Method of Moments (MOM) combining with the Kirchhoff Approximation(KA) for analysis of the problem of optical wave scattering by a stack of two one-dimensional Gaussian rough interfaces is solved. The scattered field from the upper interface is solved by MOM and the transmitted field from the lower one is expressed from the Kirchhoff approximation where the multiple scattering phenomenon is neg...

the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.

The three-dimensional digital waveguide mesh is a method for modeling the propagation of sound waves in space. It provides a simulation of the state of the whole soundfield at discrete timesteps. The updating functions of the mesh can be formulated either using physical values of sound pressure or particle velocity, also called the Kirchhoff values, or using a wave decomposition of these instea...

a class of kirchhoff type systems with nonlinear boundary conditions considered in this paper. by using the method of nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

We study spanning diverging forests of a digraph and related matrices. It is shown that the normalized matrix of out forests of a digraph coincides with the transition matrix in a specific observation model for Markov chains related to the digraph. Expressions are given for the Moore-Penrose generalized inverse and the group inverse of the Kirchhoff matrix. These expressions involve the matrix ...

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of ...

Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry dense spatial arrangements. As a result, these hold great potential for applications in materials science, catalytic chemistry, other related fields. The Kirchhoff index graph G is defined as the sum resistive distances between any two vertices G. This article f...

A frequently used broadband array imaging method is Kirchhoff or travel time migration. In smooth and known media Kirchhoff migration works quite well, with range resolution proportional to the reciprocal of the bandwidth and cross range resolution that is proportional to the reciprocal of the array size. In a randomly inhomogeneous medium, Kirchhoff migration is unreliable because the images d...

This paper describes several new methods to predict and analyze rotorcraft noise. These methods are: 1) a combined computational fluid dynamics and Kirchhoff scheme for far-field noise predictions, 2) parallel computer implementation of the Kirchhoff integrations, 3) audio and visual rendering of the computed acoustic predictions over large far-field regions, and 4) acoustic tracebacks to the K...

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the...