Sentence examples for optimal dependence from inspiring English sources

The optimal dependence of the Smagorinsky parameter on the spatial resolution is determined for second and third order accurate Galerkin methods.

We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem.

This last result was later on greatly improved by Eldan [56] who proved inequality (5.46), actually an even stronger one, with a dimensionless constant and an almost optimal dependence on (D_gamma (E)), actually just a logarithm below the optimal growth.

In [11], an optimal dependence of the parameters r and h upon the number of data, n, is obtained by minimizing an upper bound to (Delta_{h,n}^{eta,r}(hat{rho})).1.1

In Appendix C, a derivation is provided of the (L^{2} -errors and of the optimaL^{2} -errorsof h and r of the number optimal n andependenceameter β that takes intofaccount the fand decay of both the Wigner function and itheFourier tranumber fof large values of their arguments.

We conclude this section by observing that while the result by Barchiesi et al. proves the quantitative Gaussian isoperimetric inequality with an optimal dependence on the dimension and on the mass, the dependence on the dimension of the constant (gamma (n)) which appears in (4.3) is not known.

In our study, we establish the optimal C1 dependence of the stable subspaces on the parameter for very general nonuniform dichotomies (which was first introduced by Bento and Silva in [17]) for (1.1).

We also note that we can establish the optimal C1 dependence of the unstable subspaces on the parameter using the similar discussion as in [16], and we omit the detail for short.

In the case of discrete time, Barreira and Valls established the optimal C1 dependence of the stable and unstable subspaces on the parameter in [15] for the uniform exponential dichotomies and in [16] for the nonuniform exponential dichotomies.

Firing rate-based information transfer is likely to increase with temperature and we derive predictions for an optimal temperature dependence of the tympanal transduction process fostering temperature compensation.

These results suggest that the optimal particle size dependence of GNP uptake is reversed in the multilayer model in comparison to the monolayer model.