On the formation of sharp transition layers in two-dimensional reaction-diffusion models

For a singularly perturbed parabolic equation in two dimensions, the formation of a solution with a sharp transition layer from a sufficiently general initial function is considered. An asymptotic analysis is used to estimate the time required for the formation of a contrast structure. Numerical results are presented.     

Gas phase kinetic and theoretical studies of reactions of germylenes and dimethylstannylene

The results of time resolved gas phase studies of labile germylenes (GeH₂ and GeMe₂) and dimethylstannylene (SnMe₂) reactions reported to date are considered together with data of quantum-chemical investigations of the potential energy surfaces of these systems. Reaction mechanisms are discussed. A comparison of reactivity in the series of carbene analogs, ER₂ (E = Si, Ge, Sn, R = H, Me), is made.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 477–505, March, 2005.     

Synthesis of polycyclic cyclopropanecarboxylic acids and their esters based on catalytic cyclopropanation of 6,6-dimethylfulvene

Reactions of 6,6-dimethylfulvene with methyl diazoacetate in the presence of Cu compounds is accompanied by methoxycarbonylmethylenation of the endocyclic double bonds to give the corresponding mono- and diadducts in total yields of up to 85% with marked predominance ofanti-isomers. The subsequent cyclopropanation of monoadducts with diazomethane in the presence of Pd compounds also involves the endocyclic double bond and gives esters of tricyclo[4.1.0.0.^2,4]heptanecarboxylic acid in high yields. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 528–531, March, 1997.     

Spectral structure of polarization radiation from relativistic electrons in aluminum

Collective effects in polarization bremsstrahlung generated by relativistic electrons in a polycrystalline aluminum foil are studied experimentally on the basis of the 2.4-MeV electron accelerator installed at the Institute of Nuclear Physics (Moscow State University, Moscow). A peak structure found in this polarization bremsstrahlung for the first time is in agreement with theoretical predictions. __________ Translated from Yadernaya Fizika, Vol. 63, No. 11, 2000, pp. 2097–2100. __________ Translated from Yadernaya Fizika, Vol. 63, No. 11, 2000, pp. 2097–2100.     

On immediate-delayed exchange of stabilities and periodic forced canards

Singularly perturbed nonautonomous ordinary differential equations are studied for which the associated equations have equilibrium states consisting of at least two intersecting curves, which leads to exchange of stabilities of these equilibria. The asymptotic method of differential equations is used to derive conditions under which initial value problems have solutions characterized by immediate and delayed exchange of stabilities. These results are then used to prove the existence of periodic canard solutions. Published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 1, pp. 46–61. The text was submitted by the authors in English.