Influence of substituents on positron annihilation in styrene copolymers

Results of angular correlation of annihilation radiation (ACAR) and positron annihilation lifetime (PAL) measurements are presented for five styrene copolymers: poly(co-styrene-phenylmaleimide) and its three derivatives with chlorine as well as for one with the OH group substituted at the benzene ring. It occurs that the chlorine substituted at three different positions at the benzene ring poly(co-styrene-o (or-m,-p)-chlorophenylmaleimide) inhibits the formation of the positronium to different extent. The greatest effect is observed in case of the chlorine atom substituted at the benzene ring at the ortho-position towards the nitrogen atom. The two long lifetimes (₃ and ₄) observed in the lifetime spectra are connected with the bimodal distributions of the free volume radius in the samples.     

Spectral properties of operators of the theory of harmonic potential

We classify the points of the spectrum of the operatorsB andB ^* of the theory of harmonic potential on a smooth closed surfaceS ³. These operators give the direct value onS of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators inL ₂ (S). We prove that the half-interval [–2, 2) is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operatorsB andB ^* on ellipsoidal surfaces.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.This research was partially supported by the Russian Foundation for Basic Research.