arXiv subjects
Publications and source records attributed to Tomáš Vítek.
We compute the rational homology of $\mathrm{Out}(F_8)$ and $\mathrm{Aut}(F_7)$, and several related groups. We also show that the Eisenstein classes in $H_7(\mathrm{Aut}(F_5))$ and $H_{11}(\mathrm{Aut}(F_7))$ are zero.
Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \mathbb{R}^d$ onto $Δ\subset \mathbb{R}^d$ (for $d=3, 4$) such that $f\in W^{1,p}(Ω, \mathbb{R}^d)$ and $f^{-1}\in W^{1,q}(Δ, \mathbb{R}^d)$, $1\leq p ,q < \infty$ and any $ε>0$ we construct a diffeomorphism $\tilde{f}$ such that $$\|f-\tilde{f}\|_{W^{1,p}(Ω,\mathbb{R}^d)} + \|f^{-1}-\tilde{f}^{-1}\|_{W^{1,q}(Δ,\mathbb{R}^d)} < ε.$$
GRBAlpha is a 1U CubeSat launched in March 2021 to a sun-synchronous LEO at an altitude of 550 km to perform an in-orbit demonstration of a novel gamma-ray burst detector developed for CubeSats. VZLUSAT-2 followed ten months later in a similar orbit carrying as a secondary payload a pair of identical detectors as used on the first mission. These instruments detecting gamma-rays in the range of 30-900 keV consist of a 56 cm2 5 mm thin CsI(Tl) scintillator read-out by a row of multi-pixel photon counters (MPPC or SiPM). The scientific motivation is to detect gamma-ray bursts and other HE transient events and serve as a pathfinder for a larger constellation of nanosatellites that could localize these events via triangulation. At the beginning of July 2024, GRBAlpha detected 140 such transients, while VZLUSAT-2 had 83 positive detections, confirmed by larger GRB missions. Almost a hundred of them are identified as gamma-ray bursts, including extremely bright GRB 221009A and GRB 230307A, detected by both satellites. We were able to characterize the degradation of SiPMs in polar orbit and optimize the duty cycle of the detector system also by using SatNOGS radio network for downlink.