Ueber die Eigenschaft der Gammafunction keiner algebraischen Differentialgleichung zu genügen

Ohne Zusammenfassung     

I. Methoden zur Bestimmung der Totalweins?ure in Hefen und Weinsteinen unter Abscheidung der S?ure als saures Kaliumsalz

Ohne Zusammenfassung     

Quantitative Bestimmung der Chinaalkalo?de

Ohne Zusammenfassung     

Bücherbesprechungen

Ohne Zusammenfassung     

On the Possibility of Replacing Standard Chromium-Plating Electrolytes with Sulfate-Oxalate Solutions of Cr(III)

A method for preparing sulfate-oxalate chromium-plating solutions by reducing Cr(VI) from industrial chromium-plating electrolytes to Cr(III) with a Na₂SO₃ solution is proposed.     

Nonvanishing derivatives and normal families

We consider the differential operators Ψ _k , defined by Ψ₁(y) =y and Ψ _k+1(y)=yΨ _k y+d/dz(Ψ _k (y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ _k F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z ²+β z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ _k (F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ _k (f ^′/f) =f ^(k)/f, we deduce in particular that iff andf ^(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f ^′/f :f ∈F} is normal. The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999, and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank Günter Frank for helpful discussions.     

Model spectral function and superconductivity in BaxK1−xBiO3 (x=0.5-0.7)

The Eliashberg spectral density function is constructed for the superconducting compound Ba_xK_1−xBiO₃ with x=0.5, 0.6, 0.7. The functions, besides yielding some prominent structures, show widely spreading spectra that inhibit lattice instability by yielding not too large values of λ(<1.32). The resulting spectral functions show similar shape as other results, where available, and also successfully reproduce the observed critical temperature, isotope exponent, gap ratio and several other parameters.