2,704 research outputs found

    Always Improving: Turning Test Responses into Learning Opportunities

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    By using summative assessment scores and authentic student work samples, teachers can transform test grades into further opportunities for student growth. This practice allows students to continue to hone their mathematical skills, even after the test is finished. The procedures described include the incorporation of technology and "math talk" to transform everyday classroom tests into unique learning opportunities. Through the responses of their peers, students gain a clearer understanding of how to successfully respond to written response questions

    TriMinimal Parametrization of the Neutrino Mixing Matrix

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    Current experimental data on neutrino mixing are very well described by TriBiMaximal mixing. Accordingly, any phenomenological parametrization of the MNSP matrix must build upon TriBiMaximal mixing. We propose one particularly natural parametrization, which we call "TriMinimal". The three small deviations of the PDG angles from their TriBiMaximal values, and the PDG phase, parametrize the TriMinimal mixing matrix. As an important example of the utility of this new parametrization, we present the simple resulting expressions for the flavor-mixing probabilities of atmospheric and astrophysical neutrinos. As no foreseeable experiment will be sensitive to more than second order in the small parameters, we expand these flavor probabilities to second order.Comment: Typos corrected, references added, title changed; matches version appearing in PRL 100, 111801 (2008)

    X - Ray Flares and Their Connection With Prompt Emission in GRBs

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    We use a wavelet technique to investigate the time variations in the light curves from a sample of GRBs detected by Fermi and Swift. We focus primarily on the behavior of the flaring region of Swift-XRT light curves in order to explore connections between variability time scales and pulse parameters (such as rise and decay times, widths, strengths, and separation distributions) and spectral lags. Tight correlations between some of these temporal features suggest a common origin for the production of X-ray flares and the prompt emission.Comment: 7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 15 in eConf Proceedings C130414

    On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

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    We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in e+ee^+e^- annihilation. Our results are presented in terms of the EqE_q-dependence of the ttˉgt\bar tg cross section and the dependence on the cosine of the opening angle θ12\theta_{12} between top and antitop for a center of mass energy of q2=500GeV\sqrt{q^2}=500 GeV. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of sinθ12\sin\theta_{12} and cosθ12\cos\theta_{12} from the anticollinearity limits sinθ12=0\sin\theta_{12}=0 and cosθ12=1\cos\theta_{12}=-1. For a center of mass energy of 500GeV500 GeV we obtain =248.22GeV=248.22 GeV, =247.24GeV=247.24 GeV and =4.70GeV=4.70 GeV. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quark's energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at 1000\GeV. For the mean of the acollinearity angle θˉ12=1800θ12\bar\theta_{12}=180^0-\theta_{12} we obtain =1.250=1.25^0 at 500GeV500 GeV, the value of which goes up to 4.6204.62^0 at 1000GeV1000 GeV. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to 1000GeV1000 GeV showing that the gluon momentum has a large mean transverse component in this energy range.Comment: 17 pages, 7 postscript figures, to appear in Nucl. Phys.