Impact of the three-loop corrections on the QCD analysis of the deep-inelastic-scattering data

We perform the analysis of the existing inclusive deep inelastic scattering (DIS) data within NNLO QCD approximation. The parton distributions functions (PDFs) and the value of strong coupling constant $\alpha_{s}(M_Z)=0.1143\pm0.0013 (exp)$ are obtained. The sensitivity of the PDFs to the uncertainty in the value of the NNLO corrections to the splitting functions is analyzed. It is shown that the PDFs errors due to this uncertainty is generally less than the experimental uncertainty in PDFs through the region of $x$ spanned by the existing DIS data.Comment: 9 pages, LATEX, 4 figures (EPS). After fixing bug, which caused incomplete account of the NNLO corrections in the fitting program, the fitted value of \alpha_s(M_Z)(NNLO) decreased by 0.002. The PDFs values changed within their experimental errors, the conclusions remain unchange

The L^p-Poincar\'e inequality for analytic Ornstein-Uhlenbeck operators

Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure \mu_\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\'e inequality \n f - \overline f\n_{L^p(E,\mu_\infty)} \le \n D_H f\n_{L^p(E,\mu_\infty)} holds for all 1<p<\infty. Here \overline f denotes the average of f with respect to \mu_\infty and D_H the Fr\'echet derivative in the direction of H.Comment: Minor correctiopns. To appear in the proceedings of the symposium "Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics", June 2013, Herrnhut, German