We introduce a family of conditions on a simplicial complex that we call local klargeness (k ≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the nonpositive curvature: locally 6-large spaces have many properties similar to nonpositively curved ones. However, local 6-largeness neither implies nor is...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

The development of interfacial coherency stresses in TiN/AlN bilayer and multilayer films was investigated by finite element method (ABAQUS) using the four-node bilinear quadrilateral axisymmetric element CAX4R. The TiN and AlN layers are always in compression and tension at the interface, respectively, as may be expected from the fact TiN has larger lattice parameter than AlN. Both, the bi-lay...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic's surface. We will describe a prototype version of GEMM, its repeatability with tim...

OBJECTIVES The study was to compare the shaping ability of Reciproc (VDW) and WaveOne (Dentsply Maillefer) instruments compared with ProTaper, Profile and hand instrument during the preparation of simulated root canals. MATERIALS AND METHODS Five groups (n = 5) were established. Reciproc, WaveOne, ProTaper, Profile and K file (K-flexo file) were used to prepare the resin simulated canals. A s...