Related papers: Constraining Schwarzschild Models with Orbit Class…
We derive new limits on the value of the cosmological constant, $\Lambda$, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the…
This work presents an analytical perturbation method to define and study the dynamics of frozen orbits under the perturbation effects produced by the oblatness of the main celestial body. This is done using a perturbation method purely…
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…
Motivated by recent achievements of a full general relativistic method in estimating the mass-to-distance ratio of supermassive black holes hosted at the core of active galactic nuclei, we introduce the new concept redshift rapidity in…
The first half of this article is expository -- I will review, with examples, the main statements of the Langlands classification and Arthur's conjectures for real reductive groups as formulated by Adams, Barbasch, and Vogan. In the second…
Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been…
We consider physical parameters of Levin and Perez-Giz's `periodic table of orbits' around the Schwarzschild black hole, where each periodic orbit is classified according to three integers $(z,w,v)$. In particular, we chart its distribution…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
We present a data-driven method to infer the redshift distribution of an arbitrary dataset based on spatial cross-correlation with a reference population and we apply it to various datasets across the electromagnetic spectrum to show its…
Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…
We use a strong lensing inversion in the cluster of galaxies AC 114 to derive constraints on the cosmological parameters Omega_M0 and Omega_Lambda. If it is possible to measure spectroscopically the redshifts of many multiple images then…
The evolution of galaxy clusters can be affected by the repulsion described by the cosmological constant. This conclusion is reached within the modified weak-field General Relativity approach where the cosmological constant \Lambda enables…
In this manuscript I review the mathematics and physics that underpins recent work using the clustering of galaxies to derive cosmological model constraints. I start by describing the basic concepts, and gradually move on to some of the…
In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in…
A 3D steady state stellar dynamical model for the Galactic bar is constructed with 485 orbit building blocks using an extension of Schwarzschild technique. The weights of the orbits are assigned using non-negative least square method. The…
Hierarchical clustering is a common algorithm in data analysis. It is unique among many clustering algorithms in that it draws dendrograms based on the distance of data under a certain metric, and group them. It is widely used in all areas…
In this article we consider a restricted orbital counting problem for the action of certain discrete groups on suitable spaces. In particular, we present asymptotics for counting those points in an orbit restricted to a single conjugacy…
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is…