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The occurrence of toe failure (S) is the threshold between the two geotechnical issues.
By Theorem 3, we find that (r-frac {1}{2}sisma_{1}^{2}) is the threshold between weak persistence in the mean and extinction for the prey population.
Remark 1 The results of Theorem 3 illustrate that 〈 r 1 〉 ∗ is the threshold between weak persistence in the mean and extinction.
Therefore, (lim_{trightarrowinfty}frac{1}{t}int_{0}^{t}c(s),mathrm{d}s) is the threshold between the extinction and persistence in mean.
The (limsup_{trightarrowinfty}frac{1}{t}int _{0}^{t}c_{1}(s),mathrm{d}s) is the threshold between extinction and persistence for the predator-prey models.
Observe that the peaks in the value of the second Lyapunov exponent occur at spike adding transitions, when the bursting orbit comes close to the saddle which is the threshold between the spikes and the quiescent segment of the former.
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Another difference between the 2 systems is the threshold relationship between species diversity and SNV prevalence, which suggests that the shape of the dilution curve may be mechanism dependent and is the reason we proposed the term "zoonotic release".
Clearly, our condition given in this paper is the threshold condition between the extinction and the permanence of the disease.
MDC is the threshold for distinguishing between actual change and measurement error, estimated to be 10.81 on the VF-14 scale [ 15, 16].
In (18), (xi_{j}) is the threshold of the relative difference between P j and (P_{j}^{text m}).
In (15), (delta_{i}) is the threshold of difference of CPs between the i th and (i+1 th time-periods.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com