Sentence examples for monotonically decreasing sequence from inspiring English sources

In practice, to use Abel's test one begins with an infinite series and factors each term in the sequence in such a way that one of the factors produces a known convergent series and the other factor produces a monotonically decreasing sequence of positive numbers.

(A) is weakly quasi-nonexpansive with respect to ; (B) is a monotonically decreasing sequence in.

We choose a monotonically decreasing sequence of positive numbers so that (2.1).

Case 2. Assume that ({| x_{n}-x^) is not monotonically decreasing sequence.

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

Since is a monotonically decreasing sequence, the quadratic mapping satisfies (3.20) for all.

While if (A_{h}<0), then the impulsive points and its phase points of trajectory shown in Figure 8(F) are two monotonically decreasing sequences, and eventually the trajectory tends to the boundary order-1 limit cycle ((x^{T}(t),0)).

If U is the commutant of a strictly cyclic unilateral weighted shift with a monotonically decreasing weight sequence, then we show that there is a natural isomorphism of the Banach space of bounded linear maps from U into B(H) with the Banach space of bounded linear maps of the trace class operators into H, where H is a separable, infinite dimensional Hilbert space.

Then Algorithm (3) defines a monotonically decreasing matrix sequence { X n } converging to the positive definite matrix X which is a solution of matrix equation (2).

Then Algorithm (7) defines a monotonically decreasing matrix sequence { X n } converging to X ∞ which is the maximal Hermitian positive definite solution of equation (2).

(i) From (3.5) it is easy to see that the sequence {Ψ z k )} is monotonically decreasing, and hence, sequences {||H z k )||} and {β z k )} are monotonically decreasing.