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Linux distribution for smart building gateway
Nagy, Tomáš ; Komosný, Dan (referee) ; Jablončík, Lukáš (advisor)
The goal of the thesis was to create a Linux distribution for a smart home gateway. The thesis is divided into theoretical and practical parts. The theoretical part dealt with the analysis of the Linux operating system. Subsequently, single board computers are described and compared. In the next part, the gateway issues, communication protocol selection and application containerization are discussed. As a result of addressing the issue, a procedure for adding tools for home automation, the construction of scripts that automate this issue and instructions for their proper execution were proposed.
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Selfdistributive quasigroups of size 2^k
Nagy, Tomáš ; Stanovský, David (advisor) ; Kepka, Tomáš (referee)
We present the theory of selfdistributive quasigroups and the construction of non-affine selfdistributive quasigroup of size 216 that was presented by Onoi in 1970 and which was the least known example of such structure of size 2k . Based on this construction, we introduce the notion of Onoi structures and Onoi mappings between them which generalizes Onoi's construction and which allows us to construct non-affine selfdistributive quasigroups of size 22k for k ≥ 3. We present and implement algorithm for finding central extensions of self- distributive quasigroups which enables us to classify non-affine selfdistributive quasigroups of size 2k and prove that those quasigroup exists exactly for k ≥ 6, k ̸= 7. We use this algorithm also in order to better understand the structure of non-affine selfdistributive quasigroups of size 26 . 1
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Coloring knots
Nagy, Tomáš ; Stanovský, David (advisor) ; Šťovíček, Jan (referee)
The thesis deal with coloring knots by algebraical structures called quandles. We will introduce the theory that is necessary for understanding the knot coloring and we will prove that coloring is a knot invariant. The major part of the thesis is an experiment focused on coloring different knots by different classes of quandles. We will focus on knots which are hardly distinguished by other knot invariants, also the time complexity of coloring different classes of knots in dependency on the number of crossings and on the size of the quandle will be important for us. We will deal also with the connection between knot coloring and other knot invariants.
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