We prove that the manifold Mn of minimal radial curvature Kmin o ≥ 1 is homeomorphic to the sphere Sn if its radius or volume is larger than half the radius or volume of the round sphere of constant curvature 1. These results are optimal and give a complete generalization of the corresponding results for manifolds of sectional curvature bounded from below. 0. Introduction and results 0.1. A sta...

BACKGROUND The purpose of this study was to assess the effectiveness of 2% ethylenediaminetetraacetic acid (EDTA) for the treatment of band-shaped keratopathy. METHODS We studied 24 eyes of 16 patients with band-shaped keratopathy who underwent EDTA chelation treatment from April 1, 2011 to December 31, 2012. We compared preoperative and 1 month postoperative logarithm of the minimum angle of...

A classical problem in many computer graphics applications consists in extracting significant zones or points on an object surface, like loci of tangent discontinuity (edges), maxima or minima of curvatures, inflection points, etc. These places have specific local geometrical properties and often called generically features. An important problem is related to the scale, or range of scales, for ...

We reviewed the SRK-II method and introduce a new equation to calculate the intraocular lens (IOL) power for eyes which underwent laser phototherapeutic keratectomy (PTK). The Gullstrand series was used to determine the power and the radius of curvature of planoconvex IOLs which alter the focal point from the cornea to reach the conjugate point on the retina. The radius of anterior corneal curv...

Catalytic nanomotors with silica microbead heads and TiO(2) arms are systematically designed by dynamic shadowing growth. The swimming trajectories are fine tuned by altering the arm length and orientation exploiting geometry-dependent hydrodynamic interactions at low Reynolds number. The curvature, angular frequency, and radius of curvature of the trajectories change as a function of arm lengt...

This paper presents an algorithm for estimation of local curvature from gradients of a tensor field that represents local orientation. The algorithm is based on an operator representation of the orientation tensor, which means that change of local orientation corresponds to a rotation of the eigenvectors of the tensor. The resulting curvature descriptor is a vector that points in the direction ...

A novel, flexible, three-dimensional multisensor sonar system is described to localize the center of a generalized spherical target and estimate its radius of curvature. Point, line, and planar targets are included as limiting cases which are important for the characterization of a mobile robot’s environment. Sensitivity analysis of the curvature estimate with respect to measurement errors and ...

A constrained Delaunay triangle mesh method is presented to recover the surface from the three-dimensional unstructured boundary point cloud. The surfaces of different three-dimensional object models are recovered by this triangle mesh method. The radius of the tested cylinder model can be accurately estimated from the derived maximum principle curvature. The derived minimum principle curvature...

We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in R3, R the cross-section radius of a uniform tube neighborhood K, L the arclength of K, and κ the total curvature of K, then (up to some coefficient), crossing number of K ≤ L R κ . The proof generalizes to show that for smooth knots in R3, the crossing number, writhe, Möbiu...

We present direct evidence that magnetic clouds (MCs) have highly flattened and curved cross section resulting from their interaction with the ambient solar wind. Lower limits on the transverse size are obtained for three MCs observed by ACE and Ulysses from the latitudinal separation between the two spacecraft, ranging from 40 to 70. The cross-section aspect ratio of the MCs is estimated to be...