The NuTeV experiment at Fermilab has used a sign-selected neutrino beam to perform a search for the lepton number violating process $\bar{\nu}_mu e^- \to \mu^- \bar{\nu}_e$, and to measure the cross-section of the Standard Model inverse muon decay process $\nu_{\mu} e^- \to \mu^- \nu_e$. NuTeV measures the inverse muon decay asymptotic cross-section $\sigma/E$ to be 13.8 $\pm$ 1.2 $\pm$ 1.4 x $10^{-42} cm^2$/GeV. The experiment also observes no evidence for lepton number violation and places one of the most restrictive limits on the LNV/IMD cross-section ratio at $\sigma (\bar{\nu}_{\mu} e^- \to \mu^- \bar{\nu}_e) /\sigma (\nu_{\mu}e^- \to \mu^- \nu_e$) $\le$ 1.7% at 90% C.L. for V-A couplings and $\le$ 0.6% for scalar couplings.
We extract a set of values for the Gross-Llewellyn Smith sum rule at different values of 4-momentum transfer squared ($Q^{2}$), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for $1 < Q^2 < 15 GeV^2/c^2$. A comparison with the order $\alpha^{3}_{s}$ theoretical predictions yields a determination of $\alpha_{s}$ at the scale of the Z-boson mass of $0.114 \pm^{.009}_{.012}$. This measurement provides a new and useful test of perturbative QCD at low $Q^2$, because of the low uncertainties in the higher order calculations.