Sentence examples for use the same approximation from inspiring English sources

Since convection mostly takes place in the interior of the cell where the temperature is close to the interior temperature T i, we use the same approximation by expanding the exponent E/R T in the Arrhenius form so that the viscosity can be expressed as an exponential function of temperature only: eta = Bexp -gamma T), (3).

Authors in [10,35] use the same approximation approach, where its accuracy is also justified by simulation in [10].

Using the same approximation as in the CDE-PD case, and after some simple algebra, we can find the lower bound of (53) as MSE ̲ 2 CDE − SD = h 1 − ρ 2 + MSE 1 CDE − SD | Δ 2 ≤ MSE 2 CDE − SD. (56).

The well known Tchebyscheff filters can be viewed as a special case of elliptical filters and can be arrived at using the same approximation techniques.

We note that Brisson et al. (2000) used the same approximation.

In this first experiment, we study the time performance of TFM-PVALUE compared to LAZYDISTRIBUTION when using the same approximation for the distribution score.

The probability density that haplotype i is seeded at time t is given by the rate α(t) of establishing new haplotypes multiplied by the probability of having i − 1 haplotypes at time t, (3) p i (t ) = α (t ) e − λ (t ) λ (t ) i − 1 (i − 1 ) ! ∝ e − (u / s ) e s t + i s t, where we have used the same approximations as in Equation 2 and dropped factors independent of t that ensure normalization.

Using the same approximations as for the hysteresis oscillator, the repressilator cycle starts when P3 falls just below K, with P1 at its baseline level β0/ α and P2 roughly equal to (β1/ α) - K. In this regime, (50) P 1 (t ) ≈ (β 0 / α ) e − α t + (β 1 / α ) (1 − e − α t ) P 2 (t ) ≈ − K e − α t + (β 1 / α ) P 3 (t ) ≈ K e − α t + (β 0 / α ) (1 − e − α t ).

To facilitate direct comparison of the methods, we use the same initial approximations as in the case of the spectral homotopy analysis method of Yang and Liao [12]: (4.4).

The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model.

Therefore, we use the same prior P Q = c) as in the case of a single motif model as a first approximation.