Exact solutions inU 4 gravity. I. The ansatz for self double dual curvature

We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U ₄-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.     

Structural and spectroscopic studies of silylated cyclo- and bicyclosilanes

A number of cyclo-and bicyclosilanes have been prepared and structurally characterized by X-ray crystallography and Raman spectroscopy. 1,1,4,4- and 1,1,3,3-tetrakis(trimethylsilyl)octamethylcyclohexasilanes were found to exhibit unusual twist- and twisted boat-conformations. The UV absorption properties of all compounds were studied and found to show absorption maxima red shifted compared to the parent compound dodecamethylcyclohexasilane. Dedicated to Prof. Mitsuo Kira on the occasion of his reception of the Wacker Silicon Award 2005 and in recongnition of his numerous outstanding achievements in organosilicon chemistry.     

On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks

We answer some questions on the asymptotics of ballot walks raised in [S. B. Ekhad and D. Zeilberger, April 2021] and prove that these models are not D-finite. This short note demonstrates how the powerful tools developed in the last decades on lattice paths in convex cones help us to answer some challenging problems that were out of reach for a long time. On the way we generalize tandem walks to the family of large tandem walks whose steps are of arbitrary length and map them bijectively to a generalization of ballot walks in three dimensions.

     

Palladium-catalyzed electrophilic substitution of allyl chlorides and acetates via bis-allylpalladium intermediates

Palladium-catalyzed electrophilic allylic substitution of functionalized allyl chlorides and allyl acetates can be achieved in the presence of hexamethylditin under mild and neutral reaction conditions. This efficient one-pot procedure involves palladium-catalyzed formation of transient allylstannanes followed by generation of a bis-allylpalladium intermediate, which subsequently reacts with electrophiles. Using this catalytic transformation, various aldehydes and imines can be allylated providing highly functionalized homoallyl alcohols and amines. Furthermore, tandem bis-allylation reactions could be performed by employing tosyl isocyanate and benzylidenemalonitrile as substrates. A particularly interesting mechanistic feature of this reaction is that palladium catalyzes up to three different transformations in each catalytic cycle. Various allylic functionalities, including COOEt, CONH(2), COCH(3), CN, Ph, and CH(3), are tolerated in the catalytic reactions due to the application of neutral and mild reaction conditions. The substitution reaction occurs with very high regioselectivity at the branched allylic terminus. Moreover, in several reactions, a high stereoselectivity was observed indicating that this new catalytic process has a high potential for stereoselective synthesis. The regioselectivity of the reaction can be explained on the basis of DFT calculations. These studies indicate that the allylic substituent prefers the gamma-position of the eta(1)-allyl moiety of the reaction intermediate.     

Radium isotopes and <Superscript>222</Superscript>Rn in Austrian drinking waters

The activity concentrations of the Ra isotopes, ²²⁶Ra and ²²⁸Ra, as well as of ²²²Rn were measured in Austrian tap waters. Rn was extracted into a mineral oil cocktail not miscible with water and measured by liquid scintillation counting using pulse-shape analysis for α/β-separation. Ra isotopes were co-precipitated with BaSO₄ or concentrated by filtration through an element specific filter. EDTA solution was used to redissolve the precipitate as well as to release the Ra from the filter. After mixing with a cocktail, the EDTA solution was measured by liquid scintillation counting, too. From our results the effective ingestion doses for adults and 3 months old babies were calculated.     

Notes on recentU 4 theories of gravitation

Some of the proposed Lagrangians and their corresponding field equations for a gravitational theory based on a Riemann-Cartan space with metric-compatible connection (U ₄, theory) are compared and a new one is suggested. This Lagiangian, and that of P. von der Heyde and F. W. Hehl et al. are examined applying the Gordon-decomposition argument. Finally, Einstein's field equations with cosmological term are shown to be included in some sense, but the cosmological constant naturally has microphysical origin. To simplify notation, Cartan's calculus is used throughout.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in österreich, project No. 3666.Most of this work was carried out during the stay at the 6th Course of the International School of Cosmology and Gravitation at Erice, 1979.     

Instrumental neutron activation analysis of spruce needles and trees

Tree rings and needles of young spruce clones from the immission area of the Al-refinery Ranshofen (Upper Austria), which had ceased production in 1992, were investigated by INAA. Short time irradiation was performed for determining, Al, Mn, Ca and Cl, while the elements Na, K, Rb, Ba, Zn, Fe, Sc, Cr, Co, Br and in some samples also Ca were determined via middle- and long-lived radioisotopes. Irradiation and counting conditions are given. Accuracy and sensitivity are sufficient to describe the trends of the element concentrations in needles and with the exception of Cr, Sc and Br, in tree rings. Ca-concentrations derived from⁴⁹Ca (short-time irradiation) and⁴⁷Ca (long-time irradiation) are compared and show good agreement Additionally Mg was determined in some samples by ICP-AES and if possble, by INAA. The results are compared.     

Genotoxicity and Cytotoxicity of 4-Nonylphenol Ethoxylate on Lymphocytes as Assessed by the Comet Assay

Surfactants, which are prevalent at industrial sites and in the environment generally, are potential risk factors in human carcinogenesis. The widespread industrial use of surfactants such as 4-alkylphenol ethoxylates and their prevalence in many cleaning products have provoked studies about surfactant concentrations in water and their toxicity levels. Up to now, these substances have mainly been tested on aquatic organisms. Though tests on human cell lines are rare. The alkaline Comet assay was performed to evaluate the genotoxicity of 4-nonylphenol ethoxylate, a biodegradable product of 4-alkylphenol ethoxylate, in human lymphocytes. Concentrations tested ranged from 0.15 to 150 µg/mL. Test concentrations of 10 to 15 µg/mL caused an increase level of DNA migration in human cells, but without inducing excessive toxicity (viability > 80%). Though induced levels of DNA migration starting at concentrations of 30 µg/mL may have been due to excessive levels of cytotoxicity (viability < 70%). Based on these data, 4-nonylphenol ethoxylate can induce DNA damage in human lymphocytes but at higher concentrations than are normally found in river or drinking water. However, considering the prevalence of surfactants, the measured genotoxicity of these substances is of concern. Further investigations on human target cells are necessary to evaluate the carcinogenic impact of surfactants and reconsider their environmental acceptance.     

60Fe anomaly in a deep-sea manganese crust and implications for a nearby supernova source

A nearby supernova (SN) explosion in the past can be confirmed by the detection of radioisotopes on Earth that were produced and ejected by the SN. We have now measured a well resolved time profile of the 60Fe concentration in a deep-sea ferromanganese crust and found a highly significant increase 2.8 Myr ago. The amount of 60Fe is compatible with the deposition of ejecta from a SN at a distance of a few 10 pc. The well defined time of the SN explosion makes it possible to search for plausible correlations with other events in Earth's history.