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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.
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.
where It is easily checked that and This leads to If then By (2.5), we conclude that.
It is easily checked that u is indeed a solution to (1.4 - 1.5) by passing to the limit in (3.1 - 3.2 3.1 - 3.2
It is easily checked that (33) and (43) present a solution to system (1).
It is easily checked that (105) and (112) present a solution to system (1) in this case.
It is easily checked that such an admissible sequence from f to e exists if and only if there exists a reduced path from f to e of odd length in G say an admissible odd path.
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