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New Integral Formulae in Hypercomplex Analysis
Sikora, Martin ; Souček, Vladimír (advisor) ; Krýsl, Svatopluk (referee) ; Vanžura, Jiří (referee)
Title: New Integral Formulae in Hypercomplex Analysis Author: Mgr. Martin Sikora Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Vladimír Souček, DrSc., MÚ UK Supervisor's e-mail address: soucek@karlin.mff.cuni.cz Abstract: The Dirac equation for Clifford algebra-valued functions on the even-dimensional Minkowski space can be understood as a hyperbolic sys- tem of partial differential equations. We show how to reconstruct the solution from initial data given on the upper sheet of the hyperboloid. In particular, we derive an integral formula which expresses the value of a function in a chosen point as an integral over a compact cycle given by the intersection of the null cone with the upper sheet of the hyperboloid in the Minkowski space. We also treat the ultra-hyperbolic case where the Dirac equation gives the ultra-hyperbolic system of partial differential equations. An analogue of the second order Cauchy formula is proved for (n − 1)-vector-valued holo- morphic functions. It reconstructs values inside a bounded domain in the 2n-dimensional complex space by integrating over the characteristic boun- dary of the domain. 1
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Electro-thermal model and simulation of integrated circuit
Sikora, Martin ; Kledrowetz, Vilém (referee) ; Prokop, Roman (advisor)
Thermal effects in integrated circuits have increasing impact on chip's lifetime and function. For this reason, the chips must be subjected to electro-thermal simulations prior to the launch of production in order to avoid potential circuit failures. Therefore, in the first part of this diploma thesis these effects and methods of creating thermal models are described. The thesis also explores available tools for electro-thermal simulations and the way these simulators work. In the practical part of the thesis, the operation of electro-thermal simulation in the Eldo tool is verified, a method of automated thermal network creation is proposed and a application for its generation based on the circuit layout is implemented. The results of the electro-thermal simulation with the generated thermal network are compared with the results of the currently used method.
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Web App for Capturing New Shots of Historical Photographs
Sikora, Martin ; Brejcha, Jan (referee) ; Čadík, Martin (advisor)
The aim of this diploma thesis is to design and implement a web application focused on rephotography management. Analyze existing solutions, create list of features and simple graphical user interface. It also includes a design of API structure to communicate with the mobile application. Essential application requirements include adding photos on a map and combining different photos in a photo editor with enhanced auto-alignment features.
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New Integral Formulae in Hypercomplex Analysis
Sikora, Martin ; Souček, Vladimír (advisor) ; Krýsl, Svatopluk (referee) ; Vanžura, Jiří (referee)
Title: New Integral Formulae in Hypercomplex Analysis Author: Mgr. Martin Sikora Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Vladimír Souček, DrSc., MÚ UK Supervisor's e-mail address: soucek@karlin.mff.cuni.cz Abstract: The Dirac equation for Clifford algebra-valued functions on the even-dimensional Minkowski space can be understood as a hyperbolic sys- tem of partial differential equations. We show how to reconstruct the solution from initial data given on the upper sheet of the hyperboloid. In particular, we derive an integral formula which expresses the value of a function in a chosen point as an integral over a compact cycle given by the intersection of the null cone with the upper sheet of the hyperboloid in the Minkowski space. We also treat the ultra-hyperbolic case where the Dirac equation gives the ultra-hyperbolic system of partial differential equations. An analogue of the second order Cauchy formula is proved for (n − 1)-vector-valued holo- morphic functions. It reconstructs values inside a bounded domain in the 2n-dimensional complex space by integrating over the characteristic boun- dary of the domain. 1
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Design of the Computer Network at the Elementary School
Sikora, Martin ; Jordán, Vilém (referee) ; Ondrák, Viktor (advisor)
This bachelor thesis deals with the design of the computer network, specifically in the building of elementary school. It is based on the analysis of the current computer network state, school premises and requirements of the client. This thesis includes theoretical knowledge, which is used for the design of computer network. Thesis also contains cost calculations associated with the implementation of the proposal.
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Control of pneumatic press model
Sikora, Martin ; Stibor, Karel (referee) ; Štohl, Radek (advisor)
This thesis deals with improving of the pneumatic press model. The document contains short description of press model. It also focuses on completion of safety and functionality of the machine. There are an analyse and an aplication of instruments in the chapter Choice of instrumentation for change of the pressure force and for the increase of safety of this machine. The chapter Construction of the press model selects the mechanical components and solves the aplication for press model. In the section Extension of the control program there are the analyses of the control algorithms and programs for the safety PLC and PLC for vizualization. The last part of this work is devoted to vizualization, which displays the states of the sensors and safety PLC. In vizualization there is the setting of hand-operated mode or the automatic control mode with different pressing force changing in time.
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