Related papers: A Method to Extrapolate the Data for the Inverse M…
We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…
We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which…
In this paper we investigate the polarization property of the radiation amplified by astronomical masers in the presence of a strong magnetic field. Our model explicitly takes into account the broadband nature of the radiation field and the…
A general problem of magnetic sensors is a trade-off between spatial resolution and magnetic field sensitivity. With decreasing sensor size its resolution is improved but the sensitivity is deteriorated. Obviation of such the trade-off…
We consider the problem of determination of a magnetic field from three dimensional polarimetric neutron tomography data. We see that this is an example of a non-Abelian ray transform and that the problem has a globally unique solution for…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed…
The Bayesian approach to Inverse Problems relies predominantly on Markov Chain Monte Carlo methods for posterior inference. The typical nonlinear concentration of posterior measure observed in many such Inverse Problems presents severe…
We present a target field approach to analytically design magnetic fields using permanent magnets. We assume that their magnetisation is bound to a two-dimensional surface and is composed of a complete basis of surface modes. By posing the…
We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to…
Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array…
The computer processing of images of magnetic force microscopy of cobalt nanodots was performed. The solution of reverse task of magnetic force microscopy is obtained for surface points of samples. Superposition of fields, which are…
We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial…
In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\theta )$ and $f_{NN}(x;\psi)$ to approximate the solution $u^{*}(x)$ and the…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…
In the paper "Optimal control of a Vlasov-Poisson plasma by an external magnetic field - The basics for variational calculus" [arXiv:1708.02464] we have already introduced a set of admissible magnetic fields and we have proved that each of…
We study determining the posture of an in-parallel planar manipulator, which has three connectors composed of revolute, prismatic and revolute joints, from specified active joint variables. We construct an ideal in the field of complex…