Proof Along the trajectory of system (6), for the co-positive type Lyapunov-Krasovskii functional (7), we have (10).
More information about the lower bound of the (h_{1}(t)) and (h_{2}(t)) is sufficiently used in the Lyapunov functional (7).
In that case the system (1), (2) is stabilizable with respect to the state feedback shown in (43), (44), and the functional (7).
Then we assume that c + ¯ and c − ¯ are constant vectors, and then we minimize the energy functional (7) with respect to ϕ to have ∂ϕ ∂t = δ μ div ∇ ϕ | ∇ ϕ | − 1 N ∑ i = 1 N λ i + ( I i ( x, y ) − c i + ) 2 + 1 N ∑ i = 1 N λ i − ( I i ( x, y ) − c i − ) 2. (10).
Similar to the C-V model in minimizing the energy functional (7) with respect to the constants c i + and c i − for i=1,⋯,N, we obtain c i + = ∫ Ω I i ( x, y ) H ( ϕ ( x, y ) ) dxdy ∫ Ω H ( ϕ ( x, y ) ) dxdy, (8).
Consequently, condition (B3) is also satisfied and thus ρ is a b-metric on X. Example 2.5 The set l p ( R ) with 0 < p < 1, where l p ( R ) : = { { x n } ⊆ R | ∑ n = 1 ∞ | x n | p < ∞ }, together with the functional d : l p ( R ) × l p ( R ) → R +, d ( x, y ) : = ( ∑ n = 1 ∞ | x n − y n | p ) 1 p, for each x = { x n }, y = { y n } ∈ l p ( R ), is a b-metric space with coefficient s = 2 1 p > 1.
And other times I just can't go to the dinner because I know I won't be functional the next morning when I like to write.
Let LIM be a continuous linear functional on l ∞ satisfying ∥ LIM ∥ = 1 = LIM ( 1 ).
This suppression occurs only if Mre11 nuclease is functional (Figure 7).
Isolated mitochondria from neutrophils can be energised by glycerol phosphate, as demonstrated by staining with tetramethylrhodamine-methylester (TMRM), proving that the mGDP is present and functional (Figure 7).
