Sentence examples for definition of the sequence from inspiring English sources

By the definition of the sequence { x n }, we know that x n ∈ Ω.

Note that the definition of the sequence ({x_{n}}) is involved in the sequence ({y_{n}}) and the definition of the sequence ({y_{n}}) is also involved in the sequence ({x_{n}}).

From (3.23) and the definition of the sequence { λ n }, we have lim n → ∞ ∥ A x n ∥ = 0, (3.25).

Now, we give the following definition of the sequence of the BCH codes over the chain of Galois rings as in[11].

Hence, from the definition of the sequence { z n }, it follows that ∥ A x n ∥ = ∥ J z n − J x n ∥ λ n. (3.24).

Proof From the definition of the sequence { x n }, it is obvious that both H n and W n are closed convex sets.

From the definition of the sequences, it follows that.

which, by the definition of the sequences ( x m = x : m ∈ N ) and ( y m = y : m ∈ N ), gives ∀ t > 0 { M ( x, y, t ) = 1 }.

Throughout this proof, n and p will denote non-negative integers and t ∈ [ 0, ∞ ). Step 1. Definition of the sequences { x n }, { y n } and { z n }. Let x 0, y 0, z 0 ∈ X be three arbitrary points of X.

We also introduce the definition of the median sequence that is used to choose a time-scale pattern for all other sequences.

Recall the definitions of the sequences of the φ-mixing and ρ-mixing random variables.