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Robust solver of a system of nonlinear equations
Růžek, Bohuslav ; Kolář, Petr ; Kvasnička, M.
ANNIT (Artificial Neural Network Inversion Tool) is solver of a set of non- linear equations. It is implemented in MATLAB and Scilab. ANNIT is based on numerical approximation of mapping the right hand sides residuals of the original set of equations to searched parameters. A population of individuals is used for building such approximation. The shape, location and size of this population is adaptively changed during the inversion depending on the convergence of the solved problem. ANNIT has been thoroughly tested by using a set of standard problems and also by using selected geophysical problems (localization of the earthquake hypocenter, magnetotelluric inversion, inversion of group velocities of surface waves etc.).
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Modeling and approximation of absorption phenomena in dielectric materials
Raška, Jiří ; Polsterová, Helena (referee) ; Frk, Martin (advisor)
This thesis focuses on the polarization effects, that go on in the dielectric materials. It deals with physical and mathematical description of absorption effects. An important part of the thesis is a program environment, that is made by using programming language C++, which might be used for illustrative graphical displaying of physical laws of absorption effects in dielectric materials and for control of meters used for absorption current in dielectric materials measurement. This program can compute selected material constants from measured absorption currents. The proram enviroment enables creation of measurement protocol according to the norm ČSN IEC 93.
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Simulation of Stock Exchange
Šejnoha, Jiří ; Karásek, Michal (referee) ; Bálek, Martin (advisor)
The topic of this work is simulation of stock market. Studying the dependence of Prague stock exchange index PX depending on the macroeconomic parameters. It uses the connection methods, neural networks and random walks, where the random walk forward trained neural network functions as decision-making unit, normally used instead of linear approximation. Specially concerning the relationship of dependence PX on exchange rate U.S. dollar and Czech crown, gross domestic product of the Czech Republic and 2W repo rate. Simulation is performed using neural networks and linear approximation to the historical dates against them is then validated.
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Stochastická teorie katastrof
Vošvrda, Miloslav ; Voříšek, Jan
The so called Cusp deterministic catastrophe model extends the classical linear regression adding nonlinearity into a model. A property of a stochatic catastrophe model connected with stochastic differential equation could be described by density, which is known in closed-form only in stationary case. The approximation of the transition density is done here by finite difference metod.
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Design of FIR vocal tract models with linear and nonlinear phase
Vondra, Martin ; Vích, Robert
Experiences with the IIR cepstral model based on Padé approximation of the exponential function indicate some problems with stability. An experiment in designing a FIR cepstral vocal tract model has been made. The computation of the impulse response of the FIR filter that realizes the vocal tract model can be accomplished either using the window method of digital filter design or by a recursive computation directly from real cepstrum using the minimum-phase approximation.
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Least squares method using genetic algorithm
Holec, Matúš ; Tichý, Vladimír (advisor) ; Šalamon, Tomáš (referee)
This thesis describes the design and implementation of genetic algorithm for approximation of non-linear mathematical functions using the least squares method. One objective of this work is to theoretically describe the basics of genetic algorithms. The second objective is to create a program that would be potentially used to approximate empirically measured data by the scientific institutions. Besides the theoretical description of the given subject, the text part of the work mainly deals with the design of the genetic algorithm and the whole application solving the given problem. Specific part of the assignment is that the developed application has to support approximation of points by various mathematical non-linear functions in several different intervals, and then it has to insure, that resulting functions are continuous throughout all the intervals. Described functionality is not offered by any available software.
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Investigating ground state of nickel nitrides NiN and Ni2N with the help of quantum-mechanical calculations
Elstnerová, P. ; Friák, Martin ; Šob, Mojmír ; Neugebauer, J.
We have employed quantum mechanical calculations to identify ground-state structures of nickel nitrides NiN and Ni2N for which experimental data are lacking. In total 19 crystalline phases have been calculated for which not only thermodynamic but also structural and selected elastic properties have been determined. Employing density functional theory (DFT) methods, the total energies were calculated by means of a pseudopotential approach implemented in the VASP code and selected states were benchmarked by the full-potential linearized augmented plane wave (FP-LAPW) method implemented in the WIEN2k code. For the exchange-correlation energy the generalized gradient approximation (GGA) has been used.
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Studium klimatických změn v České republice
Osičková, Renata
In my Diploma Thesis are processed and analyzed values of average monthly temperatures recorded in 34 meteorological stations that are uniformly distributed in the territory of the Czech Republic. Recorded data are approximated by a series regression function F(t, x, y, h), which is based on a model . This function describe the dependence of temperature T [°C] on time t [year], geographical position x, y [km] and altitude h [m]. Unknown coefficients of the linear functions were calculated using a Maple application based on the method of least squares. The author calculated coefficients of linear correlation for each meteorological station and also the time development of the coefficient of linear correlation for the whole territory of the Czech Republic. The calculated average values for individual stations and for the whole territory were 0.97 and 0.92, respectively. This result indicates a very high standard of the developed model and the model itself indicates that the average temperatures are decreasing in approximately 80 % of the territory of the Czech Republic.
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