Study of hadronic events and measurements of αs between 30 and 91 GeV

We have studied the structure of hadronic events with a hard, %radiated isolated photon in the final state ($\mathrm{e^{+}e^{-}} \rightarrow$ Z $\rightarrow$ hadrons $+$ $\gamma$) in the 3.6 million hadronic data collected with the L3 detector at centre-of-mass energies around 91 GeV. The centre-of-mass energy of the hadronic system is in the range 30 GeV to 86 GeV. Event shape variables have been measured at these reduced centre-of-mass energies and have been compared with the predictions of different QCD Monte Carlo programs. The event shape variables and the energy dependence of their mean values are well reproduced by QCD models. We fit distributions of several global event shape variables to resummed $\cal{O} \alpha_{s}^{2})$ calculations to determine the strong coupling constant $\alpha_{s}$ over a wide range of energies. We find that the strong coupling constant $\alpha_{s}$ decreases with increasing energy, as expected from QCD.