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 ...

Estimating the relative importance of vertices and edges is a fundamental issue in the analysis of complex networks, and has found vast applications in various aspects, such as social networks, power grids, and biological networks. Most previous work focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for...

We consider a Dirichlet problem for system of equations involving Kirchhoff type $ p_i $-Laplacian differential operators and exhibiting gradient dependence in the reaction term (convection). Using subsolution-supersolution method, we establish existence weak solutions into suitable ordered intervals. Following unified approach, also provide comparison argument to obtain positive certain models.

In this work we consider a multi-dimensional higher-order Kirchhoff-type wave equation, with Dirichlet boundary conditions. We establish a blow-up result for certain solutions with positive initial energy. c © 2006 Elsevier Ltd. All rights reserved.

Abstract In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate applicability our main theoretical findings.

In this article, we study a class of Choquard–Kirchhoff type equations driven by the variable s(x,·)-order fractional p1(x,·) and p2(x,·)-Laplacian. Assuming some reasonable conditions with help variational methods, reach positive energy solution negative in an appropriate space functions. The main difficulties innovations are Choquard nonlinearities Kirchhoff functions presence double Laplace ...

Comparison theorems on resistance distances and Kirchhoff indices of the so-called S& T -isomer graphs are established. Then these results are applied to compare Kirchhoff indices of hexagonal chains, showing that the straight chain is the unique chain with maximum Kirchhoff index, whereas the minimum Kirchhoff index is achieved only when the hexagonal chain is an ‘‘all-kink’’ chain. © 2014 Els...

In this paper we study the existence, multiplicity, and regularity of positive weak solutions for following Kirchhoff–Choquard problem: M ∬ ℝ 2 N | u ( x ) − y + s d Δ = λ γ ∫ Ω μ , ∗ in 0 \ where is open bounded domain with C2 boundary, > 2s ∈ (0, 1). models Kirchhoff-type coefficient particular, degenerate case Kirchhoff zero at zero. (− Δ)s fractional Laplace operator, a real parameter, 1) c...