The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun func...The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun functions.The numerical values of energy are then obtained by fixing the zeros on "E-axis" for both complex functions Re[F(E)]and Im[F(E)].展开更多
Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structu...Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also considered,which is very important in practical systems. Finally two simulation examples showing the effectiveness of the approximation laws are proposed.展开更多
基金partially supported by the Scientific and Technical Research Council of Turkey
文摘The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun functions.The numerical values of energy are then obtained by fixing the zeros on "E-axis" for both complex functions Re[F(E)]and Im[F(E)].
基金Supported by National Natural Science Foundation of China (60674020)Natural Science Foun- dation of Shandong Province (Z2006G11).
文摘Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also considered,which is very important in practical systems. Finally two simulation examples showing the effectiveness of the approximation laws are proposed.
基金supported by NSFC(No.10971230,No.11101137 and No.11126188)the Natural Science Foundation of Hunan Province(No.10JJ6014)the Research Foundation of Education Bureau of Hunan Province(No.11C0543)
