映射定理及其约束条件的探讨与稳定判据

建立并分析了一般映射曲线的结构。从环线的意义出发,与复变函数的零、极点联系起来,从而简单地得到映射定理。而从零、极点与环线所遵守的数量制约关系,建立了映射的约束条件。由此免除了对Ｎ＝Ｚ－Ｐ结论理解的不确定性。对于映射曲线明显存在零点的情况,可免除用Ｎ＝－Ｐ来判定Ｚ是否存在的步骤;对曲线上反向环数大于给定极点数情况,由约束条件可断定题目本身是错误的。

A Probe into the Mapping Theorem and Its Restricted Conditions and Stability Criterion

The structure of the common mapping curve is established and analyzed. The mapping theorem can be obtained plainly by starting from the concept of the loop-line,followed by linking with the zeroes and poles of complex function. Based on the numeral and interactive relationship followed by zeroes, poles and the loop-line, the interactive conditions of the formation of the mapping theorem is determined, by which the uncertainty in understanding the conclusion of N=Z-P can be avoided. In the case of the clear existence of zeroes shown by the mapping curve, the procedures of judging whether the "Z" is existent or not by N=-P can also be saved. When the number of curve anti-clockwise loops is more than given poles, the title itself should be wrong According to the restricted conditions.