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With resonances treated as eigenstates of a non-Hermitian quantum Hamiltonian, the task of localization of the complex energy eigenvalues is considered. The paper is devoted to the reduced version of this task in which one only computes the…
The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…
In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by…
It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a…
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves both the interior and exterior Green's functions with the…
In the theory of inner and outer balayage of positive Radon measures on a locally compact space $X$ to arbitrary $A\subset X$ with respect to suitable, quite general function kernels, developed in a series of the author's recent papers, we…
We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on…
Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
We introduce a new method for producing both maximal green and reddening sequences of quivers. The method, called component preserving mutations, generalizes the notion of direct sums of quivers and can be used as a tool to both recover…
This work presents a complete methodology for the precise characterization of the acoustic field inside crystal-based devices driven by high-frequency ultrasounds towards the generation of tunable narrowband and directional gamma radiation…
The recently developed selected columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463, 2015] is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where…
Bragg coherent diffraction imaging (BCDI) is a unique and powerful method for tracking three-dimensional strain fields non-destructively. While BCDI has been successfully applied to many scientific research fields and receives high demands,…