The dielectric property complemented by the mechanical measurement (internal friction) in the doped Bi4Ti3O12 [Bi4−xLaxTi3O12 (x=0.5,0.75,1) and Bi4−y/3Ti3−yNbyO12 (y=0.015,0.03,0.06)] was systematically investigated from room temperature to 350 °C. In the plot of dielectric loss versus temperature for Bi4Ti3O12 (BiT), a relaxation peak was confirmed to be associated with the motion of the oxygen vacancy. It is found that the La doping at site A is in favor of improvement of the fatigue property, in contrast, the Nb doping at site B can mainly enhance the remanent polarization. Appropriate La doping at site A of perovskite-type unit in BiT enhances the chemical stability of oxygen vacancy by improving the height of the potential barrier for hopping and enhances the mobility of domain by the changing of domain structures. While the Nb doping at site B could induce the distortion of oxygen octahedral and reduce the oxygen vacancy concentration by a compensating effect so that it results in an enhancement of remanent polarization.

Pure Bi4Ti3O12 ceramics were prepared using the conventional solid-state reaction method and their dielectric properties were investigated. A dielectric loss peak with the relaxation-type characteristic was observed at about 370K at 100Hz frequency. This peak was confirmed to be associated with the migration of oxygen vacancies inside ceramics. The Cole–Cole fitting to this peak reveals a strong correlation among oxygen vacancies and this strong correlation is considered to commonly exist among oxygen vacancies in ferroelectrics. Therefore, the migration of oxygen vacancies in ferroelectric materials would demonstrate a collective behavior instead of an individual one due to this strong correlation. Furthermore, this correlation is in proportion to the concentration and in inverse proportion to the activation energy of oxygen vacancies. These results could be helpful to the understanding of the fatigue mechanisms in ferroelectric materials.

In this paper, we give a criterion for the properness of the K-energy in a general Kähler class of a compact Kähler manifold by using Song-Weinkove's result in [24]. As applications, we give some Kähler classes on CP 2 #3CP 2 and CP 2 #8CP 2 in which the K-energy is proper. Finally, we prove Song-Weinkove's result on the existence of critical points ofĴ functional by the continuity method.

For a homogeneous symmetric Cantor set C, we consider all real numbers t such that the intersection C ∩(C +t) is a self-similar set and investigate the form of the corresponding iterated function systems.