This paper applies a difference scheme to a singularly perturbed problem. The authors provide two algorithms on moving mesh methods by using Richardson extrapolation which can improve the accuracy of numerical solution. In traditional algorithms of moving meshes, the initial mesh is a uniform mesh. The authors change it to Bakhvalov-Shishkin mesh, and prove that it improves efficiency by numerical experiments. Finally, the results of the two algorithms are analyzed.
Logic programming under the stable model semantics is proposed as a non-monotonic language for knowledge representation and reasoning in artificial intelligence. In this paper, we explore and extend the notion of compatibility and the A operator, which were first proposed by Zhang to characterize default theories. First, we present a new characterization of stable models of a logic program and show that an extended notion of compatibility can characterize stable submodels. We further propose the notion of weak auto-compatibility which characterizes the Normal Forward Chaining Construction proposed by Marek, Nerode and Remmel. Previously, this construction was only known to construct the stable models of FC-normal logic programs, which turn out to be a proper subclass of weakly auto-compatible logic programs. We investigate the properties and complexity issues for weakly auto-compatible logic programs and compare them with some subclasses of logic programs.
Two six-wave mixing processes are achieved simultaneously in rubidium vapor and two channels are identified. Signal competition between the two channels is observed and phase matching conditions are analyzed for the two channels. The results show that the two six-wave mixing channels correspond to two parametric processes with weak coupling and, moreover, quantum interference and phase matching conditions primarily govern the signal competition.
