In this article, we will give a brief survey on some recent development concerning the understanding of the structure at infinity of a complete manifold whose spectrum has a positive lower bound. Throughout this paper, we denote M to be a complete n-dimensional manifold without boundary endowed with the metric ds. We assume that the Ricci curvature of M is bounded from below by some constant. R...

PURPOSE To describe longitudinal changes in corneal curvature (CC) and axial length (AL) over 14 years, and to explore the relationship between AL and CC, and the axial length/corneal radius (AL/CR) ratio. METHODS In total 469, 6 to <12-year-old, children were enrolled in COMET. Measurements of refractive error, CC (D), CR (mm), and ocular component dimensions including AL were gathered annua...

The conformal monogenic signal is a novel rotational invariant approach for analyzing i(ntrinsic)1D and i2D local features of twodimensional signals (e.g. images) without the use of any heuristics. It contains the monogenic signal as a special case for i1D signals and combines scale-space, phase, orientation, energy and isophote curvature in one unified algebraic framework. The conformal monoge...

The computing literature often draws a sharp distinction between input and output; computer scientists are used to regarding a screen as a passive output device and a mouse as a pure input device. However, nearly all examples of human-computer interaction require both input and output to do anything useful. For example, what good would a mouse be without the corresponding feedback embodied by t...

We compare curvature combs and curvature plots. © 2016 Elsevier Ltd. All rights reserved.

1.1. Connections and derivations. Let S be a scheme, and X smooth and finite type over S throughout. We have the rank-n vector bundle ΩX/S of 1-forms on X over S. We also fix some notation in the case that S is of characteristic p: in this case, we denote by FT the absolute Frobenius map for any scheme T , by X = X×S S the p-twist of X over S, where the map used in the fiber product is FS : S →...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

We prove that the Atiyah-Singer Dirac operator / Dg in L 2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map g → / Dg(1 + / D 2 g) − 12 depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commu...

Low-severity multiple damage detection relies on sensing minute deviations in the vibrational or dynamical characteristics of structure. The problem becomes complicated when reference profile healthy structure and corresponding input excitation, is unavailable as frequently experienced real-life scenarios. Detection methods that require neither undamaged (baseline-free) nor excitation informati...

in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...