A characterization of the disc by sets of uniqueness in tomography

In mathematical tomography, one wishes to reconstruct a density function on a compact set from knowledge of certain integrals. If one knowsa priori that this function is a characteristic function, some reduction in the amount of data needed may be obtained (see Fishburn et al. SIAM J. Appl. Math.50, 288–306, 1990). In such a situation we say the support regionD is a set of uniqueness. We show here that ifD is a smoothly-bounded Jordan domain which is a set of uniqueness for every pair of orthogonal directions, thenD is a disc.G.M.L.G. was supported by a Natural Sciences and Engineering Research Council of Canada grant.     

A high-pressure modification of MgVO3

The preparation of a high-pressure form of MgVO₃ has been accomplished utilizing two independent synthesis methods. The triclinic, ilmenite-type phase has been characterized by its crystallographic, magnetic, and electrical properties. Its structure is believed to be similar to that previously observed for other ilmenite-type AVO₃ derivatives (CoVO₃, NiVO₃, and MnVO₃). The properties of MgVO₃ appear to be intermediate between the localized electron model found in MnVO₃, CoVO₃, and NiVO₃, and the delocalized electron regime observed in CuVO₃.     

A structural model for barium platinum oxide,Ba3Pt2O7

A single crystal study of Ba₃Pt₂O₇ shows that the structure tolerates a variable composition which can be written Ba₃Pt_2+xO_7+2x. The crystal studied has a hexagonal cell of dimensions a = 10.108 ± 0.006 Å and c = 8.638 ± 0.009 Å, and a probable space group $\text{P}\text{6}\text{2c, Z = 4}$. The density determined by water displacement is 7.99 g/cm³; the theoretical density for Ba₃Pt₂O₇ is 7.94 g/cm³. The structure was determined from the set of 401 observed independent reflections obtained from 5189 reflections measured by automated counter methods. Refinement on F was carried to a conventional R of 8.0%. The structure has barium-oxygen layers with an essentially four-layer stacking sequence of the double hexagonal (ABAB) type. Platinum is found mainly in face-sharing octahedra, but is also distributed over some sites in which the coordination is nearly square planar and other sites in which the coordination is trigonal prismatic with three PtO bond lengths of 2.00 Å and three long PtO distances of 2.65 Å. The platinum with planar coordination is 0.08 Å from the plane of the four oxygen atoms.