Conformal Representation Based on Two Circles

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  • 2個の基円を用いた等角写像法
  • 2コ ノ キエン オ モチイタ トウカク シャゾウホウ

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Abstract

This paper deals with the general principle of conformally transforming two circles onto two segments or double-row segment lattice, based on the idea that the function for representation will be given by a general expression applicable to the circles situated outside each other or osculating or intersecting each other. The functions are uniformly composed of all the elements of the infinite group of inversion with respect to each circle by a simple rule. The structures of the functions are simplified by some transformation to rearrange their poles at periodic points. Then the double wings are represented by the elliptic function of the second kind. The foregoing principle applies to the double-row lattice. Finally the performances of the Vee-wing lattice are deduced.

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