Sentence examples for complete metrics from inspiring English sources

We study asymptotic behaviors near the boundary of complete metrics of constant curvature in planar singular domains and establish an optimal estimate of these metrics by the corresponding metrics in tangent cones near isolated singular points on boundary.

Finally, note that we cannot apply Corollary 3 to any of the complete metrics p S, p M, and p 0, since it is clear that these metrics coincide with the discrete metric on X, and for x = y = 0, u = 1, and v = 0, we have p S ( u, v ) = 1 = p S ( x, u ) = max { p S ( x, y ), p S ( x, u ), p S ( y, v ) }.

These classes are shown to be complete metric spaces with respect to the corresponding metrics.

Quantitative estimates of exposure errors can be obtained by carrying out calibration substudies where results from more complete exposure metrics are compared with results from the modeled metrics (Berhane et al. 2004; Fraser and Stram 2001; Mallick et al. 2002; Sarnat et al. 2001; Stram et al. 1995).

Mark Haskins (University of Bath), Complete noncompact metrics of special and exceptional holonomy: the first 40 years.

Complete performance metrics for a variety of score thresholds are available in Supplemental Table S1 and the ROC curve is shown in Supplemental Figure S4.

One can see that d and (d_{B}) are complete b-metrics with (s=2).

In [12] Xu-Xiong-Sheng used an affine blow up analysis to prove the Bernstein theorems for α-relative extremal hypersurfaces with complete α-metrics.

And patching won't work without the right infrastructure: modular business units, fine-grained and complete unit-level metrics, and companywide compensation parity.

In the early 90's, Bartnik defined a localization (to finite regions) of the mass of complete asymptotically flat metrics on 3-manifolds with nonnegative scalar curvature.

The complete list of metrics for measuring the quality of content metadata is presented in Domingues et al. [4].