Sentence examples for for suitably small from inspiring English sources

Theorem 1.2 If q > m, then all the solutions u ( x, t ) vanish in finite time for suitably small initial data u 0 ( x ).

In all cases, the 90-day tumor population, integrated from a fixed initial cell distribution, varied by less than 10percentt for suitably small time steps (typically 0.05-0.5 day), which was judged satisfactory for our purposes here.

If parameter sets are sampled from the set for which ρ ≤ ϵ, where ϵ is a threshold difference between the resulting model behaviour and experimental data, the posterior distribution P (θ | ρ (θ, D ≤ ϵ ) ) is sampled, which is argued to sufficiently approximate P (θ | D ) for suitably small ϵ (Marjoram et al., 2003).

In vivo studies had been hampered by a lack of suitably small and well-characterized animals.

The results indicate that for into mesh lubrication, a suitably small angle inclined to driving gear, deviation of injection position from into mesh side, and larger spray distance improve the lubrication effect.

We then repeat the process with evenly spaced polymorphisms within refined intervals until a suitably small region is identified for sequencing candidate genes.

We obtain the optimal decay rate for ∥ ∇ u t ∥ 2 2 by deriving its decay estimate from below, provided that either ε is suitably small or the initial data satisfy the proper smallness assumption.

By applying fixed point theorem, we prove the global existence and asymptotic decay estimate of solutions for all space dimensions n ≥ 1 provided that the initial value is suitably small.

For given (eta>0), we can then choose (M>1) large enough and thereafter (delta>0) suitably small such that frac{ mC_{1}}{lnfrac{M}{|Omega|}}< frac{eta}{2}quad mbox{and}quad sqrt{MTdelta}< frac{eta}{2}.

which contradicts the assumption that and hence the claim is true provided is suitably small.

if K is sufficiently large and ε 0 is suitably small and since 0 < δ < 1 2. From (4.1), we know that the estimate for N 2 ( t ) implies the desired estimate for N 1 ( t ).