Sentence examples for first observes that from inspiring English sources

Wang et al. [84] first observes that the waiting time between two consecutive comments from a user follows a upper truncated Pareto distribution.

To get this latter result, one first observes that ℕ is characterized by a single L2-sentence, and then shows that, if the result were false, then "truth in ℕ" for L2-sentences would be definable by an L2-formula, thereby violating Tarski's theorem on the undefinability of truth.

In order to prove the first assertion it suffices to show that Re ( 〈 ∂ ρ ( w ), w − z 〉 ) − ρ ( w ) > 0 for any w ∈ D ¯, z ∈ D. (9.12)Indeed, one first observes that if D is strictly convex and sufficiently smooth then Re 〈 ∂ ρ ( w ), w − z 〉 > 0 for any w ∈ D ¯ ∖ { z } (see [20] for the proof of this fact) so that Re 〈 ∂ ρ ( w ), w − z 〉 is non-negative in D ¯ and it vanishes only at w = z.

Proof First observe that (3.3).

First observe that If, then.

First observe that is an -Lipschitz monotone mapping and.

We first observe that ( R 1, ρ ) is a metric space (see Proposition 4.1 below).

First observe that (widetilde{mathscr{M}}) obviously admits the mean value property.

To apply Lemma A to f and φ, we first observe that T f ∈ Δ f, φ.

First observe that ({x_{n}}) is well defined because (S_{h(x)}) is bounded and (lambda'

To prove it, we first observe that { ( S n, j ∗, G j ), j ≤ n } is a martingale.