相关论文: Spatial Localization Problem and the Circle of Apo…

A non-trivial spatial topology of the Universe is a potentially observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological parameters.…

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…

A construction similar to Hagge's construction for circles through the orthocentre is shown to apply for any point.

Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we…

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…

A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in $S^2$. This isomorphism converts…

Reliable spatial information can be difficult to obtain in planetary remote sensing applications because of errors present in the metadata of images taken with space probes. We have designed a pipeline to address this problem on…

The Virtual Observatory is useful. I summarise some of my works where I extensively use the Aladin sky atlas. Topics cover from the search and common proper motion confirmation of very low-mass stars and brown dwarfs in wide (rho > 1000 AU)…

Rapid, accurate localization of gravitational wave transient events has proved critical to successful electromagnetic followup. In previous papers we have shown that localization estimates can be obtained through triangulation based on…

Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…

Ancient astronomers faced the problem of dealing with arcs and angles in their observations and predictions without the help of modern trigonometry. The usual method to deal with such problems was the Menelaus Theorem, explicitly discussed…

Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…

Probabilistic cross-identification has been successfully applied to a number of problems in astronomy from matching simple point sources to associating stars with unknown proper motions and even radio observations with realistic morphology.…

The configuration space of tricycles (triples of disks in contact) is shown to coincide with the complex plane resulting as a projective space costructed from the tangency and Pauli spinors. Remarkably, the fractal of the depth functions…

This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning $k$ collections of $m$ spatial…

The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…

This article discusses a computational treatment of the localization A_L of an affine coordinate ring A at a prime ideal L and its associated graded ring Gr_a(A_L) with the means of standard basis techniques. Building on Mora's work, we…

Transformers excel when dealing with sequential data. Generalizing transformer models to geometric domains, such as manifolds, we encounter the problem of not having a well-defined global order. We propose a solution with attention heads…

In this mini-review, possible manifestations of mixing between axion-like particles (ALPs) and energetic photons propagating over astronomical distances are considered. We discuss the evidence for the anomalous transparency of the Universe…

Given a regular polygonal arrangement of identical objects, turning around a central object (masses, vortices or dNLS oscillators), this paper studies the global bifurcation of relative equilibria in function of a natural parameter (central…