Related papers: Microlocal analysis of a restricted ray transform …
We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…
The windowed ray transform is a natural generalization of the "Analytic-Signal Transform" which is developed to extend arbitrary functions from $\RR^n$ to $\CC^n$. We present several inversion formulas here.
This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…
Single mode lasing is experimentally demonstrated in a transversely multi-moded InP-based semiconductor microring arrangement. In this system, mode discrimination is attained by judiciously utilizing the exceptional points in a parity-time…
The characterization of local regularity is a fundamental issue in signal and image processing, since it contains relevant information about the underlying systems. The 2-microlocal frontier, a monotone concave downward curve in $\mathbb…
We consider restricted light ray transforms arising from an inverse problem of finding cosmic strings. We construct a relative left parametrix for the transform on two tensors, which recovers the space-like and some light-like singularities…
Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…
A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated micro-resonators. 3D full…
Magnetic fields are constrained by the geometry and location of their sources, limiting the ability to freely tailor their spatial distribution. We introduce a general framework to passively convert the magnetic field generated by arbitrary…
We discuss $\theta$-deformed Maxwell theory at first order in $\theta$ with the help of the Seiberg-Witten (SW) map. With an appropriate field redefinition consistent with the SW-map we analyse the one-loop corrections of the vacuum…
We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity $(C,O)$ contained in a…
In the plane, we study the transform $R_\gamma f$ of integrating a unknown function $f$ over circles centered at a given curve $\gamma$. This is a simplified model of SAR, when the radar is not directed but has other applications, like…
We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces and tori. We give proofs of…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp…
Here we develop a general theory of mode transformation (diffraction) at the flat transverse boundary between cold magnetized electron plasma and isotropic vacuum-like medium inside a circular waveguide. The obtained results can be also…
We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to…
Solenoids induced by split sequences are introduced, as the inverse limit object of a sequence of fold maps. The topology of a solenoid is explored, and it is established that solenoids have naturally arising singular foliated structures.…
Photonic lanterns (PLs) are fiber-based waveguides that are capable of focal-plane wavefront sensing while simultaneously directing light to downstream science instruments. The optimal choice of wavefront reconstruction algorithm has yet to…
We review the method of differential renormalization, paying special attention to a new constrained version for symmetric theories.