This paper considers an M/G/1 vacation queueing system with patient server and N-policy,where the server's vacation can be interrupted.Applying the total probability decomposition technique,the renewal theory and the Laplace transform tool,the transient and steady-state queue length distributions of the system are analyzed,and the expression of the transient queue length distribution as well as the explicit recursive formulas of the steady-state queue length distribution are derived.Further-more,the stochastic decomposition property of the steady-state queue length is proved.Finally,a cost structure model is formulated and the optimal control policy N*for minimizing the long-run expected cost per unit time is discussed through a numerical example.
We consider the Cauchy problem for the modified Kawahara equation with a cubic nonlinear term in an analytic Gevrey space.Utilizing linear and trilinear estimates in analytic Bourgain-Gevrey space,we establish the local well-posedness in Gevrey space Gδ,s and show that the radius of spatial analyticity persists during the lifespan.Finally,using an approximate conservation law,we extend this to a global result in such a way that the radius of analyticity of solutions is uniformly bounded,that the uniform radius of spatial analyticity of solutions at later time t can decay no faster than 1/|t| as t → ∞.
In this paper, we consider approximate solutions (also called $\varepsilon$-solutions) for semi-infinite optimization problems that objective function and constraint functions with uncertainty data are all convex, and establish robust counterpart of convex semi-infinite program and then consider approximate solutions for its. Moreover, the robust necessary condition and robust sufficient theorems are obtained. Then the duality results of the Lagrangian dual approximate solution is given by the robust optimization approach under a cone constraint qualification.
In this paper, we mainly study the dual problem of semi-infinite programming problem with mixed constraints. we introduce the concept of higher-order (φ,ρ)-V-invexity and construct Wolfe and Mond-Weir type dual models. Weak, strong and strict converse duality theorems are discussed under the assumptions of higher-order (φ,ρ)-V-invexity.
本文研究修正的相场晶体(MPFC)方程的二阶无条件能量稳定数值格式.首先,利用标量辅助变量(SAV)法和二阶向后欧拉(BDF2)公式,得到了一个数值格式;其次,给出了能量耗散定律,严格证明了该数值格式是质量守恒的,唯一可解的,无条件能量稳定的;最后,通过数值实例验证了格式的精度和稳定性.
