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Exact(15)
Equation (A.1) can be further derived as (A.2).
Then, the displacement field while the crack coexists can be further derived.
Then, from (17) to (19), the outage probability of the jth relay transmission channel can be further derived as (20).
Doing so, the total current harmonics can be further derived to get the relationships between total current harmonics and the phase shift angle of each inverter.
The evolution of preexisted void volume and the corresponding metal line resistance change can be further derived based on the stress evolution.
For such a condition, u i in (10) can be further derived as lim N → ∞ u i = lim N → ∞ 1 2 ( N − M + 1 ) ∑ j = 1 M h j = 0. (21).
Similar(45)
The following important result, which can be called E ϵ -estimate is further derived: O (ϵ 2 ) = M ϵ 2 t, with M a constant and t the evolution time [28].
Analytical sensitivity analysis formulas are further derived.
GNR density of state (DOS) is further derived.
This study aims to quantify the acceleration and displacement response spectra of pulse-like near-fault ground motions, which can be further employed to derive the seismic force demands of a structure system or structural member.
The combined multivariate model previously fitted on the training set can be further used to derive the p-value corresponding to the null-hypothesis that the coefficient of the omics score is zero, by estimating its regression coefficients on the validation set.
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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