We investigate the Hasse principle for complete intersections cut out by a quadric hypersurface and a cubic hypersurface defined over the rational numbers.

The electron energy loss spectroscopy (EELS) technique was applied to investigate the local variation in the phase of barium titanate (BaTiO3) ceramics. It was found that the fine structure of the titanium L2,3 edge and their satellite peaks were sensitively varied with the tetragonal–cubic phase transition. The peak splitting of Ti-L3 edge of tetragonal-phased BaTiO3 ceramics was widened because of the increased crystal field effect compared with that of cubic-phased BaTiO3. In case of nanoscale BaTiO3 powders, the L3 edge splitting of the core region was found to be smaller than that of the shell region. The energy gap between peaks t2g and eg varied from 2.36 to 1.94 eV with changing the probe position from 1 to 20 nm from the surface. These results suggest that the EELS technique can be used to identify the local phase of sintered BaTiO3 ceramics.

Thermal treatment under propane at 1300-1400 °C has been used to prepare Silicon (001) wafers for subsequent growth of cubic GaN and AlN by Electron Cyclotron Resonance Plasma Assisted Molecular Beam Epitaxy (ECRMBE). Thermal treatment of Silicon wafers under propane, used in this experiment, produced a very thin (40 Å) layer of cubic SiC on the Silicon (001) surface. Despite an extremely low thickness of as-produced SiC layer, high quality cubic GaN has been successfully grown. The cubic form of AlN grown on the SiC(40Å)/Si(001) surface has also been observed despite a very high density of stacking faults.

Lower bounds are given for the independence ratio in graphs satisfying certain girth and maximum degree requirements. In particular, the independence ratio of a graph with maximum degree Δ and girth at least six is at least (2Δ − 1)/(Δ2 + 2Δ − 1). Sharper bounds are given for cubic graphs.

A previous result of the author concerning the parametric representation of infinitely many solutions of the title equation is strongly improved. New classes each containing infinitely many solutions of the equation for specified values of d are stated explicitly. The method of solution hinges heavily on solving the generalized Pell’s equation x2—Dy2=c.