Sentence examples for sequence of systems from inspiring English sources
A simulation of it solves a sequence of systems of equations which differ from each other only by the effects of the modelling of the incrementally increasing damage.
Now, should it turn out to be the case that the consistency sentences (and the other, related sentences discovered by Gödel in 1931) were the only instances of undecidable statements, then the sequence of systems in the above hierarchy would catch every problem that arises.
This allows us in corresponding cases to reduce the study of a generalized and impulsive system to the analysis of the sequence of integro-differential equations, and consequently to the analysis of the corresponding sequence of systems of ordinary differential equations.
For each k ∈ ℕ, let E k denote the Banach space of 2kT-periodic functions on ℤ with values in ℝ N under the norm | | u | | E k : = ∑ n = - k T k T - 1 ( | Δ u ( n - 1 ) | p + | u ( n ) | p ) 1 ∕ p. In order to receive a homoclinic solution of (1.1), we consider a sequence of systems: Δ ( φ p ( Δ u ( n - 1 ) ) ) + ∇ F ( n, u ( n ) ) = f k ( n ), n ∈ ℤ, u ∈ ℝ ℕ, (2.1).
The resulting sequence of system-wide performance metrics is nondecreasing and therefore monotonic.
Lemma 4.2 Let U n be the weak solution sequence of system (2.4).
For any initial value ( x 0, y 0 ), let { ( x n, y n ) } be the solution sequence of system (1.1).
In this case, the resulting sequence of system-wide performance metrics converges with probability one under perfect interference CSI information.
Convergence of the resulting sequence of system utilities follows from monotone convergence theorem, which states that a monotone increasing sequence that is bounded from above is convergent [22].
In order to investigate the type and sequence of system calls employed, the Linux Audit [40] tool has been used for capturing them.
By the same method used in Theorem 2.2, it can be proved that the solution sequence of system (1.1) converges to the positive equilibrium point P. □.
