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field of definitions
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  定义域
     in this paper, we give the position vector field of a special surface about given principal curvature function in R3 and R2.1 in field of definitions, so that the problems discussed in section [1] can be solved satisfactorily.
     本文给出了 R3,R2.1内给定主曲率函数的一类特殊曲面在定义域范围内的位置向量场,从而完满地解决了[1]中所讨论的问题.
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     The discussion on a sort of indefinite field of definitions
     对一类不定积分定义域的讨论
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Mathematical analysis is to study function by means of studing its limit. The continuous function is an important type frequently found in functions. It is Profitable and necessary to make a profound research on the concept of limit and continuity of function in order to make the elementary function continuous in its field of definition.

数学分析研究的对象是函数,研究的方法是极限,连续函数是函数中常见的重要一类,深入研究函数极限和连续的概念,使初等函数在定义域上连续是有益的和必要的。

In ancient Chinese calendar, there was a function of second degree used for calculating thevalue of celestial pole longitude. As an independent variable, right ascension was given. There wasalso such a function in the Jiyuan Calendar. But the difference from former calendar-makers was thatthe author of the Jiyuan Calendar let celestial longitude stand as an independent variable, whichmeant the right ascension could be calculated as a positive root of a second degree equation. Thecalendar-maker made clear that...

In ancient Chinese calendar, there was a function of second degree used for calculating thevalue of celestial pole longitude. As an independent variable, right ascension was given. There wasalso such a function in the Jiyuan Calendar. But the difference from former calendar-makers was thatthe author of the Jiyuan Calendar let celestial longitude stand as an independent variable, whichmeant the right ascension could be calculated as a positive root of a second degree equation. Thecalendar-maker made clear that the function's field of value was the field of definition of the formula ofa positive root. He created and used an inverse function here.

研究宋代《纪元历》的作者姚舜辅首次以赤道经度为自变量的二次函数,用以计算相应的极黄经。又取极黄经为自变量,反求其相应的赤经值,并且令函数的值域为所求二次方程之正根公式的定义域,由此创造并使用了一例精确的反函数。

in this paper, we give the position vector field of a special surface about given principal curvature function in R3 and R2.1 in field of definitions, so that the problems discussed in section [1] can be solved satisfactorily.

本文给出了 R3,R2.1内给定主曲率函数的一类特殊曲面在定义域范围内的位置向量场,从而完满地解决了[1]中所讨论的问题.

 
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