无穷网络流的顶点控制

本文研究了无穷网络上的传输过程并在一个顶点对其进行控制.描绘了所有的可控状态,并在最大可控的顶点给出了卡尔曼型判断标准.本文的结果是近期一个相似结果的推广.     

最优运输管理中的分布参数控制问题

分析了汽车运输公司的最优经营管理问题,应用分布参数控制理论和方法建立了运输问题最优控制的数学模型,并用算子半群理论和方法给出了最优控制问题的解,最后给出了最优控制问题的经济学解释.     

Quadratic optimal control of stable systems through spectral factorization

We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation.     

全样板依赖的代数性质

探讨了样板依赖的性质，明确了样板依赖与连接依赖之间的关系。证明了全样板依赖的等价类构成幺半群，进而证明了全样板依赖类与全连接依赖类是本质上相同的两个依赖类。     

映射相等问题的安全双方计算协议

安全多方计算协议是指拥有秘密输入的 方,在不泄漏各自秘密输入的前提下共同正确地计算1个函数,并且除了输出所反映的信息之外,任何一方的输入信息都不泄漏.基于可交换确定型加密体制, 在半诚实模型下给出了判断元素属于集合、集合相等及同一集合上的等价关系相等的安全双方计算协议．给出了利用核、像和核类来判断映射相等的方法,在此基础上进一步提出了判断映射相等的安全双方计算协议, 并对协议的正确性, 安全性和效率进行了说明．     

含临界参数之抽象动力方程边值问题的解

利用算子半群及其扰动理论 ,得到了含第一类临界参数的抽象动力方程边值问题的解。     

有限生成的自由阿贝尔幺半群的整体决定性

研究了有限生成的自由阿贝尔幺半群.证明了有限生成的自由阿贝尔幺半群同构于自然数集关于通常的数的加法所构成的幺半群的直和.表明了有限生成的自由阿贝尔幺半群类是整体决定的.     

由单关系式〈A;a=bua〉显示的半群的字问题

证明了由单关系式