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According to the theory of multidimensional game, the paper studies the two-dimensional game of Cournot-Bertrand model with incomplete information and its equilibrium, when the two companies have some of the old and the new alternative products. It shows that for the new and old products have no substitute, the one-dimensional static game of Cournot and Bertrand model is a special case of the two-dimensional static game model. Also, it comes to the conclusion that the equilibrium of two-dimensional static game is better than that of one-dimensional static game of Cournot and Bertrand model.

In order to solve the chaos recognition problem of short time series with noise in reality, a new method of data expansion combined with chaos theory and least square support vector machine is proposed. Then the fractal dimension and the largest lyapunov exponent are calculated on the basis of expansion data. Finally the simulation of Henon system indicats the effectiveness of this method, and explains that this method has some practical value.

A new electrostatic precipitator (ESP) for avoiding the back corona of the high resistivity dust layer is developed by fixing the barb nail discharging electrodes on the plate collecting electrodes based on the analysis of the phenomenon of the back corona of the high resistivity dust layer deposited on the grounded plate electrodes. Therefore, this ESP becomes a bipolar discharging ESP because the negative ions and the positive ions are generated simultaneously by the high voltage discharging electrodes and the grounded barb nail discharging electrodes respectively. The ionic wind is measured by a Particle Image Velocimetry (PIV) because the ionic wind plays an important role in collecting the fine dust with high Resistivity. The positive and the negative ion wind velocities in core area are about 2 m/s when the distance between the opposite electrodes is 100 mm at the voltage of 3.4 kV. In our comparison experiments, the overall efficiency of the bipolar discharging ESP for collecting the silica flour with 0.159 μm mass median diameter is higher than that of the unipolar discharging ESP at the mean electric field of 3.4 kV/cm in the room temperature and pressure. The experimental observation shows that the there is no back corona in the bipolar discharging ESP even when the very high resistivity silica flour (2.4×1014 Ω·cm) is used.

To include not only the perturbative effects but also the nonperturbative effects, the background field method is used in the OPE of two-point correlation function. The sum rules for the "moments" of pion distribution amplitude are obtained by using this method. We find that the values of "moments" are much larger than their perturbative values at intermediate Q2. This result Indicates that the behavior of pion distribution amplitude is much broader than its asymptotic behavior at intermediate Q2.

A convenient method is presented to compute the moments of the distribution amplitude for pion and a possible model form is proposed to fit the experimental data.