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\begin{eqnarray*}
f_{c,IJ}=\left\{\begin{array}{lr}
1, & r\leq r_{s,IJ} \\
\frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}<r<r_{c,IJ} \\
0, & r \geq r_{c,IJ} \\
\end{array}\right.
\end{eqnarray*} 

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