Related papers: Visibility Properties of Spiral Sets

We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which the $v_i$ are the rows. We characterize properties of $v$ in…

We investigate recent claims that the Hubble sequence of spiral galaxies is scale-free. Fundamental to this investigation is the fact that within the photometric data of 86 spiral galaxies from de Jong & van der Kruit - from which these…

Galaxies are thought to grow through accretion; as less massive galaxies are disrupted and merge over time, their debris results in diffuse, clumpy stellar halos enveloping the central galaxy. Here we present a study of the variation in the…

Vector spin chirality is one of the fundamental characteristics of complex magnets. For a one-dimensional spin-spiral state it can be interpreted as the handedness, or rotational sense of the spiral. Here, using spin-polarized scanning…

Subjective classification of spiral galaxies is not sufficient for studying the effect of bars on their physical characteristics. In reality the problem is to comprehend the complex correlations in a multivariate parametric space.…

In the past years a wealth of observations has allowed us to unravel the structural properties of the Dark and Luminous mass distribution in spirals. As result, it has been found that their rotation curves follow, out their virial radius,…

The opacity of spiral galaxies is examined by modelling the dust and stellar content of individual galaxies. The model is applied to five late-type spiral galaxies (NGC 4013, IC 2531, UGC 1082, NGC 5529 and NGC 5907). Having analyzed a…

Let $X$ be a simplicial complex on vertex set $V$. We say that $X$ is $d$-representable if it is isomorphic to the nerve of a family of convex sets in $\mathbb{R}^d$. We define the $d$-boxicity of $X$ as the minimal $k$ such that $X$ can be…

We propose a description of cluster states in nuclei in terms of representations of unitary algebras U(n+1), where n is the number of space degrees of freedom. Within this framework, a variety of situations including both vibrational and…

Using 3D global hydro simulations coupled with radiative transfer calculations, we study the appearance of density waves induced by giant planets in direct imaging observations at near infrared wavelengths. We find that a 6 MJ planet in a…

In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…

Mutual-visibility sets were motivated by visibility in distributed systems and social networks, and intertwine with several classical mathematical areas. Monotone properties of the variety of mutual-visibility sets, and restrictions of such…

Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…

Abstract Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each…

Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using…

The local space density of galaxies as a function of their basic structural parameters --like luminosity, surface brightness and scalesize-- is still poorly known. Our poor knowledge is mainly the result of strong selection biases against…

A prism is the product space $\Delta \times I$ where $\Delta$ is a 2-simplex and $I$ is a closed interval. As an analogue of simplicial complexes, we introduce prism complexes and show that every compact $3$-manifold has a prism complex…

The sphere formula states that in an arbitrary finite abstract simplicial complex, the sum of the Euler characteristic of unit spheres centered at even-dimensional simplices is equal to the sum of the Euler characteristic of unit spheres…

Here we are concerned with a special issue of billiard invisibility, where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is…

Let $\PP^d$ be the $d$-fold direct product of the set of primes. We prove that if $A$ is a subset of $\PP^d$ of positive relative upper density then $A$ contains infinitely many "corners", that is sets of the form $\{x,x+te_1,...,x+te_d\}$…