Sharp characters of finite groups

AbstractIf χ is a virtual (generalized) character of a finite group G, with n=χ and L={χ(g)|g∈G, g≠1 {χ(g)¦gϵG, g ≠ 1}, then ¦G¦ dividesfL(n), where fL(x) is the monic polynomial of least degree having L as its set of roots. (This generalises a result of the second author for permutation characters.) We say that the pair ((G,χ)) is L-sharp if ¦G¦=fL(n). We characterise the L-sharp pairs for various sets L, sometimes under additional hypotheses, and give a number of examples

V2051 Ophiuchi after superoutburst : out-of-plane material and the superhump light source

Aims. We performed a detailed spectroscopic analysis of the dwarf nova V2051 Oph at the end of its 1999 superoutburst. We studied and interpreted the simultaneous behaviour of various emission lines. Methods. We obtained high-resolution echelle spectroscopic data at ESO’s NTT with EMMI, covering the spectral range of 4000–7500 Å. The analysis was performed using standard IRAF tools. The indirect imaging technique of Doppler tomography was applied, in order to map the accretion disc and distinguish between the different emission sources. Results. The spectra are characterised by strong Balmer emission, together with lines of He i and the iron triplet Fe ii 42. All lines are double-peaked, but the blue-to-red peak strength and central absorption depth vary. The primary’s velocity was found to be 84.9 kms−1. The spectrograms of the emission lines reveal the prograde rotation of a disc-like emitting region and, for the Balmer and He i lines, an enhancement of the red-wing during eclipse indicates a bright spot origin. The modulation of the double-peak separation shows a highly asymmetric disc with non-uniform emissivity. This is confirmed by the Doppler maps, which apart from the disc and bright spot emission also indicate an additional region of enhanced emission in the 4th quadrant (+Vx, −Vy), which we associate with the superhump light source. Given the behaviour of the iron triplet and its distinct differences from the rest of the lines, we attribute its existence to an extended gas region above the disc. Its origin can be explained through the fluorescence mechanism

The Hydrogen Burning Turn-off of RS Ophiuchi 2006

We report a coordinated multi-band photometry of the RS Oph 2006 outburst and highlight the emission line free y-band photometry that shows a mid-plateau phase at y ~ 10.2 mag from day 40 to day 75 after the discovery followed by a sharp drop of the final decline. Such mid-plateau phases are observed in other two recurrent novae, U Sco and CI Aql, and are interpreted as a bright disk irradiated by the white dwarf. We have calculated theoretical light curves based on the optically thick wind theory and have reproduced the observed light curves including the mid-plateau phase and the final sharp decline. This final decline is identified with the end of steady hydrogen shell-burning, which turned out the day ~80. This turnoff date is consistent with the end of a supersoft X-ray phase observed with Swift. Our model suggests a white dwarf mass of 1.35 \pm 0.01 M_\sun, which indicates that RS Oph is a progenitor of Type Ia supernovae. We strongly recommend the y-filter observation of novae to detect both the presence of a disk and the hydrogen burning turn-off.Comment: to appear in ApJL, 4 pages including 4 figure

Deformation and cyclic strength characteristics of loose and medium-dense clean sand under sloping ground conditions: insights from cyclic undrained torsional shear tests with static shear

The effects of liquefaction on sloping ground often include the development of extremely large deformation. Although such phenomenon has been repeatedly observed following major earthquakes, the triggering conditions are not fully understood yet. To provide new insights into this issue, in this paper, results of two series of large-strain undrained cyclic torsional shear tests with initial static shear conducted on loose and medium-dense Toyoura sand specimens (relative density of 25-30% and 44-48%) are presented and analyzed. The post-liquefaction response of Toyoura sand is assessed in terms of failure modes and cyclic resistance up to 50% single amplitude shear strain. It is shown that, depending on the combined magnitude of static and cyclic shear stresses, a sand in sloping ground will likely experience a sudden development of large shear deformation (flow deformation) if initial liquefaction takes place, or a more progressive accumulation of large residual deformation, which yet may bring sand to failure, when the onset of initial liquefaction is not achieved

ASASSN-15lh: A Highly Super-Luminous Supernova

We report the discovery of ASASSN-15lh (SN 2015L), which we interpret as the most luminous supernova yet found. At redshift z = 0.2326, ASASSN-15lh reached an absolute magnitude of M_{u,AB} = -23.5+/-0.1 and bolometric luminosity L_bol = (2.2+/-0.2)x 10^45 ergs s^-1, which is more than twice as luminous as any previously known supernova. It has several major features characteristic of the hydrogen-poor super-luminous supernovae (SLSNe-I), whose energy sources and progenitors are currently poorly understood. In contrast to most previously known SLSNe-I that reside in star-forming dwarf galaxies, ASASSN-15lh appears to be hosted by a luminous galaxy (M_K ~ -25.5) with little star formation. In the 4 months since first detection, ASASSN-15lh radiated (1.1+/- 0.2)x10^52 ergs, challenging the magnetar model for its engine.Comment: Published in the January 15, 2016 Issue of Science Magazin

Nivolumab versus investigator's choice in patients with recurrent or metastatic squamous cell carcinoma of the head and neck : efficacy and safety in CheckMate 141 by age

Objectives: Many patients with squamous cell carcinoma of the head and neck (SCCHN) are 6565 years old; comorbidities and other age-related factors may affect their ability to tolerate traditional chemotherapy. Nivolumab is the only immunotherapy to significantly improve overall survival (OS) versus investigator's choice (IC) of single-agent chemotherapy at primary analysis in a phase 3 trial (CheckMate 141) in patients with recurrent/metastatic SCCHN post-platinum therapy. In this post hoc analysis, we report efficacy and safety by age. Patients and methods: Eligible patients were randomized 2:1 to nivolumab 3 mg/kg every 2 weeks (n = 240) or IC (methotrexate, docetaxel, or cetuximab n = 121). The primary endpoint of the trial was OS. For this analysis, outcomes were analyzed by age < 65 and 6565 years. The data cut-off date was September 2017 (minimum follow-up 24.2 months). Results: At baseline, 68 patients (28.3%) receiving nivolumab and 45 patients (37.2%) receiving IC were 6565 years. Baseline characteristics were generally similar across age groups. OS and tumor response benefits with nivolumab versus IC were maintained regardless of age. The 30-month OS rates of 11.2% (<65 years) and 13.0% ( 6565 years) with nivolumab were more than tripled versus corresponding IC rates of 1.4% and 3.3%, respectively. The nivolumab arm had a lower rate of treatment-related adverse events versus IC regardless of age, consistent with the overall patient population. Conclusion: In CheckMate 141, nivolumab resulted in a higher survival versus IC in patients <65 and 6565 years, with a manageable safety profile in both age groups. ClinicalTrials.gov: NCT02105636