We consider a boundary-value problem for the nonlinear integrodifferential equation $$ {u}^{\prime \prime }-m\left(\underset{0}{\overset{l}{\int }}{u}^{\prime 2} dx\right){u}^{{\prime\prime} }=f\left(x,u,{u}^{\prime}\right),\kern1em m(z)\ge \upalpha >0,\kern1em 0\le z<\infty, simulating static state of Kirchhoff beam. The is reduced to integral equation, which solved by using Picard iterative m...

Over the past two decades meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of solution field continuity, and capability to handle moving boundary and changing geometry. In this work, a meshless integral method based on the regularized boundary integral equation has been developed and applied to two-dimensional linear elasticity and elastoplas...

By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas an...

In this paper we propose a statistical integral equation model (SIEM) for shadow-corrected EM scattering from a rough surface. It treats the local coordinates and Fresnel reflection coefficients statistically over the orientation distribution of surface unit norm as characterized by the joint probability density function of its two directional slopes. In addition, it incorporates rigorously the...

Seismic imaging based on single-scattering approximation is based on analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods...

Least squares migration (LSM) is applied to 3-D synthetic data in order to test the feasibility of removing the ”recording footprint” noise from migrated sections. The LSM algorithm is implemented with a conjugate gradient algorithm. Results for simple point scatterer and meandering stream channel models suggest that LSM can significantly attenuate the recording footprint noise. For comparison,...

the reader to [1], [16], [17], [21], and their bibliographies, to get a taste of the variety of approaches used to study this descriptor. In [28], Zhou et al. studied the extremal graphs with given matching number, connectivity and the minimal Kirchhoff index. Also in [23], [25] and [26] the authors determined independently the extremality on the unicyclic graphs with respect to the Kirchhoff i...

We study solution methods for boundary value problems associated with the static Kirchhoff rod equations. Using the well known Kirchhoff kinetic analogy between the equations describing the spinning top in a gravity field and spatial rods, the static Kirchhoff rod equations can be fully integrated. We first give an explicit form of a general solution of the static Kirchhoff equations in paramet...

In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff index. During the past decade these parameters have been applied in organic chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules that have ...

In this article we state a relation between the Kirchhoff and Wiener indices of a simple connected graph G and the Kirchhoff and Wiener indices of those subgraphs of G which are induced by its blocks. Then as an application, we define a composition of a rooted tree T and a graph G and calculate its Kirchhoff index in terms of parameters of T and G. Finally, we present an algorithm for computing...