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The fast rotational alignment is based on sampling of simultaneously over all rotations R. To do so, we apply a fast 3D volumetric rotational matching (Kovacs and Wriggers, 2002; Xu et al., 2012).
By expressing the structural information in Spherical Harmonics (SH) Expansion, it is possible to formulate the rotational alignment as a fast rotational matching, which simultaneously calculates alignment scores of all rotations using FFT.
For example, in Euclidean three-dimensional space, rotations leave unaltered the distances between points; the set of all rotations about a fixed point turns out to form a Lie group, and it is one of the Lie groups in the classification.
The physical description is obviously invariant for all rotations around this axis.
The conclusion is drawn that all rotations in PEO sulfonic acid are restricted at room temperature.
The uniform pointing-constraint-ignored attitude rotation planning process is designed to solve all rotations without considering pointing constraints.
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The axis of rotation (black line) forms a singular orbit because all the rotations map the points of the axis to themselves.
"So I had to completely redo all the rotations and figure out how they worked.
Durum wheat was present in all the rotations to act as an indicator of their performance.
Tested for the ability to generalize from frontal to rotated views, prosopagnosics performed worse than controls across all rotation angles but the magnitude of the deficit didn't change with increasing rotation.
All rotation axes are coplanar and parallel.
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