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Park's conjecture
Lauschmannová, Anna ; Ježek, Jaroslav (referee) ; Stanovský, David (advisor)
A finite algebra of finite type (i.e. in a finite language) is finitely based iff the variety it generates can be axiomatized by finitely many equations. Park's conjecture states that if a finite algebra of finite type generates a variety in which all subdirectly irreducible members are finite and of bounded size, then the algebra is finitely based. In this thesis, I reproduce some of the finite basis results of this millennium, and give a taster of older ones. The main results fall into two categories: applications of Jonsson's theorem from 1979 (Baker's theorem in the congruence distributive setting, and its extension by Willard to congruence meet-semidistributive varieties), whilst other proofs are syntactical in nature (Lyndon's theorem on two element algebras, Je·zek's on poor signatures, Perkins's on commutative semigroups and the theorem on regularisation). The text is self-contained, assuming only basic knowledge of logic and universal algebra, and stating the results we build upon without proof.
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Congruence-Simple Semirings
Al-Zoubi, Khaldoun Falah Salim ; Kepka, Tomáš (advisor) ; Ježek, Jaroslav (referee) ; Philips, Jon (referee)
Následující dizertační práce je věnována podrobnému zkoumání kongrunenčně-jednoduchých (konečných) aditivně idempotentních polookruhů. sestává ze čtyř kapitol. V první kapitole jsou zkoumány kvazitriviální polomoduly a polookruhy. Speciálně jsou charakterizovány minimální a kongruenčně-jednoduché kvazitriviální polomoduly. Jsou zobeněny výsledky z knihy. Ve druhé kapitole pokračujeme ve zkoumíní polomodulů. Hlavně s důrazem na minimální a kongruenčně-jednoduché polomoduly. Ve třetí kapitole se zkoumají skoro minimální polomoduly. Klasifikujeme konečné kongruenčně jednoduché polookruhy. Ve čtvrté kapitole dokážeme, že polookruh endomorfismů netriviálního polosvazu je vždy subdirektně nerozložitelný a popíšeme jeho monolit. Polookruh endomorfismů je kongruenčně jednoduchý právě, když příslušný polosvaz má největší i nejmenší prvek. První tři kapitoly jsou souhrnem výsledků [2], [3] a [4]. Obsah poslední kapitoly je adaptován z [17]. K práci patří z ilustrativních důvodů.
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Transmission parameters of optical access networks
Ježek, Jaroslav ; Kapoun, Vladimír (referee) ; Havelka, Dušan (advisor)
The essence of this thesis is the cognition of theoretical basis for measuring on optical fibres, elements and optical wireway as well. This work describes the methods of measuring and detection of parameters of these networks. The gained knowledge is followed by its application on two laboratory tasks. The first task is focused on usage of method of embedded loss for measuring of attenuation of fibre and followed by usage of the method OTDR for localization of defect. The second task is focused on measuring of attenuation on passive optical element using only the method of embedded losses. The laboratory tasks were described and respective conclusion and findings were drawed from each other.
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Fluxmeter with graphical display of B-H curve
Ježek, Jaroslav ; Mačák, Jaromír (referee) ; Hanák, Pavel (advisor)
This work deals with simple fluxmeter which is able, together with other device, to show hysteresis loop. Hysteresis loop is a graphic expression of dependence of magnetic induction on intensity of magnetic field. Oscilloscope is used to display the hysteresis loop. This device is fully sufficient for the display. The measured objects are solenoids from various kinds of materials with the same shape. The main aim of this work is the design, realization and description of the fluxmeter. The fluxmeter consists of several partial blocks. The first one, on which this work is focused, is signal generator which is able to generace different kinds of signal. The generated signal comes on primary winding of solenoid where a magnetic field on a given intensity rises. An amplifier is used to obtain the sufficient intensity. Next thing this work is focused on is the design of the integrator which is necessary for the correct function of the fluxmeter. As suggested, there is shown the block diagram of linking of individual parts. There are described the measured results at the end of this work.
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