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.     

The preparation of 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides by the condensation/cyclization of trilithiated acetoacetanilides with lithiated methyl salicylates

Several acetoacetanilides were trilithiated in excess lithium diisopropylamide, and the resulting polylithiated intermediates were regioselectively condensed with lithiated methyl salicylates followed by acid cyclization to substituted 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides (benzopyranone-2-acetamides).     

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.     

Synthesis and Characterization of a New Quasi-One-Dimensional Copper(II) Phosphate, Ba(2)Cu(PO(4))(2)

Crystals of Ba(2)Cu(PO(4))(2) have been grown in a low-temperature eutectic flux of 32% KCl and 68% CuCl (mp = 140 degrees C). The X-ray single-crystal structure analysis shows that this barium copper(II) phosphate crystallizes in a monoclinic lattice with a = 12.160(4) ?, b = 5.133(4) ?, c = 6.885(4) ?, beta = 105.42(4) degrees, and V = 414.3(4) ?(3); C2/m (No. 12); Z = 2. The structure has been refined by the least-squares method to a final solution with R = 0.020, R(w) = 0.026, and GOF = 1.05. The framework of the title compound consists of [Cu(PO(4))(2)](infinity) linear chains with Ba(2+) cations residing between these parallel chains. The chains are composed of an array of Cu(2+) cations that are doubly bridged by PO(4) anions. Each pair of bridging PO(4) tetrahedra are in a staggered configuration above and below the CuO(4) square plane, resulting in a linear chain with a long Cu---Cu separation distance, 5.13 ? ( identical withb). This quasi-one-dimensional framework is unusual among the Cu(2+)-based phosphates. Magnetic susceptibility data shows Curie-Weiss paramagnetic behavior in the range of ca. 190-300 K and a possible antiferro-to-ferromagnetic transition at approximately 8 K. In this paper, the synthesis, structure, and properties of the title compound are presented. A structural comparison to a closely related vanadyl (VO)(2+) phosphate, Ba(2)(VO)(PO(4))(2).H(2)O, as well as Na(2)CuP(2)O(7) will be discussed.     

Comparative properties of siloxane vs phosphonate monolayers on a key titanium alloy

A direct comparison of surface loading, interface shear strength, and interface hydrolytic stability was made between a phosphonate and two siloxane monolayers formed on the native oxide surface of Ti-6Al-4V. Surface loading for the phosphonate was ca. four times greater (on a nanomole/area basis) than for the siloxanes; mechanical strengths per surface-bound molecule were comparable, but the hydrolytic stability (pH 7.5) of the siloxanes was poor. These results suggest that phosphonate monolayer interfaces are more desirable than comparable siloxane ones for applications where such interfaces contact even slightly alkaline water.     

The use of magnesium perchlorate as desiccant in the syringe injection technique for determination of mercury by cold-vapour atomic absorption spectrometry

The method developed earlier was found to suffer a loss in sensitivity when the magnesium perchlorate desiccant became damp. The most sensitive and consistent results were obtained when the magnesium perchlorate was removed from the sample injection manifold. Under most circumstances a desiccant is not required.