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The behavior of functions of several variables in terms of extremes
Beseda, Jiří ; Štarha, Pavel (referee) ; Hoderová, Jana (advisor)
Thesis deals with problems of extreme searching in multivariable calculus. Searching maxima/minima of the function can be moreover specified to local extremes, global extremes or strict extremes. Computations are mainly based on first derivations of the function that are set to be zero, in order to obtain the stationary point. Stationary point is point, where maxima or minima of the function is expected.
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Animation and calculation of cyclic curves in Maple
Novák, Jiří ; Hoderová, Jana (referee) ; Procházková, Jana (advisor)
The main goal of the thesis was to deal with the topic of cyclic curves and creating interactive maplets that would illustrate creating and characteristics of these curves. The final version includes maplet with plotting parametric curve, maplet with computing curvature, maplet for all the types of cyclic curves, set of maplets for interactive change of parameters and set of maplets that would illustrate creating each cyclic curve (with animation). The thesis also contains a theoretical part dedicated to the theory of cyclic curves.
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Integral Transformations Using Vector Operators
Joch, Lukáš ; Štarha, Pavel (referee) ; Hoderová, Jana (advisor)
This Bachelor`s thesis is devoled to the vector operotrs. The operators plays the big role in the mathematical notation of different physical processes. The main aim od this paper is to show various vector operators and their properties. At the end are the integral theorems presented, concretely Gauss-Ostrogradsky theorem, Green`s theorem and Stokes`s theorem.
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Hausdorff dimension of the lightning
Kočendová, Alžběta ; Druckmüller, Miloslav (referee) ; Hoderová, Jana (advisor)
In this thesis, the theory related to the Hausdorff dimension is described. The Hausdorff dimension is used to describe the fragmentation of a fractal. Fractals include many natural objects and phenomena. One such phenomenon is lightning, which is the focus of this work. This work involves the development of a MATLAB program to detect lightning in an image and then calculate the Hausdorff dimension of this lightning.
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Bellman's Lost in a Forest Problem and Its Analysis
Haviger, Vojtěch ; Hoderová, Jana (referee) ; Čermák, Jan (advisor)
This thesis is focused on the Bellman’s problem of searching for the shortest escape path from the planar, closed and convex set with a nonempty interior. After introduction of some notions needed to understand and solve the problem, the thesis deals with discusions of the shortest escape paths for considered shapes of the given set (circular disc, circular sector, infinite strip, rectangle, regular polygon, triangle, half-plane, circle). Finally, the obtained results are summarized, and extended by some open problems.
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Algorithm ICP and its usage for 3D registration
Fiala, Zdeněk ; Hoderová, Jana (referee) ; Procházková, Jana (advisor)
This thesis deals with the ICP algorithm used for point cloud registration. The thesis is divided into three main parts. The first part summarizes the basic concepts needed for the topic. The second part describes the basic ICP algorithm and its improvements. The last section contains the implementation of the algorithm in the C# programming language and the results of testing on real data.
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