Homogenization of some variational inequalities with restrictions on subsets <Emphasis Type="Italic">ɛ</Emphasis>-periodically located along the domain boundary

In this paper some problems concerning homogenization of variational inequalities for the Laplace operator and the biharmonic operator with restrictions on subsets ?-periodically located along the domain boundary are studied (? is a small parameter). These subsets are collections of balls of radius a _? a. An asymptotics of solutions is obtained in the so-called critical case characterized by a specific relation between the period ? and the value a _?. Strong convergence of solutions and their gradients is also established.     

Investigation of cooperative kinetics on reactions of functional groups on polymer chains

The kinetics of aminolysis of 1,2;3,4-meso-erythritol dicarbonate and 1,2;3,4;5,6-mannitol, sorbitol, and dulcitol tricarbonates by n-butylamine in dimethylformamide solution was investigated. The dicarbonate and tricarbonates are considered respectively as models of dyads and triads in the poly(vinylene carbonate) chain. The theoretical kinetic curves for the dimer and the trimers were calculated by solution of kinetic equations and close agreement with experiment was obtained. A version of the Monte-Carlo method was developed to provide a model for the reaction process by a computer calculation including the neighboring group effect in enhancing reactivity. The theoretical curve for a trimer coincides with the experimental one. These results confirm the accelerating influence of the unreacted neighboring groups. For the polymeric chain the experimental and calculated curves deviate for conversions beyond 10%. This indicates an additional polymer effect, which is as yet unexplained.     

Diffusion of topological solitons and dielectric αc relaxation in a polymeric crystal

A molecular dynamics simulation was performed to estimate the effective mass and the diffusion and friction coefficients of point defects in macromolecular chains of crystalline polyethylene. The results were compared with theoretical mass and kinetic coefficient predictions for topological solitons, with which these defects were identified. The results are used to discuss the soliton model of dielectric α_c relaxation in weakly oxidized polyethylene.     

Charge control in the formation of complexes of phenol with unsaturated compounds containing organometallic substituents from group IV

The resonance donor effect of the , conjugation of R₃M and R₃MCH₂ (M = Si, Ge, Sn; R is an alklyl group) substituents with the triple bond in compounds R₃MC=CX and R₃MCH₂CCX (X = H, R) changes on passing from isolated molecules to their H-complexes. A partial ⁺ charge on the triple bond enhances , conjugation; a partial ^– charge on the triple bond has practically no effect on the resonance properties of R₃M substituents, whereas the , conjugation of R₃MCH₂ substituents diminishes owing to the effect of negative direct resonance interaction. The effect of , conjugation on the effective negative charges of the carbon atoms in the -CC- fragments was estimated quantitatively.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1041–1046, June, 1994.This work was supported by the Russian Fundation for Basic Research (Grant 93-03-18372).