相关论文: Flocks of Cones: Star Flocks
Most stars do not form in isolation but as part of a cluster comprising anywhere between a few dozen to several million stars with stellar densities ranging from 0.01 to several 10$^5$ \Msun pc$^{-3}$. The majority of these clusters…
We compute the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the…
We define a ring whose elements are rational functions, whose addition is polynomial multiplication, and whose multiplication is a convolution operation. It is then show that this ring's endomorphisms exhibit a strong classification.…
We consider minimal compactifications of the complex affine plane. Minimal compactifications of the affine plane with at most log canonical singularities are classified. Moreover, every minimal compactification of the affine plane with at…
An orbitope is the convex hull of an orbit of a compact group acting linearly on a vector space. These highly symmetric convex bodies lie at the crossroads of several fields, in particular convex geometry, optimization, and algebraic…
Rectangulations are decompositions of a square into finitely many axis-aligned rectangles. We describe realizations of $(n-1)$-dimensional polytopes associated with two combinatorial families of rectangulations composed of $n$ rectangles.…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A $d$-dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull of $d+1$ points. This statement is equivalent…
Most stars - especially young stars - are observed to be in multiple systems. Dynamical evolution is unable to pair stars efficiently, which leads to the conclusion that star-forming cores must usually fragment into \geq 2 stars. However,…
Given a seven-element set $X = \{1,2,3,4,5,6,7\}$, there are 30 ways to define a Fano plane on it. Let us call a line of such Fano plane, that is to say an unordered triple from $X$, ordinary or defective according as the sum of two smaller…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…
We have developed a two-dimensional orbit averaged Fokker-Planck model of stellar clusters which expands on spherically symmetric one-dimensional models to include rotation and ellipticity. Physical effects such as collisions, finite…
In a linear chord diagram a short chord is one which joins adjacent vertices. We define a bubble to be a region in a linear chord diagram devoid of short chords. We derive a formal generating function counting bubbles by their size and find…
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex…
It is shown that compact groups of galaxies (HCGs, ShCGS) are stable formations, in which principal member galaxies together with faint galaxies in their environment rotate in elongated orbits around the common gravitational center of the…
A fullerene graph can be embedded in a piecewise linear 2-manifold with each non-hexagonal carbon ring corresponding to a cone vertex. Adjacent two or three such vertices can be combined as a cluster cut out from a parent cone round a…
An increasing number of photometric observations of multiple stellar populations in Galactic globular clusters is seriously challenging the paradigm of GCs hosting single, simple stellar populations. These multiple populations manifest…
Typical globular clusters (GCs - young and old) host stellar populations with little or no star-to-star variations in heavy elements (e.g., Ca, Fe) nor in age. Nuclear star clusters (NSCs), on the other hand, host complex stellar…
We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…