Intra- and intermolecular etherifications and intramolecular esterifications were detected by MALDI-TOF MS on the core molecule-containing polyesters, resulting in the formation of cycle-containing hyperbranched molecules.
In other words, there exists the possibility for the formation of cycles in the evolving networks during this network formation model, as it is defined in the following.
Notice that a node i sends an RREP to the only nodes j ∈ V ( i ) ∖ p ( l ) so as to prevent the formation of cycles in the backward propagation of RREPs.
While improving paths that start from a seed network may end in an equilibrium network, it is also possible to find the formation of cycles as the result of an improving path.
In addition, a cycle C is a closed cycle, if for all networks G∈C, there does not exist an improving path leading to a network G ′∉C. Generally, the presence of negative externalities can be seen as one of the potential reasons in the formation of cycles in linking games.
The tree diagram was formed by tracing all the states without the formation of cycles (a Hamiltonian path [32]).
Tracing all the states without the formation of cycles (a Hamiltonian path [32]) generated growing numbers of branched paths (a tree diagram).
The bistability onsets with the formation of a cycle around the stable state (fold bifurcation), and disappears when the unstable cycle becomes infinitesimally small and renders the equilibrium unstable (subcritical Hopf bifurcation).
Unlike higher organisms, many bacteria and fungi can grow on acetate or compounds such as ethanol or a fatty acid that can be catabolized to acetyl coenzyme A. Under these conditions, the net formation of TCA cycle intermediates can proceed via different ways.
Since it causes a reduction in player u's utility, u decides to sever uv that in overall leads to the formation of a cycle.
Consider the following grid-based example shown in Figure 2. In this example, we can observe the formation of a cycle in the game.
