Sentence examples for minimal element set from inspiring English sources

As mentioned above, each temporal subnet is the minimal element set at time x; and next (ii) Applying Algorithm 2 to the outputs of Algorithm 1, we construct the ASTD.

We thus define temporal subnet H'(x) at time point x as such a minimal element set consisting of usable HFPNe elements involving: (1) enabled arcs; (2) transitions connected by (1); and (3) places connected by (1) and places connected from (2).

In other words, such a minimal element set with corresponding concentration distribution M x), will return exactly the same simulation results as the original model under a precondition that the elapsed delay time of the discrete transition is given in the EDF.

Algorithm 1 aims to (i) extract a minimal element set of the HFPNe model at time x (i.e., the extracted set cannot be reduced furthermore).

That is, each node simply possesses the structural information of the entries in the minimal element set that is extracted by eliminating the disabled transitions/arcs and isolated places.

Any disturbance to the elements belonging to this minimal set will lead to different simulation results; and (ii) derive a total minimal element sets by exhaustively examining all reachable states of the HFPNe model with respect to the structural transformations along the time variations.

Since A ( C ) is compact, the family F = { A ∈ A ( C ) ; T ( A ) ⊂ A } has a minimal element K. Set K 0 = ∩ { A ; A ∈ A ( C ) and T ( K ) ⊂ A } ∩ K.

DMU E is a minimal element of partially ordered set ({A, B, C, D, E}), so it is efficient.

From Theorem 4.1, T is upper semi-continuous on P. Following the proof of Theorem 3.2 for the part of the existence of minimal element of essential sets, we obtain the following result.

An element u ∈ K is called an extended best ordered approximation of f on K, if it satisfies d X ( u, f ( u ) ) ∈ Min { d X ( s, f ( u ) ) : s ∈ K }, where Min { d X ( s, f ( u ) ) : s ∈ K } is the set of minimal elements of the set { d X ( s, f ( u ) ) : s ∈ K } with respect to the ordering ≽ X on X.

Since (A_) is a minimal element of Γ, the compact set (A_setminus V_{z}) is not in Γ, and so there exists an open set (Usubset V_) such that (( A_setminus U_{z})subset Usubset V_), (operatorname {Fix} varphi cappartial U =emptyset), (operatorname {Ind} varphi,U = 0) and (operatorname {Ind} varphi, V_)=operatorname {Ind} varphi, Ucup V_{z})).