Sentence examples for also sufficient that from inspiring English sources

For the validity of the equalities lim t → x k − 0 ω k − 6 ( t ) = 0, lim t → x k + 0 ω k ( t ) = 0, Open image in new window (2.1). it is necessary (and if ak−6 and a k are not collinear, then it is also sufficient) that lim t → x k − 0 ω j ( t ) = lim t → x k + 0 ω j ( t ) ∀ j ∈ { k − 5, k − 4, k − 3, k − 2, k − 1 }.

Instead, it is also sufficient that the reliability value be positive if null-hypothesis testing is the main objective.

It is probable (and, for a successful launch of the evolution of catalysis, also sufficient) that early ribozymes were not very efficient, but they might have possessed more than a single catalytic activity (enzyme promiscuity).

Then the sequence { x n } converges strongly to p ∈ F if and only if lim inf n → ∞ d ( x n, F ) = 0. Proof If { x n } converges to p ∈ F, then lim n → ∞ d ( x n, p ) = 0. Since 0 ≤ d ( x n, F ) ≤ d ( x n, p ), we have lim inf n → ∞ d ( x n, F ) = 0. To prove that the condition is also sufficient, assume that lim inf n → ∞ d ( x n, F ) = 0.

Recall (C_{2}=Vert T Vert _{L^{1}times L^{1}rightarrow L^{frac {1}{2},infty }}), following the same argument as in the proof of Theorem 1.1, it is also sufficient to show that bigl|bigl{ xin mathbb{R}^{n}:biglvert T_{pi b}(f_{1}, f_{2}) (x bigrvert >lambdabigr} bigr|leq Cbigl(C_{0}+C_{1}'+C_{2} bigr)^{1/2}lambda^{-1/2 1/2}lambda^{-1/2

As outlined (El-Awady et al, 2003), there is also sufficient evidence for that in the literature.

Evidence is also sufficient to conclude that male coffee drinkers have a lower risk of PD than females (Ascherio et al. 2004; Ross et al. 2000).

While critics claim that the government uses disproportionate force against protestors, there is also sufficient evidence that some of the protestors have violently attacked the police.

Despite the compelling evidence that the suppression of responses to self-generated sounds is partially accounted for by unspecific gating effects associated with the movement, there is also sufficient evidence that the N1 suppression for self-generated sounds is (at least partly) specific.

There is also sufficient evidence to support that metformin is non-inferior to insulin with regards to neonatal safety, but comparative data regarding efficacy during pregnancy are lacking [ 24, 25].

Our results are also sufficient to establish that if the C⁎-algebra of a higher-rank graph is AF, then its every ideal must be gauge-invariant.