Sentence examples for of a provided from inspiring English sources

A point x ∈ A is a diametral point of A provided that supy∈A∥x - y∥ = δ(A).

The novel part is that the company sells a self-contained pop-up tent that, with the help of a provided electric fan, deploys and becomes permanent relatively quick.

An infimum of A is similarly defined as a greatest element of the set of all lower bounds of A, provided that it exists; and the collection of all infimum elements of A is denoted by infA or ∧A.

For, the spectral radius ρ(A) is an eigenvalue of A and its eigenspace is denoted by. which includes all positive eigenvectors of A provided that the non-negative matrix A has at least one positive eigenvector(see [15]).

The purpose of this study is to determine objective vocal quality, vocal characteristics, and vocal habits in future speech language pathology (SLP) students and to evaluate the possible impact of a provided vocal counseling procedure.

They showed that the sequence { x n } generated by (7) converges strongly to a zero point of A provided the following conditions (i) and (ii) are verified: ( i ) lim n → ∞ a n = 0, ∑ n = 1 ∞ a n = ∞, lim inf n → ∞ c n > 0, lim inf n → ∞ α n > 0 ; ( ii ) either ∑ n = 1 ∞ ∥ e n ∥ < ∞ or lim n → ∞ ∥ e n ∥ a n = 0.

But shouldn't a celebration of a performer provide a bright spotlight and a big stage?

Lu, a proponent of common sense, provided a necessary counterbalance.

A consortium of foreign banks provided a construction loan.

Most of them provided a service.

But its brief injection of energy provided a welcome finish.