The recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation. Moreover, we show that the space of functions of bounded ${\mathcal D}$-variation can be turned into a commutative Banach algebra.

In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of 2×2 configuration counts. For Boolean models with balls as grains, explicit formulas for the bias of such algorithms are derived, resulting in a set of linear equations that the weights must satisfy in order to minimize the bias in high resolution. These results generalize to larger classes of random sets, as well as to the design-based situation, where a fixed set is observed on a stationary isotropic lattice. Finally, the formulas for the bias obtained for Boolean models are applied to existing algorithms in order to compare their accuracy.

The ground state electronic structures of the actinide oxides AO, A2O3 and AO2 (A=U, Np, Pu, Am, Cm, Bk, Cf) are determined from first-principles calculations using the self-interaction corrected local spin-density approximation. Our study reveals a strong link between preferred oxidation number and degree of localization. The ionic nature of the actinide oxides emerges from the fact that those oxides where the ground state is calculated to be metallic do not exist in nature, as the corresponding delocalized f-states favour the accommodation of additional O atoms into the crystal lattice.

A theory is presented which describes the photoemission spectra of actinide compounds starting from the atomic limit of isolated actinide ions. The multiplets of the ion are calculated and an additional term is introduced to describe the interaction with the sea of conduction electrons. This leads to complex mixed-valent ground states, which describes well the rich spectrum observed for PuSe. In particular, the three-peak feature, which is often seen in Pu and Pu compounds in the vicinity of the Fermi level originates from f6 → f5 emission. The theory is further applied to PuSb, PuCoGa5 and Am.

We use the self-interaction corrected (SIC) local spin-density (LSD) approximation to investigate the groundstate valency configuration of Mn impurities in p-type ZnO. In Zn1−xMnxO, we find the localized Mn2+ configuration to be preferred energetically. When codoping Zn1−xMnxO with N, we find that four d-states stay localized at the Mn site, while the remaining d-electron charge transfers into the hole states at the top of the valence bands. If the Mn concentration [Mn] is equal to the N concentration [N], this results in a scenario without carriers to mediate long range order. If on the other hand [N] is larger than [Mn], the N impurity band is not entirely filled, and carrier mediated ferromagnetism becomes theoretically possible.

The electronic structures of actinide solid systems are calculated using the self-interaction corrected local spin density approximation. Within this scheme the 5f electron manifold is considered to consist of both localized and delo-calized states, and by varying their relative proportions the energetically most favourable (ground state) configuration can be established. Specifically, we discuss elemental Pu in its δ-phase, and the effects of adding O to PuO2.

Using the Green’s function technique based on the linear muffin-tin orbital method in the atomic-spheres approximation we study the electronic structure of native defects and substitutional carbon impurities in cubic BN. To include the lattice relaxation effects a supercell approach in connection with the full-potential linear muffin-tin-orbital method is applied.

Native defects and some common dopants (Mg, Zn, and C) in cubic GaN and AlN are examined by means of ab initio theoretical calculations using two methods: i) the Green's function technique based on the linear muffin-tin orbital method in the atomic-spheres approximation; ii) a supercell approach in connection with the full-potential linear muffin-tin-orbital method. We apply the first method to look mainly at the energetic positions of the defect and impurity states in different charge states and their dependence on hydrostatic pressure. The second method allows us to study lattice relaxations. Whereas small relaxations are found near vacancies and substitutional Mg and Zn, the calculations predict large atomic displacements around antisite defects and the substitutional carbon impurity on the cation site.

The atomic and electronic structure of the radiation-induced interstitial atoms in MgO and KCl crystals representing two broad classes of ionic solids are calculated and compared. The first-principles full potential LMTO method is applied to a 16-atom supercell. For both crystals the energetically most favourable configuration is a dumbbell centered at a regular anion site. Its (110) and (111) orientations are very close in energy which permits the dumbbell to rotate easily on a lattice site. The mechanism and the relevant activation energy for thermally activated diffusion hops from the dumbbell equilibrium position to the cube face and cube center are discussed in the light of the available experimental data for MgO. In order to interpret recent experimental data on Raman spectroscopy, the local vibrational frequences are calculated for the dumbbell in KCl (the so-called H center). A strong coupling is found between its stretching molecular mode and the breathing mode of the nearest cations whose frequency is predicted.