Fusion systems containing pearls

The main theorems of this paper are generalizations of results proved by the author in her PhD thesis, under the supervision of Prof. Chris Parker. She is immensely grateful to him for his support. She would also like to show her gratitude to Dr. Ellen Henke for comments that improved this manuscript.Peer reviewedPostprin

On the structure of finite groups determined by the arithmetic and geometric means of element orders

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime p, we prove a sufficient condition for a finite group to be p-nilpotent, that is, a group whose elements of p'-order form a normal subgroup

Fusion systems on pp-groups of sectional rank 3

In this thesis we study saturated fusion systems on $p$-groups having sectional rank 3, for $p$ odd. We obtain a complete classification of simple fusion systems on p-groups having sectional rank 3 for $p$ ≥ 5, exhibiting a new simple exotic fusion system on a 7-group of order 7$^∧$5. We introduce the notion of pearls, defined as essential subgroups isomorphic to the groups C$_p$ X $_p$ and $p$$_+$$^1$$^+$$^2$ (for odd), and we illustrate some properties of fusion systems involving pearls. As for $p$ = 3, we determine the isomorphism type of a certain section of the 3-groups considered

The Probabilistic Random Forest applied to the selection of quasar candidates in the QUBRICS Survey

The number of known, bright ($i2.5$) QSOs in the Southern Hemisphere is considerably lower than the corresponding number in the Northern Hemisphere due to the lack of multi-wavelength surveys at $\delta<0$. Recent works, such as the QUBRICS survey, successfully identified new, high-redshift QSOs in the South by means of a machine learning approach applied on a large photometric dataset. Building on the success of QUBRICS, we present a new QSO selection method based on the Probabilistic Random Forest (PRF), an improvement of the classic Random Forest algorithm. The PRF takes into account measurement errors, treating input data as probability distribution functions: this allows us to obtain better accuracy and a robust predictive model. We applied the PRF to the same photometric dataset used in QUBRICS, based on the SkyMapper DR1, Gaia DR2, 2MASS, WISE and GALEX databases. The resulting candidate list includes $626$ sources with $i<18$. We estimate for our proposed algorithm a completeness of $\sim84\%$ and a purity of $\sim78\%$ on the test datasets. Preliminary spectroscopic campaigns allowed us to observe 41 candidates, of which 29 turned out to be $z>2.5$ QSOs. The performances of the PRF, currently comparable to those of the CCA, are expected to improve as the number of high-z QSOs available for the training sample grows: results are however already promising, despite this being one of the first applications of this method to an astrophysical context.Comment: Accepted for publication in MNRAS, 12 pages, 11 figures, 4 table

Spectroscopy of QUBRICS quasar candidates: 1672 new redshifts and a Golden Sample for the Sandage Test of the Redshift Drift

The QUBRICS (QUasars as BRIght beacons for Cosmology in the Southern hemisphere) survey aims at constructing a sample of the brightest quasars with z>~2.5, observable with facilities in the Southern Hemisphere. QUBRICS makes use of the available optical and IR wide-field surveys in the South and of Machine Learning techniques to produce thousands of bright quasar candidates of which only a few hundred have been confirmed with follow-up spectroscopy. Taking advantage of the recent Gaia Data Release 3, which contains 220 million low-resolution spectra, and of a newly developed spectral energy distribution fitting technique, designed to combine the photometric information with the Gaia spectroscopy, it has been possible to measure 1672 new secure redshifts of QUBRICS candidates, with a typical uncertainty $\sigma_z = 0.02$. This significant progress of QUBRICS brings it closer to (one of) its primary goals: providing a sample of bright quasars at redshift 2.5 < z < 5 to perform the Sandage test of the cosmological redshift drift. A Golden Sample of seven quasars is presented that makes it possible to carry out this experiment in about 1500 hours of observation in 25 years, using the ANDES spectrograph at the 39m ELT, a significant improvement with respect to previous estimates.Comment: 11 pages, 10 figures, accepted for publication in MNRA

Near-infrared spectroscopy of extreme BAL QSOs from the QUBRICS bright quasar survey

We report on the spectral confirmation of 18 QSO candidates from the "QUasars as BRIght beacons for Cosmology in the Southern hemisphere'' survey (QUBRICS), previously observed in the optical band, for which we acquired new spectroscopic data in the near-infrared band with the Folded-port InfraRed Echellette spectrograph (FIRE) at the Magellan Baade telescope. In most cases, further observations were prompted by the peculiar nature of the targets, whose optical spectra displayed unexpected absorption features. All candidates have been confirmed as bona fide QSOs, with average emission redshift $z\simeq 2.1$. The analysis of the emission and absorption features in the spectra, performed with Astrocook and QSFit, reveals that the large majority of these objects are broad-absorption line (BAL) QSOs, with almost half of them displaying strong Fe II absorption (typical of the so-called FeLoBAL QSOs). The detection of such a large fraction of rare objects (which are estimated to account for less than one percent of the general QSO population) is interpreted as an unexpected (yet favourable) consequence of the particular candidate selection procedure adopted within the QUBRICS survey. The measured properties of FeLoBAL QSOs observed so far provide no evidence that they are a manifestation of a particular stage in AGN evolution. In this paper we present an explorative analysis of the individual QSOs, to serve as a basis for a further, more detailed investigation

Elliptic and hyperelliptic magnetohydrodynamic equilibria

The present study is a continuation of a previous one on "hyperelliptic" axisymmetric equilibria started in [Tasso and Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. Specifically, some equilibria with incompressible flow nonaligned with the magnetic field and restricted by appropriate side conditions like "isothermal" magnetic surfaces, "isodynamicity" or P + B^2/2 constant on magnetic surfaces are found to be reducible to elliptic integrals. The third class recovers recent equilibria found in [Schief, Phys. Plasmas 10, 2677 (2003)]. In contrast to field aligned flows, all solutions found here have nonzero toroidal magnetic field on and elliptic surfaces near the magnetic axis.Comment: 9 page

CUBES : the Cassegrain U-band Efficient Spectrograph

In the era of Extremely Large Telescopes, the current generation of 8-10m facilities are likely to remain competitive at ground-UV wavelengths for the foreseeable future. The Cassegrain U-Band Efficient Spectrograph (CUBES) has been designed to provide high-efficiency (> 40%) observations in the near UV (305-400 nm requirement, 300-420 nm goal) at a spectral resolving power of R >20, 000 (with a lower-resolution, sky-limited mode of R ~7, 000). With the design focusing on maximizing the instrument throughput (ensuring a Signal to Noise Ratio (SNR) ~20 per high-resolution element at 313 nm for U ~18.5 mag objects in 1h of observations), it will offer new possibilities in many fields of astrophysics, providing access to key lines of stellar spectra: a tremendous diversity of iron-peak and heavy elements, lighter elements (in particular Beryllium) and light-element molecules (CO, CN, OH), as well as Balmer lines and the Balmer jump (particularly important for young stellar objects). The UV range is also critical in extragalactic studies: the circumgalactic medium of distant galaxies, the contribution of different types of sources to the cosmic UV background, the measurement of H2 and primordial Deuterium in a regime of relatively transparent intergalactic medium, and follow-up of explosive transients. The CUBES project completed a Phase A conceptual design in June 2021 and has now entered the detailed design and construction phase. First science operations are planned for 2028