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As the inverse is also valid, the BVP (2.2) is indeed equivalent to the BVP (1.1).
Next, we will show that the definition of semi-weak time consistency is indeed equivalent to the time consistency introduced in (Bielecki et al. 2014b).
In the circuit point of view, the proposed TFT structure is indeed equivalent to two serially connected TFTs (i.e., 10-μm-long active layer for each TFT) via the middle HECL layer (i.e., 60-μm-long conducting channel layer).
This means that f ( x ) is increasing as a function of x ∈ [ r 2, r ], i.e., the relation (26) is indeed equivalent to a ≤ x and the proof is complete.
It can be easily checked that maximizing the MI for Gaussian signals (17) is, indeed, equivalent to maximizing the squared MCCC among the N random variables, which is defined as [8] (19).
Given these definitions, and given the limitations imposed by the resolution of the assays used, that 80%% of the genome (which is indeed equivalent to close to 100%% as between 15 and 25%% of it is not uniquely mappable with short sequencing reads and is thus "invisible" in these analyses) is "functional" is indeed correct.
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The latter would indeed be equivalent to the provability in the sequent calculus described for R in Section 3 of φ ≻ ψ ↔ χ and the converse sequent.
The QR ability to fully characterize the distributional features of the response variable emerges: the QR estimated density is, indeed, almost equivalent to the observed distribution of mathematical performance, while it is evident that the approximation obtained focused only on the conditional mean.
The MASS software enables one to perform meta-analysis of score statistics for sequencing studies, which is statistically as efficient as and indeed numerically equivalent to joint analysis of individual-level data.
We reasoned that if RACK1B and RACK1C are indeed functionally equivalent to RACK1A, one would expect that overexpression of RACK1B or RACK1C complements the developmental defects of rack1a mutants.
Indeed, Trp111 (equivalent to Trp51 in CcP) on the heme distal side was shown to be part of the extended H-bonding network (white dotted trace) that plays a crucial role in the electron transfer pathways (blue dotted traces) to the two remote protein-based radical sites, Trp139 and Trp153.
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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