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Copper discs of a certain size are introduced into radioactive sodium polysulphide (sulphur-35) solutions and moved in simultaneous translation and rotation, by a small motor running at 60 rev/min.
The scene of the IR image is assumed to be completely included in the optical image and the alignment between the common scene in the two images may involve translation and rotation by a small angle, though a small scale difference may also be present.
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The symmetry group contains four symmetry transformations: the identity, a reflection about the vertical axis, rotation by 180° (which is equivalent to two successive reflections about the vertical and horizontal axes), and a combination between reflection and rotation by 180° (which is equivalent to a reflection about the horizontal axis).
Moreover, in the analyses including reflection, shape changes symmetric under reflection and rotation by 180° also take up a large share of the total shape variation.
where ⌈x⌉ and ⌊x⌋ are respectively the ceiling17 and the floor18 of x, where C_{i} = sum_{j=1}^{i} w_{i}+epsilon (7). is the cumulative sum and where (epsilon sim left [0,frac {1}{N}right ]) and C 0=0. (6) uses only element-wise operations (as described in Section 4.1) and a rotation (by a single element and as described in Section 4.2).
These were: examining the variance in trajectory angles, pairwise comparison of all MTs in the bundle, and comparison to a reference MT that represented the fiber axis, using spherical rotation and rotating by an average value.
Then, the force generated by the traffic ATPase spools a newly docked protomer into the fibre, leading to its partial extraction from the membrane and its rotation by an average 84º.
Exponential maps represent any 3D rotation by a single rotation about an axis.
The fractional Fourier transform is a generalization of the Fourier transform with a parameter α and can be interpreted as a rotation by an angle α in the time-frequency plane.
For instance, the algal cell in Figure 1A is invariant under reflections about the horizontal and vertical axes (or, equivalently, under one reflection and a rotation by 180°) and the flower in Figure 1B is invariant as a whole under five rotations.
The acceleration records were selected to be unaffected by tilts and rotation around a vertical axis.
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