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It is easily to check that.
It is easily to check that (X, d) is a complex valued metric space.
It is easily to check that sum_{t=1}^{n} biglVert mathbf{x}_{nt}mathbf{x}_{nt}^{top } bigrVert =p.
Due to assumption (A1), it is easily to check that (bar{a}(x)) is twice differentiable with bounded derivatives, and hence it is Lipschitz-continuous: biglVert bar{a}(x_{1} -bar{a}(x_{2}) bigrVert _{mathbb{R}^{n}}leq CVert x_{1} -bar{aert _{mathbb{R}^{n}},quad x_{2}, x_{2}in mathbigrVert}.
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The derived criteria are easily to check in practice.
Remark 3.4 It should be noted that the sufficient conditions ensuring the exponential stabilities of (4.1) and (4.2) are easily to check, which show the advantages of our results.
The Bayes factor developed by Verdinelli and Wasserman [ 11] from generalization of the Savage-Dickey density ratio, and adapted to the animal breeding context by García-Cortés et al. [ 18] and Varona et al. [ 12], has been easily applied to check heterogeneous residual variances in gene expression analyses when two groups of treatments are compared.
Proof of Theorem 11 Condition PIF is easily checked to be satisfied, since it has been already used to formulate the procedure.
Therefore, the necessary condition can be easily checked by checking membership of in every confining plane.
According to Theorem 2.6, the norm-to-weak continuity is easily checked.
It is easily checked that E evaluates to zero for the original network and could even reach a slightly negative value for the case of complete fragmentation, while it gives 100% if the optimum k = ni = N is reached.
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