Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

Sensitive determination of free and plasma protein-bound dipyridamole by high-performance liquid chromatography

For many years dipyridamole (DP) has been used in the treatment of hypertension as a vasodilator, but recently it has been recognised as an anti-platelet aggregation agent and to potentiate anti-metabolite activity. A rapid and sensitive (20 nM) procedure for the determination of free and protein-bound DP in plasma, using reversed-phase high-performance liquid chromatography on an Ultrasphere XL ODS (3 microns) column (70 mm x 4.6 mm I.D.) with ultraviolet detection (280 nm), is reported. Free and bound DP were separated using ultrafiltration. Concentrations of DP between 0.1 and 10 microM were measured in plasma with a relative standard deviation of less than 9.6%. The subsequent determination of DP levels in patients orally administered 450 mg per day showed that DP binding to plasma protein is higher than 90%.     

Polymer-brush stationary phases for open-tubular capillary electrochromatography

Synthesis of poly(2-hydroxyethyl methacrylate) (PHEMA) brushes from the inside of silica capillaries by surface-initiated atom transfer radical polymerization (ATRP) yields unique stationary phases for open-tubular capillary electrochromatography (OT-CEC). Although PHEMA brushes have only a small effect on the separation of a set of phenols and anilines, derivatization of PHEMA with ethylenediamine (en) allows baseline resolution of several anilines that co-elute from bare silica capillaries. Derivatization of PHEMA with octanoyl chloride (C8-PHEMA films) affords even better resolution in the separation of a series of phenols and anilines. Increasing the thickness of C8-PHEMA coatings by a factor of 2 enhances resolution for several solute pairs, presumably because of an increase in the effective stationary phase to mobile phase volume ratio. Thus, this work demonstrates that thick polymer brushes provide a tunable stationary phase with a much larger phase ratio than is available from monolayer wall coatings. Through appropriate choice of derivatizing reagents, these polymer brushes should allow separation of a wide range of neutral molecules as well as compounds with similar electrophoretic mobilities.     

Conformational and spectroscopic investigation of 3-hydroxyflavone-aluminium chelates

3-Hydroxyflavone (3HF), which is the simplest molecule of the flavonol class, possesses chelating properties towards Al(III). Spectrophotometric methods have shown that the 3HF molecule forms an Al(3HF)2 complex in pure methanol. The structure of this complex, obtained by quantum semi-empirical AM1 method, indicated that complexed 3HF adopts a pyronium form. Structural and electronic modifications induced by chelation are illustrated by the important frequency shifts observed between free and complexed 3HF FT-Raman spectra and by the chemical shifts variations in the 13C NMR spectra of the two species. Complexes with the same stoichiometry were formed when AcO- or MeO- are present in the medium. However, in acidic medium the chelate composition is Al2(3HF).     

Regioselective palladium-catalyzed alkylation of allylic halides with benzylic grignard reagents. Two-step synthesis of abietane terpenes and tetracyclic polyprenoid compounds

A highly regioselective palladium-catalyzed alpha-alkylation of allylic bromides 1a,c-e and chloride 1b with substituted and unsubstituted benzylic Grignard reagents is reported. The resulting all-trans polyenehomobenzene derivatives were obtained in excellent yields and regioselectivity. These products were easily converted to abietane-type diterpenes (10-12) and tetracyclic polyprenoid compounds (13, 14) through a Lewis acid-promoted cascade polyene cyclization reaction.