Sentence examples for mappings is needed from inspiring English sources

Remark 3.4 Note that in this result continuity of both mappings is crucial (when the space is not regular); however, no compatibility of these mappings is needed.

Two keypoint mappings are needed to determine a similarity transformation that comprises scaling and rotation.

If we are dealing with affine transformations, at least three keypoint mappings are needed to determine an affine transformation.

Using this statistically refined model, we propose a methodology for assessing where the next level of statistical refinement is needed, utilizing a data-mapping framework of 'critical descriptors'.

Since the asymptotically nonexpansive in the intermediate sense mappings are non-Lipschitzian and Bruck's Lemma [23] do not extend beyond Lipschitzian mappings, new techniques are needed for this more general case.

Since the asymptotically nonexpansive mappings in the intermediate sense are non-Lipschitzian and Bruck's lemma [35] does not extend beyond Lipschitzian mappings, new techniques are needed for this more general case.

In this short section, we recall some definitions and known results concerning set-valued mappings which will be needed throughout this paper.

Here, (y_{0}) is denoted by (P_{C}x), where (P_{C}) is called the metric projection of H onto C. Let us recall some kinds of nonlinear mappings as follows, which are needed in the next sections.

Further fine-mapping and functional analyses are needed to identify the causal genes in F. v. ssp.

Fine-mapping studies of 6q25.1 are needed to provide more insight into the independent and causal variants in this specific region.

Large-scale fine-mapping and resequencing efforts are needed to catalogue and evaluate the genetic variation from the full allele spectra in associated regions.