Sentence examples similar to noting a contraction from inspiring English sources

The research was carried out by industry watcher Strategy Analytics, which noted a marked contraction in the UK music market during the first six months of 2012.

We note that is a contraction.

Note that is a contraction of into itself with.

where By Lemma 2.2, we note that is a contraction.

Note that is a contraction mapping of into itself with coefficient.

Note that is a contraction if holds for any satisfying (2.7).

Moreover, T is called a cyclic contraction if there exists k ∈ ( 0, 1 ) such that d ( T x, T y ) ≤ k d ( x, y ) for all x ∈ A and y ∈ B. It is to be noted that although a contraction is continuous, cyclic contractions need not be.

We noted a correlation between CAF-promoted matrix contraction and their ability to promote the invasion of carcinoma cells.

"Reports noting the current contraction of the manufacturing economy and excess production capacity for durable goods underscore the need for U.S. manufacturers to adapt to permanent systemic changes taking place," said Ralph Nappi, president of the machine tool distributors' group in Rockville, Md. "No doubt business will improve, but not to prior levels".

We first note that is a contraction with coefficient.

There exists a unique x* ∈ C such that lim sup n → ∞ 〈 f ( x * ) - x *, x n - x * 〉 ≤ 0. Proof of Step 9. Note that f is a contraction mapping with coefficient α ∈ (0, 1).