Despite reproducing the general features of the statistical linearisation estimate, the approximation failed to show the presence of the poles at odd multiples of the primary resonance which are known to occur experimentally.
They are just present in much smaller amount, and when this amount grows, then the QSS approximation fails.
In contrast for bound chaotic systems the orbits start coalescing in increasing numbers on the scale of \(t_{E}\), implying that the semi-classical approximation fails by \(t_{E}\).
Remark 4.2 For the Euler equation u ″ ( t ) + R A ( t ) u ( t ) = 0 with R A ( t ) = 1 4 t 2, we have r ( t ) ≡ − 1, and the Hartman-Wintner approximation fails.
Based on the "exact" acoustic pressure wave equation, it is also concluded that flow-meter errors become independent of ultrasound frequency and cylinder radius, a point that the LPW approximation fails to predict.
Further, as we using scaling to bring our problem to the standard one, we see that in the zone ({x:,d(x asymp B^{-1/4}}), the effective semiclassical parameter is (h_{{mathsf {eff}}} = B^{1/5}Z^{-3/5} 1/5}Z^{-3/5}re unless (Bll Z^3), the semiclandical approximatherefores and the correct answer shounless expressed in completely different terms [18]; compare with [19].
We set values of µs' in accordance with Mie theory, which may cause large errors in reflectance at short SDSs where diffusion approximation fails.
When the normality approximation fails due to extremely low MAF, the p-values were validated by the Fisher's exact test.
The reasons for providing only the right-tail large deviation approximation are (i) all of the above mentioned approximations fail to approximate the extreme right-tail probabilities and (ii) the FMCI approximation provides an accurate approximation for left-tail probabilities.
But wavelet approximations fail miserably, in terms of model parsimony, if used for approximating linear or mildly nonlinear systems.
