目的:对二阶非自伴微分算子l(y)=-y″+q(x)y,0≤x<∞,在假定integral from 0 to ∞(x^2|q(x)|dx)<∞的条件下证明了特征展开。本文对方程的解做了更精确估计,然后直接采用回路积分,这样不但简化展开式的证明,且对q(x)的要求可降低...目的:对二阶非自伴微分算子l(y)=-y″+q(x)y,0≤x<∞,在假定integral from 0 to ∞(x^2|q(x)|dx)<∞的条件下证明了特征展开。本文对方程的解做了更精确估计,然后直接采用回路积分,这样不但简化展开式的证明,且对q(x)的要求可降低为integral from 0 to ∞(x|q(x)|dx)<∞。展开更多
In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation,...In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.展开更多
This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in ...This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.展开更多
Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time...Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.展开更多
文摘目的:对二阶非自伴微分算子l(y)=-y″+q(x)y,0≤x<∞,在假定integral from 0 to ∞(x^2|q(x)|dx)<∞的条件下证明了特征展开。本文对方程的解做了更精确估计,然后直接采用回路积分,这样不但简化展开式的证明,且对q(x)的要求可降低为integral from 0 to ∞(x|q(x)|dx)<∞。
文摘In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.
基金This research is supported by Natural Science Foundation of the Education Department of Sichuan Province （[2006]A067） and the Talent Introduction Foundation of Sichuan Normal University. Acknowledgments The author thanks referees for their many helpful comments and suggestions for the improvement of this paper.
文摘This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.
基金Supported by the National Natural Science Foundation of China under Grant No.11105057the Foundation of Hubei University of Education under Grant No.2009B013the Project of Excellent Teacher Team of Hubei University of Education under Grant No.2012KB302
文摘Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.
