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These time points were corresponding to the exponential growth phase (HA), the early stage of oxygen limitation (HB), the middle stage of oxygen limitation, and the late stage of oxygen limitation (HD), respectively.
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The green and blue points are corresponding to the two sets of trials, respectively, in a.
The highlighted points are corresponding to s s =1, s f =0.3, ν=0.001, T=5000.
When κ increases to a value between 10−2 and 10−1, the MST decreases to its global minimum point, and a neighborhood of this point is corresponding to the intermediate regime.
The best predictions of AUC-24 h were made when three time points were used, corresponding to Cmax, a mid-morning sample, and Cmin.
Since (mathcal{D}) and (mathcal{D}') are disjoint, we obtain two distinct fixed points, which are corresponding to two distinct T-periodic solutions of equation (4.12).
Hence by the assumption of the theorem we have that P is a contraction mapping then in view of the Banach fixed point theorem, P has a unique fixed point which is corresponding to the solution of Equation (1).
The starting points were the parameters corresponding to the minimum cost function value attained in the previous runs.
For the simulations, 6 time points were conservatively chosen, corresponding to the times 0, 2, 4, 6, 8 and 10.
The object can be broken down into innumerable points, and each object point's image is corresponding to the point spread function (PSF).
For all gene segments, the smallest allowed value of the recombination points is -4, corresponding to four P nucleotides.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com