Zur Lojasiewicz-Ungleichung für differenzierbare Funktionen

Let f be a C^∞-function satisfying a Lojasiewicz-inequality. Is it possible that the Taylor series of f is the zero-series in some point? We will show here that this is not possible.     

On single and bimodal optimum buckling loads of clamped columns

We study the problem of determining the optimum shape of a thin, elastic, clamped column of given length and volume, such that the fundamental buckling load is a maximum. The column cross-sections are assumed to be geometrically similar, and a minimum allowable value is specified for the cross-sectional area.Investigating the optimization problem parametrically in terms of this minimum constraint, we reveal a significant feature. There exists a threshold value for the constraint, beyond which the optimum columns are all associated with single mode optimum buckling loads, whereas, for any value of the constraint less than the threshold value, the optimum columns are associated with bimodal fundamental buckling loads.This bimodal behaviour necessitates an extension and a mathematical reformulation of the current optimization problem, which is outlined and solved in the paper. In particular, we revise the result hitherto considered to be the optimum solution for an unconstrained column with clamped ends.     

Über die Beziehungen zwischen der Galoisgruppe und dem Raum der Anordnungen eines formal-reellen Körpers

Ohne Zusammenfassung     

Observation of a re-entrant isotropic phase in a pure disc-like liquid crystal

We report the observation of an optically isotropic phase in the new disc-like mesogen 2,3,7,8,12,13-hexa(octadecanoyloxy)truxene. On cooling, this optically isotropic phase goes over into a nematic phase, while on heating a columnar phase grows in. To our knowledge this is the first example of a pure discotic mesogen exhibiting an isotropic phase below the temperature existence of a columnar phase. Our findings are supported by refractive index measurements of this compound as a function of temperature.