  We show that an inhomogeneous coagulation/decoagulation model can be mapped
to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum
for this inhomogeneous model is computed exactly and the spectral gap is
described for some examples. We construct our inhomogeneous model from two
different homogeneous models joined by one special bond (impurity). The
homogeneous models we started with are the coagulation/decoagulation models
studied previously using the Jordan-Wigner transformation.
