相关论文: Sharp Weyl Law for Signed Counting Function of Pos…

The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…

It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit…

We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…

We consider the interior transmission problem associated with the scattering by an inhomogeneous (possibly anisotropic) highly oscillating periodic media. We show that, under appropriate assumptions, the solution of the interior…

The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…

The spectrum of interior transmission problem is the zero set of certain entire functional determinant. It is classic that we deploy the series of exponential polynomials to approximate the distribution of the roots of the entire functions…

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We…

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…

Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…

In this paper we prove some results on interior transmission eigenvalues. First, under rea- sonable assumptions, we prove that the spectrum is a discrete countable set and the generalized eigenfunctions spanned a dense space in the range of…

This article is concerned with the time-harmonic electromagnetic (EM) scattering from a generic inhomogeneous medium. It is shown that if there is a right corner on the support of the medium, then it scatters every pair of incident EM…

This paper uses Euclidean Information Theory (EIT) to analyze the wiretap channel. We investigate a scenario of efficiently transmitting a small amount of information subject to compression rate and secrecy constraints. We transform the…

One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider…

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple…

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…

The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the transmission eigenvalue problem for…

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…

We investigate transport in type-I/type-II Weyl semi\-metal heterostructures that realize effective black- or white-hole event horizons. We provide an exact solution to the scattering problem at normal incidence and low energies, both for a…