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Other undetermined terms relate to momentum transport by velocity fluctuations about the average values.
However, standard fMRI analysis methods only quantify mean BOLD activity, and treat fluctuations about the mean as noise, thus neglecting potential effort-related changes in BOLD dynamics.
The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed.
In relation to the superspace modifications of 11D supergeometry required to describe the M-theory low-energy effective action, we present an analysis of infinitesimal supergravity fluctuations about the flat superspace limit.
The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance.
Perturbations on a smaller scale still grow parasitically on those that are first established, until the flow pattern is so grossly disturbed that it is no longer useful to define a fluid velocity for each point in space; the description of the flow has to be a statistical one in terms of mean values and of correlated fluctuations about the mean.
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Although this abstract notion of an ensemble mean is sensible and provides some insight about expected behavior of the population, under a suitable definition of "expected", that insight is limited because such models provide no measure of the fluctuations about this ensemble average one can expect to see in any real instance [ 19].
The scaling of rms and skewness of fluctuation about the mean is investigated here.
The spatial structure of the instantaneous fluctuation about the mean is investigated in terms of eigenmodes obtained using proper orthogonal decomposition with the method of snapshots.
The fluctuation about the mean is explained in terms of time-dependent oscillation of the impeller-induced jet and tip vortex components of the flow.
The mean liftoff height is shown to increase with jet-exit and coflow velocity, while the rms fluctuation about the mean increases with distance from the jet exit.
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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