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.     

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.     

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.     

On some contact problems for composite half-spaces PMM vol. 31, no. 6, 1967, pp. 1001–1008

Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.

1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.

2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.

In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.

Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.

The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].

The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials.