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In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent.

本文中，我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的。

The course content includes ordinary differential equation, linear algebra, vector calculus, Fourier analysis and partial differencial equation partial differential equation, with the aim to train students in establishing an exact perception to the meaning of theory, calculation and experimentation.

课程内容有常微分方程，线性代数，向量微积分，Fourier 分析及偏微分方程式等章节，训练同学在理论，计算及实验间建立正确的认知及意义。

The course will introduce the basic theory of Linear Algebra including linear equations, Matrix theory and vector space concept. Eigenvalues and eigenvectors are used for describing the characteristics of the system. A set of orthogonal basis vectors represent the vector components and transformation characteristics.

线性代数是利用向量与矩阵特性，解决任何以线性方程式描述之系统，譬如电路系统、通讯系统、控制系统；藉由线性代数之特征值与特征向量，更能深入了解系统之内涵；藉由线性代数正交基底，则能深入了解向量讯号之组成与其转换特性。

The construction of complex orthomorphism is created, and based on it the connection of complex f -algebra and complex orthomorphism is discussed.

详细论证了复正交射的结构，并以此为基础讨论了复f-代数与复正交射的关系。

Finally, complex orthomorphism which is intimate with complex f -algebra is fully studied.

最后，研究了和复f-代数密切相关的一类算子：复正交射。

The results obtained in the thesis are as follows: Firstly, the thesis proves that the inner measure and outer measure which defined by Fagin and Halpern are a kind of random sets, generalizes the concept of random sets to Boolean algebra's, and hence establishes the theory of the generalization of random sets.

本文的主要结果如下：①本文证明了Fagin和Halpern提出的内、外测度可表示为一种随机集合，并把随机集合的概念从幂集合推广到了布尔代数上，从而提出了广义随机集合理论。

After introducing the basic knowledge of geometric algebra such as outer product,inner product and geometric product,this paper focused on the CGA description and computation with graphic reflection,rotation,translation,rigid body motion and screw motion,and gave the experimental demonstrations.

在简单介绍外积、内积和几何积等基本概念之后，重点论述了共形几何代数在图形反射、旋转、平移等变换和刚体运动、螺旋运动等方面的描述和计算方法，并给出了实验示例。

Neumann, Successive overrelaxation methods for solving the rank deficient linear least squares problem, Linear Algebra Appl.

Miller and Neumann 提出SOR方法解决秩亏损线性最小二乘问题。

A Brief History of Algebra and Computing: An Eclectic Oxonian View - Jonathan P.

代数和计算科学简史--英国牛津大学计算实验室。

Through studying the intersection of paraboloid of revolution and cylinder , the author concluded that the horizontal projection of the intersecting lines—, is the famous Four-order algebra curve-Perseus curve.

通过对回转抛物面与圆柱面相交的研究，得出交线的水平投影曲线——为四次代数曲线——Perseus座曲线的结论。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。