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This paper reports on the first results of the study of e+e− collisions at s=27.4 GeV and s=27.7 GeV at PETRA, using the 4π-sr electromagnetic and calorimetric detector MARK-J. We obtain an average R=σ(e+e−→hadrons)σ(e+e−→μ+μ−)=3.8±0.3 (statistical)±0.6 (systematic) and a relative R=1.0±0.2 between the two energies. The R values, the measured thrust distribution, and average spherocity show no evidence for the production of new quark flavors.