三元复分析及其应用
On the ternary complex analysis and its applications
摘要：
以前介绍了复数的一种可能的扩张，以及它所连接的三角函数。本文主要讨论三进制复数的最简单情形。然后，给出了适用于三进制复数的几类全纯性以及相应的微分形式积分的结果。给出了几个物理应用，特别是一种全纯函数给出了一种新形式的定常磁场。然后研究了一个类星体在这个场中的运动，并证明了它是可积的。最后研究了三元场中的单极散射。
英文摘要：
Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are given, and in particuler one type of holomorphic function gives rise to a new form of stationary magnetic field. The movement of a monopole type object in this field is then studied and shown to be integrable. The monopole scattering in the ternary field is finally studied.
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