Sentence examples for rotation data from inspiring English sources

In many applications involving 3-D rotation data, the rotational distributions used are symmetric (or isotropic) so that they have rotationally invariant densities about a central rotation.

Thus we can test for rotational symmetry of a single 3-D rotation data set by using R as a test statistic.

Fig. 2 Plot of two simulated 3-D rotation data sets (each with n=m=50) with rotational symmetries that (a) are not significantly different and (b) are significantly different.

A small simulation study for this one-sample test is provided in Section 4. To compare the rotational symmetry in two independent 3-D rotation data sets, the absolute difference in R values can be calculated to serve as the test statistic for the permutation test of H 0 F 1=F 2 versus H a :F 1≠F 2, where F i is the degree of rotational symmetry of distribution i.

At every 5° rotation, data is recorded.

Optical rotation data are specified for each compound including intermediates.

Fig. 12 Measured rotation data of A/P-Gears (0 = 0°) Fig. 13 Measured rotation data of A/P-Gears (0 = 20°).

Resample from the 3-D rotation data set O 1,…,O n with replacement.

1. Resample from the 3-D rotation data set O 1,…,O n with replacement.

Through the incorporation of rotation, data can be clustered more appropriately than by standard elliptical basis functions.

This will provide a novel statistical approach for analyzing 3-D rotation data while also providing useful tools for practitioners.