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A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…

Differential Geometry · Mathematics 2009-03-12 Burzin Bhavnagri

Cutoff regularized subleading order ${}^1S_0$ NN potential of effective field theory (EFT) is iterated using Lippmann-Schwinger equation. It is shown that the scattering amplitudes calculated in cutoff and subtractively renormalized EFT are…

Nuclear Theory · Physics 2009-11-07 J. Gegelia , G. Japaridze

We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…

Numerical Analysis · Mathematics 2025-11-18 Markus Harju , Suvi Anttila , Teemu Tyni

In a previous article of Dos Santos Ferreira, Kenig, Salo and Uhlmann, anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a…

Analysis of PDEs · Mathematics 2011-04-04 David Dos Santos Ferreira , Carlos E. Kenig , Mikko Salo

We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…

Numerical Analysis · Mathematics 2026-03-31 Felix Bartel , Dinh Dũng

In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma stating that it is…

Analysis of PDEs · Mathematics 2012-09-18 Antoine Lemenant , Emmanouil Milakis , Laura V. Spinolo

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…

Classical Analysis and ODEs · Mathematics 2009-09-18 Dmitry Batenkov

Using a distributed representation formula of the Gateaux derivative of the Dirichlet to Neumann map with respect to movements of a polygonal conductivity inclusion, [11], we extend the results obtained in [8] proving global Lipschitz…

Analysis of PDEs · Mathematics 2020-09-01 Elena Beretta , Elisa Francini , Sergio Vessella

In this paper, we prove some exact estimates for the discrete Neumann energy of a ball and a circular ring in Euclidean space for points located on circles. The proofs are based on dissymmetrization and analysis of the asymptotic behavior…

Analysis of PDEs · Mathematics 2021-12-14 Elena Prilepkina , Anna Afanaseva-Grigoreva

We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…

Analysis of PDEs · Mathematics 2020-09-03 Tianyu Yang , Yang Yang

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…

Analysis of PDEs · Mathematics 2018-07-16 Juan A. Barceló , Carlos Castro , Teresa Luque , Mari Cruz Vilela

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

Analysis of PDEs · Mathematics 2022-03-03 Mourad Bellassoued , Houssem Haddar , Amal Labidi

We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…

Numerical Analysis · Mathematics 2022-05-04 Ben Adcock , Milana Gataric , José Luis Romero

Three-dimensional charge density maps computed by first-principles methods provide information about atom positions and the bonds between them, data which is particularly valuable when trying to understand the properties of point defects,…

Materials Science · Physics 2008-10-22 Christoph T. Koch

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…

Numerical Analysis · Mathematics 2023-11-07 Bangti Jin , Kwancheol Shin , Zhi Zhou

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…

Numerical Analysis · Mathematics 2014-10-02 Ben Adcock , Milana Gataric , Anders C. Hansen

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

Numerical Analysis · Mathematics 2010-12-01 Ben Adcock , Anders C. Hansen

Assume a time-harmonic elastic wave is incident onto a penetrable anisotropic body embedded into a homogeneous isotropic background medium. We propose an equivalent variational formulation in a truncated bounded domain and show the…

Analysis of PDEs · Mathematics 2016-12-21 Gang Bao , Guanghui Hu , Jiguang Sun , Tao Yin

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a…

Strongly Correlated Electrons · Physics 2009-10-31 V. Janis