Sentence examples for continuous branch from inspiring English sources

The branches of periodic orbits arising from the two Hopf bifurcations are joined and thus represent a single continuous branch.

Via using the method of complex analysis, we can take a continuous branch of (operatorname{log} (frac{S^{S^w_{k} )) such that ({textrm{log} (frac{S^{S^w_{k} ) }_{kin mathbb {Z}} in l^{2}).

On proceeding in this fashion, we get a continuous branch of arg c ′ Open image in new window on all of (ζ n, ζ1) satisfying the following: sup ζ ∈ ( ζ 1 -, ζ 1 ) - 2 p arg c ′ - ( ψ 1 + 2 π j 1 ) < π max { p, q } Open image in new window (22).

To this end, we first choose a continuous branch of the function arg c ′ Open image in new window on T ∖ { ζ 1, …, ζ n } Open image in new window, where z k = c ( ζ k ) Open image in new window for k = 1, …, n.

We have thus chosen a continuous branch of the function arg c ′ Open image in new window on the set T ∖ { ζ 1, …, ζ n } Open image in new window, satisfying sup ζ ∈ ( ζ k -, ζ k + ) ∖ { ζ k } - 2 p arg c ′ - ( ψ k + 2 π j k ) < π max { p, q } Open image in new window (23).

Choose the continuous branch of arg c ′ Open image in new window on ζ 2, ζ 2 +, Open image in new window such that (21) is still valid with ζ 2 -, ζ 2 Open image in new window replaced by ζ 2, ζ 2 +.

The neutral curves consist of several continuous branches, which belong to different modes of the most dangerous perturbation.

Recall that the continuous branches of the multi-valued functions under consideration are chosen in such a manner that lnθ = ln|θ| + ı arg θ with arg θ ∈ [0, 2π), J η 2 - 1 ≥ 0 Open image in new window, and more generally, z γ = | z | γ exp ( ı γ arg z ) Open image in new window with arg z ∈ [ 0, 2 π ) Open image in new window.

We shall remark that Eastham et al. employed continuous eigenvalue branch which studied in [2], in their proof.

In what follows we will always assume that each eigenvalue (lambda (omega) ) is embedded in a continuous eigenvalue branch.

We prove that if λ is an eigenvalue of the considered problem, then λ can be embedded in a continuous eigenvalue branch.