The phrase "a contraction provided" is correct and usable in written English.
It can be used in contexts where you are discussing the availability or use of a contraction in language or writing.
Example: "In the sentence, 'I can't believe it,' a contraction provided is 'can't' for 'cannot.'"
Alternatives: "a supplied contraction" or "a given contraction".
Let be a contraction provided that and Indeed, (3.2). where.
(T^{lambda}) is a contraction provided (0
(T^{lambda}) is a contraction provided (0
Let C be a nonempty subset of a real Hilbert space H. Suppose that λ ∈ ( 0, 1 ) and μ > 0. Let F : C → H be a k-Lipschitzian and η-strongly monotone operator on C. Define the mapping W : C → H by W x = x − λ μ F ( x ) for all x ∈ C. Then W is a contraction provided μ < 2 η k 2.
In association with a nonexpansive mapping (T: Crightarrow C), define the mapping (T^{lambda} Crightarrow H) by T^{lambda}x=Tx-lambdamu F T x),quad forall xin C. Then (T^{lambda}) is a contraction provided (mu
In association with a nonexpansive mapping T : C → C, define the mapping T λ : C → H by T λ x = T x − λ μ F T ( x ), ∀ x ∈ C. Then T λ is a contraction provided μ < 2 η k 2, that is, ∥ T λ x − T λ y ∥ ≤ ( 1 − λ ν ) ∥ x − y ∥, ∀ x, y ∈ C, where ν = 1 − 1 − μ ( 2 η − μ k 2 ).
The Greek economy posted its 20th consecutive quarterly decline in the three months through June, government data showed on Monday, but a slower pace of contraction provided a glimmer of hope for beleaguered Greeks.
In this view, tissue contraction provided the basis for a specific animal sensorimotor organization or ASMO.
Thus, muscle contraction provided by the swimming activity was effective at preventing the deleterious effects of unloading on bone mass, strength, trabecular, and cortical architecture, confirming the osteogenic role of mechanical stimuli on bone formation.
Thus, it is possible that TGF-β2 produced by DD fibroblasts and/or other resident cell types in vivo may be important to disease cord contraction, provided appropriate regulators of latent TGF-β activation are also present and active.
The normalization of EMG signals to those recorded during a maximal voluntary contraction provides a valid construct for comparisons of relative muscle activity.
