fffz分析Part2:BHO~BO

本词条展示fffz强度分析的第$2$部分

\begin{align}s\\&\psi_Z[\varepsilon_0](\varepsilon_0)=\psi(\psi_1(0))=(0,0)(1,1)(2,2)\\&ψ_Z[\varepsilon_0](\varepsilon_0+1)=\psi(\psi_1(0))\times\omega=(0,0)(1,1)(2,2)(1,0)\\&\psi_Z[\varepsilon_0,\varepsilon_0+\omega](\varepsilon_0+\omega)=\psi(\psi_1(0))\times\omega^\omega=(0,0)(1,1)(2,2)(1,0)(2,0)\\&\psi_Z[\varepsilon_0](\varepsilon_0+\omega)=\psi(\psi_1(0)+1)=(0,0)(1,1)(2,2)(1,1)\\&\psi_Z[\varepsilon_0](\varepsilon_0+\omega^\omega)=\psi(\psi_1(0)+\Omega^\Omega)=(0,0)(1,1)(2,2)(1,1)(2,1)(3,1)\\&\psi_Z[\varepsilon_0](\varepsilon_0\times2)=\psi(\psi_1(0)\times2)=(0,0)(1,1)(2,2)(1,1)(2,2)\\&\psi_Z[\varepsilon_0](\varepsilon_0\times3)=\psi(\psi_1(0)\times3)=(0,0)(1,1)(2,2)(1,1)(2,2)(1,1)(2,2)\\&\psi_Z[\varepsilon_0,\varepsilon_0\times\omega](\varepsilon_0\times\omega)=\psi(\psi_1(0)\times\omega)=(0,0)(1,1)(2,2)(2,0)\\&\psi_Z[\varepsilon_0](\varepsilon_0\times\omega)=\psi(\psi_1(0)\times\Omega)=(0,0)(1,1)(2,2)(2,1)\\&\psi_Z[\varepsilon_0](\varepsilon_0\times\omega^\omega)=\psi(\psi_1(0)\times\Omega^\Omega)=(0,0)(1,1)(2,2)(2,1)(3,1)(4,1)\\&\psi_Z[\varepsilon_0](\varepsilon_0^2)=\psi(\psi_1(0)^2)=(0,0)(1,1)(2,2)(2,1)(3,2)\\&\psi_Z[\varepsilon_0](\varepsilon_0^3)=\psi(\psi_1(0)^3)=(0,0)(1,1)(2,2)(2,1)(3,2)(2,1)(3,2)\\&\psi_Z[\varepsilon_0,\varepsilon_0^\omega](\varepsilon_0^\omega)=\psi(\psi_1(0)^\omega)=(0,0)(1,1)(2,2)(2,1)(3,2)(3,0)\\&\psi_Z[\varepsilon_0](\varepsilon_0^\omega)=\psi(\psi_1(0)^\Omega)=(0,0)(1,1)(2,2)(2,1)(3,2)(3,1)\\&\psi_Z[\varepsilon_0](\varepsilon_0^{\varepsilon_0})=\psi(\psi_1(0)^{\psi_1(0)})=(0,0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)\\&\psi_Z[\varepsilon_0](\varepsilon_0^{\varepsilon_0^\omega})=\psi(\psi_1(0)^{\psi_1(0)^\Omega})=(0,0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)(4,1)\\&\psi_Z[\varepsilon_0](\varepsilon_1)=\psi(\psi_1(1))=(0,0)(1,1)(2,2)(2,2)\\&\psi_Z[\varepsilon_0](\varepsilon_2)=\psi(\psi_1(2))=(0,0)(1,1)(2,2)(2,2)(2,2)\\&\psi_Z[\varepsilon_0](\varepsilon_3)=\psi(\psi_1(3))=(0,0)(1,1)(2,2)(2,2)(2,2)(2,2)\\&\psi_Z[\varepsilon_0,\varepsilon_\omega](\varepsilon_\omega)=\psi(\psi_1(\omega))=(0,0)(1,1)(2,2)(3,0)\\&\psi_Z[\varepsilon_0](\varepsilon_\omega)=\psi(\psi_1(\Omega))=(0,0)(1,1)(2,2)(3,1)\\&\psi_Z[\varepsilon_0](\varepsilon_{\varepsilon_0})=\psi(\psi_1(\psi_1(0)))=(0,0)(1,1)(2,2)(3,1)(4,2)\\&\psi_Z[\varepsilon_0](\varepsilon_{\varepsilon_{\varepsilon_0}})=\psi(\psi_1(\psi_1(\psi_1(0))))=(0,0)(1,1)(2,2)(3,1)(4,2)(5,1)(6,2)\\&\psi_Z[\varepsilon_0](\zeta_0)=\psi(\Omega_2)=(0,0)(1,1)(2,2)(3,2)\\&\psi_Z[\varepsilon_0](\zeta_0+\omega)=\psi(\Omega_2+\Omega)=(0,0)(1,1)(2,2)(3,2)(1,1)(2,1)\\&\psi_Z[\varepsilon_0](\zeta_0+\varepsilon_0)=\psi(\Omega_2+\psi_1(0))=(0,0)(1,1)(2,2)(3,2)(1,1)(2,2)\\&\psi_Z[\varepsilon_0](\zeta_0+\varepsilon_{\varepsilon_0})=\psi(\Omega_2+\psi_1(\psi_1(0)))=(0,0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,1)(4,2)\\&\psi_Z[\varepsilon_0](\zeta_0\times2)=\psi(\Omega_2+\psi_1(\Omega_2))=(0,0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)\\&\psi_Z[\varepsilon_0](\zeta_0\times3)=\psi(\Omega_2+\psi_1(\Omega_2)\times2)=(0,0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)\\&\psi_Z[\varepsilon_0,\zeta_0\times\omega](\zeta_0\times\omega)=\psi(\Omega_2+\psi_1(\Omega_2)\times\omega)=(0,0)(1,1)(2,2)(3,2)(2,0)\\&\psi_Z[\varepsilon_0](\zeta_0\times\omega)=\psi(\Omega_2+\psi_1(\Omega_2)\times\Omega)=(0,0)(1,1)(2,2)(3,2)(2,1)\\&\psi_Z[\varepsilon_0](\zeta_0\times\varepsilon_0)=\psi(\Omega_2+\psi_1(\Omega_2)\times\psi_1(0))=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)\\&\psi_Z[\varepsilon_0](\zeta_0^2)=\psi(\Omega_2+\psi_1(\Omega_2)^2)=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)\\&\psi_Z[\varepsilon_0](\zeta_0^3)=\psi(\Omega_2+\psi_1(\Omega_2)^3)=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(2,1)(3,2)(4,2)\\&\psi_Z[\varepsilon_0,\zeta_0^\omega](\zeta_0^\omega)=\psi(\Omega_2+\psi_1(\Omega_2)^\omega)=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,0)\\&\psi_Z[\varepsilon_0](\zeta_0^\omega)=\psi(\Omega_2+\psi_1(\Omega_2)^\Omega)=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,1)\\&\psi_Z[\varepsilon_0](\zeta_0^{\zeta_0})=\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)})=(0,0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,1)(4,2)(5,2)\\&\psi_Z[\varepsilon_0](\varepsilon_{\zeta_0+1})=\psi(\Omega_2+\psi_1(\Omega_2+1))=(0,0)(1,1)(2,2)(3,2)(2,2)\\&\psi_Z[\varepsilon_0](\varepsilon_{\zeta_0+2})=\psi(\Omega_2+\psi_1(\Omega_2+2))=(0,0)(1,1)(2,2)(3,2)(2,2)(2,2)\\&\psi_Z[\varepsilon_0,\varepsilon_{\zeta_0+\omega}](\varepsilon_{\zeta_0+\omega})=\psi(\Omega_2+\psi_1(\Omega_2+\omega))=(0,0)(1,1)(2,2)(3,2)(2,2)(3,0)\\&\psi_Z[\varepsilon_0](\varepsilon_{\zeta_0+\omega})=\psi(\Omega_2+\psi_1(\Omega_2+\Omega))=(0,0)(1,1)(2,2)(3,2)(2,2)(3,1)\\&\psi_Z[\varepsilon_0](\varepsilon_{\zeta_0+\varepsilon_0})=\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(0)))=(0,0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)\\&\psi_Z[\varepsilon_0](\varepsilon_{\zeta_0\times2})=\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))=(0,0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)\\&\psi_Z[\varepsilon_0](\zeta_1)=\psi(\Omega_2\times2)=(0,0)(1,1)(2,2)(3,2)(2,2)(3,2)\\&\psi_Z[\varepsilon_0](\zeta_2)=\psi(\Omega_2\times3)=(0,0)(1,1)(2,2)(3,2)(2,2)(3,2)(2,2)(3,2)\\&\psi_Z[\varepsilon_0,\zeta_\omega](\zeta_\omega)=\psi(\Omega_2\times\omega)=(0,0)(1,1)(2,2)(3,2)(3,0)\\&\psi_Z[\varepsilon_0](\zeta_\omega)=\psi(\Omega_2\times\Omega)=(0,0)(1,1)(2,2)(3,2)(3,1)\\&\psi_Z[\varepsilon_0](\zeta_{\varepsilon_0})=\psi(\Omega_2\times\psi_1(0))=(0,0)(1,1)(2,2)(3,2)(3,1)(4,2)\\&\psi_Z[\varepsilon_0](\zeta_{\zeta_0})=\psi(\Omega_2\times\psi_1(\Omega_2))=(0,0)(1,1)(2,2)(3,2)(3,1)(4,2)(5,2)\\&\psi_Z[\varepsilon_0](\eta_0)=\psi(\Omega_2^2)=(0,0)(1,1)(2,2)(3,2)(3,2)\\&\psi_Z[\varepsilon_0](\eta_\omega)=\psi(\Omega^2_2\times\Omega)=(0,0)(1,1)(2,2)(3,2)(3,2)(3,1)\\&\psi_Z[\varepsilon_0](\varphi(4,0))=\psi(\Omega_2^3)=(0,0)(1,1)(2,2)(3,2)(3,2)(3,2)\\&\psi_Z[\varepsilon_0](\varphi(5,0))=\psi(\Omega_2^4)=(0,0)(1,1)(2,2)(3,2)(3,2)(3,2)(3,2)\\&\psi_Z[\varepsilon_0,\psi_Z[\omega^\omega](\omega^\omega)](\psi_Z[\omega^\omega](\omega^\omega))=\psi(\Omega^\omega_2)=(0,0)(1,1)(2,2)(3,2)(4,0)\end{align}

\begin{align}s\\&\psi_Z[\varepsilon_0](\psi_Z[\omega^\omega](\omega^\omega))=\psi(\Omega_2^\Omega)=(0,0)(1,1)(2,2)(3,2)(4,1)\\&\psi_Z[\varepsilon_0](\psi_Z[\omega^\omega](\psi_Z(\omega)))=\psi(\Omega_2^{\psi_1(0)})=(0,0)(1,1)(2,2)(3,2)(4,1)(5,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\omega^\omega](\psi_Z[\omega^\omega](\omega^\omega)))=\psi(\Omega_2^{\psi_1(\Omega^\omega)})=(0,0)(1,1)(2,2)(3,2)(4,1)(5,2)(6,0)\\&\psi_Z[\varepsilon_0](\psi_Z(\omega^{\omega}))=\psi(\Omega_2^{\Omega_2})=(0,0)(1,1)(2,2)(3,2)(4,2)\\&\psi_Z[\varepsilon_0](\psi_Z(\omega^{\omega^{\omega}}))=\psi(\Omega_2^{\Omega_2^{\Omega_2}})=(0,0)(1,1)(2,2)(3,2)(4,2)(5,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0))=\psi(\psi_2(0))=(0,0)(1,1)(2,2)(3,3)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0)+\omega)=\psi(\psi_2(0)+1)=(0,0)(1,1)(2,2)(3,3)(1,1)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0)+\varepsilon_0)=\psi(\psi_2(0)+\psi_1(0))=(0,0)(1,1)(2,2)(3,3)(1,1)(2,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0)+\zeta_0)=\psi(\psi_2(0)+\Omega_2)=(0,0)(1,1)(2,2)(3,3)(1,1)(2,2)(3,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0)\times2)=\psi(\psi_2(0)\times2)=(0,0)(1,1)(2,2)(3,3)(2,2)(3,3)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0+1))=\psi(\psi_2(0)\times\omega)=(0,0)(1,1)(2,2)(3,3)(3,0)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0,\varepsilon_0\times\omega](\varepsilon_0\times\omega))=\psi(\psi_2(0)\times\Omega)=(0,0)(1,1)(2,2)(3,3)(3,1)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0\times\omega))=\psi(\psi_2(0)\times\Omega_2)=(0,0)(1,1)(2,2)(3,3)(3,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_1))=\psi(\psi_2(1))=(0,0)(1,1)(2,2)(3,3)(3,3)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_2))=\psi(\psi_2(2))=(0,0)(1,1)(2,2)(3,3)(3,3)(3,3)\\&\psi_Z[\varepsilon_0,\psi_Z[\varepsilon_0](\varepsilon_\omega)](\psi_Z[\varepsilon_0](\varepsilon_\omega))=\psi(\psi_2(\omega))=(0,0)(1,1)(2,2)(3,3)(4,0)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_\omega))=\psi(\psi_2(\Omega_2))=(0,0)(1,1)(2,2)(3,3)(4,1)(5,2)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_{\varepsilon_0}))=\psi(\psi_2(\psi_2(0)))=(0,0)(1,1)(2,2)(3,3)(4,2)(5,3)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](ζ_0))=\psi(\Omega_3)=(0,0)(1,1)(2,2)(3,3)(4,3)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0)))=\psi(\psi_3(0))=(0,0)(1,1)(2,2)(3,3)(4,4)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\zeta_0)))=\psi(\Omega_4)=(0,0)(1,1)(2,2)(3,3)(4,4)(5,4)\\&\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\psi_Z[\varepsilon_0](\varepsilon_0))))=\psi(\psi_4(0))=(0,0)(1,1)(2,2)(3,3)(4,4)(5,5)\\&\large\color{red}{\psi_Z(\varepsilon_0)=\psi(\Omega_\omega)=(0,0,0)(1,1,1)=\mathrm{BO}}\end{align}