Synchrotron X-rays can be a useful tool to investigate electron accelera- tion at young supemova remnants （SNRs）. At present, since the magnetic field con- figuration around the shocks of SNRs is uncertain, it is no...Synchrotron X-rays can be a useful tool to investigate electron accelera- tion at young supemova remnants （SNRs）. At present, since the magnetic field con- figuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the ac- celeration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron en- ergy is determined by SNR age, synchrotron cooling and escape from the shock. They are related to the energy dependence of the electron diffusion coefficient. Next, we discuss whether information on the cutoff shape can be provided by observations in the near future which will simply give the photon indices and the flux ratios in the soft and hard X-ray bands. We find that if the power-law index of the electron spectrum is independently determined by other observations, then we can constrain the cutoff shape by comparing theoretical predictions of the photon indices and/or the flux ratios with observed data which will be measured by NuSTAR and/or ASTRO-H. Such study is helpful in understanding the acceleration mechanism. In particular, it will supply another independent constraint on the magnetic field strength around the shocks of SNRs.展开更多
At the invitation of Professor Francois Collart-Dutilleul from the University of Nantes in France, I attendedan international academic conference fo- cusing on the EU＇s foreign policies after the Lisbon Treaty, which...At the invitation of Professor Francois Collart-Dutilleul from the University of Nantes in France, I attendedan international academic conference fo- cusing on the EU＇s foreign policies after the Lisbon Treaty, which was held at the university from Nov. 21 to Dec. 1,2011. Afterwards Professor Collart-Dutilleul asked me to give a lecture on human rights in China to his PhD. students and the following is what I got from this ex- perience in France.展开更多
In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial ...In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented. They guarantee that the Wronskian determinant and the Grammian determinant solve the （3 ＋ 1）-dimensional Jimbo-Miwa equation in the bilinear form. Then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.展开更多
基金supported in part by the fund from Research Institute,Aoyama Gakuin University(R.Y.and A.B.)grant-in-aid from the Ministry of Education,Culture,Sports,Science and Technology(MEXT)of Japan,No.24.8344(Y.O.),No.24840036(M.S.)and No.22684012(A.B.)
文摘Synchrotron X-rays can be a useful tool to investigate electron accelera- tion at young supemova remnants （SNRs）. At present, since the magnetic field con- figuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the ac- celeration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron en- ergy is determined by SNR age, synchrotron cooling and escape from the shock. They are related to the energy dependence of the electron diffusion coefficient. Next, we discuss whether information on the cutoff shape can be provided by observations in the near future which will simply give the photon indices and the flux ratios in the soft and hard X-ray bands. We find that if the power-law index of the electron spectrum is independently determined by other observations, then we can constrain the cutoff shape by comparing theoretical predictions of the photon indices and/or the flux ratios with observed data which will be measured by NuSTAR and/or ASTRO-H. Such study is helpful in understanding the acceleration mechanism. In particular, it will supply another independent constraint on the magnetic field strength around the shocks of SNRs.
文摘At the invitation of Professor Francois Collart-Dutilleul from the University of Nantes in France, I attendedan international academic conference fo- cusing on the EU＇s foreign policies after the Lisbon Treaty, which was held at the university from Nov. 21 to Dec. 1,2011. Afterwards Professor Collart-Dutilleul asked me to give a lecture on human rights in China to his PhD. students and the following is what I got from this ex- perience in France.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11202161 and 11172233)the Basic Research Fund of the Northwestern Polytechnical University,China(Grant No.GBKY1034)
文摘In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented. They guarantee that the Wronskian determinant and the Grammian determinant solve the （3 ＋ 1）-dimensional Jimbo-Miwa equation in the bilinear form. Then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.
