The diastereoselective synthesis of functionalised isoxazolidines using a Cope elimination/intramolecular nitrone cycloaddition strategy

Functionalised hydroxylamine derivatives of (S)-prolinol prepared by a Cope elimination have been found to undergo oxidation to the nitrone either in the presence of air or a catalytic quantity of TPAP. These undergo intramolecular cycloaddition to give tricyclic isoxazolidines with high diastereoselectivity.     

The synthesis of chiral functionalised morpholine N-oxides using a tandem Cope elimination/reverse-Cope elimination protocol

Hydroxylamine derivatives of (S)-prolinol have been generated using a Cope elimination. These undergo reverse-Cope elimination onto a pendant double bond to give morpholine N-oxides containing three contiguous chiral centres.     

Nuclear Fréchet spaces without bases III. Every nuclear Fréchet space not isomorphic to ω admits a subspace and a quotient space without a strong finite dimensional decomposition

The result stated in the title is proved.Research of the second author partially supported by the National Science Foundation. He would also like to thank the Banach Institute, Polish Academy of Sciences and Universität Kaiserslautern for their hospitality.     

Expedient synthesis of novel β-ketoesters from the Mizoroki–Heck coupling of ethyl 3-ethoxyacrylate with aryl and pyridyl halides

It is well known that β-ketoesters are useful intermediates for the synthesis of a range of heterocyclic templates. While there are many useful synthetic methods available to access these intermediates, there are still opportunities for the discovery of useful methodologies for their construction from novel starting materials. In this regard, we report on the discovery of a facile Pd-catalyzed Mizoroki–Heck coupling of ethyl 3-ethoxyacrylate with aryl and heteroaryl halides to form substituted alkoxyacrylates which can be hydrolyzed to form novel aryl and heteroaryl β-ketoesters.     

On a symmetry of turbulence

This paper presents results on symmetries of the spectrum of singularities for random cascades found in the statistical theory of turbulence. It is shown that empirical dimension curves possess a natural symmetry whose presence restricts the class of allowable probability distributions of the cascade generator in a simple manner. In particular, necessary and sufficient conditions on the probability distribution of the generator are obtained for symmetry of the singularity spectrum within a large class of cascade models.