A graph is called a multi-graph when E is not necessarily composed of distinct pairs of vertices (thus multiple edges are allowed in a multi-graph and E is no longer a set, but a multi-set), and is called a simple graph if no multiple edges are allowed.
This growth was fueled by a variety of factors over the decades: multi-set and color TV households increased, the selection of 24-hour programming options expanded, and such technologies as the VCR and DVR gave viewers ever increasing control.
The network design is configured as a multi-objective model in a multi-period setting and is mathematically formulated into a mixed integer programming problem with fuzzy objectives.
It should be noted that the fitting results for each curve depend on the initial guessed values, i.e. there are multi sets of c1, D1 and D2, which can all fit the stress stretch curve well (Fig. 7).
A k-set structure is a sub-linear space data structure that supports multi-set insertion and deletion operations and returns the multi-set, provided the number of distinct items with non-zero frequency does not exceed k.
Almost all of the iterations were done in a multi-room setting and required multiple observers.
In this work, we focus on multi-layer setting and we show that several important additional ingredients are needed compared to the single-layer scenario.
The existence and uniqueness of Nash equilibrium is proved in the generalized multi-period setting, and the closed-form Nash equilibrium solution is obtained when the parameters are stationary.
