We consider the classical limit of the quantum evolution, with some rough potential, of wave packets concentrated near singular trajectories of the underlying dynamics. We prove that under appropriate conditions, even in the case of BV vector fields, the correct classical limit can be selected.

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

Liquid foams have been observed to behave like immersed granular materials in at least one respect: deformation tends to raise their liquid contents, a phenomenon called dilatancy. We present a geometrical interpretation thereof in foams squeezed between two solid plates (2D GG foams), which contain pseudo Plateau borders along the plates, and in 3D foams. While experimental observations eviden...

Consider the centered Gaussian field on the lattice Z, d large enough, with covariances given by the inverse of ∑K j=k qj(−∆) , where ∆ is the discrete Laplacian and qj ∈ R, k ≤ j ≤ K, the qj satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are nonnegative on a box of side-length N has an exponential decay at rate of order...

We construct a family of two parameter quantum grou-\ps‎ ‎$U_{r,s}(mathfrak{g})$ associated with a generalized Kac-Moody‎ ‎algebra corresponding to symmetrizable admissible Borcherds Cartan‎ ‎matrix‎. ‎We also construct the $textbf{A}$-form $U_{textbf{A}}$ and‎ ‎the classical limit of $U_{r,s}(mathfrak{g})$‎. ‎Furthermore‎, ‎we‎ ‎display the equitable presentation for a subalgebra‎ ‎$U_{r...

Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...