Sentence examples for form a proximal from inspiring English sources

Given non-self-mappings S : A → B and T : B → A, the pair ( S, T ) is said to form a proximal cyclic contraction if there exists a non-negative number α < 1 such that { d ( u, S x ) = d ( A, B ), d ( v, T y ) = d ( A, B ) ⇒ d ( u, v ) ≤ α d ( x, y ) + ( 1 − α ) d ( A, B ). for all u, x ∈ A and v, y ∈ B. Definition 4.2 [1].

In animals that form a proximal tumor, GSCs enter the path to differentiation and enter into meiosis normally; however, some cells destined for the male fate fail to properly progress through meiotic prophase but rather dedifferentiate and reenter the mitotic cell cycle.

(c) The pair ((S, T)) forms a proximal cyclic contraction.

S ( A 0 ) ⊂ B 0 and T ( B 0 ) ⊂ A 0. The pair ( S, T ) forms a proximal cyclic contraction.

Moreover, the pair ( S, T ) forms a proximal cyclic contraction and the other hypotheses of Theorem 1 are also satisfied.

(b) S ( A 0 ) ⊂ B 0 and T ( B 0 ) ⊂ A 0.   (c) The pair ( S, T ) forms a proximal cyclic contraction.

Note that, if S is a self-mapping that is a contraction, then the pair the pair ((S,S)) forms a proximal cyclic contraction.

The mapping g is an isometry and the non-self-mappings S and T are proximal contractions of the first kind, and the pair ((S, T)) forms a proximal cyclic contraction.

Therefore, by Lemma 2.6, ({y_{n}}) is a Cauchy sequence and hence converges to some element y in B. Since the pair ((S, T)) forms a proximal cyclic contraction and g is an isometry, it follows that F_{x_{n+1}, y_{n+1}}(t) = F_{gx_{n+1}, gy_{n+1}}(t) geqmin biggl{ F_{x_{n}, y_{n}} biggl(frac{t}{alpha} biggr),F_{A, B} (t ) biggr} for (t>0).

The 3D structure revealed that the ∼220-nm-diameter virions are bipolar, with the capsid being positioned eccentrically, thus forming a proximal and a distal pole.

A NarW subclade was noted in clade 1a (including E. coli NarW) and formed a proximal branch from Gammaproteobacterial NarJ sequences (including E. coli NarJ), reconfirming that NarW paralogously evolved from Proteobacterial NarJ [ 9].