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Thirdly,we study certain Riemann boundary value problems and Singularintegral equations with values in a universal Clifford algebra 〓,by com-bining the classical methods of solving Riemann boundary value problems andsingular integral equations with the Taylor's expansion of regular function in Clif-ford analysis,proving a lemma which is similar to the Painleve theorem in theclassical complex analysis,and the Plemelj formula in Clifford analysis,we obtainthe better results under weaker condition than before.

第三，本文第一次借助于用来解决经典的Riemann边值问题与奇异积分方程的方法来研究Clifford分析中的某些Riemann边值问题与奇异积分方程，获得了在比以前文献中条件更弱的情况下，结论更广的结果，并且，它为更进一步地解决在Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想，为这一新的研究领域奠定了基础。

In vector algebra, addition are defined to add coordinates entries respectively,and this system of operation is the direct sum Z Z={|a,b are integers} of integers ring Z,the operations are+=,=.

向量代数加法就是这样按照分量加法在运算，再加上按照分量的乘法，这个运算体系就是整数环Z的直和Z Z={|a，b为整数}，其上的运算就是+=，=。

Mr Romney's fans are typically people who did not flunk algebra.

罗姆尼先生的支持者们属于典型的不会代数不及格的人。

Divide the whole region D into finite units and corresponding link points may be obtained. Constructing the equation of variation calculation about every element leads to the finite number of equations. Further more, algebra equation group for general synthesis are gained by adding these finite number of equations, that is,{T}={P} where is the coefficient matrix of the equation group, or say the temperature rigidity matrix,{T} is the row vector of unknown temperature and {P} is the row vector of the terms on the right side of the equation.

然后将整体区域D划分成有限个单元并得到相应的有限个节点，从而可以得到关于每个单元的变分计算方程，将这有限个方程相加就得到了总体合成的代数方程组，即{T}={P}，其中为方程组的系数矩阵，也称温度刚度矩阵，{T}为未知温度值的列向量，{P}为等式右端项组成的列向量。

The discussion of the fourth kind of quadratic equation , the use of "rule of three", the calculation of number r and some terms Algebra can be found in Indian classics introduced to Arab and some of these mathematical knowledge maybe comes from China (such as "rule of three").

花拉子米对第四种二次方程的讨论，使用的"三率法"，对圆周率的计算以及某些术语可以在早期传入阿拉伯的印度典籍中找到出处，而在这些数学知识中有一些可能是远源于中国的。

The definition of work suggests a third process of vector algebra, namely, scalar multiplication of two vectors

功的定义用到矢量代数的第三种运算，即两个矢量的标积。

From the above theorem,（1） compositional invariant security properties and constructive security properties are proved to exist, and （2） security properties are degraded under operators of process algebra, which is known as "bucket principle", i.e, a composed system cannot be securer than the weakest link of the system.

根据这一结果证明了复合不变性质和可构造安全性质在安全性质集上的存在性，并且在安全性质集合上证明了安全性质的"木桶原理"，即复合系统的整体安全性不强于系统中最弱的部分。

At the side of the semigroup algebras, gives a similar result of inverse semigroup algebra.

在第2.1节中，基于[L9]中的结论，我们给出了一个正则Yang-Baxter方程的解，同时也给出了这个解的一个分解。

Eigenvalue matrix for resolving sparse polynomial equations is constructed by deploying well arranged basis in semigroup algebra k.

本文利用半群代数k中良序基，构造了求稀疏多项式方程组解的特征值矩阵，并给出了可以构造方阵的条件。

In this paper,δ-continuous and almost continuous Q\-1Q\-2-mapping are introduced, and continuous,δ-continuous, almost continuous are equivalence in the semiregular de Morgan topological algebra.

Q1Q2 -映射的连续性已在 [2 ]中讨论过，在本文中引进了 Q1Q2 -映射的δ-连续性，几乎连续性，并在半正则德摩根拓扑代数中证明了三种连续性的等价

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷