Hayman-Miles Theorem and 2-Valued Algebroid Functions

Given an algebroid function w satisfying $$w^\nu+A_{\nu-1}(z)w^{\nu-1}+\cdot\cdot\cdot+A_0(z)=0,$$ we establish two general methods to calculate the corresponding coefficients in the defining equation for w′ in terms of the meromorphic functions A₀, …, A_ν?1 and their derivatives. We then obtain the following result: Let w be a 2-valued algebroid function. Then T(r,w′) = o(T(r,w)) can hold at most on a set of zero upper logarithmic density.     

Partial Quenching of Parametrical Tetragonality of a Chromium(III) Complex by Pressure Tuning

The ligand-field spectrum of [Cr(NH(3))(4)F(2)]AsF(6) has been pressure-tuned up to 100 kbar. The parametrical analysis shows that the absolute values of the two independent tetragonalities of the chromophoric ion both decrease with increasing isotropic pressure so that the molecular ion becomes more isotropic. Moreover, the Cr-N single bonds appear to be more compressible than the Cr-F bonds, for which it is parametrically clear that they have a partial multiple-bond character. While the spectrochemical parameter for F(-), Delta(F), increases with pressure, its two components Delta(sigma)(F) and Delta(pi)(F) decrease. It is confirmed that nephelauxetism increases with pressure.