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Measurements of cross section and asymmetry for e+e--->bb-bar and heavy quark fragmentation at KEK TRISTAN.

Using 773 muons found in hadronic events from 142 pb-1 of data at a c.m. energy of 57.8 GeV, we extract the cross section and forward-backward charge asymmetry for the e+e- --> bbBAR process, and the heavy quark fragmentation function parameters for the Peterson model. For the analysis of the e+e- --> bbBAR process, we use a method in which the behavior of the c quark and lighter quarks is assumed, with only that of the b quark left indeterminate. The cross section and asymmetry for e+e- --> bbBAR are found to be R(b) = 0.57 +/- 0.06(stat) +/- 0.08(syst) and A(b) = -0.59 +/- 0.09 +/- 0.09, respectively. They are consistent with the standard model predictions. For the study of the fragmentation function we use the variable [x(e)], the fraction of the beam energy carried by the heavy hadrons. We obtain [x(E)]c = 0.56(-0.05-0.03)+0.04+0.03 and [x(E)]b = 0.65(-0.04-0.06)+0.06+0.05, respectively. These are in good agreement with previously measured values.