Related papers: Microlocal analysis of a restricted ray transform …
This paper is concerned with the inverse problem of reconstructing a small object from far field measurements. The inverse problem is severally ill-posed because of the diffraction limit and low signal to noise ratio. We propose a novel…
We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane.…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
Local magnetic reversals are an inseparable part of magnetohydrodynamic (MHD) turbulence whose collective outcome on an arbitrary scale in the inertial range may lead to a global stochastic reconnection event with a rate independent of…
For any positive integers $r$, $s$, $m$, $n$, an $(r,s)$-order $(n,m)$-dimensional rectangular tensor ${\cal A}=(a_{i_1\cdots i_r}^{j_1\cdots j_s}) \in ({\mathbb R}^n)^r\times ({\mathbb R}^m)^s$ is called partially symmetric if it is…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…
We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction.…
Rescattering electrons offer great potential as probes of molecular properties on ultrafast timescales. The most famous example is molecular tomography, in which high harmonic spectra of oriented molecules are mapped to ``tomographic…
We develop an amended ray optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two…
The Perron-Frobenius theorem says that the spectral radius of an irreducible nonnegative tensor is the unique positive eigenvalue corresponding to a positive eigenvector. With this in mind, the purpose of this paper is to find the spectral…
Tomography can be used to reveal internal properties of a 3D object using any penetrating wave. Advanced tomographic imaging techniques, however, are vulnerable to both systematic and random errors associated with the experimental…
During the last few years, interest has arisen in using light-front Tamm-Dancoff field theory to describe relativistic bound states for theories such as QCD. Unfortunately, difficult renormalization problems stand in the way. We introduce a…
Achieving atomic resolution in electron microscopy has historically been hindered by spherical aberration, a fundamental limitation of conventional electron lenses. Its correction typically requires complex assemblies of electromagnetic…
We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…
The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural…
In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input…
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…