球面透射的进一步研究

Further Study of Homology of Sphere

在透射问题中,两内离二次曲面成透射的条件至今尚未研究,通常,该条件很难确定。笔者进一步研究了球面透射问题,得到了两内离球面的4种透射结构及其定量关系,从而为研究更一般的二次曲面内离情况下成透射的问题奠定了一定的理论基础。球面透射的研究结论,可用到相关的平面上的透射问题中。两一般二次曲线成内离和相交情况下,透射中心及透射参数如何确定的问题尚待研究。

In the problem of homology, the condition of the homology of two quadric(one quadric is inside another) is not investigated so far. In general, the condition is difficult to determine. This paper further studies the problem of homology of sphere. Four kinds of homology structures of sphere(one sphere is inside another) and their quantitative relation between one sphere and the other sphere are obtained. The results lay a theoretical foundation for solving the problem of homology of two usual quadric.The conclusion of the study of homology of sphere can be applied to solve the problem of relevant homology of plane. If two ordinary conic sections take the position of one conic section inside another or one across another, the problem of the determination of the center of homology and the parameter of homology needs further study.