We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using...

─ This paper presents an investigation into the electromagnetic scattering characteristic of two-dimensional (2-D) layered rough surfaces by using a finite-difference time-domain (FDTD) algorithm, which constitutes a three-dimensional scattering problem. The uniaxial perfectly matched layer medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used f...

The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call “contraction”, “deletion”, and “contraction-deletion...

The diffraction of electromagnetic and light waves by an aperture in a plane conducting screen is a classical boundary value problem. As is well known, theoretical analysis aims at a solution of the vector Maxwell equations, which incorporates a prescribed form of excitation and satisfies appropriate boundary conditions on the screen and in the aperture. A small measure of progress towards this...

Abstract This article deals with the degenerate fractional Kirchhoff wave equation structural damping or strong damping. The well-posedness and existence of global attractor in natural energy space by virtue Faedo-Galerkin method estimates are proved. It is worth mentioning that results this cover case possible degeneration (or even negativity) stiffness coefficient. Moreover, under further sui...

There has been an upsurge of research on complex networks in recent years. The purpose this paper is to study the mathematical properties random pentagonal chain PE C n with help graph theory. Based id="M2"> , we first obtain expected value expressions Gutman in...

The topology and dynamics of a complex network shape its functionality. However, the topologies of many large-scale networks are either unavailable or incomplete. Without the explicit knowledge of network topology, we show how the data generated from the network dynamics can be utilised to infer the tempo centrality, which is proposed to quantify the influence of nodes in a consensus network. W...

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 ...