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Voronoi cell constructions on the map
Čermák, Jan ; Hrdina, Jaroslav (referee) ; Pavlík, Jan (advisor)
This bachelor’s thesis deals with study of Voronoi cell and its representation in Voronoi diagrams and their construction on the model of Earth’s surface. At first, Voronoi diagrams and their characteristics are explained in a plane, we describe their construction using Fortune’s algorithm, then spherical geometry is explained. Then we take a look at some equations that are useful for calculating on a sphere, and we use them for calculating distances on Earth, which we approximate with a sphere. Finally we apply Fortune’s algorithm on a sphere, we explain the principles of construction of Voronoi diagrams with this algorithm on a sphere and changes compared to the planar case that must be taken care of. The goal of the thesis is to display Voronoi diagram on Google maps, thus we work with Google Maps API.
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Calculations and applications of fractional calculus
Zemčíková, Michaela ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor’s thesis deals with the calculations and applications of fractional calculus. The aim of this thesis is to mention some basic fundamentals, definitions and properties of fractional calculus, that will be used for calculations of fractional integrals and derivations of selected elementary functions focus on power functions. In next part thesis will be concerned with fractional diffusion equation, which describes subdiffusive processes. Its result will be compared with the standard diffusion.
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Applications of ordinary differential equations with boundary conditions
Felixová, Lucie ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the applications of ordinary differential equations with boundary conditions. The aim of this thesis is to find the solution of straight bar stability under different boundary conditions (hinging, clamping and their combinations), of bended bars under horizontal loading and of straight bars on an elastic foundation (Winkler's foundation). Further, the thesis deals with the derivation of the equation for temperature field in a thin rod and for mathematical pendulum.
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The solving of ordinary differential equations by means of the Laplace transform method
Klimeš, Lubomír ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
The Laplace transform is a very powerful mathematical tool for solving of ordinary linear differential equations with constant coefficients. Its usage is wide - it can be applied to first order and also to higher order equations, it is very convenient for solving of differential equations with several forcing terms (including noncontinuous terms) and of course, it can be used for solving of systems of ordinary differential equations. The Laplace transform plays the key role in control theory, where the transformation of the differential equation of the control system enables to analyse the behavior of this system, e. g. its reaction to input values. Our aim was to present essentials of the Laplace transform theory and demonstrate this strong mathematical tool in the solving of concrete problems, including the usage of the software Maple.
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The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
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HYDROGEN STORAGE IN Mg-In-C ALLOYS: EFFECT OF COMPOSITION AND AGEING
Čermák, Jiří ; Král, Lubomír
Hydrogen storage in two Mg-In-C alloys with different In concentration, c In , was studied in the temperature range from 250°C to 350°C after five-years-ageing at room temperature. The both alloys show acceptable cycling stability, however, the storage capacity of the alloys decreased from about 5 wt. % H2 to about 2,5 and 3.1 wt. % H 2 by higher c In and lower c In , respectively after 5 years. The sorption kinetics degraded much more by high c In than by c In . PCT isotherms, TPS and DSC patterns were measured for both materials. It was found that the hydrides responsible for hydrogen storage in alloy with higher c In are slightly more stable.
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