Sentence examples for shown to be invalid from inspiring English sources

Thus, as a further application, a two-sided estimate of the form c0|D+∥x t)∥R|⩽∥˙x t)∥R⩽c1|D+∥x t)∥R| can be derived, which is shown to be invalid for the norm ∥⋅∥2.

Bellman's Principle (Bellman, 1958) is shown to be invalid if the optimality or non-dominance of a path and its sub-paths is defined with respect to the complete set of departure times and joint realizations of link travel time.

Previous assumptions which consider the iron and slag to flow separately and the iron level to remain horizontal and fixed at the level of the taphole during the flow of the slag phase are shown to be invalid.

The Neck Disability Index, an advocated PRO, was recently shown to be invalid due to its bidimensional structure [ 57, 58].

Self-reported data have been shown to be invalid when compared with objective measures such as doubly labeled water (33).

Numerical methodological "quality" scores have been shown to be invalid for assessing risk of bias in clinical research (Jüni et al. 1999).

The argument forms we showed to be invalid in Adams's logic (§3.2) are invalid on Stalnaker's semantics.

In several studies, a valid endogenous cue is shown to be virtually invalid at 100 ms from its onset (affecting performance negatively) and to increase its benefit steadily until 400 ms [for example, 7].

However, the coefficient of friction has increasingly been shown to be an invalid measure of surface damage: several studies of lubricants with a low coefficient of friction report poor wear protection to mica surfaces and especially to biological tissues.

Hence, there is an asymmetry between proving arguments valid and proving them invalid: they are valid if they can be shown to be an instance of a valid form, but they are not proved invalid by showing that they are an instance of an invalid form, because both valid and invalid arguments instantiate invalid forms.

The results from animal-based research have been shown empirically to be invalid for predicting human response and this is supported and explained by theory from evolution and complexity science.