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We can represent this operation in matrix form by X ̂ T, N = B X, (21).
The governing equation of motion is cast into a matrix form by applying the Galerkin method.
The boundary and continuity conditions are expressed in a convenient matrix form by assembling the dynamic stiffness coefficients.
The kinetic and potential energy are then expressed in matrix form by using the assumed mode method.
A non-linear governing differential equation for the forced vibrations of the beam is derived in matrix form by employing the Galerkin method.
The damaged stiffness matrix C(D) can be expressed in a matrix form by using the components of undamaged stiffness matrix and the principal values of the damage tensor D I according to the Murakami-Ohno damage model (Murakami, 1988).
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Hair keratin types I and II undergo higher-ordered copolymerization-forming keratin intermediate filaments (KIFs) [ 36– 39], which are embedded into a matrix formed by keratin associated proteins (KRTAPs) involved in the formation of hard cornified resilient hair shafts [ 40– 40].
Apply SVD to the matrix formed by the DWPT coefficients.
Apply SVD on the matrix formed by the DWPT coefficients.
Thereafter, we focused on characterizing the extracellular matrix formed by the cells on various surfaces.
Since a unitary matrix formed by for any can be expressed equivalently as, we consider.
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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