两不同部件并联可修复系统的稳定性及可靠性分析

通过对两不同部件并联可修复系统的研究证明了系统的渐近稳定性,即lim t→∞p→(·,t)=p→,同时在特例的情况下初步证明了解的可靠性.     

一类可修系统的稳定性及可靠性分析

证明了系统的渐近稳定性,即limt→∞■(,.t)=■,并给出了一种方法,证明了系统的牢固可靠度不小于瞬态可靠度,即p0(t)≥p0*=limt→∞p0(t).     

一个高维loop代数及其应用

本文构造了一个7维loop代数,由此获得两个已知的Liouville可积族．利用屠格式和可积耦合定义得到了相应的四个扩展可积模型．另外,利用马格式求得了上面已知可积系之一的非等谱流．     

在常规错误下具有一个储备部件的冗余系统的稳定性分析

以在常规错误下具有一个储备部件的冗余系统为例,利用半群理论对系统算子的谱点分布进行分析,根据算子半群的稳定性原理,得出了该系统解的渐进稳定性的证明.     

The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system

A new simple loop algebra GM is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained.Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on the FM, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies.     

A family of integrable systems of Liouville and lax representation,Darboux transformations for its constrained flows

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｗｅｌｌ＿ｋｎｏｗｎｂａｓｉｓｏｆｌｏｏｐａｌｇｅｂｒａ Ａ1ｉｓｔｈａｔｈ(ｎ) =λｎ 　 00 -λｎ ,　ｅ(ｎ) =0λｎ0 0 ,ｆ(ｎ) =0 0λｎ 0 ,[ｈ(ｍ) ,ｅ(ｎ) ] =2ｅ(ｍ+ｎ) ,[ｈ(ｍ) ,ｆ(ｎ) ] =　　 -2ｆ(ｍ+ｎ) ,[ｅ(ｍ) ,ｆ(ｎ) ] =ｈ(ｍ+ｎ) .( 1 )Ｍａｎｙｅｑｕａｔｉｏｎｈｉｅｒａｒｃｈｉｅｓｗｅｒｅｏｂｔａｉｎｅｄｂｙｅｓｔａｂｌｉｓｈｉｎｇｌｉｎｅａｒｉｓｏｓｐｅｃｔｒａｌｐｒｏｂｌｅｍｖｉａｔｈｅｕｓｅｏｆ( 1 ) ,ｓｕｃｈａｓＡＫＮＳｈｉｅｒａｒｃｈｙ ,ＫＮｈｉｅｒａ…     

New periodic solutions to a generalized Hirota－Satsuma coupled KdV system

Using expansions in terms of the Jacobi elliptic cosine function and third Jacobi elliptic function, some new periodic solutions to the generalized Hirota－Satsuma coupled KdV system are obtained with the help of the algorithm Mathematica. These periodic solutions are also reduced to the bell-shaped solitary wave solutions and kink-shape solitary solutions. As special cases, we obtain new periodic solution, bell-shaped and kink-shaped solitary solutions to the well-known Hirota－Satsuma equations.     

An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system

A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz－Kaup－Newell－Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.     

A generalized SHGI integrable hierarchy and its expanding integrable model

An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov－Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered.     

修理工单重休假的Gnedenko系统主算子性质

研究了修理工单重休假的Gnedenko系统.运用C_0半群理论,通过服务率均值的观念,对系统主算子的谱上界进行了估值,并得到该谱上界即为服务率均值的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是服务率均值的相反数.