Vector laplacian and del squared confusion.

[darkpsi]

Hello all,

I am reading a research paper and have found the equation below:
[URL]http://latex.codecogs.com/gif.latex?\mathbf{z}%20=%20\mathbf{a}%20-%20%28\nabla^2E%28\mathbf{t}%29%29^{-1}\Delta%20E%28\mathbf{t}%29%29[/URL]

in which E is some function with the variable t being the vector input, and a and z being unimportant other vectors.

Now, it's my understanding that the Laplacian of a vector is the same as the divergence of the gradient, but in this equation they are being treated as separate operations, namely because division would result in 1 which would be meaningless. I'm not sure if the first part is taking an inverse, if the two operations are not the same, and/or something else entirely. I can provide more information if it turns out the equation or vectors make the difference.

Thanks for any help!

 

[darkpsi]

To clarify...

To be more specific, is the division going to give a value of 1 or is there ever a case where this doesn't happen? If it helps, the equation E is both twice differentiable and convex.