A vinyl substitution reaction in fluoroalkenes

Based on the results of CNDO and INDO quantum-chemical calculations, the possibility of a vinyl substitution (along with an addition) upon reaction of perfluoropropylene, perfluoroisobutylene, and trifluorochloroethylene with alcohols, thiols, and amines, and the absence of a similar reaction in the case of tetrafluoroethylene is explained. The calculations allow the prediction that a vinyl substitution should take place in similar reactions of 1,1-di- and trifluoroethylenes, but not with mono- and 1,2-difluoroethylenes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2802–2805, December, 1991.     

Exchange Relation Planar Algebras

An inclusion of II ₁ factors NM of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups.     

Rejoinder: Comments on a paper by Gruber

An error in Gruber's paper, Quantization in Generalised Coordinates, and the reason for this kind of error are pointed out. A partial answer to the problem posed by the paper is stated.     

A note on extended locality

Conditions for the validity of extended locality are derived within the framework of the theory of local observables. It is shown that extended locality is equivalent to the condition that the algebra of all local observables contain no non-trivial translationally invariant operators. It is then shown that the derivation of extended locality can be generalized so as to apply to a wider class of regions.