Expansion of Einstein-Yang-Mills Amplitude

In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives. Using the gauge invariance principle, we propose a recursive construction, where EYM amplitude with any number of gravitons could be expanded into EYM amplitudes with less number of gravitons. Through this construction, we can write down the complete expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes. As a byproduct, we are able to write down the polynomial form of BCJ numerator, i.e., numerators satisfying the color-kinematic duality, for Yang-Mills amplitude. After the discussion of gauge invariance, we move to the BCFW on-shell recursion relation and discuss how the expansion can be understood from the on-shell picture. Finally, we show how to interpret the expansion from the aspect of KLT relation and the way of evaluating the expansion coefficients efficiently.Comment: 50 pages, 1 figure, Revised versio

DIFFERENCES BETWEEN MALE AND FEMALE PLAYERS IN THE SAGITTAL PLANE BIOMECHANICS DURING VOLLEYBALL SPIKE LANDING

The purpose of this study was to investigate the kinematics and kinetics differences between male and female players after a volleyball spike landing. Eight male and eight female university volleyball players were recruited to participate in this study. The kinematic and kinetic data were collected by ten Vicon cameras (300 Hz) and two force plates (1500 Hz). The Visual 3D software was used to analyze the kinematic and kinetic variables. The results indicated that male players exhibited greater peak hip flexion angle, hip range of motion and hip extensor moment compared with female players. Female players exhibited greater peak ankle dorsiflexion and ankle range of motion than male players. These differences demonstrated that male and female players performed different strategies during volleyball spike landing

THE EFFECT OF SIDE STEP ON LOWER EXTREMITY BIOMECHANICS DURING BLOCK LANDING IN FEMALE VOLLEYBALL PLAYERS

The purpose of this study was to examine the effect of block and side step block on lower extremity biomechanics during landing in female volleyball players. Eight female university volleyball players participated in this study. The kinematic and kinetic data were collected by eight Vicon cameras (250 Hz) and two force plates (1000 Hz). The Visual 3D software was used to analyze the kinematic and kinetic of block and side step block landing variables. The results showed a significantly higher knee extensor moment during side step landing than the block landing at the time of peak vertical ground reaction force and peak joint moment. It was concluded that female players displayed greater knee extensor moment during the side step before block landing that may increase the loading on the knee

A strict test in climate modeling with spectrally resolved radiances: GCM simulation versus AIRS observations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95152/1/grl23741.pd

Climate policy modeling: An online SCI-E and SSCI based literature review

This study utilizes the bibliometric method on climate policy modeling based on the online version of SCI-E from 1981 to 2013 and SSCI from 2002 to 2013, and summarizes several important research topics and methodologies in the field. Publications referring to climate policy modeling are assessed with respect to quantities, disciplines, most productive authors and institutes, and citations. Synthetic analysis of keyword frequency reveals six important research topics in climate policy modeling which are summarized and analyzed. The six topics include integrated assessment of climate policies, uncertainty in climate change, equity across time and space, endogeneity of technological change, greenhouse gases abatement mechanism, and enterprise risk in climate policy models. Additionally, twelve types of models employed in climate policy modeling are discussed. The most widely utilized climate policy models are optimization models, computable general equilibrium (CGE) models, and simulation models