Asymptotic Analysis - Volume 68, issue 4

Authors: Nazarov, S.A. | Sokolowski, J. | Specovius-Neugebauer, M.

Article Type: Research Article

Abstract: Polarization matrices (or tensors) are generalizations of mathematical objects like the harmonic capacity or the virtual mass tensor. They participate in many asymptotic formulae with broad applications to problems of structural mechanics. In the present paper polarization matrices for anisotropic heterogeneous elastic inclusions are investigated, the ambient anisotropic elastic space is allowed to be inhomogeneous near the inclusion as well. By variational arguments the existence of unique solutions to the corresponding transmission problems is proved. Using results about elliptic problems in domains with a compact complement, polarization matrices can be properly defined in terms of certain coefficients in the asymptotic …expansion at infinity of the solution to the homogeneous transmission problem. Representation formulae are derived from which properties like positivity or negativity can be read of directly. Further the behavior of the polarization matrix is investigated under small changes of the interface. Show more

Keywords: asymptotic analysis, polarization matrix, elastic moment tensors, anisotropic elasticity problems, transmission conditions

DOI: 10.3233/ASY-2010-0989

Citation: Asymptotic Analysis, vol. 68, no. 4, pp. 189-221, 2010

Authors: Liu, W. | Lototsky, S.V.

Article Type: Research Article

Abstract: A multichannel model is considered, with each channel represented by a linear second-order stochastic equation with two unknown coefficients. The channels are interpreted as the Fourier coefficients of the solution of a stochastic hyperbolic equation with possibly unbounded damping. The maximum likelihood estimator of the coefficients is constructed using the information from a finite number of channels. Necessary and sufficient conditions are determined for the consistency of the estimator as the number of channels increases, while the observation time and noise intensity remain fixed.

Keywords: cylindrical Brownian motion, second-order stochastic equations, stochastic hyperbolic equations

DOI: 10.3233/ASY-2010-0992

Citation: Asymptotic Analysis, vol. 68, no. 4, pp. 223-248, 2010

Article Type: Other

Citation: Asymptotic Analysis, vol. 68, no. 4, pp. 249-249, 2010