Vitamin B1

Ohne Zusammenfassung     

Bei der Bestimmung der Komponenten der technischen Glucose

Ohne Zusammenfassung     

On the non-starlikeness of solutions to the starlike interior wake problem

We study examples of the starlike interior ``wake problem" for which no starlike solution exists relative to the natural star center of the problem. These examples show that the main result of D.E. Tepper in ``A mathematical model for a wake' (Michigan Math. J. 31 (1984), 161-165) is not correct.

     

Reactive species generated during wet chemical etching of silicon in HF/HNO3 mixtures

The role of intermediate species generated during wet chemical etching of silicon in a HF-rich HF/HNO3 mixture was studied by spectroscopic and analytical methods at 1 degrees C. The intermediate N2O3 was identified by its cobalt blue color and the characteristic features in its UV-vis and Raman spectra. Furthermore, a complex N(III) species (3NO+.NO3-) denoted as [N4O6(2+)] is observed in these solutions. The time-dependent decay of the N(III) intermediates, mainly by their oxidation at the liquid-air interface, serves as a precondition for the study of the etch rate as function of the intermediate concentration measured by Raman spectroscopy. From a linear relationship between etch rate and [N4O6(2+)] concentration, NO+ is considered to be a reactive species in the rate-limiting step. This step is attributed to the oxidation of permanent existing Si-H bonds at the silicon surface by the reactive NO+ species. N2O3 serves as a reservoir for the generation of NO+ leading to a complete coverage of the silicon surface with reactive species at high intermediate concentrations. As long as this condition is valid (plateau region), the etch rate is constant and yields a smooth silicon surface upon completion of the etching. If the N2O3 concentration is insufficient to ensure a coverage of the Si surface by NO+, the etch rate decreases linearly with the N2O3 concentration and results in a roughening of the etched silicon surface (slope region).     

How to approximate the solutions of certain free boundary problems for the Laplace equation by using the contraction principle

We show how the free boundary of an ideal fluid, subject to a generalized Bernoulli condition, can (under appropriate circumstances) be approximated. Our method is based on a class of free-boundary perturbation operatorsT , 0<<1, which are all contracting relative to a suitable norm and class of boundaries, and whose fixed points converge to the desired free boundary solution as 0+.

---

Zusammenfassung Wir zeigen, wie der freie Rand einer idealen Flüssigkeit, welcher einer verallgemeinerten Bernoulli-Bedingung genügt, unter geeigneten Umständen approximiert werden kann. Unsere Methode stützt sich auf eine Klasse freier RandperturbationsoperatorenT , 0<<1, welche relativ zu einer geeigneten Norm und Ränderklasse kontrahierend sind und deren Fixpunkte gegen die gewünschte Lösung der freien Randaufgabe mit 0+ konvergieren.

     

On the geometric form of free boundaries satisfying a bernoulli condition

In the x–y plane, let Ω denote an annular domain bounded by the simple closed curves ? and ?^*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ?. Assuming ?^* to be known, we obtain qualitative properties of ?. For example, the number of local maxima or minima of the y-co-ordinate relative to ? cannot exceed the corresponding number for ?^*.