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In the next step, an auxiliary low-dimensional system is derived whose stability implies stability of the original large-scale system.
A unique equation for the set of profile modification rendering transmission error nearly constant is presented and a number of original stress and loss factor closed-form formulae are derived whose results compare very well with those obtained by numerical simulations.
Those who celebrate Christmas without religion still commemorate the ancient saint (Nicholas, from whom "Santa Claus" is derived) whose use of church funds to rescue three young women from prostitution is one of the main reasons Christians revered him in antiquity.
Hence, a t-statistic t = Strength/Sd Strength can be derived, whose degrees of freedom Df are estimated with the Welch Satterthwaite equation [ 33, 34].
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For this reason, we now consider birds to be dinosaurs, albeit highly derived dinosaurs whose skeletons are modified for flight.
The results of this study affirmed the great potential of Mo2C derived carbons, whose EDL capacitance reaches ∼65 F cm−3 and 132 F g−1 and the 20-s discharge power density is 2.1 W cm−3.
This result has been subsequently compared to a statistically derived model whose predictor space has been built to primarily represent superficial properties.
To obtain the ergodic sum rate at the user, the joint PDF must be derived first, whose approximation is provided by the following lemma.
The principal component analysis (PCA) projects by construction the initial space spanned by the different samples into a new derived space whose axes (principal components) are each other orthogonal.
In this Account, we use glycoluril derived systems whose development can be traced to the early work of Mock, Nolte, and Rebek.
For all conditions associated with this haplotype described thus far, including TOF, the alleles conferring increased risk at the associated SNPs are the derived alleles, whose frequencies have increased in Europeans by a selective sweep (starting around 3000 years ago).
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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