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This theorem not only guarantees the existence and uniqueness of the fixed point but also shows how to evaluate this point.
Banach's result is the origin and antecedents results by the fact that he not only proved the existence and uniqueness of a fixed point of a contraction, but also showed how to evaluate this point.
Additional data are necessary to evaluate this point.
In order to evaluate this point, we took a step toward assessing the importance of mitonuclear interactions for human health.
This study was not designed to evaluate this point, but only to consider available data before ICU admission.
To evaluate this point, we compared the plants of population PFD-1 with each other for combinations of electrophoretic patterns of the five isoenzymatic systems (Table 2).
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To further evaluate this point, we plot the Bpix probability ratio of intron dot sites to active nuclei (Figure 4C).
To empirically evaluate this point, we took the data from the CaMEO Study analyzed here, and looked at two waves of data.
To further evaluate this point, we used the cell line RS4-11, derived from a Mixed Lineage Leukemia, which contains a rearrangement of the MLL1 gene with AF4: as in other MLL1 fusions, it lacks the SET domain and it is therefore devoid of H3K4 methylating activity (10).
To specifically evaluate this point, we plot the difference in hb intron dot density between two expression regions of the embryo (30% ∼40% and 20% ∼30%f embryoflembryo as a function of the pixelengthnsity threshold setting (while keeping the pixel number threshold as 4; Figure S1a).
Although we observed a marginal relationship between epithelial gap density and the number of flares in the follow-up period, our study was not designed to evaluate this end point, and may be underpowered to ascertain a significant relationship.
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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