Über das Ononin I

Ohne Zusammenfassung     

Über die Lichteinwirkung auf Stoffe vom Typus der Furo-cumarine

Ohne Zusammenfassung     

Über das Ononin II

Ohne Zusammenfassung     

Zur Bestimmung des Mangans als Schwefelmangan

Ohne Zusammenfassung     

Ueber die specifischen Gewichte einiger w?ssrigen L?sungen

Ohne Zusammenfassung     

A further study on the chiral separation power of a soluble neutral β-cyclodextrin polymer

Enantiomeric separation of some basic compounds, namely selegiline, amphetamine, and clenbuterol, was studied by capillary electrophoresis using an uncharged β-cyclodextrin polymer added to the background electrolyte at pH 2.5. Both complexation and resolution were influenced by the concentration of the chiral polymer confirming our previous results obtained in our earlier work for a wide number of pharmaceutical compounds. In this further study, we examined the influence of different organic additives to the background electrolyte on the enantioselectivity of the chiral selector, also using an extended number of analytes. In most cases, the use of an organic additive resulted in a decrease of resolution. However opposite to that, in some cases, e.g. ephedrine, the organic solvent proved to be essential to achieve enantiomeric resolution. Furthermore the influence of the capillary temperature on the resolution of the analytes was evaluated. Increase of temperature had a deleterious effect on the resolution of the enantiomers. For ephedrine, however, relatively high temperature (50 °C) proved to be advantageous, for the resolution of the optical isomers.     

Nilpotent and recursive flows

In this paper we introduce a class of nonlinear vector fields on infinite dimensional manifolds such that the corresponding evolution equations can be solved with the same method one uses to solve ordinary differential equations with constant coeficients. Mostly, these equations are nonlinear partial differential equations. It is shown that these flows are characterized by a generalization of the ‘method of variation of constants’ which is widely used for second order problems to find general solutions out of particular ones. Invariant densities are constructed for these flows in a natural way. These invariant densities are providing an essential tool for solving initial value and boundary value problems for the equations under consideration. Many applications are presented     

A proof for Theodorus' theorem by drawing diagrams

Summary In Plato's dialogue Theaetetus, the mathematician Theodorus (ca. 470-400 BC) is said to have proved the irrationality of 3, 5, ..., 17 by drawing diagrams. In this paper such a proof is presented and compared with another, more arithmetical, reconstructed proof by W. Knorr. Moreover a hypothetical early theory of similar rectangles is extracted from Euclid's Elements, which could have served as a basis for the geometrical proof of Theodorus' theorem.Herrn N. Stephanidis in Freundschaft gewidmet