Sentence examples for mappings it is from inspiring English sources

Even though we can efficiently find the highest scoring single/double regions from a given anchor set and its mappings, it is not possible to objectively compare scores of inferred single/double regions.

By using viscosity approximation methods for a finite family of nonexpansive mappings, it is shown that for any given contractive mapping, where is a nonempty closed convex subset of and for any given the iterative scheme is strongly convergent to a solution of (CFP), if and only if and satisfy certain conditions, where and is a sunny nonexpansive retraction of onto.

Based on the analysis of the velocity distribution mappings, it is concluded that SRS spontaneously generates intensive convection and vigorous shear stress under the reversing high-gravity field.

To prove existence of fixed point of such mappings, it is essential for mappings to satisfy certain contractive conditions which involve Hausdorff metric.

Since is an infinite family of closed quasi- -nonexpansive mappings, it is an infinite family of closed and uniformly quasi- -asymptotically nonexpansive mappings with sequence.

To prove the existence of a fixed point of such mappings, it is essential for mappings to satisfy certain contractive conditions which may involve the Hausdorff metric.

The problem of the existence of stationary points has remained almost unexplored for nonexpansive mappings, it being the case that most results about them require contractive like conditions on the mapping as is the case in [8 11].

For correct microarray cDNA mappings it was required for each UniGene Id that the corresponding UniGene sequence was able to identify the exact same microarray cDNA sequence as the first hit when it was compared back to a database of all microarray cDNA sequences.

In this paper, we use F ( T ) to denote the set of fixed points of T. Recall that T is said to be an α-contractive mapping iff there exists a constant α ∈ [ 0, 1 ) such that ∥ T x − T y ∥ ≤ α ∥ x − y ∥, ∀ x, y ∈ C. The Picard iterative process is an efficient method to study fixed points of α-contractive mappings. It is well known that α-contractive mappings have a unique fixed point.

Proof Let α, β : X × X → [ 0, + ∞ ) be the mapping defined by α ( x, y ) = β ( x, y ) = 1 for all x, y ∈ X. Then T is -contractive mappings. It is easy to show that all the hypotheses of Theorems 2.1 and 2.2 are satisfied. Consequently, T has a unique fixed point. □. Corollary 4.2 (Rhoades [17]).

Proposition 16 yields Φ B W ⊂ Φ P. In turn, let Φ M consist of nondecreasing mappings φ : [ 0, ∞ ) → [ 0, ∞ ) such that lim n → ∞ φ n = 0, α > 0 (Matkowski mappings). It is well known [[13], Lemma] that Φ M ⊂ Φ 0.