Sentence examples for for appropriately small from inspiring English sources

Theorem 1.3 If r < min { q, 1 } or r = q < 1 with a | Ω | < b, then all the solutions u ( x, t ) of Problem (1.1) vanish in finite time for appropriately small initial data u 0 ( x ).

We first prove the local existence and uniqueness of mild solutions for IVP (1.1) on interval ([0,a_{1}]) for an appropriately small constant (a_{1}>0), which will be given later.

For the higher-dimensional case, Wang et al. [41] proved that the Cauchy problem for (1.5) in (mathbb{R}^{n}) ((nin{2,3})) possesses globally defined classical solutions for the appropriately small initial data.

We first calculate (deg(I - K_{1}, B_{hat{r}}, 0)) for r̂ appropriately small.

If q > 1, then the solution of problem (1.1) vanishes in infinite time for any appropriately small initial data.

(2) If q > 1, then the solution of problem (1.1) vanishes in infinite time for any appropriately small initial data.  .

When the frequency at which | G jω)| peaks is ω0, the corresponding input signal takes the form (10) for an appropriately small ε, with A being a normalizing constant to ensure that the energy of u(t) is unit.

The question-and-answer session, in the Old Family Dining Room of the White House, took place over a meal that included a salad of winter greens (hand-picked from the White House garden by Sam Kass, the Obamas' chef and chief nutrition adviser), a choice of pan-roasted rockfish or seared rack of lamb and a key lime tart for dessert, all in appropriately small portions.

He takes a job at Ives's insurance company, where he devises the theory of risk management, and eventually contributes to the World War II effort, for which he is given an appropriately small, dank office in the basement of the White House by Franklin D. Roosevelt.

Shot on digital video, "Chuck and Buck" feels appropriately small and clammy, but its emotions are played for real stakes rather than for easy effects of shock and disgust.

Theorem 2.1 (1) If q = 1, then the solution of problem (1.1) vanishes in infinite time for any nonnegative initial data provided that λ > 0 is appropriately small.