Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

Local and global solutions of the Chern-Simons-Higgs system

We study low regularity solutions of the Chern-Simons-Higgs equations. The Lorentz gauge condition makes them hyperbolic equations with the null form. Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation. The div-curl decomposition is used in the temporal gauge.     

大非线性相移下光学非线性Z扫描特性的研究

采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析，通过对数值算法的优化，将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较，发现在大非线性相移的情况下，Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加，Z扫描曲线峰的变化要明显快于谷的变化，而且在谷明显存在的情况下，峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证，实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义，避免在大非线性相移下对Z扫描结果产生错误的分析. 关键词： 大非线性相移 高斯分解法 Z扫描     

Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finiteelement domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques suchas calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy methodand the theory of prior estimates are adopted.Optimal order estimates in L~2 norm are derived for the error inthe approximate solution.     

Numerical comparison of methods for solving second-order ordinary initial value problems

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C²-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

基于奇异值分解的特征跟踪方法

在传统的基于模板匹配的跟踪方法中，均是给定一个模板，然后从图像中各个位置取出一个个与模板大小一致的区域进行相似性度量，找出与模板距离最小的一个区域作为当前模板，以便进行下一步的匹配跟踪工作。在景象匹配和相关跟踪过程中，由于所面临的大多数是变化的场景，实时获取的图像与预存模板之间存在比较大的差异，传统相关匹配方法的应用就会受到限制；而且在跟踪过程中，随时更新模板会造成跟踪性能对扰动过分敏感，从而产生漂移。首先拍摄目标不同角度的图像（尽可能包含目标可能出现的所有情况），构成目标图像训练集合，抽取出特征矩阵，对它进行奇异值分解，构成一个关于目标的多维空间。然后再用匹配方法在全局范围搜索，找出目标的大致位置，并利用收敛方法在确定的大致位置内进行搜索，确定目标的仿射变换系数，从而得到一个目标位置的确切描述。     

Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients

The convergence of iterative based domain decomposition methods is linked with the absorbing boundary conditions defined on the interface between the sub-domains. For linear elasticity problems, the optimal absorbing boundary conditions are associated with non-local Dirichlet-to-Neumann maps. Most of the methods to approximate these non-local maps are based on a continuous analysis. In this paper, an original algebraic technique based on the computation of local Dirichlet-to-Neumann maps is investigated. Numerical experiments are presented for linear elasticity problems with extreme contrasts in the coefficients.     

符号几何规划的一种分解方法

针对符号几何规划提出了一种直接的分解方法,将难于求解的符号几何规划问题等价地转化为一个非线性程度很低的可分离规划,为寻求困难度高且规模较大的符号几何规划问题的求解提供了一种方法,特别是经此方法分解后的每个子问题均易于求解,最后给出了数值实例,验证了此方法的有效性．     

二氯甲烷在担载型三氧化铬催化剂上的催化降解

本文研究了二氯甲烷在不同的担载型ＣｒＯ_３催化剂上的催化降解．实验揭示：碳纤维的单丝直径粗细，吸附能力，ＺＳＭ－５沸石中晶格外铝的含量以及Ａｌ_２Ｏ_３的形貌与物相等均明显影响催化剂的催化活性与选择性．文中对不同的载体作了比较，还对活性组分ＣｒＯ_３的铬的价态，用氢气还原与空气灼烧两种预处理对催化行为的影响进行了讨论．