Related papers: The star-center of the quaternionic numerical rang…
I present a brief summary of three different types of binary star - astrometric, spectroscopic and eclipsing - and tabulate the properties of these systems that can be determined directly from observations. Eclipsing binary stars are the…
Recently, astronomers discovered unusual Einstein cross images of the galaxy HerS-3, which feature a bright central spot. Motivated by studies of images produced by regular stars, it has been proposed that optical appearances caused by…
Astronomical polarimetry is a powerful technique that can provide physical information sometimes difficult or impossible to obtain by any other type of observation. Almost every class of binary star can benefit from polarimetric…
This article is intended for undergraduate students with the aim to provide a pedagogical introduction to the physics of stellar tidal deformations. The spherically symmetric shape of any star is deformed via rotation around an arbitrary…
We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid…
On the perimeter length determination of the eight-centered oval. Several studies have shown that an eight-centered oval coincides almost perfectly with the ellipse constructed on the same axes and can be considered as a representation of…
We have computed the properties of compact objects like neutron stars based on equation of state (EOS) deduced from a core-envelope model of superdense stars. Such superdense stars have been studied by solving the Einstein's equation based…
Observations of the Galactic Centre show evidence of disc-like structures of very young stars orbiting the central super-massive black hole within a distance of a few 0.1 pc. While it is widely accepted that about half of the stars form a…
Given two symmetric convex bodies $L \subseteq K \subseteq \R^n$ with $L$ strictly convex, we prove that there exist at least $n$ hyperplanes $H$ tangent to $L$, such that the center of mass of $H \cap K$ belongs to $\partial L$. The…
The stellar inclination angle-the angle between the rotation axis of a star and our line of sight-provides valuable information in many different areas, from the characterisation of the geometry of exoplanetary and eclipsing binary systems,…
Camera calibration is fundamental to 3D vision, and the choice of calibration pattern greatly affects the accuracy. To address aberration issue, star-shaped pattern has been proposed as alternatives to traditional checkerboard. However,…
The star discrepancy $D_N^*(\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\mathcal{P}$ in the multi-dimensional unit cube which is intimately related to the integration error of…
In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a…
The inverse stellar structure problem determines the equation of state of the matter in stars from a knowledge of their macroscopic observables (e.g. their masses and radii). This problem was solved in a previous paper by constructing a…
Spherical neutron star models are studied within tensor-scalar theories of gravity. Particularly, it is shown that, under some conditions on the second derivative of the coupling function and on star's mass, for a given star there exist two…
Matter at ultra-high densities finds a physical realization inside neutron stars. One key property is their maximum mass, which has far-reaching implications for astrophysics and the equation of state of ultra dense matter. In this work, we…
Properties of rotating neutron stars with the use of relativistic mean-field theory are considered. The performed analysis of neutron star matter is based on the nonlinear Lgrangian density. The presence of nonlinear interaction of vector…
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of…
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…
Recent analysis of the distribution of clusters of galaxies is reviewed. Clusters of galaxies located in rich superclusters form a quasiregular lattice with a step size 120 Mpc. The power spectrum of clusters of galaxies has a sharp peak at…