关于有核圆汇的一个问题

A Problem on the Kernelled Field of circles

本文在以有向圆为基本元素的平面上,寻求一个非抛物型和两个抛物型有核圆汇δ(Z-Z_0)=k≠0, (1.1)δ(Z-Z_1)=0 (1.2)δ(Z-Z_2)=0 (1.3)的公共圆,前提条件是两个核圆Z_1,Z_2属于圆汇(1.1),且三圆Z_0,Z_1,Z_2不属于同一线性圆列,作者给出问题有解的充分必要条件,并用拉氏反演把问题简化,从而求得各款的解,最后就其中一款提供一个例子.

This paper is to find,on the plane,the fundamental elements of which are or-iented circles,the common circles of a non-parabolic and two parabolic kernel-led fields of circlesδ(Z-Z_0)=k≠0, (1.1)δ(Z-Z_1)=0, (1.2)δ(Z-Z_2)=0, (1.3)under the conditions that the two kernel circles Z_1,Z_2 are belonging to the field(1.1),and the three circles Z_0,Z_1,Z_2 are not belonging to a same linear range ofcircles.The author gives the necessary and sufficient condition for the problemto be solvable;the problem is simplified by using Laguerre inversion,and thenthe solutions for every case are obtained.Finally an example for one case is of-feted.