Related papers: Spatial Localization Problem and the Circle of Apo…
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…
The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based…
Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure…
The motion of astronomical bodies and the centre of mass of the system is not always well perceived by students. One of the struggles is the conceptual change of reference frame, which is the same that held back the acceptance of the…
Polar-ring galaxies (PRGs) are fascinating systems in which the central object (typically, an early-type galaxy) is encircled by a large-scale ring of stars, gas, and dust with almost perpendicular spin. PRGs are rare objects and their…
The spiral arms of the Milky Way are being accurately located for the first time via trigonometric parallaxes of massive star forming regions with the BeSSeL Survey, using the Very Long Baseline Array and the European VLBI Network, and with…
Axionlike particles (ALPs) are a common prediction of theories beyond the Standard Model of particle physics that could explain the entirety of the cold dark matter. These particles could be detected through their mixing with photons in…
In this paper, given a linear system of equations A x = b, we are finding locations in the plane to place objects such that sending waves from the source points and gathering them at the receiving points solves that linear system of…
A coordinate system is proposed for the purposes of analysis of far-field radiation from a localized source at the origin. The proposed coordinates exhibit no singularities over the far-field hemi-sphere, making them a good choice for…
Stellar occultations provide a powerful tool to explore objects of the outer solar system. The Gaia mission now provides milli-arcsec accuracy on the predictions of these events and makes possible observations that were previously…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
This work applies Mie scattering theory to provide a new perspective on the propagation of light through a spherical obstacle, offering a novel explanation for the formation of the Poisson spot (also known as the Arago or Fresnel spot). We…
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating…
We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…
Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal…
Visualising the three dimensional distribution of stars within a constellation is highly challenging for both students and educators, but when carried out in an interactive collaborative way it can create an ideal environment to explore…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of…
The light we receive from distant astrophysical objects carries information about their origins and the physical mechanisms that power them. The study of these signals, however, is complicated by the fact that observations are often a…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…