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Approximated sketches of higher order intersection curves in 2D views result in the invalidation of existing methods that need the exact projection information as input.
According to the capillary and quartz sand models, capillary forces increase with a decrease in sand grain and glass tube diameters, resulting in the invalidation of buoyancy as the most important controlling factor.
As a consequence, the platform is unable to scan the environment and move simultaneously resulting in the invalidation of all algorithms in which robot velocity is an important determinant of direction of motion [17 22].
It is shown that the deviations are mainly resulted from the overlap between the diffuse double layer and the concentration depletion layer (CDL) at nanoscale electrochemical interfaces in weakly supported media, which will result in the invalidation of the electroneutrality condition in CDL, and from the radial inhomogeneity of ET probability at nanometer-sized disk electrodes.
Yet in both decisions, the Court makes clear that this right is not likely to be something that results in the invalidation of many laws -- or perhaps even any laws other than the ones directly at issue in the case.
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A series of Supreme Court decisions, culminating in June with the invalidation of the sentencing guidelines in the Washington State, established the principle that juries, and not judges, must rule on the facts that are the building blocks of a criminal sentence.
The last great constitutional transformation of marriage in this country, the invalidation of laws against interracial marriage, moved slowly.
Additionally, Kisi's (2015) application of innovative trend method, as explained in detail by Şen (2012, 2014, 2015), has invalid confidence limits (bands) and the invalidation is explained in the comment.
On the other hand the same problem but for nilpotent singular point is far to be solved in general, due to the invalidation of classical methods.
That resulted in the latest invalidation of the state's execution protocols in 2012. .
5.01pm: Over at The Nation, Dr Sonia Nagda writes up the argument that we've seen hanging around leftie circles for the last few years and will see again, many times in the next week, about how the invalidation of the individual mandate could play out for the best: legislators will then have no other choice but to institute to a single-payer system – the one we've wanted all along!
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com