Sentence examples for as a limit point from inspiring English sources

And the desired solution u of (1.1 - 1.3) would be obtained as a limit point of u ε.

A brief study is presented of the dynamic behaviour of a system approaching a fold (also known in the literature as a limit point or saddle-node bifurcation).

We mention here that Riley and Weidman [14] reported that for the non-magnetic case ( S = 0 ), all solution curves for β > 0 have the point ( 1, 0 ) as a limit point.

Then, as noted in [20], there exists at least one subsequence { T x 2 n k } or { S x 2 n k + 1 } which is contained in P 0 or Q 0, respectively, having as a limit point z.

It shows that some novel dynamic characteristics of the model have been found in the numerical results, such as the existence of a limit point ((0,0)) when linear (q_{1},q_{2}) are in the same ranges and have opposite slopes.

Colors as in panel A. LP denotes a limit point and Hs denotes a Hopf bifurcation for the symmetric equilibrium ((1,1,1)).

Fevol can thus be classified as a limit reference point that should not be exceeded, analogs to commonly estimated reference points such as Flim (ICES 2008: the fishing rate that will eventually cause a stock collapse).

As a limit reference point, Fevol is similar to those currently used by fisheries scientists in the US (Flimit) and by International Council for the Exploration of the Sea (ICES) scientists (Flim) to identify the maximum fishing mortality deemed permissible under a harvest control rule (Cadrin and Pastoors 2008).

Similar to the case (a), we see that the monotone sequence { x ˜ n } is a Cauchy sequence and denote x ¯ as the limit point.

As the limit point z is independent of the choice of x n ∈ A n, we also get lim n → ∞ δ ( S x 2 n, z ) = lim n → ∞ δ ( T x 2 n + 1, z ) = 0. Now, we show that z is a common endpoint of S and T. Suppose, to the contrary, that δ ( z, S z ) > 0. By the assumption (2.3), x n ⪯ z for all n.

To prove that u is an endpoint of S, suppose that δ ( u, S u ) > 0. From (2.3), we have x 2 n + 1 ⪯ u for all n ∈ N. As the limit point u is independent of the choice of x n ∈ A n, we also get lim n → ∞ δ ( S x 2 n, u ) = lim n → ∞ δ ( T x 2 n + 1, u ) = 0. (2.15).