相关论文: Star-shaped distributions and their generalization…
The statistics of gravitationally lensed arcs, which can be used for a variety of cosmological tests, are sensitive to the intrinsic shapes of the source galaxies. I present an analytic formalism that makes it simple to include elliptical…
We postulate that most stars are born in aggregates of binary systems which are dynamically equivalent to the `dominant mode cluster'. The initial binary orbits are consitent with pre-main sequence data. Stellar masses are paired at random…
Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In…
The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose…
The mass function of molecular clouds and clumps is shallower than the mass function of young star clusters, gas-embedded and gas-free alike, as their respective mass function indices are $\beta_0 \simeq 1.7$ and $\beta_\star \simeq 2$. We…
In this paper, we study the spherical cardioid distribution, a higher-dimensional and higher-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial,…
Bressert et al. recently showed that the surface density distribution of low-mass, young stellar objects (YSOs) in the solar neighbourhood is approximately log-normal. The authors conclude that the star formation process is hierarchical and…
This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a…
The positions of images produced by the gravitational lensing of background sources provide unique insight in to galaxy-lens mass distribution. However, even quad images of extended sources are not able to fully characterize the central…
This chapter presents a short overview of real elliptically symmetric (RES) distributions, complemented by circular complex elliptically symmetric (C-CES) and noncircular CES (NC-CES) distributions as complex representations of RES…
This letter matches the shape of the star formation intensity distribution function to empirical laws such as the Schmidt law. The shape of the distribution at a redshift of one is reproduced from the empirical Schmidt law with a critical…
We study the distribution of projected ellipticity n(epsilon) for galaxies in a sample of 20 rich (Richness >= 2) nearby (z < 0.1) clusters of galaxies. We find no evidence of differences in n(epsilon), although the nearest cluster in the…
The statistical parameters of five generalizations of the Lindley distribution, such as the average, variance and moments, are reviewed. A new double truncated Lindley distribution with three parameters is derived. The new distributions are…
The radial distribution of globular clusters in galaxies is always less peaked to the centre than the halo stars'. Extending previous work to a sample of HST globular cluster systems in ellipticals, we evaluate the number of clusters lost…
Understanding the formation and evolution of young star clusters requires quantitative statistical measures of their structure. We investigate the structures of observed and modelled star-forming clusters. By considering the different…
We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…
The last 20 years have seen an explosion in our understanding of the large-scale distribution and motions of galaxies in the nearby universe. The field has moved from a largely qualitative, morphological description of the structures seen…
Given an elliptic curve $E$ and a point $P$ in $E(\mathbb{R})$, we investigate the distribution of the points $nP$ as $n$ varies over the integers, giving bounds on the $x$ and $y$ coordinates of $nP$ and determining the natural density of…
Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or…
We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…