谱映像定理在欧氏空间中的另类证明

以泛函分析中的谱映像定量为基础,利用矩阵可以约化为若当型的特点,用一种非常简便的方法证明了欧氏空间中的谱映像定理,给出了一类矩阵指数特征值与原矩阵特征值之间的关系,并给出具体的实例验证结果的有效性.     

一次同余方程组的一种矩阵解法

同余方程组是数论中一个极为有用的课题。文中考虑的是具有一个未知数而具有不同的模的一次同余方程组。一般可以用中国剩余定理或者递推算法等方法给出一次同余方程组的解法。利用矩阵的初等变换和矩阵的Sm ith标准形给出了求解一次同余方程组的一种矩阵解法。     

Second-Order Stiffness Matrix and Loading Vector of a Beam-Column with Semirigid Connections on an Elastic Foundation

The second-order stiffness matrix and corresponding loading vector of a prismatic beam–column subjected to a constant axial load and supported on a uniformly distributed elastic foundation (Winkler type) along its span with its ends connected to elastic supports are derived in a classical manner. The stiffness coefficients are expressed in terms of the ballast coefficient of the elastic foundation, applied axial load, support conditions, bending, and shear deformations. These individual parameters may be dropped when the appropriate effect is not considered; therefore, the proposed model captures all the different models of beams and beam–columns including those based on the theories of Bernoulli–Euler, Timoshenko, Rayleigh, and bending and shear.The expressions developed for the load vector are also general for any type or combinations of transverse loads including concentrated and partially nonuniform distributed loads. In addition, the transfer equations necessary to determine the transverse deflections, rotations, shear, and bending moments along the member are also developed and presented.     

基于判断矩阵的软件评价指标权重分配方法

本文主要讨论判断矩阵的性质和特点，阐明了利用判断矩阵为软件质量评价指标分配权重的原理，对一致性较差的判断矩阵给出了修正方法，最后给出了权重分配方法。     

Combined Petri net modelling and AI-based heuristic hybrid search for flexible manufacturing systems—part II. Heuristic hybrid search

This two-part paper presents modelling and scheduling approaches of flexible manufacturing systems using Petri nets (PNs) and artificial intelligence (AI)-based heuristic search methods. In Part I, PN-based modelling approaches and basic AI-based heuristic search algorithms were presented. In Part II, a new heuristic function that exploits PN information is proposed. Heuristic information obtained from the PN model is used to dramatically reduce the search space. This heuristic is derived from a new concept, the resource cost reachability matrix, which builds on the properties of B-nets proposed in Part I. Two hybrid search algorithms, (1) an approach to model dispatching rules using analysis information provided by the PN simulation and (2) an approach of the modified stage-search algorithm, are proposed to reduce the complexity of large systems. A random problem generator is developed to test the proposed methods. The experimental results show promising results.     

化学结构的计算机处理（Ⅱ）：化学结构的计算机内存储方式和文件格式

化学结构作为化学家最普遍使用的语言，在化学知识的记录，传播和交流中起着十分重要的作用。随着计算机的普及，广大化学工作者都希望能用计算机来帮助处理化学结构，本文介绍了目前面向计算机的化学描述方法中用得最多的几种存储方式和文件格式，它们是：邻接矩阵，邻接表，邻接多表和ＭＯＬ格式，ＳＭＤ格式，简要评述了这些存储方式和文件格式的特点，局限性的应用。     

矩阵方程 AX=B 的反问题

给出矩阵方程ＡＸ＝Ｂ的反问题具有正定实方阵解的充要条件以及解的一般形式．     

A Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras

This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to $N$ views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis.     

语言判断矩阵满意一致性的判定方法

研究语言判断矩阵的满意一致性问题．在给出语言判断矩阵及其满意一致性有关概念的基础上，提出一种关于具有严格偏好关系的语言判断矩阵满意一致性的判定方法．依据所给出的判定方法，可相应地得出关于语言判断矩阵的方案优劣的排序方法．最后通过两个算例说明了所给出方法的有效性。