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The right-hand side of equation  

LaTeX Math Block Reference
anchorpre_filnal
 can be transformed in the following way by using equality
LaTeX Math Inline
bodyf(x) \cdot \delta(x-x_0) = f(x_0) \cdot \delta(x-x_0)
:

LaTeX Math Block
anchorright_hand_side
alignmentleft
\sum_k  \rho(p(t, {\bf r}))  \cdot q_k(t) \cdot \delta({\bf r}-{\bf r}_k) 
= \sum_k  \rho(p(t, {\bf r}_k)) \cdot  q_k(t) \cdot \delta({\bf r}-{\bf r}_k) 
 = \sum_k  \rho(p(t, {\bf r})) \cdot  q_k(t)  \cdot \delta({\bf r}-{\bf r}_k)  
= \rho(p) \cdot \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k)

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