This note presents an elementary numerical scheme for discretizing the Laplace-Beltrami operator on smooth manifolds, as a difference operator of arbitrary high order. The method is coordinate-free, and involves very little geometry.

Gabor feature space is elaborated for representation, processing and segmentation of textured images. As a first step of preprocessing of images represented in this space, we introduce an algorithm for Gabor feature space denoising. It is a geometric-based algorithm that applies diffusion-like equation derived from a minimal weighted area functional, introduced previously and applied in the con...

In this article, we pursue our investigation of the connections between theory computation and hydrodynamics. We prove existence stationary solutions Euler equations in Euclidean space, Beltrami type, that can simulate a universal Turing machine. particular, these possess undecidable trajectories. Heretofore, known complete constructions steady flows dimension 3 or higher were not associated to...

Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum. In previous papers in this series [6,3,5,2,8], we have explored the occurrence of singular continuous spectrum, particularly for Schrodinger operators and Jacobi matrices. In this note, we'll construct examples of graphs whose Laplacians and Riemannian manifolds whose Laplace-Beltrami ...