[en] Published in summary form only

[en] Published in summary form only

[en] Within the scope of the approximation of a kinematic field I have been calculating the uniform paramagnetic susceptibility χ(0,0)=δR(H)/δH when H → 0 and U → ∞. It turns out that χ(0,0) < 0 in the all region, where R=0 (i.e. 0,7 > or approx. n ≥ 0). (author). 6 refs, 1 fig

[en] Cubic sublattices of cubic lattices are described which share only some of the point-symmetry operations with the original lattices; the common operations form the point groups anti 3m, anti 3, 4/m, 2/m or anti 1. Some properties of these sublattices, including the centred ones, are shown and tentative terminology, notation and classification are introduced. All the different types of inclined primitive cubic sublattices L_n for n=3, 5, ..., 31, 63, 81 (n being the length of the unit cube edge) of L₁ are listed. Several remarks and hypotheses concerning theoretical crystallography and number theory are presented. (orig.)

[en] An exact definition of the 44 lattice characters listed by Niggli is thoroughly discussed and is elucidated by examples. In order to represent the characters graphically, use is made of the projection of the Niggli-reduced basis vector c on the a, b plane. Not only is the projected end point of c restricted to certain domains in the plane by the reduction rules but for given constants A, B and F in the Niggli-reduced form this polygonal domain contains the locus of each of the characters as a vertex or an edge or the area of the polygon. For each of the cases a=b=c, a=b< c, a< b=c and a< b< c, nine figures fully cover all alternatives determined by five special values F=A/2, 0, -A/4, -A/3 and -A/2 and the four open intervals between them. Also, all normalized Buerger bases which are not Niggli-reduced bases are shown in the same figures. (orig.)

[en] The object of this paper is to show how to transfer a model from crystal physics to the solution of agricultural problems

[en] We point out that the probability law of a single domain wall separating clusters in ADE lattice models in a simply connected domain is identical to that of corresponding chordal curves in the lattice O(n) and Q-state Potts models, for suitable n or Q. They are conjectured to be described in the scaling limit by chordal SLE_κ with κ rational and >2. However in a multiply connected domain the laws can differ from those for the corresponding O(n) or Potts model. The correspondence also sheds light on the scaling limit of multiple curves

[en] Basic group-theoretical properties of the icosahedral point groups are derived. Here are given the permutations of the vertices of an icosahedron under the action of the elements of the icosahedral point groups, the icosahedral point groups' multiplication tables, subgroups, sets of conjugate subgroups, centralizers and normalizers of arbitrary subsets and closet and double coset decompositions. (orig.)

[en] Short communication

[en] A recently proposed analytic nearest-neighbour model for fcc metals is criticised and two alternative nearest-neighbour models derived from the separable potential method (SPM) are recommended. Results for copper and aluminium illustrate the utility of the recommended models. (author). 20 refs, 5 tabs