相关论文: Flocks of Cones: Star Flocks
A subset of the sphere is said short if it is contained in an open hemisphere. A short closed set which is geodesically convex is called a cap. The following theorem holds: 1. The minimal number of short closed sets covering the $n$-sphere…
Recent experimental evidence suggests that interactions in flocks of birds do not involve a characteristic length scale. Bird flocks have also been revealed to have an inhomogeneous density distribution, with the density of birds near the…
The category of (abstract) fans is to the category of monoids what the category of schemes is to the category of rings: a fan is obtained by gluing spectra of monoids along open embeddings. Here we study the basic algebraic geometry of…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, comprising only about 5.7% of anagrams in English. They can…
We define Floer homology theories for oriented, singular knots in S^3 and show that one of these theories can be defined combinatorially for planar singular knots.
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…
We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises…
Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide…
In this paper, we characterise ovoidal cones by their intersection numbers. We first show that a set of points of $\mathrm{PG}(4,q)$ which intersects planes in $1$, $q+1$ or $2q+1$ points is either an ovoidal cone or a parabolic quadric,…
This review summarizes the properties of the stellar population in bulges as observed in nearby or distant spiral galaxies. It gives a particular emphasis to the comparison with elliptical galaxies, when possible. The criteria of sample…
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection…
Derived from first physical principles, a few simple rules are presented that can help in both the planning and interpretation of CCD and IR-array camera observations of resolvable stellar populations. These rules concern the overall size…
In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order $(5^2,5)$ and give numerous further examples of hemisystems in all the known flock generalized…
The simplest way to generate a lattice of convex sets is to consider an initial set of points and draw segments, triangles, and any convex hull from it, then intersect them to obtain new points, and so forth. The result is an infinite…
The family of all $k$-independent sets of a graph containing a fixed vertex $v$ is called a {star} and $v$ is called its center. Stars are interesting for their relation to Erd\"{o}s-Ko-Rado graphs. Hurlbert and Kamat conjectured that in…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
Although originally classified as galaxies, Ultra Compact Dwarfs (UCDs) share many properties in common with globular star clusters. The debate on the origin and nature of UCDs, and the recently discovered ultra-faint dwarf spheroidal…
Recent surveys of star forming regions have shown that most stars, and probably all massive stars, are born in dense stellar clusters. The mechanism by which a molecular cloud fragments to form several hundred to thousands of individual…
Traditionally globular clusters and dwarf spheroidal galaxies have been distinguished by using one or more of the following criteria: (1) mass, (2) luminosity, (3) size, (4) mass-to-light ratio and (5) spread in metallicity. However, a few…