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For a complete derivation see [4].
(The complete derivation of the model is in Appendix 2).
The complete derivation is illustrated on an edge-preserving optical flow estimator and on image restoration.
Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation.
The complete derivation of the required mathematical models is reported in the paper.
The complete derivation of the DDM-based response sensitivity algorithm is presented.
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This paper provides more detailed (and complete) derivations along with discussions that could not be included in [21] due to space limitation.
The complete derivations are given in Supporting Information, File S1.
The complete derivations and optimization details are given in File S1.
Only Liu et al. (2011), Wang et al. (2013), Song et al. (2013), and Cui et al. (2015) in China proposed the exponential and binomial equations for the relation between the ratio of oil and water permeability and the water saturation, completed derivation of exponential, binomial, and inverse-proportion water drive curves, which have some limitations in prediction accuracy.
Complete theoretical derivation of the relationships among the capacitors, design, simulation, and measurement was conducted in this research.
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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