Self-Similar Factor Approximants

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are named the self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of the self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions which include a variety of transcendental functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.Comment: 22 pages + 11 ps figure

The Muonium Atom as a Probe of Physics beyond the Standard Model

The observed interactions between particles are not fully explained in the successful theoretical description of the standard model to date. Due to the close confinement of the bound state muonium ($M = \mu^+ e^-$) can be used as an ideal probe of quantum electrodynamics and weak interaction and also for a search for additional interactions between leptons. Of special interest is the lepton number violating process of sponteanous conversion of muonium to antimuonium.Comment: 15 pages,6 figure

Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages

Radical pluralism and free speech in online public spaces: the case of North Belgian extreme right discourses

Progressive political movements and activists are not the only ones appropriating Web 2.0 as a way to construct independent public spaces and voice counterhegemonic discourses. By looking at the other extreme of (post-)fascist movements, it will be shown that the internet also gives rise to anti-public spaces, voicing hatred and essentialist discourses. In this article, discourses of hate produced by North-Belgian (post-)fascist movements and activists will be analysed. Theoretically the analysis is informed by radical pluralism and the limits of freedom of speech in a strong democracy. The cases presented challenge the limits of freedom of speech and of radical pluralism and bring us to question whether being a racist is a democratic right, whether freedom of speech includes opinions and views that challenge basic democratic values