Sentence examples for exists an order from inspiring English sources

Then, there exists an order preserving retract P: X → M. A similar result for externally hyperconvex subsets of metric trees maybe found in [9].

If v(1)v(2) < 0, then there exists an order interval ℐ which is also a relative neighborhood of x ¯ such that for every relative neighborhood U ⊂ ℐ of x ¯ the following statements are true.

A defining characteristic of the Hilbert R-tree is that there exists an order of the nodes at each tree level, respecting the Hilbert order of the Minimum Bounding Rectangles (MBRs).

Recall that Γ is directed if there exists an order ≼ defined on Γ such that for any α,β ∈ Γ, there exists γ ∈ Γ such that α ≼ γ and β ≼ γ.

Let v = ( v ( 1 ), v ( 2 ) ) ∈ R 2 be an eigenvector of the Jacobian of T at x ¯, with associated eigenvalue μ ∈ R. If v ( 1 ) v ( 2 ) < 0, then there exists an order interval ℐ which is also a relative neighborhood of x ¯ such that for every relative neighborhood U ⊂ I of x ¯ the following statements are true.

Then, there exists an order preserving retract P : C ( M ) → M such that (1) for any x ∈ C l ( M ) we have x ≺ P x), and   (2) for any x ∈ C u ( M ) we have P x) ≺ x.  . for any x ∈ C l ( M ) we have x ≺ P x), and.

By Lemma 2.4, there exists an order-1 periodic solution of system (1) (see Figure 2(a)).

Thus there exists an order-1 periodic solution of system (1) by Lemma 2.4 (see Figure 2(c)).

For system (1), there exists an order-one periodic solution such that its trajectory is through the point (A') in the phase set (M_{I}^).

If for model (2.2) there exists an order-2 limit cycle, then the order-2 and order-1 limit cycles coexist.

Thus, we conclude that case (iii) cannot appear if for model (2.2) there exists an order-2 limit cycle under condition (SC2).