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All elements in the matrix are then extracted into a value list.
The eigenvalues of the arrowhead matrix are then estimated in terms of eigenvalues of the diagonal matrix and the special arrowhead matrix by using Weyl's theorem.
The stresses in the yarns and matrix are then used in a continuum damage model to determine localised stiffness degradation, and the cell properties are homogenised to determine the macro-scale effect.
Three methods, namely quasi-Newton, conjugate gradient, and optimization in the null and complement spaces of the measurement matrix, are then proposed to solve the l2-Sl0 uncoptimizationproblemtion problem.
The locations of a few well known threats in the matrix are then used as a basis to draw a threshold between material threats that warrant control by such criteria as legal requirement, societal expectation or corporate policy, and the other immaterial threats.
Rows and columns of the matrix are then sorted (clustered) to place the clique SNPS in the top left corner.
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Each letter's matrix is then released at the opening of its own channel in the magazine.
The ordering matrix is then defined as.
The matrix is then used as the precoding matrix,.
The constraint matrix is then invertible in order n operations.
This final matrix was then applied to all research questions.
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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