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A non-singlet QCD analysis of the structure function
$xF_3$ up to NNLO is performed based on the Bernstein polynomials
approach. We use recently calculated NNLO anomalous dimension
coefficients for the moments of the $xF_3$ structure function in
$\nu N$ scattering. In the fitting procedure, Bernstein polynomial
method is used to construct experimental moments from the $xF_3$
data of the CCFR collaboration in the region of $x$ which is
inaccessible experimentally. We also consider Bernstein averages
to obtain some unknown parameters which exist in the valence quark
densities in a wide range of $x$ and $Q^2$. The results of valence
quark distributions up to NNLO are in good agreement with the
available theoretical models. In the analysis we determined the
QCD-scale $\Lambda^ {\overline{MS}} _{QCD, N_{f}=4}=211$ MeV (LO),
$259$ MeV (NLO) and $230$ MeV (NNLO), corresponding to
$\alpha_s(M_Z^2)=0.1291$ LO, $\alpha_s(M_Z^2)=0.1150$ NLO and
$\alpha_s(M_Z^2)=0.1142$ NNLO. We compare our results for the QCD
scale and the $\alpha_s(M_Z^2)$ with those obtained from deep
inelastic scattering processes.
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