19F chemical shifts and mutual influence of ligands

By comparing the positions of ¹⁹F shifts in pentafluoro complexes of d^o transition metals and non-transition elements in higher oxidation state complexes MF₅L and EF₅L with the positions of corresponding MF₆ and EF₆, the spectra of all the pentafluoro complexes can be divided into a few types which depend on the nature of L. Correlation of chemical shifts with structural data and force constants implies that the change in the bond strength of the fluorine and the central ion has opposite effects in the ¹⁹F NMR spectra of the complexes of transition and non-transition elements.     

The capacity of the rational preimage of a compact set

It is shown that a well-known expression for the capacity of the preimage of a compact set under a polynomial map remains valid in the case of a rational map, provided that the standard capacity of the preimage is replaced by its capacity in the external field determined by the poles in C of the rational function determining the map.     

Convergence of a Limit Periodic Schur Continued Fraction

Mathematical Notes - In this paper, we show that if the parameters of a Schur continued fraction tend to zero, then the functions to which the even convergents converge inside the unit disk and the...     

三阶泛函微分方程的周期解的存在性

本文利用重合度理论研究了一类三阶泛函微分方程方程的2π-周期解的问题,获得了该方程存在2π-周期解的若干新结论,改进推广了有关文献中的已有结果．     

Description of pair potentials for which the scattering in a quantum system of three one-dimensional particles is free of diffraction effects

The coordinate asymptotics of the solution of the scattering problem for a system of three one-dimensional particles contains, besides plane and spherical waves, also Fresnel waves which arise also in the two-dimensional problem of a plane wave on a semiinfinite screen. One describes explicitly the class of potentials for which the Fresnel waves do not occur in the coordinate asymptotics. This class is somewhat wider than the class of nonrefleeting potentials.     

Spin relaxation and magnetic shielding of 93Nb nuclei in [NbCl n Br6-n ]- anions

The temperature dependence of T ₁ and T ₂ relaxation times of ⁹³Nb nuclei in octahedral [NbCl _n Br_6-n ]^-(n = 0 to 6) complexes contained in acetonitrile solution is measured. The relaxation rate is found to be controlled by quadrupole interactions in all complexes except cis-[NbCl₃Br₃]^-. The relaxation mechanism in cis-[NbCl₃Br₃]^- anion depends on exchange processes associated with intramolecular cis?trans isomerization. Calculated values of the electric field gradient (EFG) tensor invariant g _φ ² agree qualitatively with experimental values of T _1,2 ^-1. For cis-[NbCl₃Br₃]^- g _φ ² = 0. On the basis of data for T ₁ and T ₂ the assignment of resonant signals to isomers has been established. The relative chemical shift of cis and trans isomers does not correspond to that evaluated by using a pairwise additivity model. The variations of diamagnetic Δσ^d and paramagnetic Δσ^p contributions to the shielding constant of ⁹³Nb nuclei with the composition of coordination sphere are calculated. Δσ^p contribution to the chemical shifts in the [NbCl _n Br_6-n ]^- is shown to be about 70 per cent.