Related papers: Closed Form Expressions for the Potentials and Acc…
This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
We introduce a novel family of projected distributions on the circle and the sphere, namely the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular…
A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of continuity and balance of momentum density have been…
Rotation curves are often used to estimate the mass distribution of spiral galaxies, assuming circular rotation of disks. However, non-circular motions caused by a non-axisymmetric gravitational potential, such as a stellar bar, may disturb…
We present new families of bound, closed, nonelliptical orbits that are supported by various spherical potentials in clear contradiction to Newton's and Bertrand's theorems. We calculate analytically some typical closed orbits of…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
We present a relativistic model of pulsar radio emission by plasma accelerated along the rotating magnetic field lines projected on to a 2D plane perpendicular to the rotation axis. We have derived the expression for the trajectory of a…
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…
We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers of ideals in regular rings. The author recently proved these bounds in mixed characteristic using various versions of perfectoid/big Cohen-Macaulay…
We study long-time properties of reversible reaction-diffusion systems of type A + B <-> C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the…
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…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
Tsetlin Machines (TMs) capture patterns using conjunctive clauses in propositional logic, thus facilitating interpretation. However, recent TM-based approaches mainly rely on inspecting the full range of clauses individually. Such…
In this article, we obtain exponential bounds for the generalized circular and hyperbolic functions with one parameter p. Our results are natural generalizations of some existing results for classical circular and hyperbolic functions.
Inspired by the works of Hughes [17, 18], we formalize and prove the well posedness of a hyperbolic--elliptic system whose solutions describe the dynamics of a moving crowd. The resulting model is here shown to be well posed and the time of…
Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on asymptotic series has recently been developed to derive closed-form results when…
We present harmonic decompositions of the velocity fields of 19 galaxies from THINGS (The \HI Nearby Galaxy Survey) which quantify the magnitude of the non-circular motions in these galaxies and yield observational estimates of the…