On Green's Matrices of Trees

Wave propagation theory in offshore applications

A frequency-wavenumber-domain formulation is presented in this paper for calculation of the Green's functions and wave propagation modes in a stratified fluid body underlain by a layered viscoelastic soil medium. The Green's functions define the solid and fluid displacements and fluid pressures due to uniform disk loads acting in either the soil or fluid media. The solution is in the frequency ...

NUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

Green's Functions for Preconditioning

In this paper we look at the connection between Green's functions and preconditioners for systems of equations arising through the discretization of linear partial diierential equations. We nd that Green's functions, as generalized inverses of diierential operators, can sometimes ooer a useful insight into the properties of the discrete inverse operator. More precisely, their properties (singul...

Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green's functions

Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices.

Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known to be highly relevant in topics ranging from ferroelectrics to quotation networks. Combining these two points leads us to examine finite size random matrices. To obtain basic materi...