Irreducible character degrees and normal subgroups

Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For example, if N is solvable, its derived length is bounded above by a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3, then the derived length of N is at most 3

Real fields and repeated radical extensions

The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper also contains a number of other results about repeated radical extensions

X-ray induced persistent photoconductivity in Si-doped Al0.35_{0.35}Ga0.65_{0.65}As

We demonstrate that X-ray irradiation can be used to induce an insulator-metal transition in Si-doped Al$_{0.35}$Ga$_{0.65}$As, a semiconductor with {\it DX} centers. The excitation mechanism of the {\it DX} centers into their shallow donor state was revealed by studying the photoconductance along with fluorescence. The photoconductance as a function of incident X-ray energy exhibits an edge both at the Ga and As K-edge, implying that core-hole excitation of Ga and As are efficient primary steps for the excitation of {\it DX} centers. A high quantum yield ($\gg 1$) suggests that the excitation is indirect and nonlocal, due to secondary electrons, holes, and fluorescence photons.Comment: 3 pages of text, 6 figures. An error in Fig.5 was detected, so we corrected i

Conjugacy classes of p-cycles of type D in alternating groups

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.Comment: Second paragraph of subsection 2.2 rewritten. 4-th sentence of subsection 2.4 rewritten. More explanations added in Remark 2.4. Lemma 2.5 and Corollary 2.7 added. Appendix removed and put it as Remark 3.1. Remark 3.2 (former 3.1) reorganized. References: [Da], [EGSS], [H], [IS] added, [GPPS] removed. Communications in Algebra (2014

Trends in International Maths and Science Study (TIMSS) 2019 National Report for England

The Trends in International Mathematics and Science Study (TIMSS) is a survey of the educational achievement of pupils in years 5 and 9 organised by the International Association for the Evaluation of Educational Achievement (IEA). The report provides analysis of the TIMSS 2019 findings for England and compares England’s performance to performance in other participating countries

Mechanochemically synthesized Pb-free halide perovskite-based Cs2AgBiBr6–Cu–RGO nanocomposite for photocatalytic CO2 reduction

Pb-based halide perovskites have recently showed great potential in various applications such as solar cells, optoelectronics and photocatalysis. Despite their high performance, the Pb2+ toxicity along with poor stability hinders long term applications in photocatalysis. Herein, we report mechanochemically prepared Pb-free Cs2AgBiBr6 double perovskite nanoplates and their heterostructure with Cu-loaded reduced graphene oxide (Cu–RGO) for gas-phase photocatalytic CO2 reduction using water vapor as the proton source in the absence of a hole scavenger. The resulting Cs2AgBiBr6–Cu–RGO nanocomposite shows significant photocatalytic activity of 10.7 (±0.6) μmol CH4 g−1 h−1, 1.9 (±0.3) μmol CO g−1 h−1 and 1.0 (±0.2) μmol H2 g−1 h−1, with a CH4 selectivity of 93.0 (±0.5)% on an electron basis with 1 sun and a remarkable apparent quantum efficiency of 0.89 (±0.21)% at 590 nm. A further 32% enhancement in photocatalytic activity on an electron basis is achieved when the light intensity is doubled (2 suns). The high performance was attributed to their improved charge separation and suppressed electron–hole recombination, along with extended visible light absorption, better stability in a humid environment and improved CO2 adsorption. These findings support Cs2AgBiBr6 as a potential Pb-free alternative to conventional halide perovskites for photocatalytic solar-to-fuel conversion and CO2 utilization

Antimicrobial susceptibility of bacteria isolated from newborns with suspected or confirmed necrotising enterocolitis

Aim. This audit aimed to identify which bacteria were associated with necrotising enterocolitis (NEC) and determine their antibiotic sensitivities. Methods. A retrospective audit of all infants with a diagnosis of suspected NEC or confirmed NEC and a positive culture (blood/faeces/operative specimen or vascular access device) between January 2000 and September 2007 was performed. Results. Ninety nine infants had a diagnosis of suspected (45) or confirmed NEC (54). Seventeen patients had suspected (5) or confirmed (12) NEC and a positive culture result. 12 babies had positive blood cultures associated with their NEC. Only 4 of the 12 cases of NEC with a positive blood culture received adequate first line cover for their subsequently identified infecting organism. Conclusions. Due to the limitations of this study we are unable to make general recommendations on the first line antibiotic choice for babies with suspected or confirmed NEC. Our current regime of Ampicillin, Gentamicin and Metronidazole failed to adequately treat 8 of the 12 organisms subsequently isolated in blood cultures. Only the combination of Vancomycin and Meropenem would have adequately treated all the bacteria identified. The concern with this approach is the possible emergence of multi drug resistant bacteria