This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problem...This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problems are approximated byunconstrained differentible optimization problems. Numerical examples are givento show the high efficiency of the method.展开更多
The volume emission rate (VER) of airglow can be used to investigate atmospheric processes. Satellite-based limb measurement of atmosphere is able to obtain the VER profile of airglow with high vertical resolution. Ho...The volume emission rate (VER) of airglow can be used to investigate atmospheric processes. Satellite-based limb measurement of atmosphere is able to obtain the VER profile of airglow with high vertical resolution. However, the traditional one-dimensional retrieval techniques for VER inversion fail to retrieve horizontal structure of VER profile. Thus, the tomographic technique based on the maximum probability is applied to retrieving two-dimensional VER profile of airglow from infrared limb measurement. This technique could process the observed data with low signal-to-noise ratio caused by the observation angle of less than 180° due to the solid nature of the Earth. For saving the processing time and improving the computing speed of VER inversion, serial tables for storing the large sparse matrix for radiance simulation and a large dataset during iterative estimate of VER are presented. The index and weighting factor of line of sight (LOS) through each grid are saved in initial estimate to avoid being computed repeatedly. Furthermore, the product of observed radiance and corresponding weighting factor obtained in initial iteration is stored as weighted observed radiance for the iterative calculation subsequently. Based on the improved algorithm, the VER of airglow is inversed through the tomographic technique. The full width of half maximum (FWHM) of error is 1.78% and the offset of the peak percentage error is 0.22% after 40 iterations for final VER. Comparison of assumed and retrieved VER profiles suggests that VER can be retrieved with a bias of 15% between 10 km and 90 km above the LayerMin (6384 km from the Earth center), and with a bias of 8% for altitude from 30 km to 60 km with vertical resolution of 1 km after 40 iterations. After improvements, the computation speed of VER inversion for once can be improved by 29.6 times for 700 images of 1/3 orbit, and accordingly, the processing time will be reduced from 3 hours and 11 minutes to only 6 minutes. In conclusion, the improvements to tomographic inversion of VER of airglow proposed in this paper are effective and significant.展开更多
More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance m...More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.展开更多
文摘This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problems are approximated byunconstrained differentible optimization problems. Numerical examples are givento show the high efficiency of the method.
基金Under the auspices of National High Technology Research and Development Program of China(No.2006AA12Z102)Graduate Innovation Fund of Jilin University(No.20091023)
文摘The volume emission rate (VER) of airglow can be used to investigate atmospheric processes. Satellite-based limb measurement of atmosphere is able to obtain the VER profile of airglow with high vertical resolution. However, the traditional one-dimensional retrieval techniques for VER inversion fail to retrieve horizontal structure of VER profile. Thus, the tomographic technique based on the maximum probability is applied to retrieving two-dimensional VER profile of airglow from infrared limb measurement. This technique could process the observed data with low signal-to-noise ratio caused by the observation angle of less than 180° due to the solid nature of the Earth. For saving the processing time and improving the computing speed of VER inversion, serial tables for storing the large sparse matrix for radiance simulation and a large dataset during iterative estimate of VER are presented. The index and weighting factor of line of sight (LOS) through each grid are saved in initial estimate to avoid being computed repeatedly. Furthermore, the product of observed radiance and corresponding weighting factor obtained in initial iteration is stored as weighted observed radiance for the iterative calculation subsequently. Based on the improved algorithm, the VER of airglow is inversed through the tomographic technique. The full width of half maximum (FWHM) of error is 1.78% and the offset of the peak percentage error is 0.22% after 40 iterations for final VER. Comparison of assumed and retrieved VER profiles suggests that VER can be retrieved with a bias of 15% between 10 km and 90 km above the LayerMin (6384 km from the Earth center), and with a bias of 8% for altitude from 30 km to 60 km with vertical resolution of 1 km after 40 iterations. After improvements, the computation speed of VER inversion for once can be improved by 29.6 times for 700 images of 1/3 orbit, and accordingly, the processing time will be reduced from 3 hours and 11 minutes to only 6 minutes. In conclusion, the improvements to tomographic inversion of VER of airglow proposed in this paper are effective and significant.
文摘More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.
