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The genomic relationship matrix among all families was calculated as: G = W C W C 2 2 ∑ l p l q l where W C is the centered genotype matrix, and p l and q l are allele frequencies at the lth locus (Endelman and Jannink 2012).
Where I is the identity matrix, and p represents the power.
where | ⋅ | refers to the determinant of the concerned matrix and p ≤ q ≤ n.
where A is the coding matrix and P the packet vector.
Avec{P} = vec{B} (61 where A is the coefficient matrix and P and B are column vectors.
The matrix Γ ̃ Y is an M × M matrix and P s and Y are K × K diagonal matrices.
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Fracture mechanics and Lagrange equation were used to obtain crack element stiffness matrix and p-version finite element model respectively in the analysis.
The multistep tunneling process usually occurs at the HJ region of the n-ZnO matrix and p-Si substrate, which is attributed to the recombination of electrons, tunneling from ZnO into the empty gap states in the p-Si substrate, and holes, tunneling through the HJ barrier from the p-Si substrate to the n-ZnO matrix between the empty states [21, 23].
where U =UT ≥ 0 and R = RT > 0 are some prescribed real matrices and P = PT,Q =QT are positive definite matrices to be determined.
end{aligned} (4.4) Decompose the matrix a and p in the same way as the decomposition in Example 4.3.
The trends are similar in the various matrices and p-values are acceptable, with ZRes and ZNMI yielding the largest values of anti-correlation (Table 3).
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