The integrated proton-deuteron cross section {~ above letter σ} for the case of transversal polarization p_y~p of the proton and tensor polarization P_(xz) of the deuteron provides a null test signal for time-reversal invariance violating but P-parity conserving effects. The corresponding experiment is planned at COSY to measure the observable {~ above letter σ}. Here we consider in general case the status of the null-test observable in pd scattering, calculate {~ above letter σ} within the Glauber theory of the double-polarized pd scattering at 100 - 1000 MeV and study the contribution of the deuteron S- and D-waves for several type of the T-odd NN interactions.
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