Reconstruction from Projections Using Grassmann Tensors

In this paper a general procedure is given for reconstruction of a set of feature points in an arbitrary dimensional projective space from their projections into lower dimensional spaces. This extends the methods applied in the well-studied problem of reconstruction of scene points in ℘³ given their projections in a set of images. In this case, the bifocal, trifocal and quadrifocal tensors are used to carry out this computation. It is shown that similar methods will apply in a much more general context, and hence may be applied to projections from ℘ ⁿ to ℘ ^m , which have been used in the analysis of dynamic scenes, and in radial distortion correction. For sufficiently many generic projections, reconstruction of the scene is shown to be unique up to projectivity, except in the case of projections onto one-dimensional image spaces (lines), in which case there are two solutions. Projections from ℘ ⁿ to ℘² have been considered by Wolf and Shashua (in International Journal of Computer Vision 48(1): 53–67, 2002), where they were applied to several different problems in dynamic scene analysis. They analyzed these projections using tensors, but no general way of defining such tensors, and computing the projections was given. This paper settles the general problem, showing that tensor definition and retrieval of the projections is always possible.     

符号矩阵奇异值的计算机分解与广义逆计算

本文从符号计算(计算机代数)的观点,对数值矩阵计算理论中传统的奇异值分解算法及其相关的广义逆矩阵计算方法加以改进,使之适于处理符号矩阵且在计算机上实现.并指出其在矩阵理论及线性问题求解中的某些应用,还给出了一个有趣的物理实例.     

综合知识表示模型MAS的属性文法推理机制

根据文献［２］中提出了的基于属性文法和语义网络的综合知识表示模型ＭＡＳ，本文提出了关于实现该ＭＡＳ推理机制的基本算法，并且通过实例对该算法进行了说明，最后，证明了基于ＭＡＳ模板的属性文法是Ｌ－ＡＧ和ＩＭＡＳ的解是完全的结论。     

非线性可约函数方程组的展开式解

本文将可约变换的结果推广至方程组，针对方程组至少有一个可约方程的情形得到其可约变换定理，并依此推导出一类非线性可约方程组的展开式定理。     

A 3D GIS spatial data model based on conformal geometric algebra

We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are con...     

基于微分代数方程的电力市场模型的研究及应用

结合Alvarado提出的电力市场动态模型,利用特征值技术与不等式相结合的方法从理论上讨论了电力市场在Lyapunov意义下的稳定性。首先将电力市场的数学模型转化,给出两个矩阵的和及两个矩阵之积的特征值与原矩阵特征值的关系;再利用这些不等式给出了直接利用模型系数判断电力市场稳定和不稳定的一系列充分条件。利用这些条件只需少量的计算即可判定电力市场的稳定,该方法简单易行,最后用实例进行了验证。     

Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.     

分布式仿真多分辨率建模方法及一致性维护

在分布式仿真中,同一实体的多个分辨率模型并发以及不同实体的各个分辫率模型之间的交互会导致数据表现不一致的问题。在分析现有多分辨率建模方法的基础上,提出了适应分布式仿真环境的不同分辨率模型的树状结构建模方法,其主要由聚合级实体模型和平台级实体模型组成。为解决树状结构建模方法中不同分辫率模型的数据表现不一致问题,将不同分辨率模型间的交互看成分布式数据库中的事务,由此提出了一个嵌套两段式提交协议算法来有效解决不同分辨率模型的一致性维护问题。     

基于模代数的三值维持阻塞触发器及其应用

本文给出了基于模代数理论的三值维持阻塞触发器,并将其应用到时序逻辑电路设计中。由于多值模代数中的两个基本运算和运算结果均为多值信号,所以它的应用避免了以往在采用基于Ｐｏｓｔ代数的三值触发器时,由于输入、输出信号不匹配而必须增加附加编码电路的问题。设计实例表明,该触发器具有更强的逻辑功能,它使得移位寄存器类的时序电路设计得以显著简化。     

电路三要素理论和布尔代数失效原因分析

本文提出一个克服布尔代数失效的电路三要素理论。文中首先分析布尔代数在数字电路中失效的原因,接着证明开关运算定理等,它概括了文献中曾需一一证明的绝大多数开关运算等式,然后表明:数字电路的统一性既存在于门级和元件级电路间,也存在于各型元件级电路结构间,以及动态与静态电路间。此外,本文提出元件级电路设计的卡诺图方法和代数方法。