Sentence examples for mappings are needed from inspiring English sources

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.

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.

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.

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.

Thus when a fixed point of nonexpansive mappings exists, other approximation techniques are needed to approximate it.

Future fine-mapping and deep sequencing studies are needed to determine whether or not other SNPs can be found associated in African Americans as well as to identify both common and/or rare risk-causing alleles in the associated regions.