Sentence examples for mappings is provided from inspiring English sources

Essentially a new approach for finding the fixed points of nonexpansive mappings and solutions of variational inequalities for monotone mappings is provided.

Plots summarizing GO terms and the number of gene products assigned to each term are shown in Figure  3, and a file containing the GO term mappings is provided as Additional file 3. Similar to Arabidopsis [ 36] and other plants, a large number of genes were annotated with terms related to transcription factors.

Additional atom environment mappings are provided by hand curation.

The first relevant work for existence of fixed points for nonexpansive set-valued mappings was provided by Markin [1] in 1968.

Link mappings are provided with skos: exactMatch predicates, while the ChemSpider identifiers are also available via a CHEMINF representation: The InChI is a unique identifier for (small) organic molecules, and has been previously used to define unique URIs for molecules [8, 25].

Thus, T is not an ordered convex contraction of order 2 which has been used in Theorem 2.5 of [3], while by putting α ( x, y ) = 1 4 whenever x ≤ y and α ( x, y ) = 0 otherwise and a 1 = a 2 = b 1 = b 2 = 1 8, it is easy to check that the selfmap T is a generalized convex contraction of order 2. Recently, the notion of weakly Zamfirescu mappings was provided in [19] (see also Zamfirescu [20]).

The most detailed seamount mappings are provided by multibeam echosounding (sonar), however after more than 5000 publicly held cruises, the amount of the sea floor that has been mapped remains minuscule.

Finally, summaries of mappings are provided as extendable tree-views, which organize mappings by identified EC numbers.

In our model, the I/O mappings to be learned are provided sequentially, and the learning process where each mapping is provided only once is mainly analyzed.

A complete listing of GO mappings assigned for rESTs is provided in Additional File 4. Biochemical functionality was predicted by mapping all 2258 rESTs to pathways, using KOBAS implemented within ESTExplorer [ 13], with an E-value cut-off of 1.0e-5.

Feedback is provided to the linked databases if incorrect mappings are identified during the curation process.