Sentence examples for an approximation provided from inspiring English sources

Such an approximation provided following [23] is given in the Appendix.

Instead, we use the differential quotients as an approximation provided Δ is small, e.g. ∂ T j ∂ x j ( x j ) ≈ T j ( x j + Δ ) − T j ( x j ) Δ, …, ∂ ( F j l j ) ∂ x j ( x j ) ≈ ∂ F j ∂ x j ( x j ) l j + F j ∂ l j ∂ x j ( x j ), j = 1, 2, 3. Numerical experiments show, that Δ ≈ 0.1 provides a sufficiently accurate approximation of the partial derivatives.

In this paper we will show that such an approximation provides reasonable accuracy in predicting starch dynamics in O. tauri.

By comparing the solutions from this model with the solutions derived from the simpler linear driving force model it is shown that the simpler model provides an acceptable approximation provided that the coefficient [Ω in eq. (1)] is chosen correctly.

Finally, Sullivan-type health expectancies use the observed prevalence of disability/health to approximate the true period conditions, a reasonable approximation provided that disability or self-rated health is stable over time or evolves regularly (Mathers and Robine 1997).

This Bogoliubov-type expansion provides a good approximation provided the density of quantum fluctuations around the coherent background is small compared to the excitation number in the latter.

We therefore conclude that the quasi-steady state assumption for oxygen is a good approximation, provided that the values of D s and h s are as derived in section A of the Appendix (additional file 1).

The proposed method allows each silhouette map texel to represent a polygonal approximation to the actual shadowing geometry, in contrast to the jagged approximation provided by a conventional shadow map.

Here we extend this existing picture using a refined approximation, provide a more general analytical formula, and show that in principle up to N(N + 1) / 2 segments can show up experimentally.

A useful approximation provides interesting links between some well-known algorithms for the single-channel case and the general multichannel framework.

The reasons for providing only the right-tail large deviation approximation are (i) all of the above mentioned approximations fail to approximate the extreme right-tail probabilities and (ii) the FMCI approximation provides an accurate approximation for left-tail probabilities.