Sentence examples for I assures from inspiring English sources
So, by Lemma 1.9, lim n → ∞ γ n = 0 and the condition (i) assures that lim n → ∞ y n = q.
Let △ ( x ¯ 0, y ¯, y ¯ n ) be a comparison triangle for △ ( x 0, y, y n ) in S 2. Since d S 2 ( y ¯ n, [ x ¯ 0, y ¯ ] ) < π / 2, Proposition 3.1(i) assures that there is a unique point u ¯ n ∈ [ x ¯ 0, y ¯ ] nearest to y ¯ n.
Condition (i) assures the existence of a rank n 0 ∈ N such that λ n = 2 b n ′ ≤ 1 for all n ≥ n 0. Now, with the help of conditions (ii), (iii), (2.3), (2.7) and Lemma 2.2, we obtain from (2.6) that lim n → ∞ ∥ x n − q ∥ = 0, completing the proof.
Having calculated the up and down messages for each branch, we can simply calculate the marginal distributions of fitness x i by multiplying all messages going into a node i. (15) p (x i ) = 1 Z i m ↓ i (x i ) ∏ j m ↑ i j (x i ) where Z i assures normalization.
Yes, on the condition that art's attentive audience — you and I — assures our artists that their best instincts are noted and appreciated, and that more, and still better, is expected of them.
