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However, powerful mathematical tools can produce results, which although may be formally correct, are wrong if the modeller does not evaluate the specific conditions that need to be applied, such as quality of the inputted data.
If this vectors are linearly independent, taking this space as the -space of, then is a -holomorphic lift of, although may be a map into ; on the other hand, if is totally umbilic, then we may take either as the unique strictly compatible map into or into and both these maps are -holomorphic.
The volva is thin, smooth and sac-like, although may be quite extensive and contain almost half the stipe.
This is because the feature vector, although may be trained with spectrum-specific quantities, aims to categorize the whole training set into finite number of classes but does not solely reflect the properties of any individual spectrum.
Then, we consider the value VN i,i)/ for each LC6, as its aggregation measure on the map for a given vicinity radius (although may be LC6's spread on different clusters).
There was a trend towards higher frequency of microcytosis and lower MCV in children with seizures which, although may be confounded by alpha-thalassemia, suggests that our definition of iron deficiency may have been conservative.
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But although Cleo may be naive, she isn't stupid.
(See anything by Jorie Graham, although this may be my favorite).
Although Griffin may be a bit busy just now.
Although this may be enough of an incentive in itself.
Although it may be too long, the plaudits are deserved.
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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