We enumerate the number of surfaces degree $d$ in $P^3$ having a singular line order $k$, passing through $\delta$ generic points (where is dimension moduli space such surfaces).

Message-passing software systems exhibit non-trivial forms of concurrency and distribution; they are expected to follow intended protocols among communicating services, but also never “get stuck”. This intuitive requirement has been expressed by liveness properties such as progress or (dead)lock freedom various type ensure these for concurrent processes. Unfortunately, very little is known abou...

A graph G is pancyclic if G includes cycles of all lengths and G is edge-pancyclic if each edge lies on cycles of all lengths. A bipartite graph is edge-bipancyclic if each edge lies on cycles of every even length from 4 to |V (G)|. Two cycles with the same length m, C1 = ⟨u1, u2, · · · , um, u1⟩ and C2 = ⟨v1, v2, · · · , vm, v1⟩ passing through an edge (x, y) are independent with respect to th...