Catching函数分析1：BO~EBO

本条目展示Catching函数的分析。以下左为FGH，右为SGH。均用MOCF表示。

$\begin{array}{r}.\\ & f_3(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+1)\\ & f_4^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega })\\ & f_{\omega }^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}^{\mathrm{\Omega }})\\ & f_{{\omega }^{\omega }}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}})\\ & f_{\psi (0)}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1(\mathrm{\Omega }))\\ & f_{\psi (\mathrm{\Omega })[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_2))\\ & f_{\psi ({\mathrm{\Omega }}_2)[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_3))\\ & f_{\psi ({\mathrm{\Omega }}_3)[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_4))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n]}^2(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega })\times 2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n]+1}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega })\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n]\times 2}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }{)}^2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+1)}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+1))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\omega )}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\psi (0)[n])}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\psi }_1(0)))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\psi ({\mathrm{\Omega }}_{\omega }[n]))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega })))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\mathrm{\Omega })[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\mathrm{\Omega })[n\times 2]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2\times 2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+\mathrm{\Omega })}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+{\mathrm{\Omega }}^2)}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2^2\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+{\psi }_1(0))}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2(\mathrm{\Omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+{\psi }_1({\mathrm{\Omega }}_{\omega }[n]))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]+{\psi }_2({\mathrm{\Omega }}_{\omega }[n]))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }+{\psi }_3({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times 2)}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times 2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times 3)}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times 3)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times \omega )}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times \psi (0))}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_1(\mathrm{\Omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times \psi ({\mathrm{\Omega }}_{\omega }[n]))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_1({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n]\times {\psi }_1({\mathrm{\Omega }}_{\omega }[n]))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_2({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n{]}^2)}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }^2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }[n{]}^{{\mathrm{\Omega }}_{\omega }[n]})}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega }^{{\mathrm{\Omega }}_{\omega }})\\ & f_{\psi ({\psi }_n(0))}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\psi }_{\omega }(0))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n+1]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega +1})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n+2]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega +2})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n\times 2]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}(n))\sim \psi ({\mathrm{\Omega }}_{\omega \times 2})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })}^2(n)\sim \psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\omega })})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[f_{\psi ({\mathrm{\Omega }}_{\omega })}(n)+1]}(f_{\psi ({\mathrm{\Omega }}_{\omega })}^2(n))\sim \psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\omega })+1})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })}^3(n)\sim \psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\omega })})})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }})\end{array}$

$\begin{array}{r}.\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })[n]}(f_{\psi ({\mathrm{\Omega }}_{\omega })+1}(n))\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })}(f_{\psi ({\mathrm{\Omega }}_{\omega })+1}(n))\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\mathrm{\Omega }})}))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })}^n(f_{\psi ({\mathrm{\Omega }}_{\omega })+1}(n))\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })}^{n\times 2}(f_{\psi ({\mathrm{\Omega }}_{\omega })+1}(n))\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times 2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+1}^2(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+2}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+\omega }(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times {\mathrm{\Omega }}^{\omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+\omega +1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times {\mathrm{\Omega }}^{\mathrm{\Omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })+\psi (0)+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times {\psi }_1(\mathrm{\Omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })\times 2}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})\times {\psi }_1({\mathrm{\Omega }}_{\omega }))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })\times 2+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}{)}^2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })\times 2+2}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}{)}^2\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })\times 3+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}{)}^3)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega })\times \omega +1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}{)}^{\mathrm{\Omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }{)}^2+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}{)}^{{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }+1)}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}+1))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }+\psi ({\mathrm{\Omega }}_{\omega }))}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\omega })))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }+\psi ({\mathrm{\Omega }}_{\omega }))+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega })}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\mathrm{\Omega }}_2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times 2)}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}+{\mathrm{\Omega }}_{\omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times 2)+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times 2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times 3)+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times 3)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times \omega )+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times \psi ({\mathrm{\Omega }}_{\omega }))+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times {\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }}))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times \mathrm{\Omega })}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times {\mathrm{\Omega }}_2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}_2)}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times {\mathrm{\Omega }}_3)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}_3)}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times {\mathrm{\Omega }}_4)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^2)}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}\times {\mathrm{\Omega }}_{\omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^2)+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}^2)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^3)+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}^3)\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^{\omega })+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}^{\mathrm{\Omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^{\mathrm{\Omega }})+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}^{{\mathrm{\Omega }}_2})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega }^{{\mathrm{\Omega }}_{\omega }})+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }}^{{\mathrm{\Omega }}_{\mathrm{\Omega }}})\\ & f_{\psi ({\psi }_{\omega }(0))}(n)\sim \psi ({\psi }_{\mathrm{\Omega }}(0))\\ & f_{\psi ({\mathrm{\Omega }}_{\omega +1})}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }+1})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega +2})}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }+2})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega \times 2})}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }+\omega })\\ & f_{\psi ({\mathrm{\Omega }}_{\omega \times 2})+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }\times 2})\\ & f_{\psi ({\mathrm{\Omega }}_{\omega \times 3})+1}(n)\sim \psi ({\mathrm{\Omega }}_{\mathrm{\Omega }\times 3})\\ & f_{\psi ({\mathrm{\Omega }}_{{\omega }^2})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}^2})\\ & f_{\psi ({\mathrm{\Omega }}_{{\omega }^{\omega }})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}^{\mathrm{\Omega }}})\\ & f_{\psi ({\mathrm{\Omega }}_{{\omega }^{{\omega }^{\omega }}})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}}})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (0)})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1(\mathrm{\Omega })})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (1)})}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1(\mathrm{\Omega }+1)})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (1)})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1(\mathrm{\Omega }+1)\times \mathrm{\Omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (\omega )})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1(\mathrm{\Omega }\times 2)})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (\mathrm{\Omega })})}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_2)})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi (\mathrm{\Omega })})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_2\times \mathrm{\Omega })})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_2)})}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_3)})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\omega })})}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_{\omega })})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\omega })})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_{\mathrm{\Omega }})})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{{\omega }^{\omega }})})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_{{\mathrm{\Omega }}^{\mathrm{\Omega }}})})\\ & f_{\psi ({\mathrm{\Omega }}_{\psi ({\mathrm{\Omega }}_{\psi (0)})})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_1({\mathrm{\Omega }}_{{\psi }_1(\mathrm{\Omega })})})\\ & f_{\psi ({\mathrm{\Omega }}_{\mathrm{\Omega }})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_2})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_2})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_3})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_3})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_4})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})\\ & C(1)=\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})+2}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}}\times \mathrm{\Omega })\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }})\times 2+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}}\times {\psi }_1({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}}))\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}\times \mathrm{\Omega })}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}}\times {\mathrm{\Omega }}_2)\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}\times {\mathrm{\Omega }}_{\omega })+1}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}}\times {\mathrm{\Omega }}_{\mathrm{\Omega }})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }+1})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}+1})\\ & f_{\psi ({\mathrm{\Omega }}_{{\psi }_{\omega }(0)})}(n)\sim \psi ({\mathrm{\Omega }}_{{\psi }_{\mathrm{\Omega }}(0)})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega +1}})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }+1}})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\psi (0)}})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\psi }_1(0)}})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\mathrm{\Omega }}})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_2}})\\ & f_{\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}})}(n)\sim \psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}})\\ & C(2)=\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}})\\ & C(3)=\psi ({\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}}})\\ & C(\omega )=\psi ({\psi }_I(0))\end{array}$