Free constructions and coproducts of d-frames

A general theory of presentations for d-frames does not yet exist. We review the difficulties and give sufficient conditions for when they can be overcome. As an application we prove that the category of d-frames is closed under coproducts

Statistical Survey of Aerobatic Aircraft

Všeobecný přehled nejvýkonnějších akrobatických letounů v současnosti. Práce zahrnuje popis a výkonnostní údaje u jednotlivých verzí, krátké představení pravidel soutěží v letecké akrobacii a statistické srovnání uvedených parametrů letounů v podobě grafů.All round survey of higest-rating aerobatic planes. This work includes description and efficiency specifications of each single versions, short introduction into aerobatic rules and statistic comparision of mentioned characteristic in graphs.

Canonical extensions of locally compact frames

Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and choice-free way. We adapt the general algebraic technique that constructs them to the theory of frames. As a result, we show that every locally compact frame embeds into a completely distributive lattice by a construction which generalises, among others, the canonical extensions for distributive lattices and proximity lattices. This construction also provides a new description of a construction by Marcel Ern\'e. Moreover, canonical extensions of frames enable us to frame-theoretically represent monotone maps with respect to the specialisation order

A duality theoretic view on limits of finite structures

A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of measures arises --- via Stone-Priestley duality and the notion of types from model theory --- by enriching the expressive power of first-order logic with certain ``probabilistic operators''. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality-theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively.Comment: 19 page

A DUALITY THEORETIC VIEW ON LIMITS OF FINITE STRUCTURES

A systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of (finitely additive) measures arises—via Stone-Priestley duality and the notion of types from model theory—by enriching the expressive power of first-order logic with certain “probabilistic operators”. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively

Influence of fabrication and alloying on magnesium alloys

V této bakalářské práci jsou porovnávány mechanické vlastnosti hořčíkových slitin v závislosti na výrobě a složení. První část se zabývá čistým hořčíkem a jeho vlastnostmi. Druhá část obsahuje popis jednotlivých legur a přehled metod výroby. Třetí část se zabývá vybranými slitinami. Práce obsahuje fotografie mikrostruktur slitin, údaje o mechanických vlastnostech a jejich vzájemné srovnání.This bachelor thesis compares mechanical properties of magnesium alloys in dependence on their composition and fabrication. The first part deals with a pure magnesium and its properties. The second part contains information about alloying elements and an overview of the fabrication methods. The third part consists of different magnesium alloys. The thesis contains photographs of microstructures, a review of mechanical properties and their comparison.

A duality theoretic view on limits of finite structures: Extended version

A systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of (finitely additive) measures arises—via Stone-Priestley duality and the notion of types from model theory—by enriching the expressive power of first-order logic with certain “probabilistic operators”. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively