Sentence examples for using the asymptotic formula from inspiring English sources

This leads to G ( n ) < lim n → ∞ G ( n ) = 0. by using the asymptotic formula (2.3).

This leads to F ( n ) < lim n → ∞ F ( n ) = 0. by using the asymptotic formula (2.3).

An estimation of the average MFPT can be obtained using the asymptotic formula from [ 40] for r0 traps of surface area S r which are located on the boundary of a 2D medium of surface area, and gives for our standard set of parameters a MFPT value of approximatively 418.

The inverse solver performs an initial search for the location of the channels along the length of the cilium using the asymptotic formulas from Badamdorj et al. [20].

Here we have used the asymptotic formula [17], p.718, Formula 3].

Cumulative incidence risk for drop-out at 1 month, 2, 3, 6, 7, 8, 9, 10, 11, 12, 18, 24 months with confidence limits using the asymptotic method (Greenwood's formula) for standard error estimation.

Rates of treatment discontinuation were assessed as a Kaplan Meier time-to-first-event analysis and presented as: Cumulative incidence risk for drop-out at 1 month, 2, 3, 6, 7, 8, 9, 10, 11, 12, 18, 24 months with confidence limits using the asymptotic method (Greenwood's formula) for standard error estimation.

b Using the asymptotic standard error assuming the null hypothesis.

We note that in [6, 10, 11], using the obtained asymptotic formulas for eigenvalues and eigenfunctions, the basis properties of the root functions of the operators were investigated.

Now, by using the above results, derive the asymptotic formula for the eigenvalue distribution of L0.

Using these asymptotic formulas, we find conditions on the coefficients for which the root functions of this operator form a Riesz basis.