The phrase "above approximated" is not correct in standard written English.
It may be intended to refer to something that has been estimated or calculated previously in the text, but the phrasing is awkward and unclear.
Example: "The values above approximated the total cost of the project, but further adjustments are needed."
Alternatives: "previously estimated" or "mentioned above as an approximation."
Then, both static and kinematic approaches are carried out numerically on the homogenized problem using the above approximated macroscopic strength domains in an adapted finite element method.
Compare the above approximated result in Equation (10) to the exact value, U x=0,y=0)≈−3.52549 k Q q0/L from Equation (6).
There were significant main effects for modality and speed in relative energy cost of walking, which was well described as a function of speed by the above approximated parameters for both walking modalities (energy cost treadmill walking=2.028/v+1.115 v and energy cost shuttle walking on the ground=1.126/v+1.665 v; both p<0.001).
The initialization of s π ( k ) ( 0 ), for k = 1, …, i, is assigned by the above approximate solution.
Note that throughput T is described as the above approximate equation due to the maximum retransmission limit.
end{aligned} end{aligned} Choosing (alpha=1), (beta=1), and using a Taylor series expansion, the above approximate solution becomes begin{aligned} w x,t)&=sum_{n=0}^{infty}w_{n} (x,t) & =sin(x -sin(x -sinn (x t+sinl(frac{2cos(x)t^{2} }{2} +frac{(1-2cos(x))t^{2} }{2} biggl)+cdots &=sin(x)e^{-t}.
Then, after adding an appropriate error term, all of the above approximate equalities can be rephrased as inequalities.
Employing, as usual, the space-scale separation between the rapidly varying, on the lattice-constant scale, u c u v, and the slowly varying envelopes, valid for as long as L, λD ≫ a, the above is approximated by (10).
To make experimental investigation tractable and to allow the comparison between our theoretical and experimental results we proceeded as above and approximated a network of recurrently coupled SCs with a single self-coupled SC.
Contrary to the above works approximating MWM, our approach achieves throughput optimality with low-complexity and local information exchange, by avoiding solving MWM and relying on a converged Gibbs sampler for obtaining the optimal schedule at each time slot.
Under the situation where R 0 a = R 0 b and γ b + μ ≫ β a I - a which equivalently requires that the infectious period is much shorter than the duration of immunity and life span, we have Γ ≈ 1 - I - a β a / (γ b + μ ), and the above inequality is approximated as follows: (A.6) β d > [ (γ d + μ ) − 2 ϕ b (γ b + μ ) ] R 0 a.
