On the degrees of irreducible characters fixed by some field automorphism

It is known that, if all the irreducible real valued characters of a finite group are of odd degree, then the group has a normal Sylow 2-subgroup. In this paper, we prove and analogous result for solvable groups, by taking into account the degree of irreducible characters fixed by some field isomorphism of prime order $p$. We prove it as a consequence of a more general result

Character degrees in π\pi-separable groups

If a group $G$ is $\pi$-separable, where $\pi$ is a set of primes, the set of irreducible characters $\operatorname{B}_{\pi}(G) \cup \operatorname{B}_{\pi'}(G)$ can be defined. In this paper, we prove that there are variants of some classical theorems in character theory, namely the Theorem of Ito-Michler and Thompson theorem on character degrees, which involve irreducible characters in the set $\operatorname{B}_{\pi}(G) \cup \operatorname{B}_{\pi'}(G)$

Fair value accounting and financial stability

Accounting standard setters are considering the wider use of fair value accounting. This paper focuses on the financial stability implications of a move in the banking sector from the current accounting framework to full fair value accounting. A simulation exercise is performed on how various external shocks affect the balance sheet of an average European bank under the two frameworks. The paper further investigates the impact of the alternative framework on the main balance sheet items, and the interaction with banks’ risk management, supervisory tools and statistical requirements. It also examines how the application of fair value accounting to banks’ trading book has impacted their share price volatility. It is concluded that the introduction of full fair value accounting could have a significant effect in terms of income volatility, procyclicality of bank lending and more generally financial stability. Hence, any move towards this alternative accounting framework should be gradual.accounting, banks, fair value, financial regulation, financial reporting, financial stability, risk management.

Tarapacol 15-Acetate, a New Diterpenoid from Grindelia tarapacana Phil.

In the title compound, 15-acetoxy-14(S)-hydroxy-13-epi-manoyl oxide {IUPAC systematic name: 2-(dodecahydro-3,4a,7,7,10a-pentamethyl-1H-naphtho[2,1-b]pyran-3-yl)-2-hydroxyethyl acetate}, C22H38N4, rings A and B have chair conformations. Ring C adopts a boat conformation with the 16-methyl group in an axial position and the bulky glycol monoacetate group in an equatorial position. Ring systems A/B and B/C (conventional IUPAC labdane diterpenoid nomenclature) are trans fused about the C(5)-C(10) and C(8)-C(9) bonds, respectively. The present study establishes the relative stereochemistry at the C(14) position.This work was supported by a grant to the American Association for the Advancement of Science from the John D. and Catherine T. MacArthur Foundation, awarded to BNT. The structure was determined in the Molecular Structure Laboratory of the Department of Chemistry as a special class project in Chemistry 517

The Clinical Impact of the Pulmonary Embolism Severity Index on the Length of Hospital Stay of Patients with Pulmonary Embolism: A Randomized Controlled Trial.

BACKGROUND The Pulmonary Embolism Severity Index (PESI) is an extensively validated prognostic score, but impact analyses of the PESI on management strategies, outcomes and health care costs are lacking. Our aim was to assess whether the adoption of the PESI for patients admitted to an internal medicine ward has the potential to safely reduce the length of hospital stay (LOS). METHODS We carried out a multicenter randomized controlled trial, enrolling consecutive adult outpatients diagnosed with acute PE and admitted to an internal medicine ward. Within 48 h after diagnosis, the treating physicians were randomized, for every patient, to calculate and report the PESI in the clinical record form on top of the standard of care (experimental arm) or to continue routine clinical practice (standard of care). The ClinicalTrials.gov identifier is NCT03002467. RESULTS This study was prematurely stopped due to slow recruitment. A total of 118 patients were enrolled at six internal medicine units from 2016 to 2019. The treating physicians were randomized to the use of the PESI for 59 patients or to the standard of care for 59 patients. No difference in the median LOS was found between the experimental arm (8, IQR 6-12) and the standard-of-care arm (8, IQR 6-12) (p = 0.63). A pre-specified secondary analysis showed that the LOS was significantly shorter among the patients who were treated with DOACs (median of 8 days, IQR 5-11) compared to VKAs or heparin (median of 9 days, IQR 7-12) (p = 0.04). CONCLUSIONS The formal calculation of the PESI in the patients already admitted to internal medicine units did not impact the length of hospital stay

On zeros of irreducible characters lying in a normal subgroup

[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we also study certain arithmetical properties of the G-conjugacy class sizes of the elements of N which are zeros of some irreducible character of G. In particular, if N=G, then new contributions are obtained.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). The research of the second author is partially funded by the Istituto Nazionale di Alta Matematica - INdAM. The third author acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The first and third authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovacion y Universidades (Spain).Felipe Román, MJ.; Grittini, N.; Ortiz-Sotomayor, VM. (2020). On zeros of irreducible characters lying in a normal subgroup. Annali di Matematica Pura ed Applicata (1923 -). 199:1777-1789. https://doi.org/10.1007/s10231-020-00942-1S17771789199Beltrán, A., Felipe, M.J.: Prime powers as conjugacy class lengths of $$\pi$$-elements. Bull. Aust. Math. Soc. 69, 317–325 (2004)Beltrán, A., Felipe, M.J., Malle, G., Moretó, A., Navarro, G., Sanus, L., Solomon, R., Tiep, P.H.: Nilpotent and abelian Hall subgroups in finite groups. Trans. Am. Math. Soc. 368, 2497–2513 (2016)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Bianchi, M., Chillag, D., Lewis, M.L., Pacifici, E.: Character degree graphs that are complete graphs. Proc. Am. Math. Soc. 135, 671–676 (2007)Brough, J., Kong, Q.: On vanishing criteria that control finite group structure II. Bull. Aust. Math. Soc. 98, 251–257 (2018)Brough, J.: Non-vanishing elements in finite groups. J. Algebra 460, 387–391 (2016)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Grüninger, M.: Two remarks about non-vanishing elements in finite groups. J. Algebra 460, 366–369 (2016)Isaacs, I.M.: Character Theory of Finite Groups. Academic Press Inc., London (1976)Isaacs, I.M., Navarro, G., Wolf, T.R.: Finite group elements where no irreducible character vanishes. J. Algebra 222, 413–423 (1999)Malle, G., Navarro, G.: Characterizing normal Sylow $$p$$-subgroups by character degrees. J. Algebra 370, 402–406 (2012)Malle, G., Navarro, G., Olsson, J.B.: Zeros of characters of finite groups. J. Group Theory 3, 353–368 (2000)The GAP Group: GAP—Groups, Algorithms, and Programming. Version 4.10.0 (2018). http://www.gap-system.or

Photodegradation of Selected PCBs in the Presence of Nano-TiO2 as Catalyst and H2O2 as an Oxidant

Photodegradation of five strategically selected PCBs was carried out in acetonitrile/water 80:20. Quantum chemical calculations reveal that PCBs without any chlorine on ortho-positions are closer to be planar, while PCBs with at least one chlorine atoms at the ortho-positions causes the two benzene rings to be nearly perpendicular. Light-induced degradation of planar PCBs is much slower than the perpendicular ones. The use of nano-TiO2 speeds up the degradation of the planar PCBs, but slows down the degradation of the non-planar ones. The use of H2O2 speeds up the degradation of planar PCBs greatly (by >20 times), but has little effect on non-planar ones except 2,3,5,6-TCB. The relative photodegradation rate is: 2,2′,4,4′-TCB > 2,3,5,6-TCB > 2,6-DCB ≈ 3,3′,4,4′-TCB > 3,4′,5-TCB. The use of H2O2 in combination with sunlight irradiation could be an efficient and “green” technology for PCB remediation