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As the leaves of shrubby species and younger saplings of taller-growing species were consumed, only mature forms of the taller species remained, and the structure of the was thus changed with respect to the available habitat for smaller animals, the amount of light that reached the forest floor, the age breakdown of its surviving plants, and its overall biodiversity.
The indicator "expertise" was thus changed to "support for innovation", for our data revealed that the changes entailed in introducing collaborative practices are comparable to those involved in implementing innovations.
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The expression of the original problem is thus changed into a new form where the solutions of symplectic generalized eigenvalues and eigenvectors are needed.
For the cross-link from transmitter j to receiver i, the shifting is thus changed to α i,j −α j,j instead of α i,j.
The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints.
To allow contour splitting and merging naturally (i.e., a change of topology), we use a level set function to represent a contour C. The IFE functional of the contour C is thus changed into the energy functional which is directly defined on the level set functions.
Our obligations were thus: change the water weekly and feed them.
The planned pyramid was thus hastily changed into a square mastaba representing a stylized primeval hill and the accompanying mortuary temple was completed during the reign of Nyuserre.
It was thus proposed to change the selection of collector from potassium amyl xanthate (PAX) to potassium isobutyl xanthate (PIBX).
The formation and dissociation of SFs and FAs are thus drastically changed depending on intra- and extracellular mechanical conditions.
A scale model tractor was thus developed allowing changes to these factors.
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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