Complete noncompact Riemannian manifolds with nonnegative sectional curvature arise naturally in the Ricci flow when one takes the limits of dilations about a singularity of a solution of the Ricci flow on a compact 3-manifold [ H-95a]. To analyze the singularities in the Ricci flow one needs to understand these manifolds in depth. There are three invariants, asymptotic scalar curvature ratio, ...

The aim of this paper is to study a finite element numerical approximation of steady flows of an incompressible viscoelastic Oldroyd-B fluid in curved pipes of arbitrary cross-section and curvature ratio. Using rectangular toroidal coordinates, existence and uniqueness of approximated solutions are proved as well as a priori error estimates, under a natural restriction on the pipe curvature ratio.

Fiber Optic Sensors (FOS) offer numerous advantages for structural health monitoring. In addition to being durable, lightweight, and capable of multiplexing, they offer the ability to monitor strain in both static and dynamic mode. FOS also allow for instrumentation of large areas of a structure with long-gage sensors which helps enable global monitoring of the structure. Drawing upon these ben...

In this paper, we introduce the factorable surfaces in the pseudo-Galilean space G3 and completely classify such surfaces with null Gaussian and mean curvature. Also, in a special case, we investigate the factorable surfaces which fulfill the condition that the ratio of the Gaussian curvature and the mean curvature is constant in G3.

This paper proposes to incorporate boundary curvature ratio, region homogeneity and boundary smoothness into a single new merging criterion to improve the oversegmentation of marker-controlled watershed segmentation algorithm. The result is a more refined segmentation result with smooth boundaries and regular shapes. To pursue a final segmentation result with higher inter-variance and lower int...

For the retrieval of chlorophyll concentrations or the total absorption coefficients of oceanic waters based on water color, there are algorithms that use either band ratios or spectral curvatures of remote-sensing reflectance or water leaving radiance. We show that band-ratio algorithms have the potential to be applied to a wider dynamic range of oceanic waters, whereas spectral-curvature algo...

Purpose To evaluate the accuracy of IOL power calculation using adjusted corneal power according to the posterior/anterior corneal curvature radii ratio. Methods Nine hundred twenty-eight eyes from 928 reference subjects and 158 eyes from 158 cataract patients who underwent phacoemulsification surgery were enrolled. Adjusted corneal power of cataract patients was calculated using the fictitio...

In this paper we present the first globally optimal ratio-based image segmentation method allowing to impose curvature regularity of the region boundary. The proposed method is fully unsupervised and compares favorably to other such approaches. To identify the optimal foreground region in the image, the algorithm minimizes the ratio of flux over a weighted sum of length and curvature regularity...