Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-fi...Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.展开更多
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral fo...A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.展开更多
Abstract Ergosterol,（1→3）-α-D-glucan and chitosan are important biomaterials. In this research, a process has been developed to integratively extract ergosterol, （1→3）-α-D-glucan, and chitosan from Penicillium...Abstract Ergosterol,（1→3）-α-D-glucan and chitosan are important biomaterials. In this research, a process has been developed to integratively extract ergosterol, （1→3）-α-D-glucan, and chitosan from Penicillium chrysongenum mycelium. First the mycelia are pretreated with 0.1mol·L^-1 of NaOH. After recovery by centrifugation the solid portion is made to undergo saponification and deacetylation reactaons by addition of 2mol·L^-1 NaOH and et anol.After reaction, extraction is carried out by addition of petroleum ether, which separates the reaction mixture into two phases. The upper layer of petroleum ether contains extracted ergosterol, and the .bottom layer of NaOH solution contains （1→3）-α-DEglucan; the chitosan is on the mycelia residuum. After isolation, the recovery yield of ergosterol is 0.52% of dry mycelium. That of （1→3）-α-D-glucan is about 8.2%; and chitosan is 5.7% with 86% deacetylation. The compositions have been characterized by 1R, HPLC analyses.展开更多
基金0ne of author （Huang H B） was partially supported by the Natural Science Foundation of Jiangsu province, China （Grant No BK2005062）.Acknowledgement We thank Professor Tian G S for discussion
文摘Based on Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting Bose system, and adding a U（1） symmetry breaking term √V（λα0＋λα0^＋） to HB, we show by using the coherent state theory and the mean-field approximation rather than the c-number approximations, that the Bose-Einstein condensation（BEC） occurs if and only if the U（1） symmetry of the system is spontaneously broken. The real ground state energy and the justification of the Bogoliubov c-number substitution are given by solving the Schroedinger eigenvalue equation and using the self-consistent condition.
文摘A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.
基金Supported by the National Natural Science Foundation of China （No.20636010, No.50373003, No.20406002）, Beijing Natural Science Foundation （No.2071002）, and the Special Funds for Major State Basic Research Program of China （973 Program, No.2007CB714305）.
文摘Abstract Ergosterol,（1→3）-α-D-glucan and chitosan are important biomaterials. In this research, a process has been developed to integratively extract ergosterol, （1→3）-α-D-glucan, and chitosan from Penicillium chrysongenum mycelium. First the mycelia are pretreated with 0.1mol·L^-1 of NaOH. After recovery by centrifugation the solid portion is made to undergo saponification and deacetylation reactaons by addition of 2mol·L^-1 NaOH and et anol.After reaction, extraction is carried out by addition of petroleum ether, which separates the reaction mixture into two phases. The upper layer of petroleum ether contains extracted ergosterol, and the .bottom layer of NaOH solution contains （1→3）-α-DEglucan; the chitosan is on the mycelia residuum. After isolation, the recovery yield of ergosterol is 0.52% of dry mycelium. That of （1→3）-α-D-glucan is about 8.2%; and chitosan is 5.7% with 86% deacetylation. The compositions have been characterized by 1R, HPLC analyses.
