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This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo…
In this article: a) a method is developed for calculating volumetric diagrams of elastic scattering of microparticles (in particular, electrons and photons) on single-layer and multi-layer statistically uneven surfaces; b) the diffraction…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We compute the cosmological constant of a spherical space in the limit of weak gravity. To this end we use a duality developed by the present authors in a previous work. This duality allows one to treat the Newtonian cosmological fluid as…
Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.
An analytic approximation to the mass function for gravitationally bound objects is presented. We base on the Zel'dovich approximation to extend the Press-Schechter formalism to a nonspherical dynamical model. A simple extrapolation of that…
We present a detailed two-dimensional stellar dynamical analysis of a sample of 44 cosmological hydrodynamical simulations of individual central galaxies and their satellites. Kinematic maps of the stellar line-of-sight velocity, velocity…
We analyse the distribution of position angles of 1 million galaxies from the Hyperleda catalogue, a sample that presents the galaxies coordinates in the celestial sphere, information that allows us to look for a possible privileged…
Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare…
We study "distance spheres": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is "too dense" and a set of small volume, we can decompose $[0,1]^d$…
We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2…
In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond…
We generalize the spherical collapse model for the formation of dark matter halos to apply in a universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the…
We enumerate the 4(1+F)+2S independent arbitrary functions of space require to describe a general relativistic cosmology containing an arbitrary number of non-interacting fluid (F) and scalar fields (S). Results are also given for arbitrary…
From the homotopy groups of three distinct octahedral spherical 3-manifolds we construct the isomorphic groups H of deck transformations acting on the 3-sphere. The H-invariant polynomials on the 3-sphere constructed by representation…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
Cosmography is the tool that makes possible to untie the interpretation of cosmological observations from the definition of any dynamical prior. We review the constraints on the cosmographic parameter obtained using the most thorough data…
We investigate the nonlinear two- and three-point correlation functions of the cosmological density field in Fourier space and test the popular hierarchical clustering model, that the three-point amplitude Q is independent of scale. In…