The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...

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...

The k-th semi total point graph of a graph G, , ‎is a graph‎ obtained from G by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎In this paper‎, a formula for Laplacian polynomial of in terms of‎ characteristic and Laplacian polynomials of G is computed‎, ‎where is a connected regular graph‎.The Kirchhoff index of is also computed‎.

Let G 1 + G 2 , G 1 • G 2 and G 1 {G 2 } be the join, corona and cluster of graphs G 1 and G 2 , respectively. In this paper, Kirchhoff index formulae of these composite graphs are given.

Simulations of saturated-unsaturated groundwater flow in heterogeneous soil can be carried out by considering non-overlapping domain decomposition problems for the Richards equation in subdomains with homogeneous soil. By the application of different Kirchhoff transformations in the different subdomains local convex minimization problems can be obtained which are coupled via superposition opera...

Resistance distance was introduced by Klein and Randić. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all pairs of vertices. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by Cat(n; t) the set of connected cacti possessing n vertices and t cycles. In this paper, we give the first three smallest Kirchhoff indices among gra...

We describe a new imaging method that uses single-cycle pulses of terahertz (THz) radiation. This technique emulates data-collection and image-processing procedures developed for geophysical prospecting and is made possible by the availability of fiber-coupled THz receiver antennas. We use a simple migration procedure to solve the inverse problem; this permits us to reconstruct the location and...

We present results of the application of the wavelet transform method to seismic imaging. The objective of this research is to develop 3D seismic Kirchhoff imaging in the wavelet-transform domain, making use of the time-frequency property of wavelets. We propose to migrate the wavelets as units rather than single samples as in conventional Kirchhoff migration implementation. In practice, the wa...

Ž . We compare the ability of several practical ground-penetrating radar GPR array processing methods to improve Ž . signal-to-noise ratio SNR , increase depth of signal penetration, and suppress out-of-plane arrivals for data with SNR of Ž . Ž . roughly 1. The methods include two-dimensional 2-D monostatic, three-dimensional 3-D monostatic, and 3-D bistatic Kirchhoff migration. The migration a...