On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

On absolute moments of characteristic polynomials of a certain class of complex random matrices

Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a given matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.Comment: 41 page, typos correcte

Regulation of pentraxin-3 by antioxidants

Peer reviewedPublisher PD

Observation of Scaling Violations in Scaled Momentum Distributions at HERA

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of $x$ and $Q^2$ using the ZEUS detector. The evolution of the scaled momentum, $x_p$, with $Q^2,$ in the range 10 to 1280 $GeV^2$, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of $Q^2$.Comment: 21 pages including 4 figures, to be published in Physics Letters B. Two references adde

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13

Doing race: how secondary school pupils in mainly white schools construct 'race'

This article examines how ‘race’ impacts upon the lives of young people who attend secondary schools in a mainly white British area of the United Kingdom. Schools Stand up 2 Racism (SSu2R), a Big Lottery research project, brought together a community partner – the Cheshire, Halton and Warrington Race and Equality Centre – and a team from Manchester Metropolitan University to investigate racism in Cheshire secondary schools. In an area where the population is over 93% ‘white British’, the sense that ‘there's nothing to be racist about in this school’ (Year 8 pupil) was found to be common. The three-year SSu2R study used a multimethod approach to study how students ‘do race’ in these schools, where the silent advocacy of a ‘colour-blind’ approach is promulgated through the popular rhetoric of ‘everyone is unique’ and ‘we should treat everyone the same’. Race is tackled only tangentially through the curriculum, accompanied by silences that close down discussion. Perhaps unsurprisingly given this context, forms of everyday racism are endemic and yet mostly unnoticed by staff or students. The article uses Bourdieu's concepts of ‘doxa’ and ‘the game’ to examine the nature of this silence

Variation in Structure and Process of Care in Traumatic Brain Injury: Provider Profiles of European Neurotrauma Centers Participating in the CENTER-TBI Study.

INTRODUCTION: The strength of evidence underpinning care and treatment recommendations in traumatic brain injury (TBI) is low. Comparative effectiveness research (CER) has been proposed as a framework to provide evidence for optimal care for TBI patients. The first step in CER is to map the existing variation. The aim of current study is to quantify variation in general structural and process characteristics among centers participating in the Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study. METHODS: We designed a set of 11 provider profiling questionnaires with 321 questions about various aspects of TBI care, chosen based on literature and expert opinion. After pilot testing, questionnaires were disseminated to 71 centers from 20 countries participating in the CENTER-TBI study. Reliability of questionnaires was estimated by calculating a concordance rate among 5% duplicate questions. RESULTS: All 71 centers completed the questionnaires. Median concordance rate among duplicate questions was 0.85. The majority of centers were academic hospitals (n = 65, 92%), designated as a level I trauma center (n = 48, 68%) and situated in an urban location (n = 70, 99%). The availability of facilities for neuro-trauma care varied across centers; e.g. 40 (57%) had a dedicated neuro-intensive care unit (ICU), 36 (51%) had an in-hospital rehabilitation unit and the organization of the ICU was closed in 64% (n = 45) of the centers. In addition, we found wide variation in processes of care, such as the ICU admission policy and intracranial pressure monitoring policy among centers. CONCLUSION: Even among high-volume, specialized neurotrauma centers there is substantial variation in structures and processes of TBI care. This variation provides an opportunity to study effectiveness of specific aspects of TBI care and to identify best practices with CER approaches

Measurement of the View the tt production cross-section using eμ events with b-tagged jets in pp collisions at √s = 13 TeV with the ATLAS detector

This paper describes a measurement of the inclusive top quark pair production cross-section (σtt¯) with a data sample of 3.2 fb−1 of proton–proton collisions at a centre-of-mass energy of √s = 13 TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron–muon pair in the final state. Jets containing b-quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b-tagged jets are counted and used to determine simultaneously σtt¯ and the efficiency to reconstruct and b-tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be: σtt¯ = 818 ± 8 (stat) ± 27 (syst) ± 19 (lumi) ± 12 (beam) pb, where the four uncertainties arise from data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A fiducial measurement corresponding to the experimental acceptance of the leptons is also presented

Search for strong gravity in multijet final states produced in pp collisions at √s=13 TeV using the ATLAS detector at the LHC

A search is conducted for new physics in multijet final states using 3.6 inverse femtobarns of data from proton-proton collisions at √s = 13TeV taken at the CERN Large Hadron Collider with the ATLAS detector. Events are selected containing at least three jets with scalar sum of jet transverse momenta (HT) greater than 1TeV. No excess is seen at large HT and limits are presented on new physics: models which produce final states containing at least three jets and having cross sections larger than 1.6 fb with HT > 5.8 TeV are excluded. Limits are also given in terms of new physics models of strong gravity that hypothesize additional space-time dimensions