We prove a representation for the average wave function of the Schrödinger equation with a white noise potential in d = 1, 2, in terms of the renormalized self-intersection local time of a Brownian motion.

The effective dynamics of solitons for the generalized nonlinear Schrödinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is almost surely described by Hamilton’s equations for a classical particle in the random potential, plus error terms d...

The basic aspects of the momentum picture of motion in Lagrangian quantum field theory are given. Under some assumptions, this picture is a 4-dimensional analogue of the Schrödinger picture: in it the field operators are constant, spacetime-independent, while the state vectors have a simple, exponential, spacetime-dependence. The role of these assumptions is analyzed. The Euler-Lagrange equatio...

In this paper, we propose an improved motion-compensated restoration method for color motion picture films deteriorated due to flashing blotches. The method consists of an improved multiresolution block matching with log-D search, a rank ordered differences-based blotch detection and 3D vector median filtering for interpolation of missing data, and utilizes five consecutive frames. Performance ...

In the entertainment industry’s quest for the “suspension of disbelief,” two primary sensory stimuli have been engaged: sight and sound. Since the advent of digital audio, a number of new multitrack digital sound formats have appeared in the motion picture industry, all in an attempt to achieve the ultimate audio experience. However, visual presentation has not advanced at the same pace as the ...

This paper first gives a brief overview of the Chinese audio–video coding standard (AVS) especially on prediction modes of motion compensation for B-picture. Furthermore, two techniques adopted by AVS about how to improve motion compensation for B-picture coding are discussed in detail. The first one is the proposed symmetrical mode that replaces the conventional bi-directional mode, in which o...