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In this article, the FVPM is extended to viscous flows using a consistency-corrected smoothed particle hydrodynamics (SPH) approximation to evaluate velocity gradients.
In [30], the authors used this approximation to evaluate the effect of limited CSI in a MIMO broadcast channel, when spatial multiplexing is implemented in transmission using similar codebook structures (e.g., closed-loop mode 1).
Adopting a mathematical approximation, to evaluate the Reynolds number, w can be substituted by ωR with the advantage of having a mean Reynolds number independent of the angle ϑ of rotation (see Fig. 2).
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Like these papers, the paper presented here presents an analytical approximation model to evaluate and compare delivery systems.
Because p(T | F) p(F) is not a Gaussian [ 26], we use some approximation methods to evaluate it.
Therefore, we used the Comparative Fit Index (CFI), the Tucker Lewis Index (TLI), and the Root Mean Square Error of Approximation (RMSEA) to evaluate our models' global goodness of fit.
In these systems, we apply our SS probability approximation method to evaluate the probability distribution of different species and calculate the mean, standard deviation and the coefficient of variation (Λ = σ μ ; defined as the ratio between the standard deviation and the mean of any species) of the species distribution.
The model applies a control-volume finite-difference (CVFD) discretization scheme with the two-point flux-approximation (TPFA) to evaluate the transmissibility list.
To derive the BER performance of the N × L MIMO RFID channel where N > 1, since the N receiving branches at the reader are not statistically independent as we mentioned earlier, we cannot use the above distribution and its approximation to directly evaluate the performance of the MIMO channel by applying a widely used method as in[20, 21] which assumes independency of receiving branches.
For the one-QTL backcross model, we have in fact proved that already using second degree polynomials the maximal error in the approximation p is significantly smaller than the error arising from using a stepwise constant approximation corresponding to evaluating g on a standard 1 cM grid.
Because the proposed problem is too complex to apply conventional optimization algorithms, we suggest an approximation approach (AA) to evaluate the objective function.
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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