Forthcoming article in Acta Crystallographica Section A Foundations and Advances

About difference electron densities and their properties
the most popular difference syntheses have been characterized and a new difference synthesis has been proposed.

Real-time detection and resolution of atom bumping in crystallographic models
Presented here is an O(n{\rm log}n) algorithm that detects atom bonding in a unit cell. As an application of this algorithm, an evaluation function for atom bumping is proposed, which can be used for real-time elimination of crystallographic models with unreasonable bond lengths during the procedure of crystal structure determination in the direct space.

Accelerated scattering of convex polyhedra
The formulas for minn and maxn names in the classes of convex n-acra, as well as asymptotic relationships (as n → ∞) between them, are found. These explain the distribution of [minn, maxn] ranges on the real line.

Close-packed structure dynamics with finite-range interaction: computational mechanics with individual layer interaction
This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. Instead of using an Ising model over spins defined by the Hägg coding, a Hamiltonian considering direct interaction between the close-packed layers is assumed. The results of the phase diagram and the appearance of disorder are compared with the previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed.

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
The minimal-volume search space in molecular replacement can be expressed in multiple ways wherein there is a trade-off between the sizes of rotation and translation subspaces. In particular, if the space group is a semi-direct product of a point group and a Bieberbach group, then the search space can be represented as a product of two manifolds: a spherical space form and a Euclidean space form.

The wavevector substar group in reciprocal space and its representation
A new concept of the wavevector substar group and its representation is established.

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