On the symbol homomorphism of a certain Frechet algebra of singular integral operators

We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L²-Sobolev norms. The proof is based on an ⁿ of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation u/t=i|D|u, 0<<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.     

Zur Theorie der Bildung von Gelen

Colloid and Polymer Science -     

Fluorinated Musk Fragrances: The CF2 Group as a Conformational Bias Influencing the Odour of Civetone and (R)‐Muscone

The difluoromethylene (CF₂) group has a strong tendency to adopt corner over edge locations in aliphatic macrocycles. In this study, the CF₂ group has been introduced into musk relevant macrocyclic ketones. Nine civetone and five muscone analogues have been prepared by synthesis for structure and odour comparisons. X‐ray studies indeed show that the CF₂ groups influence ring structure and they give some insight into the preferred ring conformations, triggering a musk odour as determined in a professional perfumery environment. The historical conformational model of Bersuker and co‐workers for musk fragrance generally holds, and structures that become distorted from this consensus, by the particular placement of the CF₂ groups, lose their musk fragrance and become less pleasant.