The Kirchhoff integral is a fundamental in scattering theory, appearing both the approximation and small slope approximation. In this work, functional Taylor series to presented, under condition that roughness covariance function follows either an exponential or Gaussian form—in one-dimensional two-dimensional cases. Previous approximations [Gragg, Wurmser, Gauss (2001) J. Acoust. Soc. Am. 110(...

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

I propose a method for antialiasing Kirchhoff operators, which switches between interpolation in time and interpolation in space depending on the operator dips. The method is a generalization of Hale’s technique for dip moveout antialiasing. It is applicable to a wide variety of integral operators and compares favorably with the popular temporal filtering technique. Simple synthetic examples de...

In this paper, we determine the Randić energy of m-splitting graph, m-shadow graph and m-duplicate a given m being an arbitrary integer. Our results allow construction infinite sequence graphs having same energy. Further, some invariants like degree Kirchhoff index, Kemeny’s constant number spanning trees special graphs. From our results, indicate how to obtain infinitely many pairs equienerget...

A m,n -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell D n, a, b consists of the path Pn−a−b together with a independent vertices adjacent to one pendent vertex of Pn−a−b and b independent vertices adjacent to the other pendent vertex of Pn−a−b. In this paper, firstly, we show that, among m,n bipartite gra...

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

Real-time sound rendering engines often render occlusion and early sound reflection effects using geometrical techniques such as ray or beam tracing. They can only achieve interactive rendering for environments of low local complexity resulting in crude effects which can degrade the sense of immersion. However, surface detail or complex dynamic geometry has a strong influence on sound propagati...

We consider integral equation formulations of contact problems of Kirchhoff (thin) plates, discontinuously supported along arcs or segments. In the classical PDE formulation (biharmonic equation), the plate deflection is assumed as the primary unknown. The boundary conditions along the supported edge are imposed in terms of the plate deflection and its derivatives, and the reaction forces and c...