ESTIMATES OF THE HIGHER-ORDER QCD CORRECTIONS - THEORY AND APPLICATIONS

We consider the further development of the formalism of the estimates of higher-order perturbative corrections in the Euclidean region, which is based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We present the estimates of the order O(alpha(s)(4)) QCD corrections to the Euclidean quantities: the e(+)e(-)-annihilation D-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross-Llewellyn Smith sum rule. The results for the D-function are further applied to estimate the O(alpha(s)(4)) QCD corrections to the Minkowskian quantities R(s) = sigma(tot)(e(+)e(-) --> hadrons)/sigma(e(+)e(-) --> mu(+)mu(-)) and R(tau) = Gamma(tau --> nu(tau) + hadrons)/Gamma(tau --> nu(tau)<(nu)over bar>(e)e). The problem of the fixation of the uncertainties due to the O(alpha(s)(5)) corrections to the considered quantities is also discussed.