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Testing of Control and Logic Functions of Feeder Terminal
Kaplanová, Klára ; Paar, Martin (referee) ; Orságová, Jaroslava (advisor)
This work occupies itself with an analysis of operational manipulations in the feeder terminal of the distribution system and it considers the configuration of its apparatus equipment with the following configuration of the logical operations for controlling the apparatus in the feeder terminal. Further, this work occupies itself with switching high voltage equipment, their qualities and distribution, with their electrically driven mechanism, including the method of their control. Moreover, the work is aimed at the configuration of the logical operation with the aid of the Boole functions for controlling the feeder terminal apparatus within the CAP 505 software, and at its following testing on the REF 543 terminal from the ABB Company. The aim of the work is theoretical analysis of controlling and operational manipulations in a high voltage distribution system, the following creation and registration of the blocking conditions as well as with their use to create a functional configuration of the feeder terminal of the distribution system and its testing on the demonstration panel which is set with the REF 543 terminal and with further apparatus equipment that simulates the complete high voltage distributor. In the factory configuration the simulation is carried out by the LOGO! module from the Siemens Company. Therefore, our further aim is to design and subsequently to connect the feeder terminal so that the controlling and signaling panel elements could be connected directly to inputs and outputs of REF 543 terminal and could so enable its controlling and checking of the operation conditions. The main aim of the work is to elaborate a detailed description of the functional configuration creation as well as the following REF 543 terminal adjustment for testing the blocking conditions.
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Library for Boolean Functions in Algebraic Normal Form
Vasilišin, Maroš ; Mrázek, Vojtěch (referee) ; Dobai, Roland (advisor)
This bachelor thesis focuses on design and implementation of library in C language for manipulation od Boolean functions in Algebraic Normal Form. Majority of existing libraries for representation of Boolean functions is based on binary decision diagrams. Algebraic Normal Form presents several advantages over binary decision diagrams, for example Boolean value of function can be determined in linear time. Implemented library uses simple structures to effectively represent Boolean function in program. After experiments we determined that representation in Algebraic Normal Form has its applications, and in some cases it provides better results than representation in binary decision diagrams.
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Minimisation of Logical Functions
Horký, Miroslav ; Davidová, Olga (referee) ; Šeda, Miloš (advisor)
For minimisation of logical functions, laws of the Boolean algebra and the Karnaugh maps are mostly used. However, use of Karnaugh's maps is based on visual recognition of adjacent cells for functions with no more than 6 variables and, therefore, the method is not suitable for automated processing on computers. A direct application of the Boolean algebra laws is not restricted in this way, but there is no general algorithm defining the sequence of their application and thus this approach is not suitable for computer implementation either. The well-known method usable on computers is the algorithm proposed by E. J. McCluskey and W. Orman Quine.
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Theories and algebras of formulas
Garlík, Michal ; Mlček, Josef (advisor) ; Glivický, Petr (referee)
In the present work we study first-order theories and their Lindenbaum alge- bras by analyzing the properties of the chain BnT n<ω, called B-chain, where BnT is the subalgebra of the Lindenbaum algebra given by formulas with up to n free variables. We enrich the structure of Lindenbaum algebra in order to cap- ture some differences between theories with term-by-term isomorphic B-chains. Several examples of theories and calculations of their B-chains are given. We also construct a model of Robinson arithmetic, whose n-th algebras of definable sets are isomorphic to the Cartesian product of the countable atomic saturated Boolean algebra and the countable atomless Boolean algebra. 1
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Complete Boolean Algebras and Extremally Disconnected Compact Spaces
Starý, Jan ; Simon, Petr (advisor) ; Bukovský, Lev (referee) ; Thümmel, Egbert (referee)
We study the existence of special points in extremally disconnected compact topological spaces that witness their nonhomogeneity. Via Stone duality, we are looking for ultrafilters on complete Boolean algebras with special combinatorial properties. We introduce the notion of a coherent ultrafilter (coherent P-point, coherently selective). We show that generic existence of such ultrafilters on every complete ccc Boolean algebra of weight not exceeding the continuum is consistent with set theory, and that they witness the nonhomogeneity of the corresponding Stone spaces. We study the properties of the order-sequential property on σ-complete Boolean algebras and its relation to measure-theoretic properties. We ask whether the order-sequential topology can be compact in a nontrivial case, and partially answer the question in a special case of the Suslin algebra associated with a Suslin tree.
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Library for Boolean Functions in Algebraic Normal Form
Vasilišin, Maroš ; Mrázek, Vojtěch (referee) ; Dobai, Roland (advisor)
This bachelor thesis focuses on design and implementation of library in C language for manipulation od Boolean functions in Algebraic Normal Form. Majority of existing libraries for representation of Boolean functions is based on binary decision diagrams. Algebraic Normal Form presents several advantages over binary decision diagrams, for example Boolean value of function can be determined in linear time. Implemented library uses simple structures to effectively represent Boolean function in program. After experiments we determined that representation in Algebraic Normal Form has its applications, and in some cases it provides better results than representation in binary decision diagrams.
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From asymptotic density to the Riemann zeta-function
Grebík, Jan ; Balcar, Bohuslav (advisor) ; Zahradník, Miloš (referee)
We study the connection of combinatorics of natural numbers and measures extending the asymptotic density with the structures of number theory and the Riemann zeta-function. We show that the study of measures extending density via ultrafilter limits can be restricted to thin ultrafilters and we charac- terize the σ-additivity of such measures using the ∗invariance of ultrafilters. We study the generic extension obtained by forcing with the algebra P(N) modulo the density ideal. We show that this is a two-step iteration, where the first step is the known forcing with P(N)/fin adding a selective ultrafilter, while the second step kills the selectivity. We isolate the values of some cardinal invariants in this extension.
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Complete Boolean Algebras and Extremally Disconnected Compact Spaces
Starý, Jan ; Simon, Petr (advisor) ; Bukovský, Lev (referee) ; Thümmel, Egbert (referee)
We study the existence of special points in extremally disconnected compact topological spaces that witness their nonhomogeneity. Via Stone duality, we are looking for ultrafilters on complete Boolean algebras with special combinatorial properties. We introduce the notion of a coherent ultrafilter (coherent P-point, coherently selective). We show that generic existence of such ultrafilters on every complete ccc Boolean algebra of weight not exceeding the continuum is consistent with set theory, and that they witness the nonhomogeneity of the corresponding Stone spaces. We study the properties of the order-sequential property on σ-complete Boolean algebras and its relation to measure-theoretic properties. We ask whether the order-sequential topology can be compact in a nontrivial case, and partially answer the question in a special case of the Suslin algebra associated with a Suslin tree.
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Theories and algebras of formulas
Garlík, Michal ; Mlček, Josef (advisor) ; Glivický, Petr (referee)
In the present work we study first-order theories and their Lindenbaum alge- bras by analyzing the properties of the chain BnT n<ω, called B-chain, where BnT is the subalgebra of the Lindenbaum algebra given by formulas with up to n free variables. We enrich the structure of Lindenbaum algebra in order to cap- ture some differences between theories with term-by-term isomorphic B-chains. Several examples of theories and calculations of their B-chains are given. We also construct a model of Robinson arithmetic, whose n-th algebras of definable sets are isomorphic to the Cartesian product of the countable atomic saturated Boolean algebra and the countable atomless Boolean algebra. 1
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