An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measureydxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China. 相似文献
Accidental leakage of automobile oils is of great inclination to initiate pool fires in engine compartment, with threats to induce the flashover of other components and flame penetration into the passenger compartment. This paper presents experimental results of the ignition and burning behaviors of a kind of automobile oils (automatic transmission oil) using a cone calorimeter. Measurements of oil temperature, ignition time, mass loss and heat release rate are performed at different external heat fluxes and initial fuel depths. The comparison between experimental and numerical oil temperature evolutions shows that the variations of the ignition time at different experimental conditions depend on the heat dissipation process inside the liquid phase. The steady mass burning rate is nearly independent of initial fuel depth and has a linear relation with external heat fluxes. In addition, the results indicate an increase in peak heat release rate by a large margin initially, followed by a relatively small margin under thicker initial fuel depths, while its variations are proportional to external heat fluxes. Correlations are also developed to determine the peak heat release rate as a function of the initial fuel depth.
An electromechanical integrated electrostatic harmonic actuator is promising for the miniaturization of electromechanical devices. As the dimensions of the actuator decrease, the effects of the van der Waals force become obvious. In this study, by considering the nonlinearity of electrostatic and van der Waals forces, nonlinear vibration equations of the flexible ring of an electrostatic harmonic actuator are deduced. Using these equations, the nonlinear free vibration and nonlinear forced response of the actuator are investigated. The effects of the van der Waals force on the nonlinear vibration of the flexible ring are analyzed. Results show that these effects of the van der Waals force are relatively obvious under some conditions and should be considered. 相似文献