The extraction of alkoxide anions by quaternary ammonium phase transfer catalysis

Only trace amounts of hydroxide ion can be extracted from aqueous solution into non-polar organic media by quaternary ammonium salts. Addition of small amounts of primary alcohols, particularly certain diols, dramatically changes the behaviour of systems, and surprising amounts of base can be found in the organic apolar phase. The competitive extraction halide/alkoxide was investigated for various ammonium salts. Quantitative measurements were carried out for the evaluation of selectivity constants for extraction of simple primary alkoxides by tetra-n-hexylammonium chloride in benzene.     

EPR and ENDOR investigations of Sn impurities in CdS

Wurtzite type CdS single crystals with tin impurities have been reinvestigated by means of magnetic resonance. The by far strongest neighbour interaction with the rare isotope³³S is detectable by electron paramagnetic resonance (EPR), while nine weaker cadmium interactions can be resolved with the electron nuclear double resonance (ENDOR) technique. Three distinct shell symmetries are detected and can be explained by the wurtzite lattice symmetry. The parameters evaluated are interpreted in terms of the LCAO approach. An additional Sn-related spectrum, being not resolvable by ordinary EPR was identified by means of ENDOR-induced-EPR (EI-EPR) and turned out to be associated with Lithium.     

Nichtschlichte konforme Abbildung unendlich vielfach zusammenhängender Teilgebiete der Ebene

Archiv der Mathematik -     

Über die Wertannahme der Ahlfors Funktion in beliebigen Gebieten

Let B be a domain ?? that supports nonconstant bounded analytic functions, let pe B. In [1] S.Fisher posed the question: Does the Ahlforsfunction for B and p map a maximal B onto the unit disc D? We give an example of a maximal B such that in B F(z) omits two values of D.     

13C-NMR-Spektroskopie von Cyclopropenonen und Cyclopropenyliumionen (Cyclopropenonchemie: VII)

The carbon-13 NMR spectra of thirteen cyclopropenones, two cyclopropenethiones, five related cyclopropenylium salts and three cyclobutenediones are tabulated and discussed.     

An adaptive refinement method for convection‐diffusion problems

An adaptive finite difference method for singularly perturbed convection‐diffusion problems is presented. The method is introduced using a first‐order upwind scheme and a suitable error estimator based on the first derivatives. To obtain the grid structure needed for the cross stencil a special refinement strategy is considered. To avoid the slave points we change the stencil at the interface points from a cross to a skew one. After the convergence of the refinement algorithm we use a combination of a first order upwind and a second order central schemes to achieve higher order of convergence. Several numerical examples show the efficiency of our treatment. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling Spirals of Silence and Echo Chambers by Learning from the Feedback of Others

What are the mechanisms by which groups with certain opinions gain public voice and force others holding a different view into silence? Furthermore, how does social media play into this? Drawing on neuroscientific insights into the processing of social feedback, we develop a theoretical model that allows us to address these questions. In repeated interactions, individuals learn whether their opinion meets public approval and refrain from expressing their standpoint if it is socially sanctioned. In a social network sorted around opinions, an agent forms a distorted impression of public opinion enforced by the communicative activity of the different camps. Even strong majorities can be forced into silence if a minority acts as a cohesive whole. On the other hand, the strong social organisation around opinions enabled by digital platforms favours collective regimes in which opposing voices are expressed and compete for primacy in public. This paper highlights the role that the basic mechanisms of social information processing play in massive computer-mediated interactions on opinions.     

Mode coupling approximation in a model of structural phase transitions with infinite range interaction

The long-time value of the displacement-displacement correlation function and the mean square displacements are calculated within the ⁴-lattice model with infinite range interaction by use of a mode coupling approximation. Their temperature dependence is compared with exact results. While the mean square displacements (zero decoupling times) agree with exact results except the low temperature range for weak coupling, the long time correlations from MCA (infinite decoupling times) are wrong. Even a separation of the displacement function into two parts representing the two different time scales is of no use since the distribution function doesn't separate.     

Phosphor thermometry at the surface of single reacting large-diameter spherical coke particles to characterise combustion for packed bed furnaces

Packed-bed furnaces fired with large-diameter coke are important in high-temperature material processing industries such as lime and iron production. The combustion conditions are complicated by the presence of an ash layer surrounding the coke particle that remains intact during passage through the furnace and alters oxygen diffusion and heat transfer to the reacting particle core. The objective of this study is to determine the surface temperature of this ash layer using lifetime-based phosphor thermometry during combustion of single spherical 38 mm diameter coke particles in a high temperature tube furnace. Time traces of the coke particle core temperature and mass conversion rate do not significantly differ between experiments performed with and without the phosphor layer, indicating that the presence of the phosphor particles does not alter the overall combustion behaviour. Surface temperatures of up to 950 °C are measured and correlated with the fuel mass conversion rate. When the coke particle starts to react the surface temperature is up to 100 °C higher than that of the core. As the reaction front progresses toward the centre, the core temperature exceeds the surface temperature by 200 °C due to the insulating effect of the ash layer. The surface temperature of the ash layer decreases with time due to the steadily decreasing fuel mass conversion rate. The method and results can be used to provide key validation data for shrinking-core combustion models, for example by constraining the unknown transport properties of the ash layer, thereby assisting the development of complete packed-bed furnace simulations for process optimisation.