The torsion of a finite quasigroup quandle is annihilated by its order

We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the torsion of its homology. It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. From the very beginning of the rack homology (between 1990 and 1995) the analogous result was suspected. The first general results in this direction were obtained independently about 2001 by R.A.Litherland and S.Nelson, and P.Etingof and M.Grana. In Litherland-Nelson paper it is proven that if (Q;*) is a finite homogeneous rack (this includes quasigroup racks) then the torsion of homology is annihilated by |Q|^n. In Etingof-Grana paper it is proven that if (X;A) is a finite rack and N=|G^0_Q| is the order of a group of inner automorphisms of Q, then only primes which can appear in the torsion of homology are those dividing N (the case of connected Alexander quandles was proven before by T.Mochizuki). The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki and in particular, they prove that the torsion part of the homology of the dihedral quandle R_3 is annihilated by 3. In Niebrzydowski-Przytycki paper it is conjectured that for a finite quasigroup quandle, torsion of its homology is annihilated by the order of the quandle. The conjecture is proved by T.Nosaka for finite Alexander quasigroup quandles. In this paper we prove the conjecture in full generality. For this version, we rewrote the Section 3 totally and introduced the concept of the precubic homotopy. In Section 2, the main addition is Corollary 2.2 which summarizes identities observed in the proof of the main theorem as we use it later in Section 3.Comment: 13 pages, 1 figure; accepted for publication in Journal of Pure and Applied Algebr

Multi-response analysis in the material characterisation of electrospun poly (lactic acid)/halloysite nanotube composite fibres based on Taguchi design of experiments: fibre diameter, non-intercalation and nucleation effects

Poly (lactic acid) (PLA)/halloysite nanotube (HNT) composite fibres were prepared by using a simple and versatile electrospinning technique. The systematic approach via Taguchi design of experiments (DoE) was implemented to investigate factorial effects of applied voltage, feed rate of solution, collector distance and HNT concentration on the fibre diameter, HNT non-intercalation and nucleation effects. The HNT intercalation level, composite fibre morphology, their associated fibre diameter and thermal properties were evaluated by means of X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM), imaging analysis and differential scanning calorimetry (DSC), respectively. HNT non-intercalation phenomenon appears to be manifested as reflected by the minimal shift of XRD peaks for all electrospun PLA/HNT composite fibres. The smaller-fibre-diameter characteristic was found to be sequentially associated with the feed rate of solution, collector distance and applied voltage. The glass transition temperature (T g) and melting temperature (T m) are not highly affected by varying the material and electrospinning parameters. However, as the indicator of the nucleation effect, the crystallisation temperature (T c) of PLA/HNT composite fibres is predominantly impacted by HNT concentration and applied voltage. It is evident that HNT’s nucleating agent role is confirmed when embedded with HNTs to accelerate the cold crystallisation of composite fibres. Taguchi DoE method has been found to be an effective approach to statistically optimise critical parameters used in electrospinning in order to effectively tailor the resulting physical features and thermal properties of PLA/HNT composite fibres

The Vega debris disc: A view from Herschel

We present five band imaging of the Vega debris disc obtained using the Herschel Space Observatory. These data span a wavelength range of 70-500 mu m with full-width half-maximum angular resolutions of 5.6-36.9 ''. The disc is well resolved in all bands, with the ring structure visible at 70 and 160 mu m. Radial profiles of the disc surface brightness are produced, and a disc radius of 11 '' (similar to 85AU) is determined. The disc is seen to have a smooth structure thoughout the entire wavelength range, suggesting that the disc is in a steady state, rather than being an ephemeral structure caused by the recent collision of two large planetesimals

System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes in Cu+Cu and Au+Au Collisions at sqrt(s_NN) = 200 and 62.4 GeV

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from {dijets} in Cu+Cu and Au+Au collisions at sqrt(s_NN) = 62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from \Delta\phi=\pi in central and semi-central collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.Comment: 464 authors from 60 institutions, 6 pages, 3 figures, 2 tables. Submitted to Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Fire as a fundamental ecological process: Research advances and frontiers

Fire is a powerful ecological and evolutionary force that regulates organismal traits, population sizes, species interactions, community composition, carbon and nutrient cycling and ecosystem function. It also presents a rapidly growing societal challenge, due to both increasingly destructive wildfires and fire exclusion in fire‐dependent ecosystems. As an ecological process, fire integrates complex feedbacks among biological, social and geophysical processes, requiring coordination across several fields and scales of study. Here, we describe the diversity of ways in which fire operates as a fundamental ecological and evolutionary process on Earth. We explore research priorities in six categories of fire ecology: (a) characteristics of fire regimes, (b) changing fire regimes, (c) fire effects on above‐ground ecology, (d) fire effects on below‐ground ecology, (e) fire behaviour and (f) fire ecology modelling. We identify three emergent themes: the need to study fire across temporal scales, to assess the mechanisms underlying a variety of ecological feedbacks involving fire and to improve representation of fire in a range of modelling contexts. Synthesis : As fire regimes and our relationships with fire continue to change, prioritizing these research areas will facilitate understanding of the ecological causes and consequences of future fires and rethinking fire management alternatives

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio