Common-azimuth migration (CAM) is a 3-D prestack depth migration technique based on the wave equation (Biondi and Palacharla, 1996). It exploits the intrinsic narrow-azimuth nature of marine data to reduce its dimensionality and thus manages to cut the computational cost of 3-D imaging significantly enough to compete with Kirchhoff methods. Based on a recursive extrapolation of the recorded wav...

Kirchhoff showed that the number of spanning trees a graph is spectral determinant combinatorial Laplacian divided by vertices; we reframe this result in quantum setting. We prove Laplace operator on finite connected metric with standard (Neumann–Kirchhoff) vertex conditions determines when lengths edges are sufficiently close together. To obtain result, analyze an equilateral whose spectrum cl...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

We present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle-domain commonimage gathers (ADCIGs) over the aperture-angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray-based tomography, we in...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a (unit) resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices in G. For a graph G, let R(G) be the graph obtained from G by adding a new vertex co...

‎Let $G$ be a graph without an isolated vertex‎, ‎the normalized Laplacian matrix $tilde{mathcal{L}}(G)$‎ ‎is defined as $tilde{mathcal{L}}(G)=mathcal{D}^{-frac{1}{2}}mathcal{L}(G)mathcal{D}^{-frac{1}{2}}$‎, where ‎$mathcal{D}$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎G‎$‎‎. ‎The eigenvalues of‎ $tilde{mathcal{L}}(G)$ are ‎called as ‎the ‎normalized Laplacian eigenva...

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

In this paper we study the asymptotic behavior of the ground state energy E(R) of the Schrödinger operator PR = −∆ + V1(x) + V2(x−R), x, R ∈ IR, where the potentials Vi are small perturbations of the Laplacian in IR, n ≥ 3. The methods presented here apply also in the investigation of the ground state energy E(g) of the operator Pg = P + V1(x) + V2(gx), x ∈ X, g ∈ G, where Pg is an elliptic ope...