How to multiply a matrix of normal equations by an arbitrary vector using FFT

A novel full-matrix technique for crystallographic macromolecular refinement is described.

Elastic scattering of high-energy electrons by dopant atoms within a crystal in transmission electron microscopy

A Bloch-wave model that predicts electron scattering by a dopant atom is derived using perturbation theory. The results are largely confirmed by multislice simulations but subtle differences have also been observed and are attributed to the approximations made in the Bloch-wave model.

Retrieving low- and medium-resolution structural features of macromolecules directly from the diffraction intensities – a real-space approach to the X-ray phase problem

A simple mathematical algorithm is proposed to generate electron-density maps directly from the X-ray diffraction intensities. The maps can reveal the internal structures of macromolecules.

The Liga algorithm for ab initio determination of nanostructure

The Liga algorithm for ab initio determination of some solid-state nanostructures from length lists generated by the atomic pair distribution function is described. Results are demonstrated for ideal Lennard–Jones clusters and experimental C₆₀ data.

Reliability of Monte Carlo simulations of disordered structures optimized with evolutionary algorithms exemplified with diffuse scattering from La_0.70(1)(Al_0.14(1)I_0.86(1))

The reliability, reproducibility and influence of refinement parameters of evolutionary algorithm refinements of Monte Carlo simulations have been investigated in analyses of complex disorder and corresponding diffuse scattering from the compound La_0.70(1)(Al_0.14(1)I_0.86(1)). It was found that the resulting structures are qualitatively and quantitatively in good agreement independent of the strategy used. Recommendations for the best choice of the parameters are given.

Computing with almost periodic functions

An almost periodic function f is sampled at a finite number of points. A new method is developed for discrete computation of finite Fourier expansions of the function that are almost periodic and uniformly approximate f over its entire infinite domain.

Extending the S-FFT direct-methods algorithm to density functions with positive and negative peaks. XIV

The fast-Fourier-transform-based algorithm maximizing the direct-methods sum function S has been modified to allow the treatment of density functions with positive and negative peaks. Test calculations have been performed on single-crystal X-ray diffraction data, neutron diffraction data and intensities of superstructure reflections.

Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. I. Crystal families in five-dimensional space with two-, three-, four- and sixfold symmetries

The Weigel–Phan–Veysseyre symbols are explained and their properties are described. These symbols are then assigned to the point groups of several families of space E⁵.

Crystal families and systems in higher dimensions, and geometrical symbols of their point groups. II. Cubic families in five- and n-dimensional spaces

The definition, properties and symbols of the iso cubic groups are given. The mono cubic crystal families of space Eⁿ are defined and listed for n = 3 to n = 7. As an application, four crystal families of space E⁵ are studied in detail.

Bijective mapping between the eigenvalue spectrum of a Karle–Hauptman matrix and its phases

Given the eigenvalue spectrum of a Karle–Hauptman matrix, the phases are uniquely determined if a carefully chosen subset is fixed.

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