A closed Riemannian n-manifold M with Ricci M > n 1 has diameter < 7r ([M]), and equality holds only if M is isometric to the unit sphere S ~ ([Cn]). Given these results, it is natural to ask whether M is diffeomorphic to S n if the diameter of M is almost 7r. This question was answered negatively by Anderson and Otsu, who showed that even the topology of such a space can be different from the ...

PURPOSE To check whether myopic LASIK induces changes on the posterior corneal surface. METHODS A Scheimpflug system (Pentacam; Oculus, GmbH, Wetzlar, Germany) was used to measure preoperative and postoperative posterior corneal topography in 27 eyes (of 14 subjects) that had undergone standard myopic LASIK surgery (attempted corrections between -1.25 and -8.50 D) and on 18 nonoperated eyes (...

OBJECTIVE To evaluate the effect of number of uses, angle and radius of curvature and type of instrument on the fracture of ProTaper rotary instruments when used by undergraduate students. STUDY DESIGN Three hundred and seventy-six molars, with a total of 1114 root canals, extracted were instrumented by undergraduate students using ProTaper instruments according to the manufacturer´s recommen...

The digitization of a circular arc causes an inherent loss of geometrical information. Arcs with slightly different local curvature or position may lead to exactly the same digital pattern. In this paper we give a characterization of all centers and radii of circular arcs yielding the same digitization pattern. The radius of the arcs varies over the set. However, only one curvature or radius es...

Cyclic fatigue of nickel-titanium, engine-driven instruments was studied by determining the effect of canal curvature and operating speed on the breakage of Lightspeed instruments. A new method of canal curvature evaluation that addressed both angle and abruptness of curvature was introduced. Canal curvature was simulated by constructing six curved stainless-steel guide tubes with angles of cur...

PURPOSE To describe the effect of the corneal asphericity and toricity on the map patterns and best fit sphere (BFS) characteristics in elevation topography. METHODS The corneal surface was modeled as a biconic surface of principal radii and asphericity values of r1 and r2 and Q1 and Q2, respectively. The apex of the biconic surface corresponded to the origin of a polar coordinates system. Mi...