Related papers: Estimates of complex eigenvalues and an inverse sp…
We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption "a" and the scattering coefficient "k" are to be recovered from the albedo operator. We show that "gauge equivalent" pairs…
We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we…
The Korteweg-deVries (KdV) equation with step boundary conditions is considered, with an emphasis on soliton dynamics. When one or more initial solitons are of sufficient size they can propagate through the step; in this case the phase…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…
Given a set of transmission eigenvalues, its density function inversely determines the form of the indicator function. This is one application of the Cartwright's theory in inverse problems. We use the indicator function inversely to…
We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a…
We show that the interior transmission eigenvalues are discrete by proving that the interior transmission operator has upper triangular compact resolvent, and that the spectrum of these operators share many of the properties of operators…
We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that…
We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form $ T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy$. Here we consider a kernel $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$ where $\psi$ is a bounded,…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreteness of the set of eigenvalues of the transmission problem and studied their locations. In this…
In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…
The purpose of this paper is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with…
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…