Karel Domin (1882-1953) byl významný český botanik a vysokoškolský pedagog. Vystudoval a působil na Univerzitě Karlově, byl děkanem Přírodovědecké fakulty a v letech 1933-1934 dokonce univerzitním rektorem, s jeho jménem je spojen boj o insignie. Byl dlouholetým ředitelem Botanického ústavu Univerzity Karlovy. Ve své profesi byl mimořádně aktivní, v letech 1914-1945 byl předsedou České botanické společnosti, o jejíž vznik se zasloužil, publikoval řadu odborných i populárně naučných prací. Věnoval se také politické činnosti, v letech 1935-1939 byl senátorem za Národní sjednocení. Po 2. světové válce byl nařčen z kolaborace a zbaven všech funkcí. Přestože byl Národním soudem veškerých obvinění zbaven, do veřejného života se již nevrátil a roku 1949 byl penzionován., Karel Domin (1882-1953) was the important Czech botanist, politician, professor (a head of the University Botanical Institute), the dean of the Faculty of Science of Charles University in Prague and the chancellor of the University. He was very active both in his professional activities (e. g. he was a chairman of the Czech Botanical Society in 1914-1945), and in public and political activities (e. g. a National Assembly senator 1935-1939, representative of the National Democratic Party). After the World War II he was accused of collaboration and suspended from all his public and professional jobs, functions and offices. (Translated by Hana Barvíková.), and Překlad resumé: Hana Barvíková
We consider a family of conforming finite element schemes with piecewise polynomial space of degree k in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is h k + τ 2 in the discrete norms of L∞(0, T ; H1 (Ω)) and W1,∞(0, T ; L 2 (Ω)), where h and τ are the mesh size of the spatial and temporal discretization, respectively. These error estimates are useful since they allow us to get second order time accurate approximations for not only the exact solution of the wave equation but also for its first derivatives (both spatial and temporal). Even though the proof presented in this note is in some sense standard, the stated error estimates seem not to be present in the existing literature on the finite element methods which use the Newmark method for the wave equation (or general second order hyperbolic equations).
We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. ∇-relation is partly studied by means of statisch pairs.