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The final condition aids our analysis by ensuring the corresponding integral operator is compact, but is also a physically justified assumption since one could argue for the stricter assumption (int _{-1}^{1} int _{-1}^{1} |H_{ij} tau,t)|^{2},dtau,dt leq 1), since no more energy can be scattered than is transmitted.
This was expected because MST-p relies on a stricter assumption than the others (Bühlmann et al. 2014).
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Also, the comparison principle for mean-field BDSDEs is discussed when the coefficients satisfy some stricter assumptions.
For the purpose of the present paper it is important to incorporate stricter assumptions on measurability, sampling rates, and error bars.
Random effects models require stricter assumptions that are not often met, but as a sensitivity test we also obtained estimates of the year coefficients based on random effects models.
This is a strict assumption, since subcarriers which are less than apart are not fully correlated.
In this control scheme an explicit control Lyapunov function (CLF) and the strict assumption of linearly parametric uncertainties made on system structures can be avoided.
First, the multinomial probit model, unlike its logit counterpart, allows the relaxation of the strict assumption of independence of irrelevant alternatives (IIA).
The strict assumption that information flows along shortest paths (geodesics) is not always appropriate, as discussed, by Newman [18], who proposes a random walk betweenness measure computed using matrix methods.
Because traditional phylogenetic methods used in biogeographic reconstruction are based on trees rather than networks, they follow the strict assumption in which dispersal among geographical units have occurred on the basis of single dispersal routes across regions and are, therefore, incapable of modelling multiple alternative dispersal scenarios.
The only strict assumption made is that of a monotonic odor response function.
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