Sentence examples for absolutely monotonic from inspiring English sources

Next, we recall the definition of absolutely monotonic function [17].

Moreover, the functions (trightarrow-log T_{p, q}(t)), (trightarrow-[log T_{p,q}(t)]/t), and (trightarrow-[log T_{p, q}(t)]/t^{2}) are absolutely monotonic on ((0,pi/2)) if (p+q>0).

By [13, Theorem  6, page 392] it follows that if is an absolutely monotonic (resp., a completely monotonic) function, then belongs to every set with and (resp., ) for each.

Then the functions (trightarrowlog T_{p, q}(t)), (trightarrow[log T_{p, q}(t)]/t), and (trightarrow[log T_{p, q}(t)]/t^{2}) are absolutely monotonic on ((0, pi/2)) if (p+q<0).

Recall (see, e.g., Roberts and Varberg [14, pages 233-234]) that a function is called absolutely monotonic (resp., completely monotonic) if it possesses derivatives of all orders on and (4.25).

A real-valued function f is said to be absolutely monotonic on the interval I if f has derivatives of all orders on I and f^{(n)}(x)>0 for all (xin I) and (ngeq0).

The function W (F (x)) is monotonic and absolutely continuous.

The link function W : [0, 1] → ℝ is monotonic and absolutely continuous with W 0) → a and W(1) → b.

Let r(t) and R t) be the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable T ∈ [a, b], for − ∞  ≤ a < b ≤ ∞, and let F x) be the CDF of a random variable X such that the link function W : [0, 1] → [a, b] is monotonic and absolutely continuous with W 0) → a and W(1) → b.

With this approach, the skeleton map is cleaned from markers that fit one of these conditions: (i) are absolutely linked; (ii) violate monotonic growth of recombination with its subsequent neighbors; (iii) have unstable location relative to other markers (as detected by jackknife resampling).

Let (g:[alpha,beta]rightarrowmathbb{R}) be monotonic nondecreasing and (f:[alpha,beta]rightarrowmathbb{R}) be absolutely continuous with (f^{prime}in L_{infty}[alpha,beta]).