Sentence examples for u n that from inspiring English sources

Thus T 1 has two eigenvalues (counting with multiplicities) lying in U ( n ) that are the roots of (55).

It follows from x n ∈ S ( u n ) that x n ∈ A n and ϕ n ( x n, y ) ∉ − int C, ∀ y ∈ A n. (3.9).

Let q = (q(1),⋯,q(n)) be a random i.i.d sequence of Q n, u k = u k ( 1 ), ⋯, u k ( n ), k ∈ ℒ s a sequence of random variables of U n that are i.i.d given q.

Consequently, we obtain a Cauchy system of second-order integro-differential equations with smooth coefficients, so it has one and only one solution that for every n there exists a unique sequence u ( n ) that satisfies (4.3).

We can take μ ∈ ω w ( u n ), that is, there exists { u n j } such that ω − lim j → ∞ u n j = μ.

Therefore by Theorem 1(b), λ 1 and λ 2 are the eigenvalues of T 1 lying in U ( n ), that is, they are λ n, 1 and λ n, 2, which proves the simplicity of the large eigenvalues and the validity of (65).

If | I | = ∞, we can find a subsequence of { u n }, that we denote also by { u n }, such that u n = θ ( d ( T n − 1 x, T n + 1 x ) ) for  n  large enough.

Next, we show that there is a unique weak cluster point x of the sequence { u n }, that is, u n ⇀ x.