Ueber die Darstellung von Traubenzucker

Ohne Zusammenfassung     

Asymptotics of collision integral matrix elements in the isotropic case

The method of nonlinear moments, when used to solve the Boltzmann equation, necessitates the calculation of collision integral matrix elements. The matrix elements are hard to calculate numerically, especially at large indices. The asymptotics of the matrix elements are constructed. In terms of the model of pseudopower particle interaction, a formula free of summation is derived. This makes it possible to find the asymptotic behavior of linear and nonlinear elements when two indices are large. For an arbitrary interaction cross section, asymptotic expansions of linear and nonlinear matrix elements in one index are obtained. For Maxwellian molecules, asymptotic formulas are derived for three large indices.     

Absorption of electromagnetic radiation by an inhomogeneous spherical particle

The cross section of absorption of electromagnetic radiation by an inhomogeneous spherical particle is calculated. The general case of an arbitrary value of the ratio of the particle radius to the radius of the dielectric core is considered. The condition of diffuse reflection of electrons from the inner and outer surfaces of the metal layer of the particle is taken as the boundary condition of the problem. The limiting cases are considered and the results obtained are discussed.     

Some Decidability and Undecidability Results on Green's Relations for Automatic Monoids

We consider the problem of deciding Green's relations for various types of finitely presented automatic monoids. We establish some decidability as well as some undecidability results.     

A new group of fluorescent pH-indicators for an extended pH-range

Summary The pH versus fluorescence intensity profiles of a series of new pH-indicators are reported. They are characterized by two pK_a-values in the 3.7–4.9 and 6.9–7.9 range, respectively. The strong change in fluorescence intensity with pH allows the determination of pH's over a much wider range (typically 2–9) than with one-step indicators. They are therefore considered to be of potential utility for measurement of pH over the neutral and slightly acidity range which occurs, for instance, in bioliquids such as urine.

---

Eine neue Gruppe fluorescierender pH-Indicatoren für einen erweiterten pH-Bereich

Zusammenfassung Die Fluorescenzintensitätsprofile als Funktion des pH-Wertes einer Reihe von neuen pH-Indicatoren werden untersucht. Sie sind charakterisiert durch zwei pK_a-Werte im Bereich 3,7–4,9 bzw. 6,9–7,9. Die gefundene starke Änderung der Fluorescenzintensität mit dem pH-Wert erlaubt eine pH-Bestimmung über einen viel weiteren Bereich (typischerweise 2 – 9) als mit einstufigen Indicatoren. Aus diesem Grund werden sie als potentiell nützlich angesehen zur Messung von pH-Werten im neutralen und schwach sauren Bereich, wie er z.B. in biologischen Flüssigkeiten, etwa im Urin, gegeben ist.