Related papers: Bounds on positive interior transmission eigenvalu…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…
We investigate the problem of information theoretically secure communication in a line network with erasure channels and state feedback. We consider a spectrum of cases for the private randomness that intermediate nodes can generate,…
We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the…
This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…
Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical…
A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…
Consider the eigenvalue problem generated by a fixed differential operator with a sign-changing weight on the eigenvalue term. We prove that as the negative part of the weight is rescaled towards negative infinity on some subregion, the…
We consider families of finite quantum graphs of increasing size and we are interested in how eigenfunctions are distributed over the graph. As a measure for the distribution of an eigenfunction on a graph we introduce the entropy, it has…
We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
We generalize and analyse the method for computing lower bounds of the principal eigenvalue proposed in our previous paper (I. Sebestova, T. Vejchodsky, SIAM J. Numer. Anal. 2014). This method is suitable for symmetric elliptic eigenvalue…
We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, i.e. the equation $\nabla\cdot(A \nabla u ) + k^2 n u =-f$ where both $A$ and $n$ are functions of position. We prove new a priori bounds on the solution…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
This work proposes a novel outer bound for the Gaussian cognitive interference channel in strong interference at the primary receiver based on the capacity of a multi-antenna broadcast channel with degraded message set. It then shows that…
We investigate the localization and vanishing of $L^2$ interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at non-convex corners. This phenomenon has, however, not been…
We consider the Laplace equation in a domain of $\mathbb{R}^n$, $n\ge 3$, with a small inclusion of size $\epsilon$. On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For $\epsilon$ small enough…
We investigate energy and momentum non-contact exchanges between two arbitrary flat media separated by a gap. This problem is revisited as a transmission problem of individual system eigenmodes weighted by a transmission probability…