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Finally, we give a result corresponding to Theorem G. Theorem 1.9.
Remark 1 If in (2) we take k = 1, f 1 ( x ) = x and L 1 ( x ) = λ ∈ [ 0, 1 ) for x ∈ X, then Theorem 1 becomes a result corresponding to the classical Banach contraction principle.
As a result, corresponding gene is upregulated (activating mutation) or downregulated (suppressing mutation) (for detailed review, see [ 2]).
As shown in Figure 4b, plotting the first versus the second principal component also generates a result corresponding to that obtained for the published FPKM/RPKM values with the heart samples separated from brain and kidney samples, but this time a tendency toward a separation of all three tissue types is visible in the second component.
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a Results corresponding to the samples displayed in panel b (FL3-A: red fluorescence intensity proportional to Nile-red staining; SSC-A: side scatter intensity).
These filter coefficient and input data products make up a partial result, the sums of which generate a local result corresponding to the centroid of the filter.
To obtain a test result corresponding to the true physical situation the minimum column length should be four half-wavelengths of the local instability.
They reported the presence or absence of acid-fast bacilli (AFB) using the WHO/IUATLD scale, with a positive result corresponding to ≥ 1 AFB per 100 high-power fields (HPFs) [ 29].
The most frequent chromosome abnormality found was trisomy 21 (n = 13, representing 81.25% of the total abnormal findings), but we also found an abnormal result corresponding to Cat Eye microduplication syndrome (22q11).
As a result, the corresponding modelled time series are slightly higher than the corresponding measured time series during most of the day.
As a result, the corresponding kernel matrix will be an identity matrix as illustrated by the corresponding plot in the second row.
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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