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where K C i is reduced rigidity matrix of i th part.
where V T denotes the modal matrix of I T ′ corresponding to an arbitrary ordering of its eigenvalues.
where R i denotes the M-rank covariance matrix of I, and 0 M denotes an M-rank zero matrix.
By association with etc., it is enough to measure a single column (or row) from the matrix of i, j response functions which relate velocities at points i to excitations at points j.
where H i is the Hessian matrix of I i : H i = ∂ 2 I i / ∂ x 2 ∂ 2 I i / ∂ x ∂ y ∂ 2 I i / ∂ y ∂ x ∂ 2 I i / ∂ y 2. To sharpen the color images, the shock filter is applied on each image channel I i only in one direction φ+ of the vector discontinuities[39].
where Hσ is a matrix of i.i.d.i.d
Similar(48)
Table 1 List of variables used in the analysis Δ Channel determinant 11 bits ampx_trk Scale for amplitude tracking 7 bits ratefield_rx Modulation order indicator 1 bit x ̂ i Estimated transmit symbol of i-th stream 18 bits ||W i ||2 Norm of pseudo inverse matrix of i-th row 17 bits.
Let D i denote the eigenvalue matrix of H i in SVD; thus, D i = D i - 1 i ⋯ D 01, (21).
B= Bhatacharyya index; i= first spectral signature vector; j= second spectral signature vector; Σ i = covariance matrix of sample i; and Σ j = covariance matrix of sample j.
Additionally, e f represents the I f -dimensional vector of infectivity environmental effects with e f | σ E, f 2 ∼ N (0, σ E, f 2 I f ), where I f is an identity matrix of dimension I f.
where D 2 f i is the Hessian matrix of f i with respect to (x,y,z 1,…,z d ).
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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