We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on E corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain a state smearing theorem for these effect algebras, as well as the continuity of ⊕-operation in the order and interval topologies on them.
Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.
The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.
This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.
We show that whenever the $q$-dimensional Minkowski content of a subset $A\subset \mathbb R^d$ exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in $\mathbb R^d$, $d\geq 3$.
This study on Alois Klar (1763-1833) focuses mainly on his achievements as a pedagogue and his work for the visually impaired. Methodologically, it draws on Theodor Adorno, Max Horkheimer and Michel Foucault, enabling us to view the evolution of social care as a concomitant of the emerging modern state and integral to its structure. The study presents an analysis of the beginnings of Klar’s Prague institute for the visually impaired against a background of rapid changes in medicine, the scope of the state, and educational thinking. At a time of compulsory school attendance and new approaches to education, when the state demanded the active participation of its subjects/citizens in propagating its aims and the values of society as a whole, the blind and partially sighted were given access to a full and systematic education. We also present data concerning Klar’s educational work and thinking (he taught in Litoměřice and at Prague University), and examine the internal workings of the newly established institute - one of the first of its kind in Europe - and its contacts with the medical discourse of the emerging science of ophthalmology., Marek Fapšo., and Obsahuje bibliografické odkazy
Alois Musil, the Czech Old Testament scholar, priest, topographer and explorer of the unexplored Arabic lands of the Near East before World War I left the scholarly world an immense wealth of information about the Biblical, historical, ethnographical, and archaeological sites he visited, described, noted, and commented on during the years ca. 1896 to 1917. During that time he served as a valuable mediator to the Central Powers (Mittel-Mächte) and the Ottoman Empire seeking to make peace between rival Arab tribes in Arabia. Since he knew the sheikhs of all tribes, and since he was acknowledged by the tribe of the Rualla as sheikh Musa, he was successful in making peace between the tribes of the Rualla, Ibn Rashid, and Ibn Saud. In this way he raised approximately 30,000 camel riders to aid the Ottoman Empire in the fight against the British army in Arabia. Initially his efforts were successful, however due to the shortsightedness of the Ottoman Empire, the British and French military and policy finally triumphed over the tribal confederacies by turning them away from Constantinople. The various episodes of Alois Musil’s sojourn into the Arabian desert, as well as his negotiations with the tribes from November/December 1914 until the middle of April 1915, are described and commented on in this article.
Beside Antonín Švehla, it was - without question - Alois Rašín, who influenced the process of the coup the most. His vision of the coup was not dull, simple or technological; it was a perfectly prepared and managed action, which was also to be enjoyed by its participants. In the centre of Rašín's thoughts were the preparations of the law drafts (also called The Founding Law of the State and above all The First Law), which should have given a legal framework to the new state. A coup that did not get out of hand and which was, once completed, immediately sealed by a law was his ideal but attainable vision. Rašín was probably the only one who tried to prepare such a law. No other proposal is known. All of this attests to his capabilities as statesman and his ability to act. and Článek zahrnuje odkazy pod čarou