Floating origin

In polar space groups, which have a floating origin (e.g. PI where the origin is entirely arbitrary, or P2i where the origin can be anywhere on the b axis), a shift of the entire atomic model along a polar axis does not violate the space group symmetry. In the presence of a heavy atom in the stmcture, this atom s coordinates can be constrained to certain values (e.g. (0,0,0) for PI or (x, 0, z) for P2i). Alternatively, the sum of the coordinates of all atoms in the stmcture can be constrained to remain constant, which removes one parameter per polar axis. 

SHELXL uses a mathematically different and somewhat more stable approach, restraining the weighted sum over all coordinates to remain constant as introduced by Flack and Schwarzenbach (1988). A relatively high weight for this floating origin restraint makes it almost equivalent to a constraint. 

After about 4 to 12 hours the hides are drained, then floated with lime without additional sulfides. The dmm or hide processor is mn at slow speeds intermittently during the unhairing process. The continued action of the lime solution on the hides brings the pH to 12—13. At this pH the hides swell to about twice the original thickness. This swelling has a beneficial opening of the fibers to permit better tannage (Fig. 3a). 

At any level, rejection means revisions and another climb up the approval ladder. This can be frustrating when the reviewers are less qualified than the originators to evaluate a complex proposal. Expertise grows progressively more rarefied as the proposal floats higher into the upper stratospheres of authority. 

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