Always Improving: Turning Test Responses into Learning Opportunities

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

A New Correlation Between GRB X-Ray Flares And The Prompt Emission

From a sample of GRBs detected by the $Fermi$ and $Swift$ missions, we have extracted the minimum variability time scales for temporal structures in the light curves associated with the prompt emission and X-ray flares. A comparison of this variability time scale with pulse parameters such as rise times,determined via pulse-fitting procedures, and spectral lags, extracted via the cross-correlation function (CCF), indicate a tight correlation between these temporal features for both the X-ray flares and the prompt emission. These correlations suggests a common origin for the production of X-ray flares and the prompt emission in GRBs.Comment: 5 pages, 3 figures, Accepted for publication in ApJ

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

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 $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $\theta_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. 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 $\sin\theta_{12}$ and $\cos\theta_{12}$ from the anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a center of mass energy of $500 GeV$ we obtain $=248.22 GeV$, $=247.24 GeV$ and $=4.70 GeV$. 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 $\bar\theta_{12}=180^0-\theta_{12}$ we obtain $=1.25^0$ at $500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. 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 $1000 GeV$ 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.

TriMinimal Parametrization of the Neutrino Mixing Matrix

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

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

Multiloop String-Like Formulas for QED

Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the last decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous article; the latter will be elaborated in this paper. We show here how to write multiloop string-like formulas in the Feynman-parameter representation for any process in QED, including those involving other non-electromagnetic interactions. The general connection between the Feynman-parameter approach and the superstring/first-quantized approach is discussed. In the special case of a one-loop multi-photon amplitude, these formulas reduce to the ones obtained by the superstring and the first quantized methods. The string-like formulas exhibits a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram-by-diagram with the seagull vertex neglected.Comment: 25 pages in Plain Tex, plus four figures in a postscript file; McGill/92-5

Undergraduate Research Opportunities in Microelectronics at Boise State University

Several opportunities exist for undergraduates in the Microelectronics area at Boise State University. This paper will describe the Research Experience for Undergraduates (REU) program funded by the National Science Foundation and other opportunities that have resulted for undergraduates due to external support. BSU became a NSF REU site for Microelectronics research in 1999. Each year 10 students are recruited nation-wide from various engineering and science disciplines to come to BSU for 8 weeks. The students work intensively with various faculty advisors and graduate student mentors. Another unique feature of our program is the tie to local industry. In 1999-2001, three students have and will benefit from an interaction with a local company, SCP Global Technologies, and this will be described