Noting that s - r ¯ ∈ supp ( s ) ∪ supp ( r ), we have either s - r ¯ ∈ supp ( s ) or s - r ¯ ∈ supp ( r ).
Thus, every rule in equivalence class ({mathcal A}{mathcal R}, L,SS)) has identical support and confidence, (supp(S),suppp(S /supp(L),) respectively.
Lemma 3.3 If ( s n ), ( t n ) ∈ Δ +, then supp ( s n ⋆ t n ) ⊂ supp s n + supp t n.
Then, (r L{^prime })(rightarrow )(R{^prime }) is a rule created by (L{^prime }), (R{^prime }) (or by (L{^prime }), (S{^prime })) and its support and confidence are determined by supp(r) (equiv ) supp((S{^prime })) and conf(r) (equiv ) supp((S{^prime }))/supp((L{^prime })), respectively.
Furthermore, by observing the Markov state chains corresponding to the equilibrium points found by the LH method, it may indeed be observed that supp ( x ∗ ) = supp ( y ∗ ) = n f · n C T, i.e., the equilibriums are completely mixed.
From now on, we assume that M = ⋃ i ≠ j Supp ( a i j ) ∪ Supp ( c i ) is a nonempty compact set.
After a finite number of steps, we get v 1, v 2, …, v m such that supp ( v i ) ∩ supp ( v j ) = ∅, i ≠ j, and | supp ( v j ) ∩ Ω 0 | > 0 for all i, j ∈ { 1, 2, …, m }.
The result is a smeared field φ(f) = ∫ φ(x f(x dx with supp(f) ⊂ O, where supp(f) is the support of the test function f and O is a bounded open region in Minkowski space-time.
We denote the support of the k-sparse signal h by supp(h), i.e., supp ( h ) : = { i ∈ { 1, 2, …, n } | h ( i ) ≠ 0 }, where h(i) is the i th element of vector h.
end{aligned} Thus, for (forall (L, S in {mathrm{NFCS}}({s}_{{0}},{s}_{{1}},{c}_{{0}}, {c}_{{1}})), all rules in the same equivalence class (mathrm{AR}(L, S)) have the same support supp(S) and confidence supp(S /supp L).
We consider the smooth functions g j = g j ( x ) with respect to φ j on D j that equal 1 on supp φ j, where supp g j ⊂ D j and | g j ( x ) | < 1.
