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Provided that j, k ∈ { 1 , ..., N } and j ̸ = k , 

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Thus, ∇ $^{2}$G$_{·}$$_{,k}$ in (82) shows the k th column of ∇ $^{2}$G . ∇ $^{2}$G$_{·}$$_{,}$$_{1}$ denotes the first column, ∇ $^{2}$G$_{·}$$_{,}$$_{2}$ denotes the second column, and so forth. 

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