45 research outputs found
Overview of (pro-)Lie group structures on Hopf algebra character groups
Character groups of Hopf algebras appear in a variety of mathematical and
physical contexts. To name just a few, they arise in non-commutative geometry,
renormalisation of quantum field theory, and numerical analysis. In the present
article we review recent results on the structure of character groups of Hopf
algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild
assumptions on the Hopf algebra or the target algebra the character groups
possess strong structural properties. Moreover, these properties are of
interest in applications of these groups outside of Lie theory. We emphasise
this point in the context of two main examples: The Butcher group from
numerical analysis and character groups which arise from the Connes--Kreimer
theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on
"New Developments in Discrete Mechanics, Geometric Integration and
Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai
Association between days alive without life support/out of hospital and health-related quality of life
CubeSpec, A Mission Overview
CubeSpec is an in-orbit demonstration CubeSat mission in the ESA technology programme, developed and funded in Belgium. The goal of the mission is to demonstrate high-spectral-resolution astronomical spectroscopy from a 6-unit CubeSat. The prime science demonstration case for the in-orbit demonstration mission is to unravel the interior of massive stars using asteroseismology by high-cadance monitoring of the variations in spectral line profiles during a few months. The technological challenges are numerous. The 10x20cm aperture telescope and echelle spectrometer have been designed to fit in a 10x10x20cm volume.
Under low-Earth orbit thermal variations, maintaining the fast telescope focus and spectrometer alignment is achieved via an athermal design. Straylight rejection and thermal shielding from the Sun and Earth infrared flux is achieved via deploying Earth and Sunshades. The narrow spectrometer slit requires arcsecond-level pointing stability using a performant 3-axis wheel stabilised attitude control system with star tracker augmented with a fine beam steering mechanism controlled in closed loop with a guiding sensor. The high cadence, long-term monitoring requirement of the mission poses specific requirements on the orbit and operational scenarios to enable the required sky visibility.
CubeSpec is starting the implementation phase, with a planned launch early 2024