used to restrict the precision of the geometry on small scales without postulating discrete structure; or it may be used as an effective description of a probabilistic geometry resulting from a full-fledged quantum gravity computation.
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Volumetric Efects Accelerated on GPU
Kubovčík, Tomáš ; Tóth, Michal (referee) ; Starka, Tomáš (advisor)
This thesis deals with simulation and rendering of fluid based volumetric effects, especially effect of fire and smoke. Computations are accelerated on graphics card using modern graphics API with motivation to achieve realistic visual results as well as physically correct calculations. Implemented volumetric effects are distributed as dynamic library which allows addition of these effects to existing applications.
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Korteweg fluids - modeling, analysis and computer simulations
Blaškovičová, Monika ; Málek, Josef (advisor) ; Řehoř, Martin (referee)
We present two possible thermodynamical approaches towards a derivation of a model, proposed by Korteweg at the beginning of the 20th century, that is suitable to describe phase transitions liquid-vapor with non-sharp interfaces. The first approach (Dunn, Serrin (1985)) is based on classical rational continuum thermodynamics. The second approach (Heida, Málek (2010)) stems from the principles of classical nonequilibrium continuum thermodynamics. We compare both approaches in favor of the second one. The considered constitutive equation for the Cauchy stress is nonlinear. Nonlinearity and higher order derivatives of the density makes the analysis of relevant problems for the Navier-Stokes- Korteweg (NSK) fluid more difficult in comparison to problems concerning Navier-Stokes equations. Special attention is devoted to the appropriate choice of the boundary conditions. We also investigate the influence of compressibility on the stability of bubbles by comparing numerical simulations for compressible NSK fluid and its incompressible variant. Instabilities observed for a compressible NSK fluid are due to the pressure that has a different meaning for incompressible fluid. Powered by TCPDF (www.tcpdf.org)
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Recursive calculation of compound distributions
Sekera, Michal ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
The aim of this work is the calculation of compound distributions by using the algorithm known as the Panjer recursion. This algorithm is limited to dis- crete distributions and the (a, b, 0) and (a, b, 1) classes of distributions. The thesis shows which distributions are members of these classes. The thesis then descri- bes the discretization of continuous distributions by using the rounding method and the method of local moments matching; everything is explained on exam- ples. These methods are then applied to the calculation of the premium for mo- del of excess of loss reinsurance with reinstatements (XL-reinsurance with re- instatements), and the calculating the solvency capital requirement. Numerical illustrations are included. 1
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Non-linear normal modes in dynamics-continuous systems
Náprstek, Jiří ; Fischer, Cyril
The paper presents a continuation of an effort started last year, when the authors briefly informed about the Non-linear normal modes (NNM) concerning the version dealing with discrete systems. Although many features of the continuous formulation from the mathematical viewpoint are similar to the discrete case, a couple of specifics should be highlighted from the viewpoint of a real applicability of this tool to investigate particular dynamic systems. Three approaches are mentioned in the paper and the Galerkin-Petrov based procedure is outlined in more details. As a particular subject the cantilever prismatic beam is discussed. Non-linear normal modes for several amplitudes are shown to demonstrate the dependence of their shapes on the actual effective amplitude. Comparison with adequate linear counterpart is done.
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Web Page Classification
Kolář, Roman ; Burget, Radek (referee) ; Bartík, Vladimír (advisor)
This paper presents problem of automatic webpages classification using association rules based classifier. Classification problem is presented, as a one of datamining technique, in context of mining knowledges from text data. There are many text document classification methods presented with highlighting benefits of classification methods using association rules. The main goal of work is adjusting selected classification method for relation data and design draft of webpages classifier, which classifies pages with the aid of visual properties - independent section layout on the web page, not (only) by textual data. There is also ARC-BC classification method presented as a selected method and as one of intriguing classificators, that derives accuracy and understandableness benefits of all other methods.
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Preprocessing Methods in Knowledge Discovery
Pokorný, Lubomír ; Lukáš, Roman (referee) ; Bartík, Vladimír (advisor)
This thesis discusses preprocessing methods in knowledge discovery. There are four methods of discretization, filling in the missing values and normalization is investigated. There is closer view on building the application which discretizate numeric atribute in database. All methods were successfully tested and the results were added.
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