Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

The K\"ahler-Ricci flow with positive bisectional curvature

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.Comment: 15 page

The perseverance of Pacioli's goods inventory accounting system

This paper details sources of the 'undoubtedly strange' (Yamey, 1994a, p.119) system of goods inventory records described in Pacioli’s 1494 bookkeeping treatise and traces the longevity and widespread use of this early perpetual inventory recording (EPIR) system in English language texts. By doing so and contrasting this system with the bookkeeping treatment of modern texts, it is shown that the EPIR system persisted as the dominant form of goods inventory accounting for between 400 and 500 years and that the reasons for its demise are worthy of further consideration and research

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR

The performance of the jet trigger for the ATLAS detector during 2011 data taking

The performance of the jet trigger for the ATLAS detector at the LHC during the 2011 data taking period is described. During 2011 the LHC provided proton–proton collisions with a centre-of-mass energy of 7 TeV and heavy ion collisions with a 2.76 TeV per nucleon–nucleon collision energy. The ATLAS trigger is a three level system designed to reduce the rate of events from the 40 MHz nominal maximum bunch crossing rate to the approximate 400 Hz which can be written to offline storage. The ATLAS jet trigger is the primary means for the online selection of events containing jets. Events are accepted by the trigger if they contain one or more jets above some transverse energy threshold. During 2011 data taking the jet trigger was fully efficient for jets with transverse energy above 25 GeV for triggers seeded randomly at Level 1. For triggers which require a jet to be identified at each of the three trigger levels, full efficiency is reached for offline jets with transverse energy above 60 GeV. Jets reconstructed in the final trigger level and corresponding to offline jets with transverse energy greater than 60 GeV, are reconstructed with a resolution in transverse energy with respect to offline jets, of better than 4 % in the central region and better than 2.5 % in the forward direction

Relationship of edge localized mode burst times with divertor flux loop signal phase in JET

A phase relationship is identified between sequential edge localized modes (ELMs) occurrence times in a set of H-mode tokamak plasmas to the voltage measured in full flux azimuthal loops in the divertor region. We focus on plasmas in the Joint European Torus where a steady H-mode is sustained over several seconds, during which ELMs are observed in the Be II emission at the divertor. The ELMs analysed arise from intrinsic ELMing, in that there is no deliberate intent to control the ELMing process by external means. We use ELM timings derived from the Be II signal to perform direct time domain analysis of the full flux loop VLD2 and VLD3 signals, which provide a high cadence global measurement proportional to the voltage induced by changes in poloidal magnetic flux. Specifically, we examine how the time interval between pairs of successive ELMs is linked to the time-evolving phase of the full flux loop signals. Each ELM produces a clear early pulse in the full flux loop signals, whose peak time is used to condition our analysis. The arrival time of the following ELM, relative to this pulse, is found to fall into one of two categories: (i) prompt ELMs, which are directly paced by the initial response seen in the flux loop signals; and (ii) all other ELMs, which occur after the initial response of the full flux loop signals has decayed in amplitude. The times at which ELMs in category (ii) occur, relative to the first ELM of the pair, are clustered at times when the instantaneous phase of the full flux loop signal is close to its value at the time of the first ELM

Measurement of prompt D0^{0} and D‾\overline{D}0^{0} meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at root SNN\sqrt{S_{NN}} = 5.02 TeV

The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapiditydependent difference (Av2) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, v2) between D0 (uc) and D0 (uc) mesons. Motivated by the search for evidence of this field, the CMS detector at the LHC is used to perform the first measurement of Av2. The rapidity-averaged value is found to be (Av2) = 0.001 ? 0.001 (stat)? 0.003 (syst) in PbPb collisions at ?sNN = 5.02 TeV. In addition, the influence of the collision geometry is explored by measuring the D0 and D0mesons v2 and triangular flow coefficient (v3) as functions of rapidity, transverse momentum (pT), and event centrality (a measure of the overlap of the two Pb nuclei). A clear centrality dependence of prompt D0 meson v2 values is observed, while the v3 is largely independent of centrality. These trends are consistent with expectations of flow driven by the initial-state geometry. ? 2021 The Author. Published by Elsevier B.V. This is an open access article under the CC BY licens

Observation of electroweak production of Wγ with two jets in proton-proton collisions at √s = 13 TeV

A first observation is presented for the electroweak production of a W boson, a photon, and two jets in proton-proton collisions. The W boson decays are selected by requiring one identified electron or muon and an imbalance in transverse momentum. The two jets are required to have a high dijet mass and a large separation in pseudorapidity. The measurement is based on data collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results at 8 TeV, the observed (expected) significance is 5.3 (4.8) standard deviations. The cross section for the electroweak W$_{γjj}$ production in a restricted fiducial region is measured as 20.4 +/- 4.5 fb and the total cross section for W$_{γ}$ production in association with 2 jets in the same fiducial region is 108 +/- 16 fb. All results are in good agreement with recent theoretical predictions. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-8 effective field theory operators