Sentence examples for failure of approximation from inspiring English sources

One cannot compare the failure of approximation of separate components, such as is seen in rachischisis of the spine or cleft palate, with a structure originating as a single mesenchymal mass, differentiating originally as a continuous structure which separates into its conjugate parts after a growth of the foetus to 30 millimeters.

The failure of Tafel approximation in the middle plates (even when the cell current is large) is illustrated.

Figures 4, 5 and 6 demonstrate that the selected conductivity and thickness values make the approximate formulas (16) and (21) of the surface impedance quite accurate, and so the above arguments about the reasons for the failure of the approximations in Figs. 1, 2 and 3 are shown to be correct.

Moreover, the deviations cannot be attributed either to a failure of the quasisteady approximation introduced in Eq. (7) because the larger the diffusion, the more accurate that approximation is.

However, the failure of the depletion approximation in the near surface region implies that conventional MOS C V measurements yield erroneous doping profiles in that region.

Conventional dielectrophoresis (DEP) force on cell and particle is altered in the proximity of the electrodes due to the failure of the dipole approximation.

Thus, the failure of the Condon approximation provides the mechanism for the influence of PT at the hydrogen-bonded interface on the long-distance ET. The effects of the R coordinate on the reorganization energy are not included.

The much larger value of the vibronic coupling distance decay factor compared to the decay factor for an ET matrix element explains the failure of the Condon approximation for the H coupling in the presence of X fluctuations.

That is, we inspect the magnitudes of the nuclear kinetic nonadiabatic coupling terms (eqs 5.48 and 5.49) that can lead to the failure of the adiabatic approximation near an avoided crossing, and we compare these terms with relevant features of the BO adiabatic PESs (in particular, the minimum adiabatic splitting value).

Even for probabilities of failure as low as 10−5, the quality of approximation obtained by the method is also acceptable.

This suggests the discrepancies are due to failures of the LNL approximation for large fluctuations in the instantaneous spiking rates (r(t)) (see Fig. 3(b)); these fluctuations are smaller at lower correlation values, which lead to smaller signal currents in the LNL formulation.