Related papers: Spatial statistics for lattice points on the spher…
We briefly present a new coordinate-invariant statistical test dedicated to the study of the orientations of transverse quantities of non-uniformly distributed sources on the celestial sphere. These quantities can be projected spin-axes or…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
We find exact and asymptotic formulas for the average values of several statistics on set partitions: of Carlitz's $q$-Stirling distributions, of the numbers of crossings in linear and circular representations of set partitions, of the…
This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with…
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interval, whose admissible length depends on whether or not we…
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We…
We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…
For a given wave function one can define a quantity $\mu_E$ having a meaning of its inverse spatial size. The Laplace transform of the distribution function $P(\mu_E)$ is calculated analytically for a 1D disordered sample with a finite…
We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive improved upper and lower bounds based on the entropy of a…
Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to…
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…