Let G be a connected graph with vertex set V.G/. The degree Kirchhoff index of G is defined as S .G/D P fu;vg V.G/ d.u/d.v/R.u;v/, where d.u/ is the degree of vertex u, and R.u;v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result fo...

and many authors have studied the existence and uniqueness of global solution, the blowup of the solution (see [–] and the references therein). WhenM is not a constant function, equation (.)without the damping and source terms is often called a Kirchhoff-type wave equation; it has first been introduced by Kirchhoff [] in order to describe the nonlinear vibrations of an elastic string. When...

in this paper‎, ‎we consider the following kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{r}^{3}}|nabla u|^{2}right)delta u+v(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$uin h^{1}(mathbb{r}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎the aim of this paper is to study the existence of positive ...

Wave-equation migration is an accurate and robust alternative to Kirchhoff migration when multipathing and other complex wave phenomena occur, such as in subsalt exploration. In these situations, images obtained by wave-equation migration are often superior to images obtained by Kirchhoff methods. However, 3-D wave-equation prestack imaging is an immature technology compared with Kirchhoff imag...

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q n by utilizing spectral graph theory. More...

The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution ...

Firstand second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the secondorder reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized el...

coustructing masonry building has been done in a large scale in our country. a ccording to the recorded statistics. it comprises the majority of building in our country. the loss of life and property as the result previous earthquakes reveals that masonry building have not functioned properly. meanwhile, their complex behaviors resulted from the heterogenons, nonlinear, and plate behavior of it...

‎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.