Sentence examples for suppose a sequence from inspiring English sources

Suppose a sequence of functions { g n } n = 1 ∞ in C1 converges uniformly to a function g.

Definition 1 Suppose a sequence x(n) = (x0, x1, ⋯, xN - 1) with length N, x(n) is defined as the binary sequence, if x(n) ∈ {−1,1} holds.

(1) Traditional interpretation Suppose a sequence Q t for historical natural gas production of a given oil & gas field: Q_{t} = (Q_{ 1},Q_{ 2}, ldots,Q_{n} ),quad t = 1, 2, ldots,n.

In fact, suppose a sequence ({u_{m}}) is a (PS) sequence, that is, ({ varphi u_{m})}) is bounded and (varphi' u_{m})rightarrowmathbf{0}) as (mrightarrow+infty), then the proof of Theorem 1.1 (or Theorem 1.2) tells us that φ is coercive, which implies that ({u_{m}}) is bounded.

Definition 3 Suppose a sequence x(n) = (x0, x1, ⋯, xN - 1) with length N and its imbalance satisfies I ∈ {−1, 0, 1}, x(n) is considered as a zero-mean or a closely approximate zero-mean stationary random process, then the third-order cumulant of cyclic autocorrelation binary sequence x(n) is defined as c 3 x τ 1, τ 2 = 1 N ∑ n = 1 N x n x n + τ 1 x n + τ 2 (2).

Suppose that a sequence (an) converges to some unknown limit a.

Suppose that a sequence of satisfies (2.34).

Suppose that a sequence (x=(x_{n})in{omega}) is Fibonacci I-convergent to some number (Lin{mathbb{R}}).

Suppose that a sequence ({x_{n}}) in X Δ-converges to x such that (r p,{x_{n}})< D_{kappa}/2).

Suppose that a sequence of source samples {U n ∈ℝ} has to be quantized, given that the sequence {Y n ∈ℝ}, is available at the decoder as side-information, where n = 1, 2,... denotes the discrete-time.

Let X be a metric space with a metric d and let p be a u-distance on X. Suppose that a sequence {x n } of X satisfies lim n → ∞ sup p x n, x m, : m > n = 0, (14).