# Asymptote

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Related to asymptotically: Asymptotically stable

## Asymptote

In geometry, a line associated with a curve in such a way that the distance between the line and the curve approaches zero as both reach toward infinity. Asymptotes are used in calculus and are computed using limits.
References in periodicals archive ?
then (23) with [lambda] < 0 and the increasing order function v() is asymptotically stable.
[[rho].sub.a](k, L,[eta],[p.sub.1],[p.sub.2])) is positive and asymptotically increasing in k for 0 < k < [cL.sup.-1/2] and L small enough if
It is said that f [member of] [L.sup.p.sub.S]([0, [infinity]) : X) is asymptotically Stepanov p-almost periodic, asymptotically S^-almost periodic for short, iff [??] : [0, [infinity]) [right arrow] [L.sup.p]([0,1] : X) is asymptotically almost periodic.
Therefore, for [R.sup.*.sub.1] < [R.sup.thr.sub.1], system (1) presented the locally asymptotically stable low-criminality equilibrium [P.sub.l].
Obviously if [R.sub.0] < 1 disease-free equilibrium [E.sub.02] is locally asymptotically stable; otherwise [E.sub.02] is unstable.
Xie, "Global attractivity of asymptotically almost periodic Nicholson's blowflies models with a nonlinear densitydependent mortality term," International Journal of Biomathematics, vol.
By the method in , the point [E.sup.*]([x.sup.*], [y.sup.*]) is globally asymptotically stable (see Figure 1.)
By the LaSalle's invariance principle, [E.sub.1] is globally asymptotically stable.
By Lyapunov global asymptotic stability theory, we can conclude system (12) is globally asymptotically stable.
We remark here that, in the discussion above, the cavity radius is introduced as a state parameter to test the thermodynamic properties near the critical point of the RN black hole in the asymptotically flat space-time.
For a given [gamma] > 0, the time-delay system (14) is asymptotically stable with [[parallel][T.sub.wz](s)[parallel].sub.[infinity]] < [gamma], if there exist positive definite matrices P, [Q.sub.1], [Q.sub.2], [R.sub.1], [R.sub.2], [S.sub.1], and [S.sub.2] and matrices [M.sub.1], [M.sub.2], [N.sub.1], [N.sub.2], [U.sub.1], [U.sub.2], [V.sub.1] and [V.sub.2] with appropriate dimensions such that
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