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     

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.     

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.     

Synthesis, characterization, and stability of Fe-MCM-41 for production of carbon nanotubes by acetylene pyrolysis

Fe-substituted MCM-41 molecular sieves with ca. 1, 2, and 3 wt % Fe were synthesized hydrothermally using different sources of colloidal silica (HiSil and Cab-O-Sil) and characterized by ICP, XRD, N2 physisorption, UV-vis, EPR, TPR, and X-ray absorption. Catalysts synthesized from Cab-O-Sil showed higher structural order and stability than those from HiSil. The local environment of Fe in the mesoporous material as studied by UV-vis reveals the dominance of framework Fe in all the as-synthesized Fe-MCM-41 samples. Dislodgement of some Fe species to extraframework location occurs upon calcination, and this effect is more severe for Fe-MCM-41 (2 wt %) and Fe-MCM-41 (3 wt %), as confirmed by EPR and X-ray absorption. These materials have been used as catalytic templates for the production of carbon nanotubes (CNTs) by acetylene pyrolysis at atmospheric pressure. A relationship between the Fe loading in MCM-41 and the carbon species produced during this reaction has been established. Using our optimized conditions for this system, Fe-MCM-41 with ca. 2 wt % Fe showed the best results with particularly high selectivity for single-wall carbon nanotube (SWNT) production. This catalyst was selective for carbon nanotubes with a low amount of amorphous carbon for a narrow range of temperatures from 1073 to 1123 K. To account for the different selectivity of these catalysts for CNTs production, the local environment and chemical state of Fe in the used catalyst was further probed by X-band EPR.