Zum chemischen Transport von Fe2O3 mit Tellurtetrachlorid

Chemical Transport of Fe₂O₃ by TeCl₄ The behaviour of the transport of Fe₂O₃ by TeCl₄ is calculated by the aid of the solubulities in the gas phase. TeOCl₂ existing in the gas phase is the essential species for the transport of oxygen. According to the calculations a reversion of the transport direction appears in the temperature range of about 800°C, which was confirmed experimentally. Stoichiometric single crystals of α-Fe₂O₃ were obtained showing in most cases rhombic plates of maximum dimensions 15° 10 · 1 mm.     

Schnitt- und überdeckungszahlen kombinatorischer Sphären

Ohne Zusammenfassung     

Zur Relativgeometrie: Symmetrische Zusammenhänge auf Hyperflächen

Ohne Zusammenfassung     

Characterizability of Free Motion in Special Relativity

The concept of forcefree motion is primitive, i.e., unexplained, in special relativity. The paper demonstrates a way to characterize it by more primitive, directly operationally interpreted notions. These are the worldlines of (more or less) pointlike, but non-quantum bodies and of light signals, clock parametrizations of the former kind of worldlines and the direction, in which an observer sees a light signal go out. Already at this general level one can define the radar distance and the radar (initial) velocity of one body with respect to another, and can define in a reasonable manner that two bodies move in opposite directions with respect to an observer. These concepts are then used to formulate a certain criterion for path structures which can experimentally be tested without presupposing inertial frames, atomic clocks, etc. It is demonstrated that the path structure of free motion in gravity-free regions of space-time, i.e., in the domain of validity of special relativity, satisfies that criterion.     

W-band31P-ENDOR on the high-affinity Mn2+ binding site in the minimal and tertiary stabilized hammerhead ribozymes

The catalytic activity of the tertiary stabilized hammerhead ribozyme (tsHHRz) is by three orders of magnitude higher than the one of the long-known minimal construct (mHHRz). This gives rise to the question whether the single high-affinity manganese(II) binding site present in both ribozymes is located closer to the cleavage site and the transition state in the tsHHRz than in the mHHRz, which would make a direct involvement of this metal(II) ion in the bond-breaking step more likely. Here, we used W-band³¹P-Davies-ENDOR (electron-nuclear double resonance) to complement earlier reported¹⁴N-ESEEM/HYSCORE (electron spin echo envelope modulation/hyperfine sublevel correlation) studies. The³¹P-ENDOR spectrum of the mHHRz revealed a doublet with a splitting of 8.4(±0.5) MHz but unresolved hyperfine anisotropy. Such a large splitting indicates an inner-sphere coordination of a phosphate backbone group with a significant amount of spin density on the phosphorous nucleus. This is in good agreement with the³¹P isotropic hyperfine constant,A _iso(³¹P), of +7.8 MHz obtained by density functional theory calculations on the structure of the Mn²⁺ binding site as found in crystals of the same ribozyme. This supports the idea that the structure and location of the binding site in the mHHRz is in frozen buffer similar to that found in the crystal. Since the W-band ENDOR spectrum of the tsHHRz also shows a³¹P splitting of 8.4(±0.5) MHz, the local structures of both binding sites appear to be similar, which agrees with the coincidence of the¹⁴N data. An involvement of the high-affinity Mn²⁺ ion in the catalytic step seems therefore unlikely.     

Left Euclidean (2, 2)-Algebras

The concept of a commutative and zero-divisor-free Euclidean ring, defined via an Euclidean function, has been generalized to arbitrary left Euclidean rings and than to various other structures as semirings, nearrings and semi-near-rings. As first shown in the dissertation (Hebisch, 1984 Hebisch , U. ( 1984 ). (2, 2)-Algebren mit Euklidischen Algorithmen . Ph.D. thesis, TU Clausthal . [Google Scholar]), these different investigations can be combined considering arbitrary (2, 2)-algebras (S, +, ·), defined as left Euclidean in a suitable way. Here we present and investigate an improved version of this concept. Moreover, Motzkin (1949 Motzkin , T. ( 1949 ). The Euclidean algorithm . Amer. Math. Soc. 55 : 1142 – 1146 . [Google Scholar]) gave a criterion which characterizes a commutative and zero-divisor-free ring as Euclidean by certain chains of product ideals, without the use of Euclidean functions. In the central part of this paper we obtain a corresponding characterization and two further criterions, necessary and sufficient for an algebra (S, +, ·) to be left Euclidean. Based on this we prove several results on these algebras.