This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

We have determined refractive indices of rubrene crystals in the wavelength regions where their emissions were observed. For this purpose, we grew in a vapor phase the rubrene crystals having both horizontal and vertical pairs of parallel crystal facets. The facets functioned as optical resonators that produced interference fringes in the emission and reflectance spectra. From the fringes in the emission spectrum, we estimated the dispersion of the phase refractive index along the crystal a-axis. The anisotropic group refractive indices were evaluated along the b-and c-axes from the fringes in the reflectance spectra. The experimental indices were compared with those computed from the density functional theory.