  The authors have presented in \cite{IN2} a technique to generate
transformations $\cal T$ of the set ${\Bbb P}_n$ of $n$th degree polynomials to
itself such that if $p\in{\Bbb P}_n$ has all its zeros in $(c,d)$ then ${\cal
T}\{p\}$ has all its zeros in $(a,b)$, where $(a,b)$ and $(c,d)$ are given real
intervals. The technique rests upon the derivation of an explicit form of
biorthogonal polynomials whose Borel measure is strictly sign consistent and
such that the ratio of consecutive generalized moments is a rational $[1/1]$
function of the parameter. Specific instances of strictly sign consistent
measures that have been debated in \cite{IN2} include $x^\mu\D\psi(x)$,
$\mu^x\D\psi(x)$ and $x^{\log_q\mu}\D\psi(x)$, $q\in(0,1)$. In this paper we
identify all measures $\psi$ such that their consecutive generalized moments
have a rational $[1/1]$ quotient, thereby characterizing all possible
zero-mapping transformations of this kind.
