Related papers: The Moment Generating function for ray lengths in …
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of electrically-conducting fluid with stress-free electrically perfectly conducting boundaries for…
Advanced accelerator-based light sources such as free electron lasers (FEL) accelerate highly relativistic electron beams to generate incredibly short (10s of femtoseconds) coherent flashes of light for dynamic imaging, whose brightness…
We obtain a representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion $H$ with a drift that is affine linear in the local time accumulated by $H$ at its current level. As…
In the study of amyloid fiber formation, the fiber length distribution plays a central role. From this microscopic distribution, all macroscopic statistical quantities, like the fiber number concentration P(t) and mass concentration M(t),…
We study the distribution of the durations of gamma-ray bursts (GRBs) in the unified model of short and long GRBs recently proposed by Yamazaki, Ioka, and Nakamura. Monte Carlo simulations show clear bimodal distributions, with…
We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a…
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…
A branching random tessellation (BRT) is a stochastic process that transforms a coarse initial tessellation of $\mathbb{R}^d$ into a finer tessellation by means of random cell divisions in continuous time. This concept generalises the…
We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in $\mathbb{R}^2$ with radii determined by an underlying stationary and ergodic random field $\varphi:\mathbb{R}^2\to[0,\infty)$,…
We consider Gaussian approximation in three particular models of Poisson-Laguerre tessellations, namely, the $\beta$-, $\beta'$- and Gaussian-Voronoi tessellations. The tessellations are constructed based on inhomogeneous Poisson point…
We investigate parametric X-ray radiation (PXR) under condition of the extremely asymmetric diffraction, when the ultra-relativistic electron bunch is moving in \textit{vacuum} parallel to the crystal-vacuum interface, close to the crystal…
Including destructively interfering off-diagonal transitions of diffraction-dissociation type, we arrive at a formulation of GVD for exclusive vector-meson production in terms of a continuous spectral representation of dipole form. The…
We consider the process of atomic ionization driven by a laser pulse with varying ellipticity. We study distribution of the momenta of the photoelectrons, ionized by a strong laser field, emitted in the direction perpendicular to the…
We present a theoretical investigation of the resonant elastic scattering of twisted light, carrying angular momentum, by partially stripped ions. Special emphasis is placed on a question of whether the scattered radiation is also twisted.…
The cross section for elastic vector meson production in photon-proton interactions at large $t$ is considered using the exact analytic solution of the BFKL equation in the azimuthally symmetric $n=0$ limit. We use a non-relativistic model…
The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points in the plane with which are associated directions. At time 0, each line-segment starts…
We theoretically investigate droplet quasi-Bessel beams for different shapes of the round-tip axicon. Exact solutions for the Fresnel diffraction integrals describing the axial distribution of the electric field amplitude behind the axicon…
The aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an…
We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our…