  This paper is an attempt to construct a special kind of Hopf pairing
$\langle-,-\rangle:H^\bullet\otimes H\rightarrow\Bbbk$. Specifically,
$H^\bullet$ and $H$ should be both affine, noetherian and of the same
GK-dimension. In addition, some properties of them would be dual to each other.
We test the ideas in two steps for all the affine prime regular Hopf algebras
$H$ of GK-dimension one: 1) We compute the finite duals $H^\circ$ of them,
which are given by generators and relations; 2) the Hopf pairings desired are
determined by choosing certain Hopf subalgebras $H^\bullet$ of $H^\circ$, where
$\langle-,-\rangle$ becomes the evaluation.
