the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.

In order to estimate elastic parameters of the subsurface, geophysicists need reliable information about angle-dependent reflectivity. In this paper, we describe how to image nonzero offsets during shot-profile migration so that they can be mapped to the angle domain with Sava and Fomel’s (2000) transformation. CIGs also contain information about how well focused events are at depth, and so pro...

Current algorithms for imaging seismic reflection data can be subdivided into two classes: Kirchhoff (generalized Radon transform) and wave-equation (double-square-root and reverse-time) migration. Kirchhoff type methods rely on asymptotic and ray-geometrical considerations. Wave-equation imaging algorithms (one-way or twoway) appear to be more robust in the case of complicated velocity models ...

We analyze the resolution and statistical fluctuations of images when the ambient medium is random and scattering can be modeled primarily by wavefront distortion. We compare the coherent interferometric imaging method to the widely used Kirchhoff migration and show how the latter loses statistical stability at an exponential rate with the distance of propagation. In Kirchhoff migration we form...

Stacking operators are widely used in seismic imaging and seismic data processing. Examples include Kirchhoff datuming, migration, offset continuation, DMO, and velocity transform. Two primary approaches exist for inverting such operators. The first approach is iterative least-squares optimization, which involves the construction of the adjoint operator. The second approach is asymptotic invers...

A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,

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...

We prove the existence of critical points vortex type Hamiltonians \[ H(p_1,\ldots, p_N) = \sum_{{i,j=1}\atop{i\ne j}} ^N \Gamma_i\Gamma_jG(p_i,p_j)+\Psi(p_1,\dots,p_N) \] on a closed Riemannian surface $(\Sigma,g)$ which is not homeomorphic to sphere or projective plane. Here $G$ denotes Green function Laplace-Beltrami operator in $\Sigma$, $\Psi\colon \Sigma^N\to\mathbb{R}$ may be any class $...