Related papers: Star configurations in $\mathbb P^n$
We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating…
We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…
The physical conditions in molecular clouds control the nature and rate of star formation, with consequences for planet formation and galaxy evolution. The focus of this review is on the conditions that characterize regions of star…
This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other…
Direct determination of fundamental stellar parameters has many profound and wide-ranging impacts throughout astrophysics. These determinations are rooted in high angular resolution observations. In particular, as long-baseline optical…
The basic processes of the formation of the first stars in the primordial Universe are outlined and the implications for cosmological structure formation discussed. By employing theoretical and numerical models of cosmic structure evolution…
Understanding the formation of the first stars is one of the frontier topics in modern astrophysics and cosmology. Their emergence signaled the end of the cosmic dark ages, a few hundred million years after the Big Bang, leading to a…
We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…
We introduce and study integral planes associated with crystallographic and non-crystallographic integral systems in real composition algebras. For an integral order $\Order$ in such an algebra we define the plane $\Order^{2}$ with…
In this article we prove in main Theorem A that any infinity type real hyperplane arrangement $\mathcal{H}_n^m$ (Definition 2.11) with the associated normal system $\mathcal{N}$ (Definitions [2.2,2.4] can be represented isomorphically…
Any realistic theory of galaxy formation must be set in the context of a model for the formation of structure in the universe. We describe a powerful approach -- semi-analytic modelling -- that combines a set of simple rules describing the…
In this paper, I review to what extent we can understand the photometric properties of star clusters, and of low-mass, unresolved galaxies, in terms of population synthesis models designed to describe `simple stellar populations' (SSPs),…
The goal of the paper is to study a topology generated by the star order on von Neumann algebras. In particular, it is proved that the order topology under investigation is finer than $\sigma$-strong* topology. On the other hand, we show…
An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are…
We study the problem of crescent configurations, posed by Erd\H{o}s in 1989. A crescent configuration is a set of $n$ points in the plane such that: 1) no three points lie on a common line, 2) no four points lie on a common circle, 3) for…
The King and the EFF (Elson, Fall & Freeman 1987) analytical models are employed to determine the structural parameters of star clusters using an 1-D surface brightness profile fitting method. The structural parameters are derived and a…
This study aims to provide an analytical scheme for computing equilibrium configurations of relativistic stars by solving the Tolman-Oppenheimer-Volkoff equations directly in isotropic polar coordinates, as opposed to the commonly applied…
Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric…
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…
In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3.…