Sentence examples for equivalent to demonstrating from inspiring English sources

We note that the formation of bands in the model (4) is equivalent to demonstrating the existence of the converging travelling wave solutions (U z)) and (V z)).

Because Problem III is a linear equation about unknown function ϖ, to prove the existence and uniqueness of solutions of Problem III is equivalent to demonstrating that it has only a zero solution when (g=f=u_{0}=0).

Blum et al.'s result is equivalent to demonstrating that all functions over denumerable domains — including the uncountably many functions that are not Turing-computable — are computable by Blum et al.'s "computing" systems, which are allowed to manipulate the exact values of arbitrary real numbers.

We also note that neither observing behavioural variation in root responses to neighbours, nor modelling fitness differentials associated with different behavioural types is equivalent to demonstrating these behaviours are adaptive.

The electrochemical behaviour at various immersion times was modelled by equivalent circuits to demonstrate the effect of silica nanoparticle loading on corrosion.

Included within the remit was an assessment of whether "the knowledge and skills demonstrated by a pass in the PLAB test continue to be equivalent to those demonstrated by successful completion of [Foundation Year 1] training".

As the authors are aware straight lines in log-log plots are not equivalent to having demonstrated a power law distribution and least squares fitting frequently generate biased estimates.

Second, equivalence test as applied in this study began with a null hypothesis that the two mean values were not equivalent, and attempted to demonstrate that they were equivalent within a practical, preset limit.

In addition to other metrics, we have evaluated the performance of the desalination process from power point of view with a new metric, Electricity Equivalent Water (EEW) to demonstrate the marginal energy penalty of desalination.

The belite melilite cement was found to have good fluidity, and the belite melilite cement mixed with OPC at up to 30% exhibited a satisfactory long term strength equivalent to the OPC, demonstrating the potential as an alternative to OPC.

First, de novo protein design has complicated the assertion that biological function is equivalent to biological structure — demonstrating the capacity to abstract active sites from natural contexts and paste them into non-native topologies without loss of function.