Equation 9.11.31593FB9025947

\begin{equation} \begin{gathered} \beta _ a=(1-a)\beta +a\sigma ,\qquad V=d(1-a^ n),\qquad c_ a=V/M,\\ P_ a(s)=\left(a^ n+c_ an\int _0^ s k(r)r^{n-1}\, \mathrm{d} r\right)^{1/n},\\ Q_ a'(s)=\frac{P_ a(s)-a-(1-a)s}{s(1-s)},\qquad Q_ a(1)=0,\\ q_ a=a\psi +(1-a)\ell +Q_ a(s),\qquad A_ a=\beta _ a+\mathrm{dd}^{\mathrm{c}}q_ a. \end{gathered} \end{equation}