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In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the…
The purpose of this paper is to extend the notions of generalised Poincar\'e series and divisorial generalised Poincar\'e series (of motivic nature) introduced by Campillo, Delgado and Gusein-Zade for complex curve singularities to curves…
Fix $n \geq 2$ an integer, and $F$ be a totally real number field. We reduce the shifted convolution problem for $L$-function coefficients of $\operatorname{GL}_n({\bf{A}}_F)$-automorphic forms to the better-understood setting of…
We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming…
This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar…
We report a new resummation procedure for the partial wave series (PWS) representation of the scattering amplitude, when a basis set of Legendre polynomials is used for the expansion. The effect of the resummation is to remove from the PWS…
Diffusion models have been widely utilized for image restoration. However, previous blind image restoration methods still need to assume the type of degradation model while leaving the parameters to be optimized, limiting their real-world…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koornwinder polynomials are introduced on the reference…
The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…
Diffusion-weighted imaging (DWI) is a powerful non-invasive tool which is widely used in clinical routine. Mostly, apparent diffusion coefficient maps are acquired, which cannot be directly related to cellular structure. More recently it…
An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contains some isolated substructures, was expanded to account quadratic potential terms. Based on this approach, the…
In Optics it is common to split up the formal analysis of diffraction according to two convenient approximations, in the near and far fields (also known as the Fresnel and Fraunhofer regimes, respectively). Within this scenario, geometrical…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important…