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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
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Simulation of pharmacokinetic models
Hejč, Jakub ; Jiřík, Radovan (referee) ; Mézl, Martin (advisor)
The theoretical part of this project is occupied with analysis of pharmacokinetic actions and also basic attributes of mathematical models used in pharmacokinetics. This description is mainly focused on models used for perfusion imaging methods. The aim of this project is to create an algorithm that simulates chosen models based on assigned parameters and also an algorithm that serves to fit experimentally measured data with a chosen model with a calculation of basic pharmacokinetic parameters. The next step of this solution is graphic interface realization which enables a full use of created algorithm in more accessible surroundings for the user. The result of this work is a program that can be used to obtain real data parameters and as well as a visual sample of the influence of these parameters on a process in a chosen functions.
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Application of Bessel functions
Lorenczyk, Jiří ; Lomtatidze, Aleksandre (referee) ; Dosoudilová, Monika (advisor)
The purpose of this work is the introduction to the theory of Bessel differential equation and Bessel functions and its application to the problem of the vibration of a circular plate. In order to tackle this problem succesfully, it is needed to find a solution to the Bessel differential equation in the form of the eponymous Bessel functions and it will be shown how to do so. After that, some characteristics of the obtained Bessel functions of the first kind will be thoroughly demonstrated. Then the other solutions to the Bessel differential equation will be introduced, namely Bessel functions of the second kind, Hankel functions and modified Bessel functions which are obtained as a solution to the modified Bessel equation. In the second chapter, the area of interest will be the application of Bessel functions to the problem of the vibration of a circular plate. However, this problem will be severely restricted since the board will be considered to be perfectly fixed around its circumference, there will be no holes in it and there will be no external force acting on its surface. To solve this problem, it will be needed to make a use of each of the aformentioned Bessel functions.
|
|
|
Simulation of pharmacokinetic models
Hejč, Jakub ; Jiřík, Radovan (referee) ; Mézl, Martin (advisor)
The theoretical part of this project is occupied with analysis of pharmacokinetic actions and also basic attributes of mathematical models used in pharmacokinetics. This description is mainly focused on models used for perfusion imaging methods. The aim of this project is to create an algorithm that simulates chosen models based on assigned parameters and also an algorithm that serves to fit experimentally measured data with a chosen model with a calculation of basic pharmacokinetic parameters. The next step of this solution is graphic interface realization which enables a full use of created algorithm in more accessible surroundings for the user. The result of this work is a program that can be used to obtain real data parameters and as well as a visual sample of the influence of these parameters on a process in a chosen functions.
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