Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

The Supremum Norm of the Discrepancy Function: Recent Results and Connections

A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at least (log N) ^{(d-1)/2}. It is conjectured that the L-infty bound is significantly larger, but the only definitive result is that of Wolfgang Schmidt in dimension d=2. Partial improvements of the Roth exponent (d-1)/2 in higher dimensions have been established by the authors and Armen Vagharshakyan. We survey these results, the underlying methods, and some of their connections to other subjects in probability, approximation theory, and analysis.Comment: 15 pages, 3 Figures. Reports on talks presented by the authors at the 10th international conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Sydney Australia, February 2011. v2: Comments of the referee are incorporate

Electron spin as a spectrometer of nuclear spin noise and other fluctuations

This chapter describes the relationship between low frequency noise and coherence decay of localized spins in semiconductors. Section 2 establishes a direct relationship between an arbitrary noise spectral function and spin coherence as measured by a number of pulse spin resonance sequences. Section 3 describes the electron-nuclear spin Hamiltonian, including isotropic and anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the effective Hamiltonian for nuclear-nuclear coupling mediated by the electron spin hyperfine interaction. Section 4 describes a microscopic calculation of the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops with quasiparticle broadening included. Section 5 compares our explicit numerical results to electron spin echo decay experiments for phosphorus doped silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low dimensional structures", edited by Marco Fanciulli. To be published by Springer-Verlag in the TAP series. 35 pages, 9 figure

Propylene Carbonate Reexamined: Mode-Coupling β\beta Scaling without Factorisation ?

The dynamic susceptibility of propylene carbonate in the moderately viscous regime above $T_{\rm c}$ is reinvestigated by incoherent neutron and depolarised light scattering, and compared to dielectric loss and solvation response. Depending on the strength of $\alpha$ relaxation, a more or less extended $\beta$ scaling regime is found. Mode-coupling fits yield consistently $\lambda=0.72$ and $T_{\rm c}=182$K, although different positions of the susceptibility minimum indicate that not all observables have reached the universal asymptotics

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

Science-Technology-Society (STS): a new paradigm in Science Education

publication-status: Publishedtypes: ArticleChanges in the past two decades of goals for science education in schools have induced new orientations in science education worldwide. One of the emerging complementary approaches was the science-technology-society (STS) movement. STS has been called the current megatrend in science education. Others have called it a paradigm shift for the field of science education. The success of science education reform depends on teachers' ability to integrate the philosophy and practices of current programs of science education reform with their existing philosophy. Thus, when considering the STS approach to science education, teacher beliefs about STS implementation require attention. Without this attention, negative beliefs concerning STS implementation and inquiry learning could defeat the reform movements emphasizing STS. This article argues the role of STS in science education and the importance of considering science teachers' beliefs about STS in implementing significant reforms in science education

Measurement of the correlation between flow harmonics of different order in lead-lead collisions at √sNN = 2.76 TeV with the ATLAS detector

Correlations between the elliptic or triangular flow coefficients vm (m=2 or 3) and other flow harmonics vn (n=2 to 5) are measured using √sNN=2.76 TeV Pb+Pb collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of 7 μb−1. The vm−vn correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, v3 is found to be anticorrelated with v2 and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities, ε2 and ε3. However, it is observed that v4 increases strongly with v2, and v5 increases strongly with both v2 and v3. The trend and strength of the vm−vn correlations for n=4 and 5 are found to disagree with εm−εn correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to vn and a nonlinear term that is a function of v22 or of v2v3, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to v4 and v5 are found to be consistent with previously measured event-plane correlations

Search for W′→tb→qqbb decays in pp collisions at √s=8 TeV with the ATLAS detector

A search for a massive W′ gauge boson decaying to a top quark and a bottom quark is performed with the ATLAS detector in pp collisions at the LHC. The dataset was taken at a centre-of-mass energy of √s=8 TeV and corresponds to 20.3 fb−1 of integrated luminosity. This analysis is done in the hadronic decay mode of the top quark, where novel jet substructure techniques are used to identify jets from high-momentum top quarks. This allows for a search for high-mass W′ bosons in the range 1.5–3.0 TeV. b-tagging is used to identify jets originating from b-quarks. The data are consistent with Standard Model background-only expectations, and upper limits at 95 % confidence level are set on the W′→tb cross section times branching ratio ranging from 0.16pb to 0.33pb for left-handed W′ bosons, and ranging from 0.10pb to 0.21pb for W′ bosons with purely right-handed couplings. Upper limits at 95 % confidence level are set on the W′-boson coupling to tb as a function of the W′ mass using an effective field theory approach, which is independent of details of particular models predicting a W′boson

Search for vectorlike B quarks in events with one isolated lepton, missing transverse momentum, and jets at √s = 8 TeV with the ATLAS detector

A search has been performed for pair production of heavy vectorlike down-type (B) quarks. The analysis explores the lepton-plus-jets final state, characterized by events with one isolated charged lepton (electron or muon), significant missing transverse momentum, and multiple jets. One or more jets are required to be tagged as arising from b quarks, and at least one pair of jets must be tagged as arising from the hadronic decay of an electroweak boson. The analysis uses the full data sample of pp collisions recorded in 2012 by the ATLAS detector at the LHC, operating at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb −1 . No significant excess of events is observed above the expected background. Limits are set on vectorlike B production, as a function of the B branching ratios, assuming the allowable decay modes are B → Wt/Zb/Hb. In the chiral limit with a branching ratio of 100% for the decay B → Wt, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 810 GeV (760 GeV). In the case where the vectorlike B quark has branching ratio values corresponding to those of an SU(2) singlet state, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 640 GeV (505 GeV). The same analysis, when used to investigate pair production of a colored, charge 5/3 exotic fermion T 5/3 , with subsequent decay T 5/3 → Wt, sets an observed (expected) 95% C.L. lower limit on the T 5/3 mass of 840 GeV (780 GeV)