Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

An Alternative Procedure for the Aluminum-Mediated Conversion of Esters to Amides

A convenient method has been developed for directly converting esters to amides using reagents derived from the reaction of trimethylaluminum with ammonium chloride, methylamine hydrochloride or dimethylamine hydrochloride.     

Energy Scaling Laws for Conically Constrained Thin Elastic Sheets

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h|logh|, where h?1 is the thickness of the sheet, we establish matching upper and lower bounds of order h ²|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.     

A New Insight into the Stereoelectronic Control of the Pd0-Catalyzed Allylic Substitution: Application for the Synthesis of Multisubstituted Pyran-2-ones via an Unusual 1,3-Transposition

Pyran-2-ones 3 undergo a novel Pd⁰-catalyzed 1,3-rearrangement to afford isomers 6 . The reaction proceeds via an η²-Pd complex, the pyramidalization of which (confirmed by quantum chemistry calculations) offers a favorable antiperiplanar alignment of the Pd−C and allylic C−O bonds ( C ), thus allowing the formation of an η³-Pd intermediate. Subsequent rotation and rate-limiting recombination with the carboxylate arm then gives isomeric pyran-2-ones 6 . The calculated free energies reproduce the observed kinetics semi-quantitatively.     

Some stable homology calculations and Occam's razor for Hodge structures

Motivated by motivic zeta function calculations, Vakil and Wood in [10] made several conjectures regarding the topology of subspaces of symmetric products. The purpose of this note is to prove two of these conjectures and disprove a strengthening of one of them.