Determination of the impulsive Dirac systems from a set of eigenvalues

In this work, we consider the inverse spectral problem for the impulsive
Dirac systems on $(0,\pi)$ with the jump condition at
the point $\frac{\pi}{2}$. We
conclude that the matrix potential $Q(x)$ on the whole interval can be
uniquely determined by a set of eigenvalues for two cases: (i) the
matrix potential $Q(x)$ is given on
$\Big(0,\frac{(1+\alpha)\pi}{4}\Big)$;
(ii) the matrix potential $Q(x)$ is given on
$\Big(\frac{(1+\alpha)\pi}{4},\pi\Big)$,
where $0<\alpha<1$.