If ((H_{21})) holds, we can conclude that equation (14) has at least a positive root (omega_{10}) such that equation (12) has a pair of purely imaginary root (pm iomega_{10}).
end{aligned} (6) (A_{4}<0), so equation (5) has at least a positive root (u^).
That is to say, Eq. (11) has at least a positive root.
When condition (1) holds, Eq. (4.1) has at least a positive real root, and the equilibrium point ( 0, 0, 0 ) of system (2.1) is unstable.
(ii) If (cu_{ast}>1), applying Lemma 3, we know that all roots of (2.10) have modulus less than one when (tauin 0,tau_{0}) ), and (2.10) has at least a couple of roots with modulus greater than one when (tau>tau_{0}).
Arison takes exception, though, when someone who has lived in South Florida for at least a decade still roots openly for the Knicks against the hometown team.
(2) If (bu_{ast}>2+frac{1-alpha}{alpha c}), applying Lemmas 2 and 4, we know that all roots of Eq. (4.8) have modulus less than one when (tauin 0,tau_{0})), and Eq. (4.8) has at least a couple of roots with modulus greater than one when (tau>tau_{0}).
By a simple calculation, we have the following: (12) and (13) both have a positive root if (H1) holds, (14) has at least a positive one positive root, as (tau=0).
T is an rth-order non-expansive mapping if the polynomial (p z):=z^{r}-sum_{k=0}^{r-1}c_{k}z^{k}) is tamely unstable, that is, there exists at least a magnitude-wise dominating root (lambdainmathbb{C} ) such that (p lambda)=0 ) and (|lambda|=1).
He's gone back to his roots, or at least a mythicized version of his roots.
