The singularity category of a Nakayama algebra

Let A be a Nakayama algebra. We give a description of the singularity category of A inside its stable module category, which provides a new approach to the singularity category of a Nakayama algebra. We prove that there is a duality between the singularity category of A and the singularity category of its opposite algebra. As a consequence, the resolution quiver of A and the resolution quiver of its opposite algebra have the same number of cycles and the same number of cyclic vertices.