Sentence examples for be an increasing sequence from inspiring English sources

Let P be a differential operator with analytic coefficients and elliptic, or more generally of principal type and hypoelliptic, in an open Ω of Rn and let (kj) be an increasing sequence of positive integers.

As a consequence, for p∈[1,2], if Y is a closed non-trivial Γ-invariant subspace of ℓp and let Yn be an increasing sequence of closed Γ-invariant subspace such that ⋃Yn¯="ℓp(Γ V), then there exist a k such that Yk∩Y≠{0}.

where {t i } is assumed to be an increasing sequence.

and let { a n, n ≥ 0 } be an increasing sequence of positive numbers.

In fact, for t ∈ I, let {x n } ⊂ [v0 (t), w0 (t)] be an increasing sequence.

Let be a martingale-difference sequence and be an increasing sequence of positive numbers.

For let be a increasing sequence and be a decreasing sequence.

where is an increasing sequence in such that and.

Since is an increasing sequence,, for and for all.

Since (C_{k}) is an increasing sequence, (lambda_{k}) is a decreasing sequence.

That is, the sequence { M k ( 1 ) } is an increasing sequence.