We find new facet-defining inequalities for the linear ordering polytope generalizing the well-known Möbius ladder inequalities. Our starting point is to observe that the natural derivation of the Möbius ladder inequalities as {0, 1 2 }-cuts produces triangulations of the Möbius band and of the corresponding (closed) surface, the projective plane. In that sense, Möbius ladder inequalities have ...

Abstract The Born–Fock theorem is one of the most fundamental theorems quantum mechanics and forms basis for reliable efficient navigation in Hilbert space a system with time-dependent Hamiltonian by adiabatic evolution. In absence level crossings, i.e. without degeneracies, under time evolution all eigenstates keep their energetic order, labeled conserved integer number. Thus, controlling orde...

The q− difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.

a graph g = (v,e) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : v (g) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ v (g), xy ∈ e(g), and the total number of 0, 1 and 2 are balanced. that is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). in thi...