A route from a source S i to a destination D j is a set of nodes such that there exists an ordering of these nodes where the first one is S i, the last one is D j, and any two consecutive nodes in this ordering are connected by an edge in the graph.
There exists an ordering of the rows and columns of B, which yields a canonical matrix.
Lacunarity analysis suggests there may exist an ordering of irregularity based on an images' singular lacunarity value.
Lacunarity analysis suggests there may exist an ordering of irregularity in melanocytic lesions, and further investigation is required to determine whether this ordering has any clinical utility.
In particular, there must exist an ordering of the states = s1,..., s S such that the probability t(s i, s j ) of transitioning from state i to state j is zero unless j ≥ i and (j - i) ≤ k for some fixed small constant k.
In addition a split system Ϭ' ⊆ Ϭ(X) is circular if there exists an ordering Θ of X such that Ϭ' is compatible with Θ.
Formally, a collection of splits of X is circular if there exists an ordering x1,⋯, x n of X such that every split is of the form { x i, x i +1,⋯, x j}| X - { x i,⋯,x j} for some i and j, 1 ≤ i ≤ j ≤ n.
By Lemma 2.4, there exists an order-1 periodic solution of system (1) (see Figure 2(a)).
Thus there exists an order-1 periodic solution of system (1) by Lemma 2.4 (see Figure 2(c)).
If (xleq x_{0}) and (0< h_{1}<frac{c}{rb}<x_{0}), there exists an order-1 periodic solution of system (1).
