Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system are used to define a global phase time in terms of the canonical coordinates and momenta of the minisuperspaces. The procedure clearly shows how the geometry o...

The vertex set of the resonance graph of a hexagonal graph G consists of 1-factors of G, two 1-factors being adjacent whenever their symmetric difference forms the edge set of a hexagon of G. A decomposition theorem for the resonance graphs of catacondensed hexagonal graph is proved. The theorem intrinsically uses the Cartesian product of graphs. A canonical binary coding of 1-factors of cataco...

In this paper, a new dynamic developable surface model is proposed. The proposed model represents developable surfaces using triangle meshes. A novel algorithm is proposed to introduce the Hamilton principle into these meshes such that the resulting developable model is dynamic, i.e., it can offer a time-dependent continuous path to deform the model. Applications with examples are presented; th...

The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to answer for the first time an old question of quantum mechanics in curved spaces raised in 1957 by DeWitt: The Hamiltonian of a particle in a curved space must not contain an additional term proportional to the curvature scalar R, since this would change the level spacings in the...