Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

Paramagnetic defects in BaTiO3 and their role in light-induced charge transport — Optical studies

On the basis of a previous identification of paramagnetic defects in nominally undoped as grown BaTiO₃ single crystals, we have investigated the changes of the concentrations of these centers and their optical absorptions under illumination with light of varying wavelengths. The most pronounced charge transfers occur by hole ionization of Fe⁴⁺ and — to a lesser extent — of Cr⁵⁺ and Cr⁴⁺. At low temperatures the created holes are trapped in the form of O^–-ions next to Al³⁺ or unknown acceptor defects. Corresponding Fe⁴⁺ and O^– absorptions have been identified.     

TERAHERTZ QUALITY CONTROL OF POLYMERIC PRODUCTS

We report on experiments that evaluate the potential of terahertz (THz) time-domain spectroscopy (TDS) for quality control of polymeric compounds. We investigate specimens out of a polyethylene compound with silver-coated titanium dioxide nanospheres and a glass-fiber reinforced epoxy composite. We further examine an industrial polymer product produced by injection molding. Our data demonstrates that THz imaging is a powerful tool for contactless quality control in the polymer industry.     

The course scheduling problem at Lufthansa Technical Training

Lufthansa Technical Training GmbH (LTT) performs training courses for Lufthansa Technik AG as well as for several other international airlines. Courses of about 670 different types are offered of which several hundred take place each year. The course scheduling problem faced by LTT is to construct a yearly schedule which maximizes the profit margin incurred while meeting a variety of complex precedence, temporal, and resource-related constraints. A “good” operational schedule should also meet a number of additional subordinate objectives. We formalize the problem and develop a heuristic scheme along with several priority rules, as well as a local search algorithm to determine well-suited weights for weighted composite rules. The operational planning situation of 1996 served as our major test instance; additional test instances were constructed by modifying this data. Several computational experiments were carried out to evaluate the performance of the algorithms. It turned out that the best so-found schedule is substantially better in terms of the profit margin incurred than the solution manually constructed by LTT.     

LiTiCl3: Synthesis and thermal behaviour

LiTiCl₃ is obtained as one example within an ample solid solution, Li_24–2nTi_nCl₂₄ (?4?n?10), by synpropotionation of TiCl₃ and Ti in the presence of LiCl (2:1:3 molar ratio) in sealed tantalum tubes at 750°C. It crystallizes with the inverse spinel-type structure according to (Li_0.67)^[4](Li_0.67Ti_1.33)^[4]Cl₄ with, at 25°C, a = 1048.62(4) pm, space group Fd3m. Thermal expansion is linear with α = 4.85 × 10^?5K^?1 up to about 300°C and thereafter, when the migration of Li⁺ from tetrahedral to octahedral interstices becomes increasingly important, it exhibits a relative decrease resulting, finally, in the phase transition to a NaCl-type structure that is observed for the first time at about 575°C.     

Stereochemie von Metallocenen, 13. Mitt.: Optisch aktive Derivate des Methylcymantrens: Darstellung,Rotationsdispersion und konfigurative Korrelation

Zusammenfassung Optisch aktive Methylcymantren-- und--carbonsäuren wurden durch Racematspaltung ihrer Phenäthylaminsalze erhalten. Bei der Umwandlung in die entsprechenden Acetyl- bzw. Vinyl-methylcymantrene treten charakteristische Drehwertänderungen auf. Aus diesen, vor allem aber aus der Rotationsdispersion, ließ sich auf Grund von Konformationsanalysen und Vergleichen zwischen offenkettigen und cyclischen Verbindungen sowie mit analogen Methylferrocenderivaten für die -substituierten Produkte mit großer Sicherheit die absolute Konfiguration ableiten: (1S) für (+)-Methylcymantren--carbonsäure und ihre Folgeprodukte. Dieser Befund wurde durch kinetische Racematspaltung des Anhydrides der racem. Säure mit (–)--Phenäthylamin gestützt.

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Optically active methylcymantrene-- and--carboxylic acids were obtained by resolution of their salts with -phenethylamine. Upon transformation into the corresponding acetyl and vinyl methylcymantrenes, characteristic shifts of the optical rotation are observed. From these data, and especially from the rotatory dispersions, on the basis of conformational analyses and comparisons between open chain and cyclic compounds as well as with analogous methylferrocene derivatives, the absolute configurations of the -substituted products could be deduced with reasonable probability: (1S) for (+)-methylcymantrenecarboxylic acid and its subsequent products. This result was supported by kinetic resolution of the anhydride of the racemic carboxylic acid with (–)--phenethylamine.

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Mit 3 Abbildungen     

Chronocoulometric study of the electrochemistry of Prussian blue

During the electrochemical oxidation of Prussian blue (PB) to Prussian yellow (PY), an electrocatalytic oxygen production proceeds at the electrode when aqueous electrolyte solutions are used. The formed oxygen is scavenged by the PY, probably by absorption, and it is consumed during the electrochemical reduction of PY to PB by a heterogeneous chemical reaction of PB with oxygen to PY and hydrogen peroxide. Because of this catalytic regeneration of PY, it is impossible to determine the amount of low-spin iron by chronocoulometry using a potential program in which PB is first oxidized to PY and then the charge is measured to reduce PY to PB. The latter charge is biased by the electrocatalytic PY regeneration.