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Optimization of Basic Magnetic Field Homogeneity in MR Tomography
Hadinec, Michal ; Brančík, Lubomír (referee) ; Frollo, Ivan (referee) ; Bartušek, Karel (advisor)
This thesis is concerned with problems of measuring and mapping of magnetic field in MR tomograph, for purpose of magnetic flux density homogeneity optimization. Attention is paid to mapping techniques on rotary symmetric volume and to ways of magnetic fields optimization with utilization of passive and active correction systems. Theoretical analysis of magnetic field decomposition with utilization of spherical harmonics and numerical decomposition is made. Mapping and approximation techniques of basic magnetic field are verified by experiments in the laboratory at the Institute of Scientific Instruments AS CR in Brno.
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Specialized Computer System Automatic Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.
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Electronic Representation of Line Reflex
Yousifová, Hanen ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
It would be difficult to imagine a world without communication systems . In order to optimise guided communication systems , it is necessary to determine or project power and signal losses in the system, since all systems have such losses . To determine these losses and eventually ensure a maximum output, it is necessary to formulate some kind of equation with which to calculate these losses . A mathematical derivation for the telegraph equation in terms of voltage and current for a section of a transmission line will be investigated .
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Hardware Realization of Higher Order Numerical Integrator
Matečný, František ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
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Stiff Systems Analysis
Šátek, Václav ; Dalík, Josef (referee) ; Horová, Ivana (referee) ; Kunovský, Jiří (advisor)
The solving of stiff systems is still a contemporary sophisticated problem. The basic problem is the absence of precise definition of stiff systems. A question is also how to detect the stiffness in a given system of differential equations. Implicit numerical methods are commonly used for solving stiff systems. The stability domains of these methods are relatively large but the order of them is low. The thesis deals with numerical solution of ordinary differential equations, especially numerical calculations using Taylor series methods. The source of stiffness is analyzed and the possibility how to reduce stiffness in systems of ordinary differential equations (ODEs) is introduced. The possibility of detection stiff systems using explicit Taylor series terms is analyzed. The stability domains of explicit and implicit Taylor series are presented. The solutions of stiff systems using implicit Taylor series method are presented in many examples. The multiple arithmetic must be used in many cases. The new suitable parallel algorithm based on implicit Taylor series method with recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is proposed.
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Autonomous Electronic Circuits Simulation Method
Minárik, Michal ; Konvalina, Jiří (referee) ; Kunovský, Jiří (advisor)
This work deals with a methodology of description of linear electrical circuits through the use of differential equations and autonomical method. It compares commom numerical methods with Taylor series method implemented in TKSL. It's focused on analysis of applicability of autonomical method to various circuits, complexity of circuit diagram transformation to system of equations and transcription to TKSL.
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Automatic Computation Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of numerical calculations. The reader is acquainted with the numerical solution of differential equations and the parallel, serial, and series-parallel numerical integrator. The practical aim of this work is to design control circuits for the three mentioned variants of integrators. The design includes the development of a software simulator of the control circuit for the series-parallel integrator in a fixed point.
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Aircraft Modelling - The Kinematics and Dynamics of Aircraft Motion
Kutal, Jiří ; Kaluža, Vlastimil (referee) ; Kunovský, Jiří (advisor)
This bachelor's thesis is focused on general aircraft motion. Main terms connected to modelling continous systems, principles of control theory, linear systems, feedback systems and basic types of regulators are analyzed in the first part of the thesis. Second part mentions mathematical basics connected to modelling, mainly focused on differential equations and Taylor series. Reader can also find out about A/D and D/A convertors. The last part of this bachelor's thesis is dedicated to aircraft motion and the simulation of it's kinetic equations in TKSL program.
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