Tetraaryl-methane analogues in group 14—V. Distortion of tetrahedral geometryin terms of through-space π–π and π–σ interactions andNMR sagging in terms of π–σcharge transfer

44 members of thecompound series Ph_4−nMR_n (M=Si, Ge, Sn, Pb; R=o-, m-, p-Tol; n=0–4) were synthesized (15 newcompounds). The crystal structures of Ph₃Sn (o-Tol) and PhSn (o-Tol)₃ were determined and compared to 16 known structures. Subject to the distanced (M–C), an interplay between through-space π–π repulsion and π–σ attraction leads to either elongated or compressed tetrahedral geometry. ²⁹ Si-, ¹¹⁹ Sn- and ²⁰⁷ Pb-NMR chemical shifts were determined in solution and in the solid state. ⁷³ Ge chemical shifts were measured only in solution. Anupfield or downfield sagging of the chemical shifts along each series is rationalized in terms of a π–σcharge transfer which is constrained by torsion of the aromatic groups.     

Ueber eine neue Methode zur Bestimmung des Eisens im Harn

Ohne Zusammenfassung     

Variational problems with obstacles and integral constraints

Various problems in mathematics and physics can be formulated in terms of a variational problem with obstacles and integral constraints, e.g. finding a surface of minimal area with prescribed volume in a bounded region.We are concerned with the regularity of solutions of variational problems: We show that the minima of a variational integral under all Sobolewfunctions with prescribed boundary values, lying between two obstacles, and fulfilling some integral constraints, are bounded and Hölder-continuous. We do not assume any differentiability or convexity of the integrand, but only a Caratheodory and a growth condition.This research has been supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft.     

A selection lemma for sequences of measurable sets,and lower semicontinuity of multiple integrals

In the present paper we show that the integral functional is lower semicontinuous with respect to the joint convergence of y_k to y in measure and the weak convergence of u_k to u in L₁. The integrand f: G × ^N × ^m , (x, z, p) f(x, z, p) is assumed to be measurable in x for all (z,p), continuous in z for almost all x and all p, convex in p for all (x,z), and to satisfy the condition f(x,z,p)(x) for all (x,z,p), where is some L₁-function.The crucial idea of our paper is contained in the following simple