  We use quantum and Floer homology to construct (partial) quasi-morphisms on
the universal cover of the group of compactly supported Hamiltonian
diffeomorphisms for a certain class of non-closed strongly semi-positive
symplectic manifolds $(M,\omega)$. This leads to construction of (partial)
symplectic quasi-states on the space of continuous functions on $M$ that are
constant near infinity. The work extends the results by Entov and Polterovich,
which apply in the closed case.
