相关论文: Spatial Localization Problem and the Circle of Apo…
There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What…
Ultra-light axion-like particles (ALPs) can be a viable solution to the dark matter problem. The scalar field associated with ALPs, coupled to the electromagnetic field, acts as an active birefringent medium, altering the polarisation…
Henri Poincar\'e formulated the mathematics of the Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is shown that these two mathematical instruments can be combined…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze spherical roots, colors and their interrelation. At the end, we…
We start from the author's metric for a rotating and accelerating Universe and we calculate the force acting on a particle in it. This force consists of two parts: one is derived from a potential, and the other describes a Coriolis force…
A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…
We introduce and study the Marco Polo problem, which is a combinatorial approach to geometric localization. In this problem, we are told there are one or more points of interest (POIs) within distance $n$ of the origin that we wish to…
We consider the sound ranging, or source localization, problem - find the source-point from the moments when the wave-sphere of linearly, with time, increasing radius reaches the sensor-points - in the proper metric spaces (any closed ball…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
We consider the search for axion-like particles (ALPs) by using time series data of the polarization angle of the light. If the condensation of an ALP plays the role of dark matter, the polarization plane of the light oscillates as a…
The morphology and kinematics of the spiral structure of the Milky Way is a long-standing problem in astrophysics. In this review we firstly summarize various methods with different tracers used to solve this puzzle. The astrometry of…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically…
Polarization is a basic property of light and is fundamentally linked to the internal geometry of a source of radiation. Polarimetry complements photometric, spectroscopic, and imaging analyses of sources of radiation and has made possible…
Observing the list of compatible second order equations of Absolute Parallelism (AP) found by Einstein and Mayer (they used D=4), we choose the one-parameter class of equations which take on a 3-linear form (when contra-frame density of…
Here I present results from individual galaxy studies and galaxy surveys in the Local Universe with particular emphasis on the spatially resolved properties of neutral hydrogen gas. The 3D nature of the data allows detailed studies of the…
Over 3 billion astronomical objects have been detected in the more than 22 million orthogonal transfer CCD images obtained as part of the Pan-STARRS1 $3\pi$ survey. Over 85 billion instances of those objects have been automatically detected…
Why is it that after so many years matrices continue to play such an important roll in Physics and mathematics? Is there a geometric way of looking at matrices, and linear transformations in general, that lies at the roots of their success?…
Astrophysics and cosmology can be used to test the standard model of particle physics under conditions and over distance and time scales not accessible to laboratory experiments. Most of the astrophysical observations are in good agreement…