Related papers: Visibility Properties of Spiral Sets
Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\mathcal{I}$ contains either a separatrix at $p$ or an invariant real…
We prove a relatively simple combinatorial characterization of simplicial $d$-spheres on $d+4$ vertices. Our criteria are given in terms of the intersection patterns of a simplicial complex's family of minimal non-faces. Namely, let…
We construct a polygonal spiral by arranging a sequence of regular $n$-gons such that each $n$-gon shares a specified side and vertex with the $(n+1)$-gon in the construction. By offering flexibility for determining the size of each $n$-gon…
The number of apparent double points of a smooth, irreducible projective variety $X$ of dimension $n$ in $\Proj^{2n+1}$ is the number of secant lines to $X$ passing through the general point of $\Proj^{2n+1}$. This classical notion dates…
We present a model for the dark matter in spiral galaxies, which is a result of a static and axial symmetric exact solution of the Einstein-Dilaton theory. We suposse that dark matter is a scalar field endowed with a scalar potential. We…
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…
We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…
We evaluate determinants of "spiral" matrices, which are matrices in which entries are spiralling from the centre of the matrices towards the outside, with prescribed increments from one entry to the next depending on whether one moves…
The spiral is one of Nature's more ubiquitous shape: it can be seen in various media, from galactic geometry to cardiac tissue. In the literature, very specific models are used to explain some of the observed incarnations of these dynamic…
Among the most fundamental properties of a dark matter halo is its density profile. Motivated by the recent proposal by Garc\'ia et al. [R. Garc\'ia et. al., MNRAS 521, 2464 (2023)] to define a dynamical halo as the collection of orbiting…
Deep HI observations of the outer parts of disc galaxies demonstrate the frequent presence of extended, well-developed spiral arms far beyond the optical radius. To understand the nature and the origin of such outer spiral structure, we…
A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of circles with fixed radius. Most previous study of Tangles has dealt with the case where these arcs are quarter-circles, but Tangles comprised of thirds and sixths…
The fundamental plane of spiral galaxies was searched from observational data, which can be approximately represented in observational parameters by $ L \propto V^2 R $, where $L$, $R$, and $V$ are the luminosity, the linear size of…
Given a sphere of any radius $r$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average…
In spiral galaxies, we explain their non-Keplerian rotation curves (RCs) by means of a non-luminous component embedding their stellar-gaseous disks. Understanding the detailed properties of this component (labelled Dark Matter, DM) is one…
Let K be a simplicial complex with vertex set V = {v_1,..., v_n}. The complex K is d-representable if there is a collection {C_1,...,C_n} of convex sets in R^d such that a subcollection {C_{i_1},...,C_{i_j}} has a nonempty intersection if…
We derive the atomic hydrogen content for a total of 1900 spirals in the fields of eighteen nearby clusters. By comparing the HI deficiency distributions of the galaxies inside of and outside of one Abell radius of each cluster, we find…
The disks of spiral galaxies are generally elliptical rather than circular. The distribution of ellipticities can be fit with a log-normal distribution. For a sample of 12,764 galaxies from the Sloan Digital Sky Survey Data Release 1 (SDSS…
We report the analysis of HST WFPC2 F606W images of 40 spirals belonging to the sample introduced in Carollo et al. (paper I), where 35 other targets were discussed. We describe the optical morphology of the new 40 galaxies, derive the…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…