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Implicitní aproximace Bellmanovy rovnice
Pištěk, Miroslav
In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. It approximate the Bellman equation without omitting the principial uncertainty stemming from an uncomplete knowledge. An integral part of the proposed solution is a reduction of memory demands using HDMR approximation. The result of this method is a linear algebraic system for an approximated upper bound on the Bellman function. One illustrative example has been completely resolved.
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Poznámka k reptační teorii
Kharlamov, Alexander ; Filip, Petr ; Švrčinová, Petra
Avoiding the Independent Alignment (IA) approximation in the classical Doi-Edwards model causes the computation extremely time and hardware consuming. Nevertheless some flow situations cannot be modelled with the IA approximation. This contribution presents a probabilistic approach not taking into account the IA approximation.
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Dvě rovnice popisjící kyvadlový tlumič
Fischer, Cyril ; Náprstek, Jiří
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the previous paper is performed. Both approaches are compared and conclusions are drawn.
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Dental enamel hypoplasia in early medieval population of Rajhrad.
Zahradníková, Mariana ; Trefný, Pavel (advisor) ; Stránská, Petra (referee)
The objective of this study was the assessment of linear enamel hypoplasia (LEH) in early medieval Great Moravian population sample - Rajhrad. Linear enamel hypoplasia represents the disruption of enamel matrix secretion during the growth of the tooth crown, which is related to a generalized growth disturbance. This is why it is considered as a nonspecific stress marker. The incidence of LEH could reflect stress factors during the life of early medieval population. The aim of this study was to asses the frequency and timing of the LEH. The incidence of LEH was supposed to be high because of poorer nature of this cemetery. The results of our study could confirm or falsify this assumption and determine relation between LEH and socio-economic status. The timing of LEH was estimated from regression equations consisting of distance from LEH to CEJ (cemento-enamel junction) and crown height of upper and lower canines. 108 individuals from approximately 4 - 15 years were observed. The frequency was high according to the assumption - 88 %. That confirms poorer life conditions. The range of mean age of LEH formation was from 2,94 - 4,72 years in individuals with multiple LEH incidence. The mean age of single LEH formation was approximately 3,98 years. The earliest onset of LEH in the pooled sample occurred...
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Ray-based Born approximation
Šachl, Libor ; Klimeš, Luděk (advisor) ; Bulant, Petr (referee)
Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1
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The Selected Stochastic Programs in Engineering Design
Čajánek, Michal ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than deterministic problem and assess the quality of approximations based on Monte Carlo simulation method and the theory of interval estimates. The resulting mathematical models are implemented and solved in the general algebraic modeling system GAMS. Graphical and numerical results are presented.
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Approximation function implementation into PIC microprocessor
Petřík, Tomáš ; Sysel, Petr (referee) ; Šmirg, Ondřej (advisor)
This bachelor‘s thesis deals with the implementation of approximation function into the PIC microprocessor. Thesis is focused on microprocessor architecture and analysis of approximation functions. Then for actual implementation is chosen the method of least squares, and because of its relative simplicity and accuracy in comparison with other methods. Microcontroller is using the A/D converter to measure the dependence of non-linear system, which is connected to the microprocessor. Measure the voltage on a logarithmic potentiometer, which represents non-linear system, depending on the position of the slider track resistance. Then, using the method chosen microprocessor calculates the characteristic non-linear system. The measured values are compared with the theoretical, calculated the chosen method. The values measured, and their theoretical difference is then displayed on the display, connected to the microprocessor. In conclusion, then discuss the results together with the possibility of further developing this work.
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Smooth approximation spaces based on a periodic system
Segeth, Karel
A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $exp(-ii kx)$. A 1D numerical example is presented.
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Rezonanční chování kulového kyvadlového tlumiče
Fischer, Cyril ; Náprstek, Jiří
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the previous paper is performed. Both approaches are compared and conclusions are drawn.
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Výpočetní srovnání diskretizační a iterační chyby
Vejchodský, Tomáš
The paper presents the Poisson equation and its solution by the finite element method. A numerical example is show, where besides the exact solution also the exact discrete solution is explicitely known. This allows to compare the discretization error and the error in the approximate solution of the system of linear algebraic system.
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