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Then inverse transform the solutions of the algebraic equations, the Green's functions can be expressed by contour integral.
By providing those matrices to StOMP, we are able to reconstruct the wavelet sampled data, (varvec{s}) in Fig. 3, and then inverse transform (varvec{s}) to reconstruct the original data (varvec{f}).
After having finished obtaining x R (f) for all f's, one can then inverse the x R (f) function to obtain f(x R ), which is the same as f R (x) in its meaning.
end{aligned} Using (lambda^{alpha}(lambda^{alpha} +mathscr{A})^{-1} = I-mathscr{A}(lambda^{alpha} +mathscr{A})^{-1}), the above equation is then inverse Laplace transformed to obtain x t) = mathbb{T}_{alpha}(t)x_{0} + int_{0}^{t}mathbb{S}_{alpha } t-s) mathscr{F} t-sds.
We use the availability of CSI at the subcarrier levels, as shown in Fig. 7, to measure the ESNR at the jth network client I4, by averaging the subcarriers' bit error rate (BER) and then inverse mapping the BER to the SNR.
As in [26], I log-transformed these displacements, calculated the mean (or CEP) and then inverse transformed the results (see [31]).
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The two dimensional offsets were rounded to the nearest pixel integer, then inversed and used to displace the red and green stimulus locations relative to the infrared location which was selected in the stabilized retinal display.
(By contrast, as noted earlier, while the proposition, "if a Keplerian ellipse exactly, then inverse-square exactly," is true, the proposition, "if a Keplerian ellipse quam proxime, then inverse-square quam proxime," is not true when the eccentricity of the ellipse is not large, as explained in Smith, 2002).
This essentially ranks the scores (with missing/could-not-perform set as the highest rank and missing-at-random left blank) and then inverse-normal transforming the ranks.
Individual channel 50 Hz noise was further removed by transforming signals into the Fourier domain, attenuating the peak of 50 Hz by smoothing from 48 to 52 Hz, and then inverse-Fourier transforming the data back into the time domain.
Then the inverse function (Phi^{-1} alpha )) is called the inverse uncertainty distribution of ξ.
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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