Exact(10)
The plant is shown to experience instability as the bifurcation parameter takes value in the working region of the reactor.
Then, the solution y ( ⋅ ; z, w ∗ ) takes value in the target set B ( 0, 1 ) at time T ∗ ( z ).
Moreover, by Lemma 2.2 we know that the extended operator takes value in (L_{G}^{2}(Omega _{T})), (p=1,2).
Then, the solution y h ( ⋅ ; z h, w h ∗ ) takes value in B h ( 0, 1 ) at time T h ∗ ( z h ).
Clearly, u ¯ ∈ U a d, and the solution y ( ⋅ ; y 0, u ¯ ) takes value in B ( 0, 1 ) at time T h ∗ ( P h y 0 ) + T ∗ ( z ).
In the first case, the solution y ( T h ∗ ( P h y 0 ) ; y 0, u h ∗ ) takes value in B ( 0, 1 ) at time T h ∗ ( P h y 0 ).
Similar(50)
Interestingly, (3) also makes sense when c is not binary-valued but takes values in (mathbb {R}).
where takes values in.
where the function takes values in.
Here the function takes values in.
where (here the mod function takes values in ).
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