Sentence examples for stable equation from inspiring English sources

By the mid-13th century a stable equation between gold and silver was attained, resulting in a coinage impressive in both quality and volume.

Theorem 3.3 is exact in the sense that if (2.2) is a homogeneous linear stable equation with constant matrices, then, and condition (3.29) is always fulfilled.

If 0 < τ < τ 0, Eq. (3) has an EE E ∗ which is locally asymptotically stable; Equation (3) can undergo a Hopf bifurcation if τ > τ 0, and a periodic orbit exists in the small neighborhood of the EE E ∗. Proof From Lemma 4.1, we have the conclusion in case (i).

The method consists in a transformation of a given differential equation to an operator equation by the substitution x t)= int_{0}^{t} W t,s) z(s),ds, where (W t,s)) is the Cauchy function for some known exponentially stable equation.

In view of the tight regulation on stem cells by various signals from both epithelial and mesenchymal cells [27], the marginally stable equation (1) hardly captures the homeostatic feature of the stem cells [28].

We assumed that each individual spends exactly Ti days in stage i, that all individuals in the last day of that stage (Ti - 1) graduate to the next stage, and that the age distribution within the stage is stable (equation 6.100 in [ 12]).

(i) If 0 < τ < τ 0, Eq. (3) has an EE E ∗ which is locally asymptotically stable;   (ii) Equation (3) can undergo a Hopf bifurcation if τ > τ 0, and a periodic orbit exists in the small neighborhood of the EE E ∗.  .

As g_{k}-g_=expbigl - mu+delta Tbigr) (g_{k}-g_=expbigl - mu+delta TbigrTbig_{k}-g_=expbigl - mu+delta Tbigrasymptotically stable for equation (9).

We prove that if the eigenvalues of the infinitesimal generator of the righthand side of (4) are in the left part of the complex plane, the stationary state U = 0 is asymptotically stable for equation (4).

It reveals that there can be a zero solution for the oscillator under the effect of parametric excitation, while it is impossible to have a stable zero equation without parametric excitation.

To study the stable region, Equations (3)–(5) are linearized at the equilibrium point (τ i *, W i *) for each variable.