Über den Verteilungsmechanismus der Verunreinigungen bei der kriechenden Kristallisation,wenn keine chemische Verbindung und keine Mischkristalle gebildet werden; 2. Mitt.

Zusammenfassung Der vorgeschlagene Mechanismus wird in entsprechender analytischer Form dargestellt. Die Versuchsergebnisse stimmen mit den theoretischen Berechnungen überein.

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A suitable mathemathical form has been given to the proposed mechanism. The experimental results are in good agreement with the theoretical ones.

     

Some tendencies of the synergistic extraction of lanthanides with mixtures of thenoyltrifluoroacetone and trioctylamine

Solvent extraction of Pr, Gd and Yb with mixtures of HTTA andTOA has been investigated. The values of the synergistic equilibrium constant have been calculated. Some tendencies of the synergistic extraction of lanthanides have been discussed.

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Einige Tendenzen in der synergistischen Extraktion von Lanthaniden mit einer Mischung aus Thenoyltrifluoraceton und Trioctylamin (Kurze Mitteilung)

Zusammenfassung Es wurde die synergistische Extraktion von Pr, Gd und Yb mit einer Mischung aus HTTA undTOA untersucht. Die synergistishcen Gleichgewichtskonstanten wurden berechnet und die Auswirkungen spezifischer Versuchsbedingungen auf das Extraktionsgleichgewicht diskutiert.

     

Universal lattices and unbounded rank expanders

We study the representations of non-commutative universal lattices and use them to compute lower bounds of the τ-constant for the commutative universal lattices G _d,k =SL _d (ℤ[x ₁,...,x _k ]), for d≥3 with respect to several generating sets. As an application we show that the Cayley graphs of the finite groups can be made expanders with a suitable choice of generators. This provides the first example of expander families of groups of Lie type, where the rank is not bounded and provides counter examples to two conjectures of A. Lubotzky and B. Weiss.     

Richardson-extrapolated sequential splitting and its application

During numerical time integration, the accuracy of the numerical solution obtained with a given step size often proves unsatisfactory. In this case one usually reduces the step size and repeats the computation, while the results obtained for the coarser grid are not used. However, we can also combine the two solutions and obtain a better result. This idea is based on the Richardson extrapolation, a general technique for increasing the order of an approximation method. This technique also allows us to estimate the absolute error of the underlying method. In this paper we apply Richardson extrapolation to the sequential splitting, and investigate the performance of the resulting scheme on several test examples.     

Effects of emulsifier charge and concentration on pancreatic lipolysis. 1. In the absence of bile salts

An in vitro study is performed with sunflower oil-in-water emulsions to clarify the effects of type of used emulsifier, its concentration, and reaction time on the degree of oil lipolysis, α. Anionic, nonionic, and cationic surfactants are studied as emulsifiers. For all systems, three regions are observed when surfactant concentration is scaled with the critical micelle concentration, C(S)/cmc: (1) At C(S) < cmc, α ≈ 0.5 after 30 min and increases up to 0.9 after 4 h. (2) At C(S) ≈ 3 × cmc, α ≈ 0.15 after 30 min and increases steeply up to 0.9 after 2 h for the cationic and nonionic surfactants, whereas it remains around 0.2 for the anionic surfactants. (3) At C(S) above certain threshold value, α = 0 for all studied surfactants, for reaction time up to 8 h. Additional experiments show that the lipase hydrolyzes molecularly soluble substrate (tributirin) at C(S) > cmc, which is a proof that these surfactants do not denature or block the enzyme active center. Thus, we conclude that the mechanism of enzyme inhibition by these surfactants is the formation of a dense adsorption layer on an oil drop surface, which displaces the lipase from direct contact with the triglycerides.     

The Dehn function of Baumslag’s metabelian group

Baumslag??s group is a finitely presented metabelian group with a ${\mathbb Z \wr \mathbb Z}$ subgroup. There is an analogue with an additional torsion relation in which this subgroup becomes ${C_m \wr \mathbb Z}$ . We prove that Baumslag??s group has an exponential Dehn function. This contrasts with the torsion analogues which have quadratic Dehn functions.     

On the scattering of torsional elastic waves from axisymmetric defects in coated pipes

Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field.