A light ray in space is characterized by two vectors: (i) a transverse spatial vector associated with the point where intersects given spherical cap; (ii) an angular-frequency which defines direction of propagation. Given propagating from emitter to receiver, linear equation established that links its representative vectors on and receiver. The link expressed means matrix not homogeneous, since...

We review the classical Principle of the Least Action in a general context where the Hamilton function H is possibly non convex. We show how van Groesen [6] principle follow as particular cases where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application. 2000 Mathematics Subject Classification. 70H03, 70H05, 70H30, 37J05.

In this paper, we study diagonal dominance of the stiffness matrix resulted from piecewise linear finite element discretisation integral fractional Laplacian under global homogeneous Dirichlet boundary condition in one spatial dimension. We first derive exact form frequency space which is extendable to multi-dimensional rectangular elements. Then give complete answer when can be strictly diagon...

Linear hyperbolic partial differential equations in a homogeneous medium, e.g., the wave equation describing the propagation and scattering of acoustic waves, can be rewritten as a time-domain boundary integral equation. We propose an efficient implementation of a numerical discretization of such equations when the strong Huygens’ principle does not hold. For the numerical discretization, we ma...

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...