Sentence examples for transformations need from inspiring English sources

Observe that "something remaining the same under some transformations" need not depend on coordinates, metric, dimension or orientation of the space.

These transformations need not, of course, be literal.

Not all transformations need to be bold and bright.

If data require a transformation prior to the analyses then all such transformations need to be documented and clearly justified.

Regardless of whether or not these transformations need to be reversed during decoding, they lead to improvements in compression that overcome the cost of storing the 'sideband' information necessary to reverse them.

Therefore, the phase-locked loop and control strategy without any frame transformations needs further investigation.

However, the social-ecological transformations needed to effectively implement these management options are not sufficiently understood.

Smolke also emphasizes that researchers remain a considerable distance from putting together the full chain of chemical transformations needed for yeast to make morphine.

The tool would first work out the transformations needed to convert the current solution to the desired pattern (in the paper a plausible precursor was chosen first).

Thus, finding the sequence of transformations needed to stationarize a time series often provides important clues in the search for an appropriate forecasting model.

as an example of someone seeking transformational economic change, along with professor Stephanie Kelton, whose work argues sovereign governments cannot run out of money, thus debunking the argument that economies cannot afford to make the transformations needed to address climate change.