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Transcendentally frequency-dependent complex valued non-symmetric mobility matrices are treated.
Computational issues, as the construction of the nonlocal element and global stiffness matrices, are treated in detail.
The purely non-proportional damping matrix and possible modification matrices are treated as the perturbation matrix to the proportionally damped system.
For proteins, amino acids that are considered very similar, for example using the PAM [ 6] or BLOSUM [ 7] matrices, are treated as complete mismatches.
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The matrices were treated using NaOH 1 N at 65 °C for various durations (ranging from 20 min to 24 h).
The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems.
Based on the knowledge of the Hessian matrix symmetry, only the off-diagonal elements of Hessian matrix are treated mathematically.
However, extra effort is required to obtain the correct real and imaginary combination of the mixing matrix since the real and imaginary parts of the mixing matrix are treated separately, leading to an increased computational cost due to the increased dimension of the matrix that needs to be processed.
Furthermore, bisphosphonates can inhibit the adhesion of tumor cells to mineralized matrices in vitro, both when the cells or the matrix are treated [ 13, 14].
ZA downregulates adhesion molecules on bone marrow stromal cells and inhibits tumor cell adhesion to the bone matrix whether the tumor cells or the matrix are treated with bisphosphonate [ 12].
This was possible because the non-observed fraction of the design matrix was treated as an unknown model parameter.
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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