Related papers: Gradient Estimates for the Perfect and Insulated C…
We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a…
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…
It is investigated how graded variants of integral and complete integral closures behave under coarsening functors and under formation of group algebras.
We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
The inverse problem of antiplane elasticity on determination of the profiles of $n$ uniformly stressed inclusions is studied. The inclusions are in ideal contact with the surrounding matrix, the stress field inside the inclusions is…
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…
In this article we compare solutions to elliptic problems having rapidly oscillated conductivity (permeability, etc) coefficient with solutions to corresponding homogenized problems obtained from two-scale extensions of the initial…
A brief history of the impurity theories in semiconductors is provided. A bound exciton model is proposed for both donor- and acceptor- like impurities and point defects, which offers a unified understanding for "shallow" and "deep"…
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruction of the critical index for superconductivity from the…
We present a closed description of the charge carrier injection process from a conductor into an insulator. Common injection models are based on single electron descriptions, being problematic especially once the amount of charge-carriers…
In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between…
In this paper we estimate the size of a measurable inclusion in terms of power measurements for a single applied boundary current. This problem arises in medical imaging for the screening of organs. For this kind of problem one has to deal…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrised version of the classical fidelity). These are crucial for establishing global linear…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective on the set of pairs of sparse vectors if the number of…
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the…
Let $(\Sigma, g)$ be a closed Riemann surface, and let $u$ be a weak solution to equation \[ - \Delta_g u = \mu, \] where $\mu$ is a signed Radon measure. We aim to establish $L^p$ estimates for the gradient of $u$ that are independent of…