} \\ & = - { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! a \cdot \nabla _v \psi { \chi \left ( \frac{|v|}{\delta}\right)}f} - { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! a \cdot \