We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.
Ein dorniger Weg zu Versöhnung und Gerechtigkeit. Sigismund von Luxemburg als Schiedsrichter in Streit zwischen dem Deutschen Orden und Polen (1412-1420).
The structure of the human microsporidium found by Yachnis and colleagues in two AIDS patients (Am. J. Clin. Pathol. 106: 535-43, 1996) (hereafter referred to as HMY) was investigated by light and transmission electron microscopy and compared with Thelohania apodemi Doby, Jeannes et Raoult, 1963, a microsporidian of small rodents. The fine structure of the HMY was found to be similar to that of Trachipleistophora hominis Hollister, Canning, Weidner, Field, Kench et Marriott, 1996. Characteristic is the presence of a thick layer of electron dense material on the outer lace of the meront plasmalemma, which is maintained during the whole life cycle and which later persists as an electron dense coat on the sporophorous vesicle (SPOV). However, HMY is distinguished from T. hominis during sporogony, as two types of SPOV and spores are formed in HMY. One type of SPOV contains thick-wallcd spores (usually 8 or more in number) with anisofilar polar filaments of 7 + 2 pattem, while the other type contains only two thin-walled spores with a smaller number (3-5) of isofilar polar filament coils. The HMY differs from T. apodemi which also forms SPOV with 8 spores inside, but the spores of which are larger in size and have 9 + 2 polar filament pattern.
Fiedler and Markham (1994) proved {\left( {\frac{{\det \hat H}}{k}} \right)^k} \geqslant \det H, where H = (H_{ij})_{i,j}^{n}_{=1} is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and \hat H = \left( {tr{H_{ij}}} \right)_{i,j = 1}^n. We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove \det \left( {{I_n} + \hat H} \right) \geqslant \det {\left( {{I_{nk}} + kH} \right)^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}}}., Minghua Lin., and Obsahuje seznam literatury
A (finite) acyclic connected graph is called a tree. Let W be a finite nonempty set, and let H(W) be the set of all trees T with the property that W is the vertex set of T. We will find a one-to-one correspondence between H(W) and the set of all binary operations on W which satisfy a certain set of three axioms (stated in this note).