A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random two-phase heterogeneous media with a target two-point correlation function. However, not every hypothetical two-point correlation function corresponds to a realizable two-phase medium. Here we collect all of the known necessary conditions on the two-point correlation functi...

In this paper, we study one-Lee weight and two-Lee weight codes over Z2Z2[u], where u = 0. Some properties of one-Lee weight Z2Z2[u]-additive codes are given, and a complete classification of one-Lee weight Z2Z2[u]-additive formally self-dual codes is obtained. The structure of two-Lee weight projective Z2Z2[u] codes are determined. Some optimal binary linear codes are obtained directly from on...

Relations are found between grain boundary character distribution, misorientation distribution and two-point orientation distribution. Some of these relations are analogies for polycrystals of the Debye-Anderson-Brumberger formula and Berryman formula established for two-phase composites.