It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ωh is localized either at the whole lateral surface Γh of the domain, or at a point of Γh, while the eigenfunction decays exponentially inside Ωh. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and N...

In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if uln is an eigenfunction associated with the nth variational eigenvalue, ln, then uln has at most 2n−2 nodal domains. Also, if uln has n+k nodal domains, then there is another eigenfunction with at most n−k nodal domains. © 2002 Elsev...

A novel method for estimating the shear wave speed from crawling waves based on the amplitude modulation-frequency modulation model is proposed. Our method consists of a two-step approach for estimating the stiffness parameter at the central region of the material of interest. First, narrowband signals are isolated in the time dimension to recover the locally strongest component and to reject d...

We construct the Hadamard Green’s function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the Sn−1 of a n-dimensional closed, static universe. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. Solving of eigenfunction and eigenvalues of the corresponding field equation is inte...

The mode-matching applications to scattering from circular and annular apertures in a thick perfectly conducting plane are reviewed. The Hankel and Weber transforms are utilized to solve the boundary-value problems of circular and annular apertures. Simple electrostatic problems are presented to illustrate the mode-matching method in terms of the Hankel and Weber transforms. Various types of We...

The dyadic Green's function for cylindrical waveguides of circular or rectangular cross section with a moving, isotropic, homogeneous medium is developed using the method of eigenfunction expansion. The orthogonality properties of the vector mode functions are discussed. In contrast to waveguides with a stationary medium, it is seen that the normalization factor in the case of the E mode introd...