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When the phase point is on the strong canard, δ = 0. Let δ > 0 when the phase point is in the singular funnel and δ < 0 when the phase point is outside the singular funnel.
Through PSR, the M LF-MDCT coefficients are mapped into M- m-1)τ phase points, where the diM- m-1n nuM- m-1f each phase point is m.
From the above analysis, it is obvious that due to the complicated range expression in the CTSSAR where the simple quadratic range equation does not hold, the stationary phase point is difficult to approach and the 2D spectrum is hard to obtain.
If f d (k) > fD, the phase point y k NN is determined as the false nearest neighbor of the phase point y k, where fD is a threshold value used for verifying whether the nearest neighbor of phase point is false or not.
To verify whether the nearest neighbor of each phase point is false or not, the relative change of Euclidean distance between phase point and its nearest neighbor is denoted as f d (k) when the dimension number of phase space is changed to d + 1 from d, i.e., f d (k) is defined by [14] f d k = D 2 d + 1 k - D 2 d k D 2 d k 1 2 = x k + τd - x NN k + τd D d k. (6).
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The result shows that the reference trigger point of two different sinusoidal RF signals for an arbitrary phase point was acquired with a matched phase error below 1° (approximately 2.1 ns), and the step delay time better than 2 ns were realized.
Furthermore, the percentage of the false nearest neighbors in all nearest neighbors of all phase points is defined as β(d).
By comparing f d (k) with fD, the false nearest neighbors for all the phase points are verified.
The phase inversion point is shown to depend on the wettability of the shearing surfaces by the liquid phases and the viscosity difference between the liquids.
From Fig. 10, when ( {widehat{k}}_s=40 ), the phase search pseudo-spectrum Phase k s ) reaches its maximum and this peak corresponds to the phase change point of the third and the fourth codes in [-1 -1 1-1 -1 1 1-1 1 1], which means the position of the phase change point is (p − 1) × N s + k s = (8 − 1) × 80 + 40 = 600.
The primary A-phase end point is a composite of all-cause mortality, myocardial infarction (MI), and documented refractory ischemia at 7 days.
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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