Related papers: Spindle Starshaped Sets
We describe a set $\mathcal{R}^{\infty}$ consisting of tuples of integer sequences and provide certain explicit maps on it. We show that this defines a semiregular crystal for $\mathfrak{sl}_{n+1}$ and $\mathfrak{sp}_{2n}$ respectively.…
Whether the spiral structure of galaxies is trailing or leading has been a subject of debate. We present a new spin parity catalog of 146 spiral galaxies that lists the following three pieces of information: whether the spiral structure…
We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of…
We construct the first infinite families of locally arc transitive graphs with the property that the automorphism group has two orbits on vertices and is quasiprimitive on exactly one orbit, of twisted wreath type. This work contributes to…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
Globular clusters provide a unique probe of galaxy formation and evolution. Here I briefly summarize the known observational properties of globular cluster systems. One re-occurring theme is that the globular cluster systems of spirals and…
The simulation of rich star clusters presents challenging problems of several kinds, including the design of suitable hardware and software, and numerous theoretical problems in stellar dynamics and stellar physics. Great progress has been…
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.
This paper makes a modest contribution to the family of starlike univalent mappings in the open unit disk, by the introduction of some new subclasses of them via certain convolution operators. A new univalence condition is given with…
In this paper, we address the topic of envelopes created by pseudo-circle families in the Minkowski plane, which exhibit some different properties when compared with the Euclidean case. We provide solutions to all four basic problems…
We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly…
Spiral galaxies are axi-symmetric objects showing 2D-chirality when projected onto a plane. Features in common with tetrahedral molecules are pointed out, in particular the existence of a preferred chiral modality for genetic galaxies as in…
In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure…
I review recent and less recent work on globular cluster systems in early-type galaxies. Explaining their properties and possible assembly scenarios, touches on a variety of astrophysical topics from cluster formation itself to galaxy…
We study tangential families, i.e. systems of rays emanating tangentially from given curves. We classify, up to Left-Right equivalence, stable singularities of tangential family germs (under deformations among tangential families) and we…
The spin point groups are finite groups whose elements act on both real space and spin space. Among these groups are the magnetic point groups in the case where the real and spin space operations are locked to one another. The magnetic…
In traditional astronomies across the world, groups of stars in the night sky were linked into constellations -- symbolic representations rich in meaning and with practical roles. In some sky cultures, constellations are represented as line…
Given a graph whose edges are labeled by ideals in a ring, a generalized spline is a labeling of each vertex by a ring element so that adjacent vertices differ by an element of the ideal associated to the edge. We study splines over the…
A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorff spaces and continuous maps. As an application, we show that there exists a…