In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorph...In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.展开更多
The spatial resolution of the gamma-rays camera was measured on a60Co gamma-rays source with edge method. The gamma-rays camera is consisting with rays-fluorescence convertor, optical imaging system, MCP image intensi...The spatial resolution of the gamma-rays camera was measured on a60Co gamma-rays source with edge method. The gamma-rays camera is consisting with rays-fluorescence convertor, optical imaging system, MCP image intensifier, CCD camera, electronic control system and other devices, and is mainly used in the image diagnostics of the intense pulse radiation sources [1]. Due to the relatively big quantum detective efficiency (DQE) and quantum gain of the gamma-rays, etc., the experimental data were processed by averaging multiple images and fitting curves. According to the experimental results, the spatial resolution MTF (modulation transfer function) at the 10% intensity was about 2lp/mm. Meanwhile, because of the relatively big dispersion effects of the fluorescence transmissions in the scintillator and the optical imaging system, the maximal single-noise ratio (SNR) of the camera was found to be about 5:1. In addition, the spatial resolution of the camera was measured with pulse X-rays with 0.3MeV in average energy and exclusion of the effects of secondary electrons from consideration. Accordingly, the spatial resolution MTF at the 10% intensity was about 5lp/mm. This could be an additional evidence to verify the effects of secondary electrons induced by the 1.25MeV gamma-rays in the scintillator upon the spatial resolution. Based on our analysis, the dispersion sizes of the secondary electrons in the scintillator are about 0.4mm-0.6mm. Comparatively, as indicated by the detailed analysis of the spatial resolutions of the MCP image intensifier and CCD devices, both of them have little effect on the spatial resolution of the gamma-rays camera that could be well neglected.展开更多
基金supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai Universitythe support with the NSF of China (No. 11271090, 11326083)+2 种基金NSF of Guangdong Province (S2012010010121)Shanghai university young teacher training program (ZZSDJ12020)projects 10XKJ01, 12C401 and 12C104 from the Leading Academic Discipline Project of Shanghai Dianji University
文摘In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.
文摘The spatial resolution of the gamma-rays camera was measured on a60Co gamma-rays source with edge method. The gamma-rays camera is consisting with rays-fluorescence convertor, optical imaging system, MCP image intensifier, CCD camera, electronic control system and other devices, and is mainly used in the image diagnostics of the intense pulse radiation sources [1]. Due to the relatively big quantum detective efficiency (DQE) and quantum gain of the gamma-rays, etc., the experimental data were processed by averaging multiple images and fitting curves. According to the experimental results, the spatial resolution MTF (modulation transfer function) at the 10% intensity was about 2lp/mm. Meanwhile, because of the relatively big dispersion effects of the fluorescence transmissions in the scintillator and the optical imaging system, the maximal single-noise ratio (SNR) of the camera was found to be about 5:1. In addition, the spatial resolution of the camera was measured with pulse X-rays with 0.3MeV in average energy and exclusion of the effects of secondary electrons from consideration. Accordingly, the spatial resolution MTF at the 10% intensity was about 5lp/mm. This could be an additional evidence to verify the effects of secondary electrons induced by the 1.25MeV gamma-rays in the scintillator upon the spatial resolution. Based on our analysis, the dispersion sizes of the secondary electrons in the scintillator are about 0.4mm-0.6mm. Comparatively, as indicated by the detailed analysis of the spatial resolutions of the MCP image intensifier and CCD devices, both of them have little effect on the spatial resolution of the gamma-rays camera that could be well neglected.
基金Acknowledgements This work was supported by the Visiting Scholar Program of Chern Institute of Mathematics at Nankai University when the first and third authors worked as visiting scholars. The authors wish to thank the anonymous referees for their very helpful comments and useful suggestions. This work was also supported by the National Natural Science Foundation of China (Grant No. 11271090), the Tianyuan Youth Fund of the National Natural Science Foundation of China (Grant No. 11326083), the Shanghai University Young Teacher Training Program (ZZSDJ12020), the Innovation Program of Shanghai Municipal Education Commission (14YZ164), the Natural Science Foundation of Guangdong Province (S2012010010121), and the Projects (13XKJC01) from the Leading Academic Discipline Project of Shanghai Dianji University.