Tomography in the post-migrated domain is quickly becoming the standard approach for obtaining velocities in complex areas. The standard flow to update the velocity through tomography in the post-migrated domain begins by migrating the data using some initial velocity model. This migration method can be Kirchhoff (Etgen, 1990), downward continuation methods (Clapp, 2001b; Mosher et al., 2001), ...

Abstract: We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented b...

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is...

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions. For graphs with...

We have recently introduced a modification of the multiple signal classification method for synthetic aperture radar. This incorporates user-defined parameter, ϵ, that allows tunable quantitative high-resolution imaging. However, this requires relatively large single-to-noise ratios (SNR) to work effectively. Here, we first identify fundamental mechanism in produces images. Then introduce Kirch...

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 ...

In recent years, various Kirchhoff type problems have been extensively investigated by many authors due to their theoretical and practical importance, such problems are often referred to as being nonlocal because of the presence of the integral over the entire domain Ω. It is well known that this problem is analogous to the stationary problem of a model introduced by Kirchhoff [1]. More precise...