Sentence examples for monotonically increasing sequence from inspiring English sources

Then (Omega_{t}) is a monotonically increasing sequence.

Now, we have shown that is a monotonically increasing sequence while is a monotonically decreasing sequence.

Also, the sequence { Y n } defined in Algorithm (3) defines a monotonically increasing sequence converging to X − 1.

Proposition 3.3 The sequence { g 2 n − 1 } is a monotonically increasing sequence and the sequence { g 2 n } is a monotonically decreasing sequence.

A solution to the fixed point equation (6) is the limit of the monotonically increasing sequence rho_{k+1}=Krho_{k}+F, qquad rho_{0}=0,quad kge1.

Step 2. There exists a monotonically increasing sequence ({m_{k}} ) such that the sequence (bar{delta}_{m_{k}}) is increasing on (m_{k}).

Then there exist (epsilon> 0) and monotonically increasing sequences of natural numbers ({m_{k}}) and ({ n_{k}}) such that (n_{k} > m_{k}).

In (1.1), { x n }, { y n } are monotonically increasing sequences and the positive equilibrium point of system (1.1) is unique, we get M = x ∗, N = y ∗.

To confirm the main results obtained in Theorem 6.3, we fixed the parameter values as those in Figure 8, and we can see that if (A_{h}>0), then the impulsive points and its phase points of trajectory shown in Figure 8(C) are two monotonically increasing sequences, and eventually the trajectory approaches a closed orbit which frees it from impulsive effects.

The sequence ({u_{n}= underline{w}^{(n)}, underline{z}^{(n)})}) is monotonically increasing and bounded above by ((overline {w}_{0},overline{z}_{0})). The bounded monotonic increasing sequence shows convergence to its least upper bound, say ((w_, z_)).

where {γ k } is a positive monotonically increasing scalar sequence [26].