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Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
Two-dimensional, resonant scanners have been utilized in a large variety of imaging modules due to their compact form, low power consumption, large angular range, and high speed. However, resonant scanners have problems with non-optimal and…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is…
We present a new technique - photon folding - for imaging in non-focusing telescopes. Motivated by the epoch-folding method in timing analysis, the photon folding technique directly provides the statistical significance of signals in…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…
The demand for higher resolution telescopes leads to segmented primary mirrors which need to be phased for operation. A phasing sensor applying a wavelength sweep technique provides a large capture range without modulating the position of…
We introduce orthogonal ring patterns consisting of pairs of concentric circles generalizing circle patterns. We show that orthogonal ring patterns are governed by the same equation as circle patterns. For every ring pattern there exists a…
In applications, choices of orthonormal bases in Hilbert space H may come about from the simultaneous diagonalization of some specific abelian algebra of operators. It was noticed recently that there is a certain finite set of non-commuting…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
For the filtering of peaks in periodic signals, we specify polynomial filters that are optimally localized in space. The space localization of functions having an expansion in terms of orthogonal polynomials is thereby measured by a…
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
Superquadrics provide a compact representation of common shapes and have been used both for object/surface modelling in computer graphics and as object-part representation in computer vision and robotics. Superquadrics refer to a family of…