Mathematical Theory of Elasticity of Quasicrystals and Its Applications by Tian-You Fan

Author:Tian-You Fan
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

(9.8.11)

From Eqs. (9.8.2), (9.8.3) and (9.8.8), we have

(9.8.12)

Multiplying the second formula of (9.8.12) by and adding it to the first, one obtains

(9.8.13)

By Eqs. (9.8.2), (9.8.3) and (9.8.9), one has

(9.8.14)

in which

(9.8.15)

However, the further calculation will be very difficult at the z-plane owing to the complicity of the manipulation; we must employ the conformal mapping

(9.8.16)

to transform the region with the ellipse at the -plane onto the interior of the unit circle at -plane, referring to Sect. 8.​4.​2, in which

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