Sentence examples for a trivial path from inspiring English sources

Thus, we suggest that metabolic pathways are extensively reflected in conserved metabolic correlations, although not exclusively in a trivial path length-dependent fashion.

Whenever there exists a directed path (including the trivial path) from a node u to v, we will say that v is a descendant of u, or that u is an ancestor of v.

This includes the possibility where a ∈ X (in which case the trivial path at a satisfies the condition).

We say that A ≪ B if there exists at least one directed path from A to B. There always exists a trivial directed path from any node to itself so that A ≪ A is true for any node A in G.

By simple calculation, we derive an equation which describes all such viable paths of the projected centers of mass, as opposed to the one trivial path of a single point.

To see this, if v ∈ X, then the trivial path is a normal path from v to X.

We consider that there is always a trivial directed path from any node A to itself.

Any vertex v is considered a path of length 0. A non-trivial path (mu ) (=e_{1}dots e_{n}) in E is closed if (r(e_{n} )=s(e_{1})), in which case (mu ) is said to be based at the vertex (s(e_{1})).

It seems that such global bifurcations with trajectories passing through the saddles of the trivial path are due to the interaction of the first and second buckling modes which occur in the aforementioned small region of adjacent equilibria.

The trivial path 3 is normal.

If x is normal in N, let Q be the trivial path z0 = x.