Ytterbium and holmium titanates have been synthesized and their dielectric and magnetic properties have been investigated. The frequency dependences of the permittivity at T = 77 and 300 K, and measured magnetization curves and temperature dependences of the magnetic susceptibility in fields up to 30 kOe and at temperatures from 2 K to 50 K have been obtained. The properties of the doped and undoped titanates have been compared. Based on the temperature dependences of the magnetic susceptibility, the magnetic dipole and exchange couplings in the titanates have been analyzed.

Quasiclassical calculations of the effective cyclotron mass and the spectrum of Landau levels have been carried out for carriers of the sizequantized H2 subband with a nonmonotonic dispersion law, which forms a valence band of 20.5-nm-wide HgTe quantum well with an inverted band structure. The model of the so-called "extremum loop", previously developed by Rashba and Sheka for semiconductors with a wurtzite lattice, has been used for calculations. The results obtained are compared both with the empirical picture and with quantummechanical calculations of the Landau level spectrum for the HgTe quantum well in the semimetallic phase.

An anisotropy of the magnetoresistance with respect to the direction of the current is observed experimentally when the magnetic field lies in the plane of a two-dimensional system and is perpendicular to the direction of the current. This effect is related to the combined action of the Lorentz force, which causes a shift in the peak of the electron density from the center to different walls of a quantum well for opposite directions of the current, and to a difference in the contributions of scatterers from different sides of the quantum well to the resistance. It is shown that the difference between the resistances for different directions of the current is an effect with odd parity with respect to the direction of the magnetic field and that the magnitude of this effect increases as the current is raised. The behavior of the differences in the resistance for different directions of the current is observed as a function of the magnetic field strength and current. It is shown that the sign of this effect provides information on the ratio of the scattering intensities from the substrate side and the surface.