相关论文: Spatial Localization Problem and the Circle of Apo…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
We present a map of the spiral structure of the Galaxy, as traced by molecular CS emission associated with IRAS sources which are believed to be compact HII regions. The CS line velocities are used to determine the kinematic distances of…
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
The spiral structure in the Solar neighborhood is an important issue in astronomy. In the past few years, there is significant progress in observation. The distances for a large number of good spiral tracers, i.e. giant molecular clouds,…
In this paper, an efficient algorithm to find the center of the biggest circle inscribed in a given polygon is described. This work was inspired by the publication of Daniel Garcia-Castellanos & Umberto Lombardo and their algorithm used to…
Pythagoras' theorem, the area of a triangle as one half the base times the height, and Heron's formula are amongst the most important and useful results of ancient Greek geometry. Here we look at all three in a new and improved light, using…
We give detailed predictions for the spectral signatures arising from photon-particle oscillations in astrophysical objects. The calculations include quantum electrodynamic effects as well as those due to active relativistic plasma. We show…
A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
We provide upper bounds for the sum of the multiplicities of the non-constant irreducible factors that appear in the canonical decomposition of a polynomial $f(X)\in\mathbb{Z}[X]$, in case all the roots of $f$ lie inside an Apollonius…
We consider the effect of spatial correlations on sources of polarized electromagnetic radiation. The sources, assumed to be monochromatic, are constructed out of dipoles aligned along a line such that their orientation is correlated with…
Ultra-light bosons such as axions or axion-like particles (ALPs), are promising candidates to solve the dark matter problem. A unique way to detect such ALPs is to search for the periodic oscillation feature of the position angles of…
This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system,…
The depth function of three numbers representing curvatures of three mutually tangent circles is introduced. Its 2D plot leads to a partition of the moduli space of the triples of mutually tangent circles/disks that is unexpectedly a…
In this paper the two dimensional abelian Higgs model is revisited. We show that in the physical sector, the solutions to the Euler-Lagrange equations include solitons.
Circular photon orbits have become an attractive topic in recent years. They play extremely important roles in black hole shadows, gravitational lensings, quasi-normal modes, and spacetime topological properties. In our recent work,…
Based on the most complete sample of Galactic open star clusters up to 1.8 kpc, we performed statistical analysis of the distribution of open cluster parameters in order to understand the Galactic structure. The geometrical characteristics…