相关论文: Optimal Shape Design by Partial Spectral Data

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…

We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…

When material parameters are fixed, optical responses of nanoresonators are dictated by their shapes and dimensions. Therefore, both designing nanoresonators and understanding their underlying physics would benefit from a theory that…

In unilateral pelvic fracture reductions, surgeons attempt to reconstruct the bone fragments such that bilateral symmetry in the bony anatomy is restored. We propose to exploit this "structurally symmetric" nature of the pelvic bone, and…

This paper reports some novel and intriguing discoveries about the localization and geometrization phenomenon in plasmon resonances and the intrinsic geometric structures of Neumann-Poincar\'e eigenfunctions. It is known that plasmon…

We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it $I_0$) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the…

We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad-Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of…

Measurements on a subset of the boundary are common in electrical impedance tomography, especially any electrode model can be interpreted as a partial boundary problem. The information obtained is different to full-boundary measurements as…

This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity in the input data. A converging hierarchy of semidefinite relaxations for eigenvalue and trace optimization is provided. This…

This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and…

Consider Bernoulli(1/2) percolation on $\mathbb{Z}^d$, and define a perfect matching between open and closed vertices in a way that is a deterministic equivariant function of the configuration. We want to find such matching rules that make…

The elastic Neumann--Poincar\'e operator is a boundary integral operator associated with the Lam\'e system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two…

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…

Today, three-dimensional reconstruction of objects has many applications in various fields, and therefore, choosing a suitable method for high resolution three-dimensional reconstruction is an important issue and displaying high-level…

This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordstr\"{o}m space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general…

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…

Digital holographic microscopy based on Gabor in-line holography is a well-known method to reconstruct both the amplitude and phase of small objects. To reconstruct the image of an object from its hologram, obtained under illumination by…

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 subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme…