We provide techniques for studying the nonnegatively curved leftinvariant metrics on a compact Lie group. For “straight” paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity property of the initial derivative of curvature. We apply this result to obtain a partial classification of the nonnegatively curved left-inv...

Curved π-conjugated molecules have attracted considerable interest because of the unique properties originating from their curved π surface. However, the synthesis of such distorted molecules requires harsh conditions, which hamper easy access to heteroatom-containing curved π systems. Here we report the synthesis of a π-extended azacorannulene with nitrogen in its centre. The oxidation of 9-am...

OBJECTIVES To compare the efficacy of Reciproc(®) (VDW GmbH) and ProFile(®) (Dentsply Maillefer) instruments at removing gutta-percha from straight and curved root canals ex vivo filled using the cold lateral condensation and GuttaMaster(®) (VDW GmbH) techniques. MATERIAL AND METHODS Forty mesial roots of mandibular molars with two curved canals and 80 single-rooted teeth with straight root c...

Impact resistance and damage tolerance remain major concerns in the design of laminated composite structures. Impact on flat panels has been the subject of extensive experimental and theoretical studies [1]. The work on curved panels is more limited although most laminates in aircraft wings and fuselages, as well as in other vehicles, are more or less curved. The existence of a delamination thr...

In the early 1990s Steve Gersten and Hamish Short proved that compact nonpositively curved triangle complexes have biautomatic fundamental groups and that compact nonpositively curved square complexes have biautomatic fundamental groups. In this article we report on the extent to which results such as these extend to nonpositively curved complexes built out a mixture of triangles and squares. S...

This paper describes computer modeling and testing of phased arrays curved in the passive axis to improve focusing on small diameter pipe welds; in practice, a couple of curvatures satisfy most diameter and wall thickness applications. The modeling was followed by experimental testing using one of the curved arrays. Not surprisingly, the curved array showed significant improvements over a flat ...

A set of monocular images of a curved painting is taken from di erent viewpoints around its curved surface. After deriving the surface localization in the camera coordinate system we backproject the image on the curved surface and we atten it. We analyze the perspective distortions of the scene in the case when it is mapped on a cylindrical surface. Based on the result of this analysis we deriv...

Humans have a preference for curved over angular shapes, an effect noted by artists as well as scientists. It may be that people like smooth curves or that people dislike angles, or both. We investigated this phenomenon in four experiments. Using abstract shapes differing in type of contour (angular vs. curved) and complexity, Experiment 1 confirmed a preference for curvature not linked to perc...

Local disparity signals must interact in visual cortex to represent boundaries and surfaces of three-dimensional (3D) objects. We investigated how disparity signals interact in 3D contours and in 3D surfaces generated from the contours. We compared flat (single disparity) stimuli with curved (multi-disparity) stimuli. We found no consistent differences in sensitivity to contours vs. surfaces; f...