In a recent paper [1], the authors suggest a novel Riemannian framework for comparing shapes. In this framework, a simple closed surface is represented by a field of metric tensors and curvatures. A product Riemannian metric is developed based on the L norm on symmetric positive definite matrices and scalar fields. Taken as a quotient space under the group of volume-preserving diffeomorphisms, ...

The metric entropy of absolute convex hulls of sets in Hilbert spaces is studied for the general case when the metric entropy of the sets is arbitrary. Under some regularity assumptions, the results are sharp.

In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such s...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...

Introduction: Following dental avulsion, the immediate recommended treatment is tooth replantation to avoid adverse effects. Therefore, the tooth must be stored in a physiological storage medium to preserve the viability of the periodontal ligament fibroblast (PDLF) cells during transportation to dental office. The aim of this study was to determine the effect of several storage media in preser...