[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] 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] 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] 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] The discovery of quasi-crystals and their 1-dimensional modeling have led to a deep mathematical study of Schroedinger operators with an arbitrary deterministic potential sequence. In this work we address this problem and find trace maps for an arbitrary substitution sequence. our trace maps have lower dimensionality than those of Kolar and Nori, which make them quite attractive for actual applications. (authors)

[en] Short communication