Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix r new rows and columns, so that the original Jacobi matrix is shifted downward. The r new...

In this work, we consider the nonequilibrium thermodynamics of a reaction-diffusion system at a given temperature, using the Master equation. The information potential is defined as the logarithm of the stationary state. We compare the approximations, given by the Fokker–Planck equation and the Wentzel-Kramers-Brillouin method directly applied to the Master equation, and prove that they lead to...

The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour. PACS: 03.65-w, 03.65Pm, 03.65.-b

Abstract We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born–Oppenheimer type of expansion, in analogy to the case of the usual Wheeler–DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton–Jacobi eq...

We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one–dimension is sufficient to fix the Schwarzian equation [6], implies a fundamental higher dimensional Möbius invariance which in turn univocally fixes the quantum version of the Hamilton–Jacobi equation...

In this paper we study the convergence of the Galerkin approximation method applied to the Generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman ...