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A topological constraint on the possible values of the universal quantization parameter is revealed in the case of geometric quantization on (boundary) curves diffeomorphic to $S^1$, analytically extended on a bounded domain in…
We show that metrics that maximize the k-th Steklov eigenvalue on surfaces with boundary arise from free boundary minimal surfaces in the unit ball. We prove several properties of the volumes of these minimal submanifolds. For free boundary…
We study a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local variant to be bounded on…
In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The `factoring' approach alleviates this difficulty by deriving a PDE for a new (locally smooth) variable while…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
We consider the problem of joint reconstruction of both attenuation $a$ and source density $f$ in emission tomography in two dimensions. This is sometimes called the Single Photon Emission Computed Tomography (SPECT) identification problem,…
By considering an optically denser medium with a flat surface, but with natural roughness instead of abstract geometrical boundary which leads to mathematical discontinuity on the boundary of two adjacent stratified media, we have thus…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
In this article, we consider the limited angle problem in computed X-ray tomography. A common practice is to use the filtered back projection with the limited data. However, this practice has been shown to introduce the artifacts along some…
Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a…
We prove a uniqueness result for finite-dimensional representations of the Kauffman skein algebra $\mathcal{S}_A(S)$ of a surface $S$, when $A$ is a root of unity and when the surface $S$ is a sphere with at most four punctures or a torus…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the…
A core-softened model of a glass forming fluid is numerically studied in the limit of very low temperatures. The model shows two qualitatively different behaviors depending on the strength of the attraction between particles. For no or low…
This study examines the roughness of mechanically cleaved edges in 2D crystals and glasses using molecular dynamics simulations with chemically accurate machine-learning force fields. Our results show that ultra-flat armchair and zigzag…
We study sharp asymptotics of the first eigenvalue on Riemannian surfaces obtained from a fixed Riemannian surface by attaching a collapsing flat handle or cross cap to it. Through a careful choice of parameters this construction can be…
In this paper we consider the question of whether the doubling character of a measure supported on a subset of $\RR^m$ determines the regularity of its support (in a classical sense). This problem was studied by David, Kenig and Toro for…
In this paper we show that for metrics with conormal singularities that correspond to class C^{1,\alpha} with \alpha>0, the reflected wave is more regular than the incident wave in a Sobolev sense. This is helpful in the analysis of the…
The k-space data generated from magnetic resonance imaging (MRI) is only a finite sampling of underlying signals. Therefore, MRI images often suffer from low spatial resolution and Gibbs ringing artifacts. Previous studies tackled these two…