Fluctuations in an averaging scheme for parabolic boundary-value problems

The initial/boundary value problem for a parabolic equation in which the lower-order terms have random coefficients depending on a small parameter is studied. In doing this the joint distribution of the coefficients, normalized by dividing by , converges to a limit distribution. It is proved that under certain natural additional hypotheses the distribution of the difference between the solution of the equation being studied and that of the limit equation converges to a distribution that can be easily expressed in terms of the limit distribution of the coefficients.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 15–21, 1986.     

Solution of a Pólya-Szegö isoperimetric problem

There is given the solution of the problem of the maximum inner radius in the family of n-gons D_n, n3, of fixed area, and of some related extremal problems. The proof is carried out by the method of the modules of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 168, pp. 140–153, 1988.     

On the asymptotics of convolutions of complex measures in Banach spaces

We study the problem of the asymptotics of the integral of a functiong with respect to a normalized and centeredn-fold convolution of finite complex measures _n on a separable reflexive Banach spaceX. Conditions for existence are given under the assumption that the functiong(x) is the Fourier transform of a finite complex measure on the conjugate spaceY and the corresponding limit is calculated.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 34–37, 1987.     

Chemical structure of iodine-doped polyisoprene

A nonconjugated conducting polymer (1,4-rans-polyisoprene) at different iodine doping levels has been studied with the 27.7-keV Mössbauer resonance of¹²⁹I. At the light doping level, almost all iodines are covalently bonding to the carbon atoms, breaking the double bonds of the main chain. At the medium doping level, other iodine species are found, which are idendified as anion species, l^?, l ₃ ^? and l ₃ ^? .At the heavy doping level, polyiodide anions, l ₃ ^? and l ₅ ^? , increase as compared to the covalently bonding iodine atoms and addtionally molecular iodine l₂ exists.