一般代数

The algorithm is simple and fast as compared with the Boolean algebra algorithm of adjacency matrix .

本文给出一种判断有向连接图中节点是否可达的算法，与一般相邻矩阵的布尔代数算法相比，具有简便快速的优点。

For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

Consider the identification of a continuous linear system The identification of its algebraic equivalent system or transfer function can be obtained.

在一般情况下，对于连续线性系统可以获得其代数等价系统或传递函数的辨识。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

We study the properties of $BR_0$-algebra and the total complication triple I method on complete $BR_0$-algebra, and we apply the results to $R_0$-Unite interval $\overline{W}$. Not only we have simplified the proof of the results of $R_0$-type triple I method on $R_0$-Unite interval $\overline{W}$, but also we make the proof to combine with the formal deductive system for fuzzy propositional calculus. This work also explains that the $R_0$-type triple I method is a matching fuzzy inference with $B{\cal L}^*$ system.

研究了基础$BR_0$-代数的性质和基于完备基础$BR_0$-代数的全蕴涵三I算法，对一般蕴涵算子给出了三I算法解存在的一个充分条件，并将结果应用于$R_0$-单位区间$\overline{W}$，不但极大的简化了$R_0$-单位区间$\overline{W}$的$R_0$-型$\alpha$-三I算法结果的证明，而且使其证明过程与相应的模糊命题演算系统结合起来，说明了$R_0$-型三I算法是与$B{\cal L}^*$系统相匹配的模糊推理方法。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

After studying the applications of image algebraic feature thoroughly, we found that when algebraic feature is used to face recognition, projective transformation is generally used to compress the dimension of extracted image feature, then classifier is designed to recognize.

对图象代数特征应用作了深入研究之后，发现在应用代数特征进行人脸识别研究时，一般用投影变换来压缩提取的图象特征维数，然后设计分类器进行识别。

Third,the paper sets up a mathematical model for indirect tax shifting through algebraic method, it concludes a general rule on indirect tax shifting from VAT payers to others, the buyers only takes the full tax burden when there isn't any demand elasticity or full supply elasticity, and the sellers only takes the full tax burden when there is full supply elasticity or no demand elasticity, sellers and buyers share the tax burden respectively, the tax share amount has a straight line dependence to the commodity demand or supply elasticity, the proportion of indirect tax burden of sellers equal to the proportion between demand elasticity and the sum of demand and supply elasticity.

第三，本文用代数推理的办法推导出测算间接税税负转嫁的代数模型，从而得出增值税纳税人间接税税负转嫁的一般规律：销售者和购买者各自负担部分税负，其负担的份额取决于商品供求弹性的对比关系，销售者负担的间接税税负比例等于需求弹性系数占供求弹性系数之和的比例。

Under the condition of knowing zero eigenvalue algebraic multiplication ,the authors have discussed the use and necessary relationship between matrix zero eigenvalue algebraic multiplication and matrix rank.

在已知零特征值代数重数时，给出了矩阵零特征值代数重数与矩阵秩之间的内在必然联系，及其一般应用。

In third part, I discussed R0 algebra in two different aspect:(1) Defined Boole element in R0 algebra. Gave the properties of Boole element and distributive rules of Boole element about finite R0 algebra. Study the filter and the stone filter of L are filters of M.

元的分布规律：研究了民代数M的滤子和民代数M作为有界分配格（记这个有界分配格为L（MO 的滤子之间的关系，得出结论：L的极小素滤子以及 L的 Stone滤子都是 M的滤子，但 L的滤子一般不必是M的滤子。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。