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If such a pair exists and is unique, the decoder declares that.
It's because those pants weren't made for my ass -- but somewhere out there, a pair exists that will fit perfectly.
If such a pair exists move u to the cluster P i and v to the cluster P j.
We will call such a subgraph W a witness of S. Therefore, the right way to look at the problem is that we need to find a pair (S, W), where is S is a T-join and W is the witness of S. It is clear that the problem has a solution if and only if such a pair exists.
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However, for a given resonance frequency, an optimal pair exists of the passive damping coefficient of the IA and the feedback gain.
After this procedure, some proteins are represented in more than one cluster, which indicates that a nonreciprocal pair exists in the filtered set.
The results show that the correlation coefficient between pairs of gene homologs diminishes significantly with an increase in rank, with usually the largest decrease from rank 1 to rank 2. This suggests that, for most clusters, a best pair exists that has significantly higher conservation than with any of the remaining potential functional orthologs.
By performing multiple iterations and collecting pairs that pass a given threshold, we assure with high probability that if an interacting pair exists, it is included in the candidates list and will be reported during validation stage.
Moreover, only a free-end vortex pair is exhibited behind the forward inclined cylinder whereas a base vortex pair exists behind the backward inclined cylinder.
In the following discussion, a function Φ represents the two-variable function on R ¯ + × R ¯ + defined by Φ ( x, y ) : = α − 1 ( x ) β − 1 ( y ), provided that a pre-Hölder pair exists.
We also checked whether a different base pair exists at these positions in bacterial tRNAAsp and if so, whether it affects the recognition mode by their respective AARS enzymes.
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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