Sentence examples for approximation fails from inspiring English sources

This conceptually clean approach is very general and can be applied to various settings where the Newtonian approximation fails or becomes inaccurate, ranging from simulations of models with dynamical dark energy3 or warm/hot dark matter4 to core collapse supernova explosions5.

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.

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.

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].

They are just present in much smaller amount, and when this amount grows, then the QSS approximation fails.

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.

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.

Smith's and Fatti's approximations failed to estimate reservoir porosity because of associated uncertainties.

As classical approximations fail to describe carrier quantization, charge inversion and potential profile of a device at sub-100 nm regime, here for the first time an analytical model in quantum mechanical aspect for COI/CON devices has been derived.