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Discretely normed orders of quaternionic algebras
Horníček, Jan ; Skula, Ladislav (oponent) ; Kureš, Miroslav (vedoucí práce)
This thesis summarizes author's research on the field of theory of the quaternion algebras, their isomorphisms and maximal orders. The new point of view to this issue is received by using the concept of the discrete norm. The three following statements could be taken as the main results of the thesis: - Proof of the uniqueness of the discrete norm for integers, for the orders of the quadratic field extension and also for the orders of quaternion algebra - Theorem, which enables us to construct isomorphisms between quaternion algebras in explicit matrix form - Proof of the existence of infinitely many mutually distinct orders of the quaternion algebra Results given in this thesis will be also used in a scientific article.
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Exploiting Structures in Automated Planning
Kuckir, Ivan ; Barták, Roman (vedoucí práce) ; Chrpa, Lukáš (oponent)
Tato práce se zaměřuje na zlepšení procesu automatického plánování skrze rozbití symetrií. Cílem je popsat symetrie, které jsou často zřejmé pro programátory, ale nebyly řádně teoreticky formalizovány. Po analýze dostupných zdrojů se zavedou nové definice v kontextu klasického plánování, jako je např. ekvivalence stavů, T1 automorfizmy a obecnější automorfizmy konstant. Bude dokázáno několik vět o symetriích. Ve výsledku bude navržen algoritmus pro detekci speciální třídy symetrií spolu s metodou využití těchto symetrií během plánování. Budou provedeny experimenty, které ukáží efekt rozbití symetrií na výkon plánovače. Powered by TCPDF (www.tcpdf.org)
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Discretely normed orders of quaternionic algebras
Horníček, Jan ; Skula, Ladislav (oponent) ; Kureš, Miroslav (vedoucí práce)
This thesis summarizes author's research on the field of theory of the quaternion algebras, their isomorphisms and maximal orders. The new point of view to this issue is received by using the concept of the discrete norm. The three following statements could be taken as the main results of the thesis: - Proof of the uniqueness of the discrete norm for integers, for the orders of the quadratic field extension and also for the orders of quaternion algebra - Theorem, which enables us to construct isomorphisms between quaternion algebras in explicit matrix form - Proof of the existence of infinitely many mutually distinct orders of the quaternion algebra Results given in this thesis will be also used in a scientific article.
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