Synthesis of pulvinones via tandem Dieckmann condensation-alkoxide β-elimination

A series of pulvinones were prepared in three steps from a common precursor, methyl 3-phenylglycidate. This compound was readily converted to several diesters containing an ether function. Then, treatment of these compounds with lithium hexamethyldisilazide afforded the corresponding pulvinones, via tandem Dieckmann condensation-alkoxide β-elimination. The use of a 2,2,2-trifluoroethyl ether instead of a methyl ether facilitated the β-elimination and led to better yields of product.     

Unordered and ordered sample from dirichlet distribution

Consider the random Dirichlet partition of the interval inton fragments with parameter π>0. Explicit results on the statistical structure of its size-biased permutation are recalled, leading to (unordered) Ewens and (ordered) Donnelly-Tavaré-Griffiths sampling formulae from finite Dirichlet partitions. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what are the intervals between new sampled categories when sampling is from Dirichlet populations? The results obtained are in accordance with the ones found in sampling theory from random proportions with GEM(γ) distribution. These can be obtained from Dirichlet model when considering the Kingman limitn↑∞, π↓0 whilenπ=γ>0.     

Large Deviations for the Yang-Mills Measure on a Compact Surface

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the scaled Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energy.     

On Entropic Reduction of Fluctuations

We point out that there is no general relation between ground state degeneracy and finite-temperature fluctuations for tilted interfaces.     

On topological set theory

This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)