On mixed Abelian groups with periodic groups of automorphisms

In the paper, sufficient conditions for the splittability of mixed Abelian groups with periodic automorphism groups are established. Classes of mixed splittable Abelian groups with perfect holomorphs are distinguished. Translated fromMaternaticheskie Zametki, Vol. 61, No. 4, pp. 483–493, April, 1997. Translated by A. I. Shtern     

Acid hydrolysis of 2-alkoxyperfluoropropenes

Conclusions A new method for the synthesis of perfluoro-2-propenol from perfluoroisobutylene oxide was developed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1672–1673, July, 1978.     

Prediction of solvent activities using the UNIFAC-FV model

A UNIFAC group contribution method with an explicit temperature dependent free volume term has been developed. The systems used in the development were benzene-polyethylene oxide from 319 to 423 K and n-hexane—n-hexadecane from 303 to 333K. The addition of temperature dependence to the proportionality factor in the free volume expression decreased the average error in prediction of the solvent activities from 15% to 6%.     

A Suzuki coupling based route to 2,2'-bis(2-indenyl)biphenyl derivatives.

Because of the promising performance in olefin polymerization of 2,2'-bis(2-indenyldiyl)biphenyl zirconium dichloride, we developed a new and broadly applicable route to 2,2'-bis(2-indenyl)biphenyl derivatives. Reaction of the known 2,2'-diiodobiphenyl (26) with the new 2-indenyl boronic acid (23) did not result in the desired 2,2'-bis(2-indenyl)biphenyl (10); instead an isomer thereof, (spiro-1,1-(2,2'-biphenyl)-2-(2-indenyl)indane) (27), was obtained. It was found that compound 10 could be made via a palladium-catalyzed reaction of 2,2-biphenyldiboronic acid (31) with 2-bromoindene (21) under standard Suzuki reaction conditions. However, the yield of this reaction was low at low palladium catalyst loadings, due to a competitive hydrolysis reaction of 2,2-biphenyldiboronic acid (31). HTE techniques were used to find an economically viable protocol. Thus, use of the commercially available 1.0 molar solution of (n-Bu)(4)NOH in methanol with cosolvent toluene led to precipitation of the pure product in a fast and clean reaction, using only 0.7 mol % (0.35 mol % per C-C) of the expensive palladium catalyst.     

Distinguished isogenies for formal groups in local fields with small ramification

The existence of distinguished isogenies is proved for formal groups defined over the ring of integers of a local field with ramification index less than the characteristic of the residue field. This generalizes the result of Demchenko for Honda formal groups. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 93–100.     

Nonlinear transmission of a single-mode optical fiber with a sharp change of core diameter

Nonlinear transmission of a cylindrically symmetric weakly guiding single-mode optical fiber with a sharp change of core diameter is estimated in the approximation of weak nonlinearity of the fiber material and is calculated by direct numerical simulation of light propagation. It is shown that an increase or a decrease of nonlinear transmission in comparison with the linear value depends on the way in which the width of the radial mode distribution changes with changing diameter of the structure. Domains of fiber diameters corresponding to an increase of nonlinear transmission in comparison with the linear value are determined.