8,042 research outputs found

    The Work of the Complaints Section of the Antitrust Division

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    Principals Partnering to Build a Vision for School Mathematics

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    Crop phenology literature review for corn, soybean, wheat, barley, sorghum, rice, cotton, and sunflower

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    Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop

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    By applying the known expressions for SYM and SUGRA tree amplitudes, we write generating functions for the NNMHV box coefficients of SYM as well as the MHV, NMHV, and NNMHV box coefficients for SUGRA. The all-multiplicity generating functions utilize covariant, on-shell superspace whereby the contribution from arbitrary external states in the supermultiplet can be extracted by Grassmann operators. In support of the relation between dual Wilson loops and SYM scattering amplitudes at weak coupling, the SYM amplitudes are presented in a manifestly dual superconformal form. We introduce ordered box coefficients for calculating SUGRA quadruple cuts and prove that ordered coefficients generate physical cut amplitudes after summing over permutations of the external legs. The ordered box coefficients are produced by sewing ordered subamplitudes, previously used in applying on-shell recursion relations at tree level. We describe our verification of the results against the literature, and a formula for extracting the contributions from external gluons or gravitons to NNMHV superamplitudes is presented.Comment: 46 pages, 2 figures, additional references and clarifications include

    Tree-level Split Helicity Amplitudes in Ambitwistor Space

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    We study all tree-level split helicity gluon amplitudes by using the recently proposed BCFW recursion relation and Hodges diagrams in ambitwistor space. We pick out the contributing diagrams and find that all of them can be divided into triangles in a suitable way. We give the explicit expressions for all of these amplitudes. As an example, we reproduce the six gluon split NMHV amplitudes in momentum space.Comment: 20 pages, 16 figures; minor changes; clarifications added, 22 pages, 16 figure

    Magnetic properties of Yb2Mo2O7 and Gd2Mo2O7 from rare earth Mossbauer measurements

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    Using 170-Yb and 155-Gd Mossbauer measurements down to 0.03K, we have examined the semiconducting pyrochlore Yb2Mo2O7 where the Mo intra-sublattice interaction is anti-ferromagnetic and the metallic pyrochlore Gd2Mo2O7 where this interaction is ferromagnetic. Additional information was obtained from susceptibility, magnetisation and 172-Yb perturbed angular correlation measurements. The microscopic measurements evidence lattice disorder which is important in Yb2Mo2O7 and modest in Gd2Mo2O7. Magnetic irreversibilities occur at 17K in Yb2Mo2O7 and at 75K in Gd2Mo2O7 and below these temperatures the rare earths carry magnetic moments which are induced through couplings with the Mo sublattice. In Gd2Mo2O7, we observe the steady state Gd hyperfine populations at 0.027K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intra-sublattice interaction is ferromagnetic.Comment: 9 pages, 9 figure
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