Conservation properties of higher order time stepping schemes based on variational integrators

This paper deals with higher order accurate variational integrators for finite element systems. The variational integrator (VI) is based on higher order LAGRANGE polynomials as shape functions and a higher order GAUSSIAN quadrature rule. The goals of this paper are to implement a discrete gradient to preserve the balance of total energy and fulfill the constraints with the LAGRANGE multiplier method and a NEWTON-COTÊS quadrature rule. We show the calculation of bearing forces from the LAGRANGE multipliers, which are essential for the balance of total linear momentum and the balance of total angular momentum. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Studies on pectin coating of liposomes for drug delivery

The present study investigated the surface coating of charged liposomes by three different types of pectin (LM, HM and amidated pectin) by particle size determinations and zeta potential measurements. The pectins and the pectin coated liposomes were visualized by atomic force microscopy. The adsorption of pectin onto positive liposomes yielded a reproducible increase in particle size and a shift of the zeta potential from positive to negative side for all three pectin types, whereas the adsorption of pectin onto negative liposomes did not render any significant changes probably due to electrostatic repulsion. The positive liposomes coated with HM-pectin gave the largest pectin coated particles with the least negative zeta potential, while the opposite was observed for the LM-pectin coated positive liposomes. Furthermore, results from dynamic light scattering revealed narrow size distributions, indicating that the degree of aggregation was low for the pectin coated liposomes. As liposomes are able to encapsulate drugs and pectin has been found to be mucoadhesive, these pectin coated liposomes may be potential drug delivery systems.     

Synthesis of fully substituted polyhydroxylated pyrrolizidines via Cope-House cyclization

Total synthesis of the proposed structure of (-)-hyacinthacine C(5) and its epimers at C6 and C7 is described. A key step of the synthesis was the construction of the bicyclic pyrrolizidine system by means of a nucleophilic addition of a dithiane to a cyclic nitrone followed by a Cope-House cyclization.     

Vibrational analysis of 1-methyl-pyridinium-2-aldoxime and 1-methyl-pyridinium-4-aldoxime cations

Pyrimidinium aldoximes are administered intravenously in cases of acute organophosphate poisoning. Since questions regarding their morphology and active conformation in the solution are still open, an effort was made to establish correspondence between their crystal state conformers and vibrational spectra, thus facilitating the future work on the assignment of bands in solution. Normal coordinate analysis including the potential energy distribution for all modes was performed for 1-methyl-pyridinium-2-aldoxime (PAM2AN) and 1-methyl-pyridinium-4-aldoxime (PAM4AN) cations (charge=+e, spin=0). Positions of infrared and Raman bands of corresponding chloride salts agree rather well with predicted values, except for modes taking part in hydrogen bonding to anions. The strength of hydrogen bonding is estimated to be of medium strength in both salts, the bonding in PAM2AN being stronger. The calculated and observed values of the characteristic stretching modes for the aldoxime moiety have been in accordance with the stronger acidity of PAM2AN structural isomer.     

Idempotente (automorphe) Zahlen in q-Stellenwertsystemen

Zusammenfassung Idempotente Zahlen bezeichnen hier Zahlen, die mit den letzten Ziffern all ihrer Potenzen übereinstimmen, was offenbar vom zugrunde liegenden Stellenwertsystem abhängt. Der Artikel untersucht den mathematischen Mikrokosmos dieser Zahlen: ihre Eigenschaften und Beziehungen untereinander sowie zu verschiedenen Stellenwerten. All dies geschieht auf elementarem Niveau, um zu belegen, dass die Beschäftigung mit diesen speziellen Zahlen auch für interessierte Schüler lohnend sein kann.     

Influence of oleic acid on the structure of a mixture of hydrated model stratum corneum fatty acids and their soaps

The phase behaviour of a hydrated (32% (w/w) water) mixture of saturated and unsaturated fatty acids and their soaps has been examined. By progressively increasing the proportion of oleic acid, it could be shown that this unsaturated component exists partly as a separate phase within the others. The unsaturated fatty acids form an H_II phase at 25°C, whereas the saturated fatty acids form a fatty acid—soap crystal under the conditions employed. The results help to explain the role played by the fatty acids (and also cholesterol) within the lipid fraction of human stratum corneum. A feature of this study is a comparison of the results obtained by X-ray diffraction, differential scanning calorimetry and Fourier transform infrared spectroscopy.     

Minimum information estimation of allocation models of different sizes

For allocation models consisting of n = 10, 6 and 4 equations, constrained generalized least squares coefficient estimates are compared with those obtained from the minimum information (MI) criterion in the sense of statistical information theory. The MI estimates are more efficient for n = 10. The bootstrap procedure is illustrated for the assessment of the variability of these estimates.