  We establish a duality of the non-periodic Gaudin model associated with
superalgebra $\mathfrak{gl}_{m|n}$ and the non-periodic Gaudin model associated
with algebra $\mathfrak{gl}_k$.
  The Hamiltonians of the Gaudin models are given by expansions of a Berezinian
of an $(m+n)\times(m+n)$ matrix in the case of $\mathfrak{gl}_{m|n}$ and of a
column determinant of a $k\times k$ matrix in the case of $\mathfrak{gl}_k$. We
obtain our results by proving Capelli type identities for both cases and
comparing the results.
