The Einstein tensor Gij is symmetric, divergence free, and a concomitant of the metric tensor gab together with its first two derivatives. In this paper all tensors of valency two with these properties are displayed explicitly. The number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.

All tensors of contravariant valency two, which are divergence free on one index and which are concomitants of the metric tensor, together with its first two derivatives, are constructed in the four-dimensional case. The Einstein and metric tensors are the only possibilities.

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A generic Monte Carlo model of a photon therapy machine is described. The model, known as McRad, is based on EGS4 and has been in use since 1991. Its primary function has been the characterization of the incident photon fluence for use by dose calculation algorithms. The accuracy of McRad is examined by comparing the dose distributions in a water phantom generated using only the Monte Carlo data with measured dose distributions for two machines in our clinic; a 6 MV Varian Clinac 600C and the 15 MV beam from a Clinac 2100C. The Monte Carlo generated dose distributions are computed using a dose calculation algorithm based on the use of differential pencil beam kernels. It was found that the match to measured data could be improved if the model is tuned by adjusting the energy of the electron beam incident on the target. The beam profiles were found to be more sensitive indicators of the electron beam energy than the depth dose curves. Beyond the depths reached by contaminant electrons, the computed and measured depth dose curves agree to better than 1%. The comparison of beam profiles indicate that in regions up to within 1 cm of the field edge, the measured and computed doses generally agree to within 2%-3%.

The masses, total widths, and leptonic widths of three triplet s-wave Estates Y(4S), Y(5S), and Y(6S) are determined from measurements of the e + e~~ annihilation cross section into hadrons for 10.55 < W< 11.25 GeV. The resonances are identified from potential model results and their properties are obtained with the help of a simplified coupled-channels calculation. We find M(4S) = 10.577 GeV, r(4S) = 25 MeV, 1^(45) = 0.28 keV; M(5S) = 10.845 GeV, r(5S) = 110 MeV, r«,(5S) = 0.37 keV; M(6S) = 11.02 GeV, T(6S) = 90 MeV, 1^(65) = 0.16 keV.