算子代数

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

Within the round function, the logistic chaotic map and three algebraic group operations are mixed.

在轮函数巾用Logistic混沌映射和3个代数群算子进行混合运算，此外还特别设计了子密钥生成算法。

Within the round function, the logistic chaotic map and three algebraic group operations are mixed. Moreover, the subkeys schedule is specially designed for the consideration of the security.

在轮函数中用Logistic混沌映射和3个代数群算子进行混合运算，此外还特别设计了子密钥生成算法。

This paper discussed the algebraic multiplicity of the complex eigenvalues of population operator.

讨论了人口算子复本征值的代数重数问题。

This method is developed based on Algebra of Systems, an algebraic system modeling language.

并对系统代数提出"Merge"算子，使其更适合建立较复杂系统的仿真模型。

Letbe Ra PID. M_n the n×n full matrix algebra over R,and f denotethe linear bijection over M_n.

设R是主理想整环，M_n是尺上全矩阵代数，f为M_n上的可逆线性算子。

Therefore, for every perfect Lie algebra L(E_1,E_2,E_3) with v = 2, its uniersal central extension has the vertex operator represention.

于是，对于每一个perfect李代数L(E_1，E_2，E_3)，当v=2时它的泛中心扩张都存在顶点算子表示。

Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory.

主要成果，如Sz。，纳吉扩张定理，外尔，冯诺依曼，伯格定理与冯诺伊曼代数的分类，覆盖，就像一个Fredholm算子理论的待遇。

The Laplace matrix is an active and important subject in Algebra Graph Theory. It is a discrete form of the Laplace operator on the compact Rimannian manifold acting on the graphs. It has been widely used in many fields such as Physics, Chemistry, Biology, Computer net science and Information theory ,etc. Some results on the Laplace matrix are given in this thesis.

本文主要研究了代数图论中的一个课题：单圈图的Laplace谱，它是黎曼流形上的拉普拉斯算子在图上的离散形式，Laplace矩阵在物理、化学、生物和计算机通信网络研究等学科中有着广泛的应用。

The thesis studies the difference between GWSs composition and traditional workflow applications, proposes the implement mechanism and technical architecture of GWSs composition and defines the reference model of GWSs composition platform, which provide holistic framework and top-level guidance for studying dynamic GWSs composition technology, designing GWSs composition platform, and implementing representative composite service applications.2、Theories and methods of composite process modeling and process analysis. This thesis proposes a meta-model of Geo-spatial Web services composition process defining from two aspects, i.e. process and resource. According to the process definition meta-model, we propose a new Geo-spatial Web services composition Process/Resource model based on extended WF-net, which effectively resolves the problems on uncertain activity option and dynamic variation of service in composite process model. A notion with regard to soundness of process model is proposed from three aspects, i.e. the structural correctness of process model, validity of data link and validity of resource. The notion of soundness definitely gives a dividing line on correctness of composite GWS process. This thesis analyzes sufficient and essential terms of soundness, and studies compositional property of WSCP/R-net models which provides an effective method to construct a soundness WSCP/R-net model. According to WSCP/R-net, the thesis proposes composition algebra and studies the properties of it. Based on the composition algebra, 6 kinds of composite process reduction rules are induced to optimize the process.3、Geo-spatial Web service QoS model and its application architecture. This thesis proposes an extendable GWS QoS model from three aspects, i.e. Geo-spatial Web Service itself, networking conditions and service consumer which can be used to distinguish GWSs with overlapping or identical functionality. We work over the QoS evaluation methods of composite GWS process which can be used to guide the execution, monitor and service selection of composition process. Aming at some disadvantages in traditional Web service discovery model for its lacking of QoS supporting, this thesis proposes a new service discovery model SDMQ supporting QoS constraints.4、Technologies of composite service executing. SSPL, a new composite service process language, is defined to overcome the disadvantages of existing composite services process languages which can not adapt to the dynamic variation of Geo-spatial Web Services. An algorithm is described to translate WSCP/R-net model into SSPL. The thesis studies the model of dynamic services selection with QoS global optimization, presenting an algorithm GODSS to resolve dynamic services selection with QoS global optimization in GWSs Composition.5、Design and implement experimental system and representative applications. According to the research findings presented above, we design and implement an experimental system and construct two representative applications to show that our achievements are effective and practical.

针对当前空间信息服务聚合研究中存在的若干不足，本文重点在基于工作流的空间信息服务聚合框架、空间信息服务聚合流程建模和分析技术、空间信息服务QoS模型及应用体系以及空间信息服务聚合流程执行等几个方面进行深入研究，主要工作和创新点包括：1、基于工作流的空间信息服务动态聚合框架：研究了空间信息服务动态聚合和传统工作流应用的不同，在此基础上提出了基于工作流技术的空间信息服务动态聚合实现机制、技术体系和参考模型，为研究空间信息服务聚合的关键技术、开发服务聚合支撑平台以及在此基础上构造特定的空间信息服务聚合应用提供了总体框架和顶层指导。2、空间信息服务聚合流程建模和分析技术：首先基于动态服务聚合流程建模的需求和空间信息服务动态变化的应用实际，从服务聚合的过程维和资源维出发定义了服务聚合流程定义元模型；与之相对应，对基本的WF-net进行扩展，提出服务聚合流程/资源网作为空间信息服务聚合流程的形式化描述模型，有效解决了现有的基于基本Petri网和工作流网的服务聚合建模方法所不能解决的不确定路径选择和服务的动态变化性问题；从流程结构正确性、数据依赖有效性和资源实现有效性三个方面提出了WSCP/R-net健壮性的概念，明确界定了聚合流程正确性的标准，并对WSCP/R-net模型的健壮性分析方法和WSCP/R-net模型的组合特性进行了研究；提出了空间信息服务聚合代数算子并对其性质进行了研究，在此基础上提出了6种聚合流程约简规则，从而可达到优化聚合流程、提高聚合流程执行效率的目的。3、空间信息服务QoS模型和应用体系：从服务本身、网络环境和服务消费者三个层次出发，提出了一个可扩展的空间信息服务QoS模型GSQM，实现了对空间信息服务的度量和评价，并对GSQM不同质量要素信息的客观、公正采集方法进行了研究；研究了空间信息服务聚合流程QoS评价方法，有效支持了空间信息服务聚合流程的执行、监控以及服务选择等操作；针对目前的服务发现模型仅支持服务功能性描述、不能有效满足空间信息服务应用需求的现状，提出了一种新的支持QoS约束的服务发现模型SDMQ，并对模型的实现框架进行了研究。4、空间信息服务聚合流程执行技术：针对现有的服务聚合流程描述语言不能有效满足空间信息服务动态聚合流程描述的特点，基于BPEL4WS提出了一种新的空间信息服务聚合流程描述语言SSPL；研究了满足健壮性要求的WSCP/R-net模型向SSPL的转换算法，在此基础上可以满足用户无显式编码来实现空间信息服务聚合应用的目的；研究了服务动态选择QoS全局优化模型，并在此基础上提出了一种解决服务动态选择QoS全局优化问题的实现算法GODSS.5、基于论文研究成果，设计实现了"空间信息服务聚合实验系统"，并构建了"矿产资源评价"和"城市消防应急响应"两个典型应用案例，对论文所述模型、方法的可行性和有效性进行了验证。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。