Fifty years of the Siberian Division of the Russian Academy of Sciences

This is a write-up on the foundation of the Sobolev Institute of Mathematics in 1957.     

On the Isoperimetric Type Problems with Current Hyperplanes

Analytical approach is presented to the isoperimetric type problems of finding convex figures separated by current hyperplanes.     

Synthesis of 3,6-dialkyl-4,5-dihydro-4,5-dichloro-2,1-benzisoxazoles from o-nitrophenylcyclopropanes

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 130–131, January, 1992.     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.     

Conversion of 2,1-benzisoxazolinium ions to anthranils by treatment with hydrohalic acids

2,1-Benzisoxazolinium ions, obtained from o-nitrophenylcyclopropanes, react with hydrobromic and hydrochloric acids to give halo-substituted benzo[c]isoxazoles.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1563–1568, November, 1990.     

Leibnizian,Robinsonian, and Boolean valued monads

This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities. Two approaches to combining nonstandard set-theoretic models are sketched and illustrated by order convergence, principal projection, and polyhedrality.