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Sectors at centre of affine quadrics with point symmetry are investigated over arbitrary fields of characteristic different from two. As an application we demonstrate nice formulas for the area and the volume of such planar and spatial…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Many new types of sensing or imaging surfaces are based on periodic thin films. It is explained how the response of those surfaces to partially coherent fields can be fully characterized by a set of functions in the wavenumber spectrum…
Given two subsets of R^d, when does there exist a projective transformation that maps them to two sets with a common centroid? When is this transformation unique modulo affine transformations? We study these questions for 0- and…
We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…
This paper continues the study of a class of compact convex hypersurfaces in Euclidean space $R^{n+1}, ~n \geq 1$, which are boundaries of compact convex bodies obtained by taking the intersection of (solid) confocal paraboloids of…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space…
An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…
In this paper we offer a complete methodology for sufficient dimension reduction called the test function (TF). TF provides a new family of methods for the estimation of the central subspace (CS) based on the introduction of a nonlinear…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
In adaptive optics, the tracker and wavefront sensor commonly measure irradiance centroids (in their respective focal planes) to estimate the turbulence-degraded wavefront in the pupil plane. Several factors affect the accuracy of these…
This paper contributes a novel cognitively-inspired method for RGB-D indoor scene classification. High intra-class variance and low inter-class variance make indoor scene classification an extremely challenging task. To cope with this…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
We study the continuous solutions of several classical functional equations by using the properties of the spaces of continuous functions which are invariant under some elementary linear trans-formations. Concretely, we use that the sets of…
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that for any point set $P$ of $n$ points in $\mathbb{R}^d$, there is a point $c$, not necessarily from $P$, such that each halfspace containing…
We describe an affine transformation on the (CIE) color matching functions and map the spectral locus as a circle. We then homogenize the right circular cylinder erected by the circle, with respect to a normalizing plane and develop an…