It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n...It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.展开更多
In the Hellings Nordtvedt theory, we obtain some expressions of energy radiation and mass defect effect for a kind of the active galactic nuclei, which is meaningful to calculating the energy radiation in the processi...In the Hellings Nordtvedt theory, we obtain some expressions of energy radiation and mass defect effect for a kind of the active galactic nuclei, which is meaningful to calculating the energy radiation in the procession of forming this kind of celestial bodies. This calculation can give some interpretation for energy source of the jet from the active galactic nuclei.展开更多
Si-Jie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expecte...Si-Jie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expected number of particles in any wave packet belonging to spontaneously produced from the state , which confirms the traditional belief that extremal black holes do not radiate particles. Making some modifications, we demonstrate that the analysis can go through for a charged scalar field.展开更多
The Ring effect refers to the filling in of Fraunhofer lines, which is mainly attributed to the rotational Raman scattering of solar spectra by N2 and O2 molecules in the atmosphere. The Ring effect is one of the most...The Ring effect refers to the filling in of Fraunhofer lines, which is mainly attributed to the rotational Raman scattering of solar spectra by N2 and O2 molecules in the atmosphere. The Ring effect is one of the most significant factors affecting the accuracy of retrieving concentrations of atmospheric trace gases, such as NO2 and SO2, from satellite observations through differential optical absorption spectroscopy. First in this study, the solar spectrum measured by the Ozone Monitoring Instrument onboard NASA Aura is convolved with the rotational Raman cross section of the atmosphere, which is calculated from the rotational Raman cross sections of N2 and O2 molecules, and divided by the original solar spectrum. The slowly varying term is removed by fitting it with a cubic polynomial to obtain the differential Ring spectrum. The results agree well with the calculations using a radiative transfer model (R2=0.9663). Second, the differential Ring spectrum is computed using two fixed wavelengths of 410 nm and 488 nm, and the resulting differential Ring spectra are similar to that calculated with varying wavelengths and agree well with the calculation using the radiative transfer model (R2=0.9624 and 0.9639 respectively). The computation time using the fixed wavelength is about 0.128% of that using a varying wavelength. Finally, we found that the frequency spectrum of the Raman cross sections for the atmosphere, N2 molecules and O2 molecules are similar; thus, the Raman cross section of N2 or O2 molecules can be used to compute the approximate Ring effect for simplicity.展开更多
基金Supported by the Natural Science Foundation of Hubei Province(2004X157).
文摘It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.
基金The project supported by National Natural Science Foundation of China under Grant No.19975018+2 种基金National Basic Research Program of China under Grant No.2003CB716300Natural Science Foundation of Hunan Province of China under Grant No.01JJY2084
文摘In the Hellings Nordtvedt theory, we obtain some expressions of energy radiation and mass defect effect for a kind of the active galactic nuclei, which is meaningful to calculating the energy radiation in the procession of forming this kind of celestial bodies. This calculation can give some interpretation for energy source of the jet from the active galactic nuclei.
基金The project supported in part by National Natural Science Foundation of China under Grant No.90103019+2 种基金the Doctoral Programme Foundation of Institute of Higher Educationthe Ministry of Education of China under Grant No.2000000147
文摘Si-Jie Gao has recently investigated Hawking radiation from spherically symmetrical gravitational collapse to an extremal R-N black hole for a real scalar field. Especially he estimated the upper bound for the expected number of particles in any wave packet belonging to spontaneously produced from the state , which confirms the traditional belief that extremal black holes do not radiate particles. Making some modifications, we demonstrate that the analysis can go through for a charged scalar field.
文摘The Ring effect refers to the filling in of Fraunhofer lines, which is mainly attributed to the rotational Raman scattering of solar spectra by N2 and O2 molecules in the atmosphere. The Ring effect is one of the most significant factors affecting the accuracy of retrieving concentrations of atmospheric trace gases, such as NO2 and SO2, from satellite observations through differential optical absorption spectroscopy. First in this study, the solar spectrum measured by the Ozone Monitoring Instrument onboard NASA Aura is convolved with the rotational Raman cross section of the atmosphere, which is calculated from the rotational Raman cross sections of N2 and O2 molecules, and divided by the original solar spectrum. The slowly varying term is removed by fitting it with a cubic polynomial to obtain the differential Ring spectrum. The results agree well with the calculations using a radiative transfer model (R2=0.9663). Second, the differential Ring spectrum is computed using two fixed wavelengths of 410 nm and 488 nm, and the resulting differential Ring spectra are similar to that calculated with varying wavelengths and agree well with the calculation using the radiative transfer model (R2=0.9624 and 0.9639 respectively). The computation time using the fixed wavelength is about 0.128% of that using a varying wavelength. Finally, we found that the frequency spectrum of the Raman cross sections for the atmosphere, N2 molecules and O2 molecules are similar; thus, the Raman cross section of N2 or O2 molecules can be used to compute the approximate Ring effect for simplicity.
