Exact(11)
Let the other vertices in T be totally dominated by at most m−k vertices in N ( Ω 1 ( G ) ) ∩ N ( T ) Open image in new window.
The total particle-number operator is defined by N = ∑ t N t Open image in new window.
We take X ― = X 1 ― ∪ X 2 ― ∪ … ∪ X T ― Open image in new window and N = N 1 + N 2 +.... + N T Open image in new window.
It is easy to know that, φ n ( t, t ) = sin sin … sin ⏟ n t, Open image in new window and lim n → ∞ φ n ( t, t ) = 0, ∀ t ∈ R + Open image in new window.
Decision vector X t ―, t = 1, 2, …, T Open image in new window is the control of the t- th level DM having N t Open image in new window number of decision variables.
In the iteration process of Equation 3.4, we can guarantee that the approximation u n ( t ) Open image in new window always satisfies the boundary conditions of Equation 2.1.
Similar(49)
The system of linear differential equations for the vector P t = P 1 t P 2 t.... P N t T Open image in new window is presented by P ′ t = dP t dt = Q.
Define ∥ y ∥ = sup t ∈ [ ν − N, b + M + ν ] N ν − N y ( t ) Open image in new window.
If the pairs (A, S) and (B, T) enjoy the (CLR S T ) property, then two sequences {x n } and {y n } in X exist such that lim n → ∞ A x n = lim n → ∞ S x n = lim n → ∞ B y n = lim n → ∞ T y n = t, Open image in new window.
Liu, 2005 [28] Two pairs (A, S) and (B, T) of self-mappings of a metric space (X, d) are said to satisfy the common property (E.A) if two sequences {x n } and {y n } in X exist such that lim n → ∞ A x n = lim n → ∞ S x n = lim n → ∞ B y n = lim n → ∞ T y n = t, Open image in new window.
Imdad, 2012 [31] Two pairs (A, S) and (B, T) of self-mappings of a metric space (X, d) are said to satisfy the common limit range property with respect to mappings S and T, denoted by (CLR S T ) if two sequences {x n } and {y n } in X exist such that lim n → ∞ A x n = lim n → ∞ S x n = lim n → ∞ B y n = lim n → ∞ T y n = t, Open image in new window.
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