Sentence examples for mappings to two from inspiring English sources

Extend the mappings from one family of mappings to two families of mappings; Extend the mappings from the class of asymptotically nonexpansive mappings to the class of generalized asymptotically nonexpansive mappings.

(1) Extend the mappings from one family of mappings to two families of mappings;   (2) Extend the mappings from the class of asymptotically nonexpansive mappings to the class of generalized asymptotically nonexpansive mappings.  .

Corollary 3.3 improves Theorem 3.1 of Cai and Hu [22] from a finite family of of relatively weak quasi-nonexpansive mappings to two finite families of relatively weak quasi-nonexpansive mappings.

(c) We extend a countable family of closed and uniformly L i -Lipschitz continuous and uniformly total quasi-ϕ-asymptotically nonexpansive mappings to two countable families of closed and uniformly L i -Lipschitz continuous and uniformly total quasi-ϕ-asymptotically nonexpansive mappings.  .

If a read's mappings to two or more pseudogenomes are identical, Suspenders merges the mappings into one logical unit and tags the mapping with a bit vector to identify the origin.

Fig. 15 The Dashboard displays mappings between the linear alkylbenzenesulfonate surfactant (CASRN: 42615-29-2) and the mappings to five related chemicals.

(1) Our main results generalize Theorem 1, Theorem 2 and Theorem 3 of Khan-Abbas [4] from one nonexpansive mapping to two nonexpansive mappings involving the convex and lower semi-continuous function in (operatorname{CAT}(0)) spaces.

Remark 2.6 Corollary 2.4 improve and extend the corresponding results in Ye and Gu [[15], Theorem 2.5] from three self-mappings to six self-mappings.

Remark 2.7 Corollary 2.5 improve and extend the corresponding results in Ye and Gu [[15], Corollary 2.7] from three self-mappings to six self-mappings.

Remark 2.1 Theorems 2.1 and 2.2 improve and extend the corresponding results in Ye and Gu [[15], Theorem 2.1, Corollary 2.2] from three self-mappings to six self-mappings.

As the mappings to the three reference genomes yielded qualitatively similar results, we chose to base subsequent analyses on the A. thaliana reference as it is the plant genome which is currently best annotated.