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The semi-random spikes of the direct runoff coefficient series are approximated sufficiently.
Figure 5 Example of COV-OBS.x1 MF (right) and SV (left) coefficient series (blue) and comparison with CHAOS4plus_v4 (red).
Indeed, regularized field models tend to provide a smoothed estimate (i.e., weighted time average) of the SV coefficient series towards high degrees.
Maps (centered on the Greenwich meridian) of the Z component at the Earth's surface for the first four normalized eigen modes, ({mathcal {Z}}_{1}) to ({mathcal {Z}}_{4}), obtained from the (tilde {z}_{n}^{m}) coefficient series in dipole coordinates.
Thus, we build matrices R h and R v from the variances of the coefficient series ({h_{n}^{m}}(t)) and ({v_{n}^{m}}(t)) in dipole coordinates, first obtained over the period 1960 to 2010 for which the model is weakly sensitive to the a priori matrices (we would underestimate the variances of the model parameters by considering the era before 1960, where fewer, less accurate data are available).
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Specifically, we investigate whether the I-O coefficients series could contain sets of attractor points.
Due to these two circumstances—high volatility and serial correlation the possible presence of attractors in the technical coefficients series was taken into consideration.
As it can be seen from Eq. (19) for a given voxel pair i− j and frequency, the element is in effect the z-transform of the MAR coefficients series across time lags a ij, modeling the effect of voxel j on voxel i.
We access some relations about the coefficient sine series and cosine series.
The technique of proper orthogonal decomposition is used to convert measured point pressure coefficient time series to loading time series at specific frame loading points.
In this paper, we first consider a time-varying coefficient time series model with potential time-varying endogeneity.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com