x,y)] is the Jacobian determinant for the forward transformation.
The Jacobian determinant is a combination of partial derivatives.
The Jacobian determinant of the inverse transformation, from the rectangular region to the irregular region, defined as (7b), is a combination of partial derivatives in the rectangular region.
Let us define Jacobian determinant of the image registration mapping 0(x) as f (x).
2]) holds for every e> 0 in Q where J([phi])(x) is the Jacobian determinant of [phi](x).
Because the Jacobian determinant did not vanish, Samuelson therefore concluded that "the equilibrium is unique" (Ibid.
The non-vanishing of the Jacobian determinant discussed in equation (7) satisfied that factor intensity condition.
As an example, we may give the Jacobian determinant L = J(x)(t) associated to a diffeomorphism x: [R.
Iwaniec: Jacobian determinants and null Lagrangians, The Art of Integration by Parts, preprint.
An important special case is furnished by the Jacobian determinant
L = J(x)(t) associated to a diffeomorphism x: [R.