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Moreover, the function ∂Nw/∂Nu ~ (Nu b−1 is a monotonically decreasing function for b < 1, demonstrating the decreasing marginal need for additional words as a corpora grows.
Thus, (f(x)) is a decreasing function for (1leq xleq n-3).
Thus (f(x)) is a monotonically decreasing function for (x>0).
Suppose that the following assumptions are satisfied: 1. (u(x)) is a continuous, positive, decreasing function for (xgeq n). 2.
The fluctuations are observed in the figure because an average number of transmissions is a decreasing function for Bob's received SNR.
Then R_{n}leq int_{n}^{infty}u(x),dx. (u(x)) is a continuous, positive, decreasing function for (xgeq n).
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If both and are strictly decreasing functions for,, and then one has the following equivalent inequalities: (1.3).
Let (X= [ {a,b} ]), (alpha= m= 0 ) and f, g be two decreasing functions for all (x in X).
Because when and, is a decreasing function of for, this follows from Lemma 3.1.
Previous association studies of increased breast cancer risk for BRCA2 N372H and decreased function for APEX D148E variants were not in agreement with our findings of decreased risks.
It is easy to show that expression (30) is a decreasing function of β (for g of interest, i.e., g > 1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com