代数

This paper tries to discuss the probability, conditional probability and conditional expectation on MV-algebra of fuzzy sets.

为此，本文试图建立一套较完备的关于MV-代数中的概率、条件概率和条件期望的理论体系。

Because it emphasizes on algebraic method, geometric intuition are lose. Especially in the unit of conic section, although "the unity of geometrical material and algebraic symbol "is the teaching objective of text books, but according to the material of text books, it is difficult for students to arrive.

本文首先试著分析目前高中数学教科书中，对於几何部份的教材编写上，由於编写者的意识型态不同，理念不同，数学教师对教科书的诠释就会因此而有不同，因而造成目前高中几何教学著重在代数方程式上的一些问题。

This article takes the teaching of conic sections as an example. By designing worksheets, teachers can introduce the historical material about conic sections to students. By way of using Apollonius' definition of parabola, ellipse and hyperbola, teachers can introduce the geometric aspect of "conic section" to students. By using the concept of " latus rectum " in Conics , we can connect "conic sections"-- representation of geometrical aspect, with "the equation of conic sections"-- representation of algebraic aspect to improving insufficiency of text books.

同时本文也试著从历史文本中寻找材料，简单举例说明数学教师可以如何应用这些史料在几何单元教学上，例如三角函数的正余弦定理，最后再以圆锥曲线的正焦弦为例，说明如何利用数学史料於此单元的教学，尤其是阿波罗尼斯的《锥线论》中对圆锥曲线的3个命题，将此3个命题的内容与意涵，尤其是正焦弦在圆锥曲线的几何意义上所扮演的角色，将其适当地融入教学中，将可使学生真正学习圆锥曲线的几何知识，而不再只是代数形式的几何知识。

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。

As an important content in mathematics, Conjugation can be studied and discussed from different aspects such as differential coefficient, algebra, geometry and so on.

摘要共轭是数学中一个重要的内容，讨论也有不同的方法，可以用微分、代数、几何等方法。

We give a purely algebraic method to add uniton numbers for harmonic maps from a simply connected domain into the unitary group.

对于从单连通区域到酉群的调和映射，我们给出了一个增加酉子数的纯代数方法。

In order to prevent the deformation of the physical domain, the geometrical consistency conditions were used.

为提高紊流计算精度，对κ-ε模型结合壁面函数法同LVEL、Baldwin-Lomax这两种代数紊流模型进行了比较。

It is proved that the algorithm is convergenced for arbitrary consistent systems of linear algebraic equations.

本文利用行处理法[2～4]和分治策略[5]探讨这一问题。将任意的n×m阶线性代数方程组=bi，∥αi∈R1×m∥i=1，2，…，n。

In this paper, an important property and a theorem have been given about the matrix Thiele's continued fraction which is used to approximate the function of e. Based on the property, the Thiele algorithm is improved. A numeral example is also provided.

文章利用代数知识给出了矩阵指数函数e的连分式逼近函数的一个重要性质和定理，并在此基础上对矩阵指数函数e的连分式算法进行改进，最后用数值例子来验证其可行性。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

They go to town. Would you just ask them?

他们在城里你能问他们吗？

Ossein pretreated for a2 weeks period exhibited the maximum% yield incase of bone gelatin, while the yield from intact skin was higher than that realized incase of de-scaled skin.

预处理时间达2星期的骨胶原表现出最高的骨明胶百分产量，然而从未处理鱼皮中得到的产率比去鳞的鱼皮得到的要高。