Marriage of Clifford Algebra and Finsler Geometry: A Lineage for Unification?

The teleparallel Finsler connections on Riemannian metrics are more compatible with algebraic structure than the usual metric-compatible connections. Tangent and cotangent Clifford algebras come together with Finslerian teleparallelism to give rise to a Kaua—Klein structure endowed with a canonical connection. The implications of this convergence for unification are explored.     

Critical flocculation density of dilute water-in-CO2 emulsions stabilized with block copolymers

The critical flocculation density (CFD), that is, the CO(2) density below which flocculation occurs, was studied for dilute water-in-CO(2) (W/C) miniemulsions stabilized with poly(1,1-dihydroperfluorooctyl methacrylate)-b-poly(ethylene oxide) (PFOMA-b-PEO) surfactants. The CFD, which was measured by turbidimetry, decreased as the PFOMA molecular weight was increased, the average droplet size was decreased, the surfactant loading was increased, and the temperature was increased. A simple model, which addressed both the van der Waals attraction between droplets and osmotic solvent-tail interactions, was in good qualitative agreement with the experimentally observed trends for the CFD and predicted a decrease in emulsion stability as the CO(2) density was lowered toward the theta density for PFOMA in bulk CO(2).     

A novel azulene synthesis from the Ramirez ylide involving two different modes of its reaction with activated alkynes

The Ramirez ylide undergoes electrophilic substitution with acetylenedicarboxylates to form Z and E adducts. The latter can react by cycloaddition with another equivalent of the alkyne to provide a new route to novel tetra-substituted azulenes, which show interesting bond localisation and crystal packing effects.     

Enhanced photoluminescence from poly(phenylene vinylene):dendrimer polyelectrolyte assemblies in solution

Poly(2,5-methoxy-propyloxy sulfonate phenylene vinylene)(MPS-PPV) and DAB-Am-16, a generation 3.0 polypropylenimine hexadecamine dendrimer (DAB), are shown to form a tunable photoresponsive polyelectrolyte assembly in aqueous solution with an enhanced emission signal of up to 18-times that of MPS-PPV alone.     

Chalcogen-chalcogen bonds in edge-sharing square-planar d8 complexes. Are they possible?

A theoretical study of the formation of X-X bonds in complexes with the general formula [M(2)(mu-X)(2)L(4)] (M = group 10 and X = group 16 elements) having d(8) transition-metal atoms is presented. The existence of two energy minima for some complexes, with short and long X-X distances, is shown by density functional theory calculations, and the factors responsible for it are analyzed, including a strong influence of the nature of the metals and ligands on the relative stability of the two isomers. The influence of the bite angle of chelating terminal ligands and the nature of the donor atom on the relative stabilities of the two isomers are also discussed.     

An optimal Poincaré inequality in for convex domains

For convex domains with diameter we prove

for any with zero mean value on . We also show that the constant in this inequality is optimal.