LONG-TIME BEHAVIOR OF A CLASS OF REACTION DIFFUSION EQUATIONS WITH TIME DELAYS

The present paper devotes to the long-time behavior of a class of reaction diffusion equations with delays under Dirichlet boundary conditions. The stability and global attractability for the zero solution are provided, and the existence, stability and attractability for the positive stationary solution are also obtained.     

A stability of the steady flow of compressible viscous fluid with respect to initial disturbance (v∞ ≠ 0)

We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ?³. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula (Math. Ann. 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H³‐norm of the initial disturbance is small enough, then the solution to the non‐stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in L_q‐norm for any number q? 2. Copyright © 2006 John Wiley & Sons, Ltd.     

期货经纪公司保证金的一种确定方法

本文基于马尔可夫链在存储论中的应用，结合Ergodic定理，得到确定期货经纪公司保证金的Ergodic模型，即一个双目标规划问题，然后应用乘积最大化准则，将该模型转化为单目标规划问题来求解。该方法考虑期货经纪公司承担的风险和对投资者的吸引程度，为保证金的确定提供新的思路。     

Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

酸糖蛋白手性柱分离6种手性化合物

通过考察缓冲液种类、浓度及其pH值对对映体在手性柱上的保留和分离行为的影响,以及流动相中加入不同种类、不同浓度的不带电荷的有机溶剂乙腈、甲醇、正丙醇、异丙醇、流动相流速和柱温对对映体分离能力的影响,优化了含碳手性中心的碱性药物苯丙哌林、酸性化合物MT-A5及MT-酸和含硫手性中心的质子泵抑制剂奥美拉唑、泮托拉唑、雷贝拉唑对映体分离条件,最佳手性分离条件为:苯丙哌林,0.05 mol/L磷酸二氢铵缓冲液(pH 3.0)-乙腈(95∶5,V/V)为流动相,流速为0.7 mL/m in,柱温为20℃;MT-A5及MT-酸,流动相为0.01 mol/L醋酸铵缓冲液(pH 5.0)-乙腈(74∶26,V/V),流速为0.9 mL/m in,柱温为20℃;泮托拉唑,流动相为10 mmol/L醋酸铵缓冲液(pH 5.5)-乙腈(93∶7,V/V),流速为0.9 mL/m in;柱温为20℃;奥美拉唑和雷贝拉唑,流动相为0.01 mol/L醋酸铵缓冲液(pH 3.0)-乙腈(95∶5,V/V),流速为0.7 mL/m in,柱温为20℃。实现了应用高效液相色谱法在α1-酸糖蛋白手性柱上对上述化合物的对映体分离,并成功用于手性药物合成中的对映体过量百分率的测定。     

On the structure of stationary sets

We isolate several classes of stationary sets of [k]ωand investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.     

弱混强平稳序列随机容量、随即秩次序统计量的极限分布律

设W(1n)W2(n)…W(nn)是严平稳随即序列{Xn,n 1}的前几个变量的顺序统计量,Nn Mn是两正整值r.v,n 1.在较弱一些的混合条件下,本文给出了W(NMn)n标准化后的极限分布,从而使一些提法更趋一般化,主要结果推进了Rao(1984)和张国胜(1993)的工作.由于混合条件的减弱,使得对m-相关和正态平稳过程的具体应用讨论更加充分.