Homogenization of two-phase flow: high contrast of phase permeabilityHomogénéisation d'écoulement diphasique : grand contraste de perméabilité d'une phase

The steady-state two-phase flow non-linear equation is considered in the case when one of phases has low effective permeability in some periodic set, while on the complementary set it is high; the second phase has no contrast of permeabilities in different zones. A homogenization procedure gives the homogenized model with macroscopic effective permeability of the second phase depending on the gradient and on the second order derivatives of the macroscopic pressure of the first phase. This effect cannot be obtained by classical (one small parameter) homogenization. To cite this article: G.P. Panasenko, G. Virnovsky, C. R. Mecanique 331 (2003).     

An approximate solution to the integral radiative transfer equation in an optically thick slab

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ₀?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ₀. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd.     

1, 5-Rearrangement of enol acylates of aryl 1H.-1, 2, 4-triazol-1-ylmethyl ketones

The rearrangement of enol acylates of aryl 1H-1, 2, 4-triazol-1-ylmethyl ketones at 140–150°C in acetic anhydride is studied. The migration of the acyl group to the C(5) atom of the heterocycle is found to be intramolecular. The characteristics of the original and final products are presented. X-ray structural studies of the enol acetates of 2, 4-dichlorophenyl 1H-1, 2, 4-triazol-1-ylmethyl ketone and 2, 4-dichlorophenyl 5-acetyl-1H-1, 2, 4-triazol-1-ylmethyl ketone are carried out.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 560–564, March, 1993.     

1H and13C NMR spectra and structure of 2,3,4-trisubstituted sulfolanes

Conclusions The¹H and¹³C NMR spectra were studied for 2,3,4-trisubstituted sulfolanes and the isomerism of these compounds was determined, The use of chemical shift information is more convenient to determine the isomerism of polysubstituted cyclic compounds by PMR spectroscopy, while use of the direct carbon-proton coupling constants is more convenient for this problem when employing¹³C NMR spectroscopy.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2498–2501, November 1984.     

13C NMR spectra of polycyclic compounds: Stereochemistry of trimers of bicyclo[2.2.1]heptadiene

¹³C NMR spectra have been obtained for six isomers of bicyclo[2.2.1]heptadiene (norbornadiene) trimers, and a complete stereochemical assignment of these isomers has been made by means of a computer-assisted calculation of chemical shifts.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 1973–1978, September, 1990.     

13C NMR Spectra of polycyclic compounds: spiro(bicyclo[2.2.1]heptane-7,1′-cyclopropane) derivatives

The¹³C NMR spectra of 15 spirocyclopropane derivatives in the (C⁷)-norbornane series have been investigated, signal assignments made, and the stereochemistry of isomeric products has been determined. It was found that the methylene group signals in the cyclopropane fragment may be used as criteria in making the stereochemical assignments.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 555–559, March, 1990.     

13C NMR Spectra of polycyclic compounds: stereochemistry of spiro(bicyclo[2.2.1]hepta-2,5-diene-7,1′-cyclopropane) dimers

The structures of the dimerization products of spiro(bicyclo[2.2.1]hepta-2,5-diene-7,1-cyclopropane) have been solved using¹³C NMR spectroscopy and their stereochemical assignments made. The methylene carbon atom signals for the spirocyclopropane fragment can be used as diagnostic signals in making the stereochemical assignments.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 559–564, March, 1990.     

13C NMR spectra of some 1,2-disubstitutedN-vinyl-1H-1,2,4-triazoles

¹³C NMR spectra (20 and 75 MHz, in DMSO-d₆) of a series of 1,3-diaryl-3-(1H-1,2,4-triazol-1-yl)- and 1,3-diaryl-2-(1H-1,2,4-triazol-1-yl)prop-2-en-1-ones were registered. It was shown that the chemical shifts of both the carbon atom of the alkene group and C(3) reflect regio- and stereoisomerism of these compounds. Taking this into account the isomeric structures of several 1,3-diaryl-3-(1H-1,2,4-triazol-1-yl)prop-2-en-1-ones were identified and the configurations relative to the double bond of a number of 1,3-diaryl-2-(1H-1,2,4-triazol-1-yl)prop-2-en-1-ones were determined.