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Li2MgTiO4 ceramics were prepared with Li2CO3, TiO2 and MgO by high energy ball mill method. After mixtures ball-milling 30 h and calcining at 700°C, the homogenate Li2MgTiO4 powders with average particle size of 160 nm were obtained. The pure phase obtained temperature was about 300°C lower than that by a conventional solid-state reaction process. Due to Li+ evaporation, the Li2MgTiO4 ceramics sintered at high temperature existed with some Mg2TiO4. The Li2MgTiO4 ceramics at 1250°C had an excellent microwave dielectric properties ϵr = 12.17, Q × f = 42000 GHz and an τf = −23 ppm/°C

The AWO4 (A = Ca, Sr, Ba) compounds with scheelite structure were synthesized by high energy ball milling for 30 min and the average particle size was reduced to about 120 nm after milling 30 h. AWO4 ceramics were well sintered at relatively low temperatures of 900–1000 °C, 200–400 °C lower than those required by a conventional solid state reaction technique. The samples of CaWO4, SrWO4, and BaWO4 ceramics have dense microstructures and excellent microwave dielectric properties, ɛr = 10.7, 8.6, 8.4; Q × f = 62,100 GHz, 57,500 GHz, 58,800 GHz; and τf = −48 ppm/°C, −52 ppm/°C, −64 ppm/°C, respectively.

The transverse and longitudinal relaxations from the excited electronic levels of rare earth ions (Ln 3+ ) in nanocrystals are reviewed. Employing the frequency up-converted emission, we have studied the ion–ion interactions and the distribution of the ions within Pr 3+ :LaF 3 nanocrystals embedded in oxyfluoride glass. The phonon-assisted energy transfer between Pr 3+ ions is discussed and the relation between the energy transfer rate and the buildup of the up-converted emission is established. The results suggest that the Pr 3+ concentration inside the nanocrystals is 5–10 times that of the average concentration. A jump in the energy transfer rate is observed as the concentration increases, and the possible processes behind it are discussed.

The multiple devil's staircase, that was observed in 1997 in a one-dimensional map with two discontinuous regions, showed a kind of consonant tower-like structures. All the branches that connected top and bottom phase-locked steps of the towers could be divided into two kinds. Our recent study found that actually 16 different kinds of tower branches existed in most parts of parameter space. 14 of them belong to the so-called dissonant structures. The number of types of corresponding dissonant branches is employed to describe the dissonance of the staircase. When the number of discontinuous regions, n, in the system function develops, the dissonance of the staircase increases with 2n3−n rule.

A multifractal measure for the relaxation time distribution in Davidson–Cole dielectric relaxation is analytically obtained. A general first-order multifractal phase transition is reported. It is characterized by the existence of three different phases and the corresponding triple point.

This letter reports the specific phase-locking property of a 1-d map that includes two discontinuous regions. The devil's staircase observed in the system loses monotonicity, self-similarity, and the “Farey tree rule” for description of the plateau length distribution. However this staircase is composed of many conventional devil's staircases that have all three characteristics.

An interior crisis with striking new characteristics has been observed in a one-dimensional piece-wise linear map. Induced by the collision between a chaotic attractor and a “hole”, the crisis exhibits a scaling law of the characteristic time as 〈 τ 〉 ∼ ϵ −1 . The analytical calculation shows that this scaling behavior sensitively depends on the function form of the map and suggests that a different and more complicated scaling behavior may be observed in some non-linear maps.