The dual Brunn-Minkowski theory for bounded Borel sets: Dual affine quermassintegrals and inequalities

This paper develops a significant extension of E. Lutwak's dual Brunn-Minkowski theory, originally applicable only to star-shaped sets, to the class of bounded Borel sets. The focus is on expressions and inequalities involving chord-power integrals, random simplex integrals, and dual affine quermassintegrals. New inequalities obtained include those of isoperimetric and Brunn-Minkowski type. A new generalization of the well-known Busemann intersection inequality is also proved. Particular attention is given to precise equality conditions, which require results stating that a bounded Borel set, almost all of whose sections of a fixed dimension are essentially convex, is itself essentially convex.     

Some new methods for preparing 2,3- and 3,4-diaminopyridines

New methods of preparing 2,3-diaminopyridine ( 13 ) from 2-chloro-3-nitropyridine ( 11 ) and 3,4-diaminopy-ridine ( 8 ) from 4-ethoxy-3-nitropyridine hydrochloride ( 5 ) have been explored and evaluated.     

N-labelling studies of the reaction of 2,6-di-t-butyl-4-methyl-4-nitrocyclohexa-2,5-dienone with nitrogen dioxide; A revised mechanism

Reaction of the ¹⁵N-4-nitrodienone (1) with excess nitrogen dioxide in benzene for 16 h gives the 4,5,6-trinitro ketone (2), labelled (¹⁵NO₂) at C6 but not at C4, and recovered 4-nitrodienone (1) in which extensive loss of ¹⁵NO₂ has occurred. The mechanistic implications of these and related results are discussed.     

Stereoselective synthesis of unnatural α-amino acid derivatives through photoredox catalysis

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids. The developed protocol allows the use of ubiquitous carboxylic acids as radical precursors without prior derivatization. The protocol utilizes near-stoichiometric amounts of the imine and the acid radical precursor in combination with a catalytic amount of an organic acridinium-based photocatalyst. Alternative mechanisms for the developed transformation are discussed and corroborated by experimental and computational studies.

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids.     

Multiple nitrene insertions into metal-sulfur bonds of dithiocarbamate complexes: synthesis of sulfido-amido and zwitterionic tetraamido complexes

The iodine(III) reagent, PhI[double bond, length as m-dash]NTs, acts as a source of the nitrene fragment NTs, which undergoes facile insertion into the metal-sulfur bonds of a range of dithiocarbamate complexes. Addition of two equivalents of PhI=NTs to [M(S(2)CNR2)2] affords sulfido-amido complexes [M{SC(NR2)SNTs}2](M=Ni, Cu), which insert two further nitrene fragments to afford zwitterionic tetraamido complexes [M{TsNSC(NR2)SNTs}2](M=Co, Ni, Cu). Crystallographic studies have been carried out on both types of complex allowing possible resonance hydrids of the new ligand types to be assessed.     

High-performance liquid chromatographic analysis of free long chain fatty acids produced during lipolysis by anaerobic digestor sludge

The development of sample extraction techniques in conjunction with application of a modified version of an established HPLC technique allowed the rapid estimation of concentrations of long chain fatty acids (LCFA) produced by the lipolytic activity of bacteria in anaerobic digestor sludges or experiments using the sludges as inocula. It was established that free long chain fatty acids will preferentially partition into certain phases in the sludge or experimental cultures. These data, and application of the developed techniques for monitoring of LCFA, may lead to the avoidance of toxicity and failure of full-scale anaerobic digestors treating high lipid content waste in the future.