Sentence examples for is not longer valid from inspiring English sources

However, this deflation step is not trivial in the dependent case since the sources are not orthogonal and the classical deflation technique used in ICA is not longer valid.

For the asymmetric CCEiCP, this reduction is no longer valid.

Therefore, for high solid concentrations, as it is the case for the simulation with 35 wt% and 55.8 wt% sand concentration, the consideration of the suspension as a Newtonian fluid is not any longer a valid assumption.

After a resampling step, this is not valid any longer.

When air is somehow trapped between the solid and the liquid, the Wenzel model is not valid any longer, and a more accurate description of the phenomenon is given by the Cassie Baxter equation that considers both solid liquid and liquid air interface fractions of the overall interface (see Figure 2 f.ii).

So, (i) is not intuitionistically valid.

Jaimie: "That is not a valid question.

That is not a valid opinion.

The moon is not a valid one.

Wanting attention is not a valid one.

For general (sparse) graphs, the system is no longer exchangeable, and the mean field approximation is not valid.