Sentence examples for the same approximations as from inspiring English sources

In the same manner, we can obtain further approximations (v_{3} x,t), ldots) Setting (beta=1) in the first approximation (24) and the second approximation (25) and after some simplifications, we obtain the same approximations as (15) and (16) on returning to the original variable.

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 ).

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.

Furthermore, the thermodynamic properties of the generated candidates are within the same approximation as the customised trans-acting switching molecules reported in the laboratory.

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).

Thus, other design classes previously proposed with the same approximation aim such as RDGs, SRDGs and NBIBDs of type I can be viewed as particular cases of MBMUDs.

Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach.

The authors established L2 error estimates of the proposed methods and also presented a criterion for the choice of basis functions of the non-polynomial spaces to have the same approximation rates as those of polynomial finite element spaces of the same dimension.

It is worth pointing out that Algorithm 8 achieves the same approximation ratio on AB(R) as Algorithm 7, as long as R greedily chooses a vertex u of the largest (|{u_vdash }^P|) at each synchronous update.

Theoretical analysis proves that the scheme has the same approximation ratio and complexity as the previous best algorithm for the MLBSDC problem.

It was found that in order to achieve the same approximation quality with RSNNs as with PRSs, a higher number of simulations may be required.