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We report on our on-going study of the lower moments of iso-vector polarised and unpolarised structure functions, $g_A$ and $\langle x\rangle_{u-d}$, respectively, and the iso-vector scalar and tensor charge, for $N_f=2$ non-perturbatively improved clover fermions. With pion masses which go down to about 150 MeV, we investigate finite volume effects and excited state contributions.

Moments of structure functions for $N_f=2$ near the physical point.